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Multitweezers generation using dark soliton pulses and applications
Optik 122 (2011) 1492–1499
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Optik journal homepage: www.elsevier.de/ijleo
Multitweezers generation using dark soliton pulses and applications B. Jukgoljun a,b , S. Pipatsart b , M.A. Jalil c,d , P.P. Yupapin b,∗ , J. Ali d a
Department of Physics, Faculty of Science, Burapha University, Bangsaen, Cholburi 20131, Thailand Nanoscale Science and Engineering Research Alliance, Advanced Research Center for Photonics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand c Ibnu Sina Institute for Fundamental Science Studies (IIS), Universiti Teknologi Malaysia (UTM), 81300 Johor Bahru, Malaysia d Institute of Advanced Photonics Science, Nanotechnology Research Alliance, Universiti Teknologi Malaysia (UTM), 81300 Johor Bahru, Malaysia b
a r t i c l e
i n f o
Article history: Received 25 July 2010 Accepted 8 October 2010
Keywords: Quantum tweezers Dynamic tweezers Tweezers transportation Multi-tweezers
a b s t r a c t Multi-dark soliton pulses have been successfully generated by using forward and backward pumping of the S-band erbium doped fiber in the fiber optic loop, where the Stimulated Brillouin Scattering (SBS) is a nonlinear interaction between pump fields with Stokes field through acoustic wave. Results obtained have shown that the dark soliton trains can be generated and configured as the multi-optical tweezers. The advantage is that the generated tweezers are in the form of dynamic tweezers, where they can transmit/transport via the soliton communication link. The single dark soliton is also experimentally generated by using the different fiber optic scheme. We have also theoretically shown that the dynamic tweezers can be controlled and tuned, which is available for trapping and transportation in the communication link via a wavelength router. The quantum states of the transported atoms/molecules by the dynamic tweezers can be performed by using the quantum processing unit incorporating in the system. © 2010 Elsevier GmbH. All rights reserved.
1. Introduction Atom trapping tool is likely to be one of the key components of future information technology. The envisioned quantum computer and network consist of major components such as quantum information processor, quantum memory and quantum channel for communication between nodes. In order to realize these components, active research work has been going on to identify suitable candidates for fundamental building blocks – quantum states to realize logic states (qubits), quantum processors to realize logic processing and quantum carrier to realize logic transport. Many earlier works with different trapping techniques have been reported, where the creation of a photon–atom bound state was first envisaged for the case of an atom in a long-lived excited state inside a high-quality microwave cavity [1,2], In practice, however, light forces in the microwave domain are insufficient to support an atom against gravity. Although optical photons can provide forces of the required magnitude, atomic decay rates and cavity losses are larger too, and so the atom–cavity system must be continually excited by an external laser [3,4]. Optical tweezer is a powerful tool in the three-dimensional rotation of and translation (location manipulation) of nano-structures such as micro- and nano-particles as well as living micro-organisms [5]. The benefit offered by optical tweezer is the ability to interact
with nano-scaled objects in a non-invasive manner, i.e. there is no physical contact with the sample, thus preserving many important characteristics of the sample, such as the manipulation of a cell with no harm to the cell. Optical tweezers are now widely used and they are particularly powerful in the field of microbiology to study cell–cell interactions [6–8], manipulate organelles without breaking the cell membrane and to measure adhesion forces between cells. However, the dynamic tweezer is needed instead of the static one. Recently, quantum tweezer has been proposed as the interesting tool in the trapping atom research areas, where the motion of atom for long distance flight can be realized, which can provide many aspects of applications, especially, in the quantum information processing [9]. Therefore, in this paper, the quantum tweezer generation scheme is proposed, where the dark soliton pulse can be experimentally generated by using a pumped laser in a fiber optic system. The obtained dark soliton can be amplified and tuned by using the nonlinear ring resonator system analytically. The dynamic behavior of soliton conversion, i.e. tunable optical tweezer within an add/drop filter is analyzed. A concept of quantum tweezer using the entangled photon (dark soliton pulse) to trap atom is also discussed for long distance atom trapping transportation. Finally, the concept of the atomic collision is also plausible by using two systems of dark soliton generation. 2. Operating principle
∗ Corresponding author. Fax: +66 2 3264 354. E-mail address: [email protected] (P.P. Yupapin). 0030-4026/$ – see front matter © 2010 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2010.10.003
We assume that the experimentally generated dark soliton pulse (even a Gaussian pulse) can be amplified and formed the soliton propagation within a nonlinear media. Therefore, we are looking for
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as shown in Fig. 1, which consists of a series MRRs. The resonant output is formed, thus, the normalized output of the light field is the ratio between the output and input fields [Eout (t) and Ein (t)] in each roundtrip, which is given by[14]
Eout (t) 2 = (1 − ) Ein (t)
1− (1 − x
(1 − (1 − )x2 )
2 √ √ 2 1 − 1 − ) + 4x 1 − 1 − sin (/2) (3)
Fig. 1. Schematic of a dark–bright soliton conversion system, where Rs is the ring radii, s is the coupling coefficient, and 41 and 42 are the add/drop coupling coefficients.
a stationary dark soliton pulse, which is introduced into the multistage micro-ring resonators as shown in Fig. 1. The input optical field (Ein ) of the dark soliton pulse input is given by [10,11] Ein (t) = A tanh
T T0
exp
z 2LD
− iω0 t
(1)
where A and z are the optical field amplitude and propagation distance, respectively. T is a soliton pulse propagation time in a frame moving at the group velocity, T = t − ˇ1 z, where ˇ1 and ˇ2 are the coefficients of the linear and second-order terms of Taylor expansion of the propagation constant. LD = T02 /|ˇ2 | is the dispersion length of the soliton pulse. T0 in equation is a soliton pulse propagation time at initial input (or soliton pulse width), where t is the soliton phase shift time, and the frequency shift of the soliton is ω0 . This solution describes a pulse that keeps its temporal width invariance as it propagates, and thus is called a temporal soliton. When a soliton peak intensity (|ˇ2 /T02 |) is given, then T0 is known. For the soliton pulse in the microring device, a balance should be achieved between the dispersion length (LD ) and the nonlinear length (LNL = 1/NL ), where = n2 k0 , is the length scale over which dispersive or nonlinear effects makes the beam become wider or narrower. For a soliton pulse, there is a balance between dispersion and nonlinear lengths, hence LD = LNL . When light propagates within the nonlinear material (medium), the refractive index (n) of light within the medium is given by n = n0 + n2 I = n0 +
n2 P, Aeff
(2)
where n0 and n2 are the linear and nonlinear refractive indexes, respectively. I and P are the optical intensity and optical power, respectively. The effective mode core area of the device is given by Aeff . For the microring resonator (MRR) and nanoring resonator (NRR), the effective mode core areas range from 0.50 to 0.10 m2 [12,13]. When a soliton pulse is input and propagated within a MRR,
The close form of Eq. (3) indicates that a ring resonator in this particular case is very similar to a Fabry–Perot cavity, which has an input and output mirror with a field reflectivity, (1 − ), and a fully reflecting mirror. is the coupling coefficient, and x = exp(−˛L/2) represents a roundtrip loss coefficient, 0 = kLn0 and NL = kLn2 |Ein |2 are the linear and nonlinear phase shifts, k = 2/ is the wave propagation number in a vacuum, where L and ˛ are waveguide length and linear absorption coefficient, respectively. In this work, the iterative method is introduced to obtain the results as shown in Eq. (3), and similarly, when the output field is connected and input into the other ring resonators. To retrieve the signals from the chaotic noise, we propose to use the add/drop device with the appropriate parameters. This is given in the following details. The optical circuits of ring-resonator add/drop filters for the throughput and drop port can be given by Eqs. (4) and (5), respectively [15].
2 Et = Ein
(1 − 1 ) − 2
1 − 1 ·
1 − 2 e−(˛/2)L cos (kn L) + (1 − 2 )e−˛L
1 + (1 − 1 )(1 − 2 )e−˛L − 2
1 − 1 ·
(4)
1 − 2 e−(˛/2)L cos (kn L)
and
2 Ed = Ein
1 2 e−(˛/2)L 1 + (1 − 1 )(1 − 2
)e−˛L
−2
1 − 1 ·
(5) 1 − 2 e−(˛/2)L cos (kn L)
where Et and Ed represent the optical fields of the throughput and drop ports, respectively. ˇ = kneff is the propagation constant, neff is the effective refractive index of the waveguide, and the circumference of the ring is L = 2R, with R as the radius of the ring. In the following, new parameters is used for simplification with = ˇL as the phase constant. The chaotic noise cancellation can be managed by using the specific parameters of the add/drop device, and the required signals can be retrieved by the specific users. 1 and 2 are the coupling coefficient of the add/drop filters, kn = 2/ is the wave propagation number for in a vacuum, and where the waveguide (ring resonator) loss is ˛ = 0.5 dB mm−1 . The fractional coupler intensity loss is = 0.1. In the case of the add/drop device, the nonlinear refractive index is neglected.
a 7.7 km DCF
1400nm RP
30 m DC-EDF 10%
3
2
50%
OC1
1400/1500nm WSC
980/1500nm WSC
980/1500nm WSC
2
50%
1
980nm LD
9.4dBm BP
980nm LD
3
OC2
90%
1
b 1400nm RP
7.7 km DCF
30 m DC-EDF
10% 90%
OC2
3
2 1
50%
OC1
1400/1500nm WSC
980/1500nm WSC
980/1500nm WSC
2
3
50%
9.4dBm BP
980nm LD
980nm LD
1
Fig. 2. The experimental set up for (a) forward pumping and (b) backward pumping, where OSA: optical spectrum analyzer, OCs: optical circulators, BP: Brillouin pumping, RP: Raman pumping, WDM: wavelength division multiplexing, DCF: dispersion compensated fiber, LDs: laser diodes. DC: depressed cladding, EDF: erbium doped fiber.
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Fig. 3. Result of ASE of the bi-directional pump in the depressed cladding fiber.
Fig. 5. Results of the multi-Brillouin lasing spectrum with BP wavelength set at 1500 nm.
3. Optical tweezers generation Fig. 2(a) and (b) shows the experimental setup for multiwavelength BEFL in the forward and backward pumping configuration respectively. Both the setup consists of a Brillouin pump (BP) with a 9.4 dBm output power, a Raman pump (RP) with a 296 mW output power that pumps the 7.7 km dispersion compensated fiber (DCF) and two laser diodes (LDs) with an output power of 48 mW and 121 mW respectively. These LDs were bi-directionally pumped a 30 m length depressed cladding fiber with a spooling diameter of 7 cm. A linear resonator consisting of two optical circulators (OC) at both ends of the setup is used. These two optical circulators also create a double pass configuration inside the cavity. Three wavelength division multiplexers (WDM) are used to combine the different wavelength inside the cavity. A 3 dB OC1 couples the signal from the BP into the cavity. A 90:10 output coupler that is being placed at different locations as shown in Fig. 2(a) and (b) is tapped 10% of this signal. This output signal is directly observed using an optical spectrum analyzer (OSA) with a resolution of 0.02 nm. The amplified spontaneous emission (ASE) of the DC-EDF fiber was pumped bi-directionally by the two LDs as shown in Fig. 3. This scheme gives efficient amplification resulting in a higher ASE spectrum being obtained. The fundamental cut-off wavelength of the fiber is dependent on the spooling diameter of the fiber. It must be between the S-band and the longer wavelength bands of the Cband and the L-band region. Thus from Fig. 3, it can be observed that the 7 cm spooling diameter of the DC-EDF used in this experiment has a cut-off wavelength between 1490 nm and 1510 nm. The ASE shows that the emission is suppressed in the c-band region, which it is at a wavelength of 1510 nm. This suppression gives a significant gain in the S-band region. Fig. 4 shows the tunable multiple-Brillouin lasing at different settings of wavelengths at BP. Note that this multi-wavelength Brillouin lasing are obtained from the experimental setup in Fig. 1(a). The power setting of the BP is kept constant at 9.4 dBm but the wavelength of the signal is varied at 1500 nm, 1502 nm and 1504 nm. From the output spectrum of 13, 12 and 11 peaks are obtained at 1500 nm, 1502 nm and 1504 nm respectively. The lasing peaks at 1500 nm are more stable and fluctuates less as compared to 1502 nm and 1504 nm lasing. Due to the less numbers of fluctuations of the lasing spectrum and the highest number of peaks obtained at 1500 nm, the multi-
Fig. 4. The tunable multiple-Brillouin lasing peaks at different wavelengths of Brillouin pumping.
Fig. 6. The stability of the multi-Brillouin lasing spectrum at 1500 nm.
Brillouin lasing at this wavelength is chosen for close scrutiny. Fig. 5 shows the 13 Brillouin peaks generated with a constant spacing of 0.08 nm. The peak power of this multiple Brillouin pulses is stable at a power of 46 mW with about 1 dB fluctuation in each peak except for the second peak on the left hand side of the spectrum and the last peak at the right hand side of the lasing spectrum. The highest output power of the second peak is due to the first Stokes. The high power value of the first Stoke is essential for the generation of the multi-Brillouin peaks. In order to ensure the stability of the multi-Brillouin lasing, the results are repeated a number of times from 00 to 04 ns. Fig. 6 shows the stability and evolution of the lasing spectrum. It can be seen that the same spectrum is almost reproducible. The time interval between two spectrums is 60 s. The generation of multi-Brillouin lasing is much dependent on the pumping power that interacts with the acoustic wave. Fig. 7 shows the changes in the multi-Brillouin lasing spectrum obtained when the power of RP is varied between 296 mW and 225 mW. It can be observed that the numbers of multiBrillouin peaks obtained varies from 13 peaks to 6 peaks when the RP power is decreased. These results indicate that the number of Brillouin peaks and anti-stokes are also reduced when RP power is decreased. The generation of multi-Brillouin lasing is much dependent on the pumping power that interacts with the acoustic wave. Fig. 8 shows the changes in the multi-Brillouin lasing spectrum obtained when the power of RP is varied between 296 mW and 225 mW. It can be observed that the numbers of multi-Brillouin
Fig. 7. Multi-Brillouin lasing spectrum at different Raman pump power.
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Fig. 8. The multi-Brillouin peaks obtained at different wavelength setting of Brillouin pumping.
Fig. 9. Multi-Brillouin lasing spectrum with BP wavelength set at 1504 nm.
peaks obtained varies from 13 peaks to 6 peaks when the RP power is decreased. Fig. 1(b) shows the multi-wavelength BEFL setup for the backward pumping configuration. The 90:10 output coupling is placed after the OC2 coupler in this configuration. In the forward pumping configuration, the highest numbers of multi-Brillouin peaks are obtained at the 1500 nm BP wavelength. In the backward pumping scheme, the numbers of multi-Brillouin peaks are obtained when the setting wavelengths of BP are at 1502 nm and 1504 nm as compared to the number of peaks when the BP wavelength are set at 1500 nm wavelength. Fig. 9 shows, 8 number of peak obtained at the wavelength of 1500 nm, where 10 peaks are observed when the wavelength of the BP is set at 1502 nm and 1504 nm. From Fig. 10, an optical spectrum analyzer (OSA) with a resolution of 0.07 nm is used to analyze the output of the proposed setup. The operation of the experimental setup is also follows; the BP generates a 1500 nm signal at 1.96 dBm, where it enters Port 1 of the first OC. The signal then travels onward to the DCF, where the nonlinear interaction provides the first Stokes wavelength. The BP and Stokes then travels onwards to the second OC where it is reflected back to the DCF and again to Port 2 of the first OC, where it will now exit via Port 3 which is connected to the OSA. The experimental setup is shown in Fig. 10. The dark soliton generator consists of a fiber laser based on a non-linear gain medium that is placed in a linear cavity. The non-linear gain medium is a 7.7 km dispersion compensating fiber (DCF) which is pumped by a 1500 nm Brillouin pump (BP) at 1.96 dBm. An optical circulator
Fig. 10. Shows an experimental setup.
Fig. 11. Shows dark soliton propagation over time, which is similar to a potential well, where (a) a dark soliton train and (b) a modulated soliton train.
(OC) is used at one end of the setup to act as a fiber based mirror, with Port 3 connected to Port 1 while Port 2 is connected to the rest of the experimental setup. Another OC is also used in the experimental setup to guide the incoming and outgoing signals. From Fig. 11, the soliton propagation over time can be obtained. As can be seen in the figure, the soliton pulse maintains its shape through the time of testing with no observable fluctuation in the power or wavelength. This is critical as any slight fluctuation cause the beam to lose its hold over the transported atom or molecule, effectively dropping it. 4. Dynamic tweezers In operation, the generated dark soliton pulse, for instance, with 50-ns pulse width, and a maximum power of 0.65 W is input into the dark–bright soliton conversion system as shown in Fig. 1. The suitable ring parameters are used, such as ring radii where R1 = 10.0 m, R2 = 7.0 m, and R3 = 5.0 m. In order to make the system associate with the practical device [12,13], whereas the selected parameters of the system are fixed to 0 = 1.50 m, n0 = 3.34 (InGaAsP/InP). The effective core areas are Aeff = 0.50, 0.25, and 0.10 m2 for a MRR and NRR, respectively. The waveguide and coupling loses are ˛ = 0.5 dB mm−1 and = 0.1, respectively, and the coupling coefficients s of the MRR are ranged from 0.05 to 0.90. However, more parameters are used as shown in Fig. 1. The nonlinear refractive index is n2 = 2.2 × 10−13 m2 /W. In this case, the waveguide loss used is 0.5 dB mm−1 . The input dark soliton pulse is chopped (sliced) into the smaller signals, where the filtering signals within the rings R2 and R3 are seen. We find that the output signals from R3 are smaller than from R1 , which is more difficult to detect when it is used in the link. In fact, the multistage ring system is proposed due to the different core effective areas of the rings in the system, where the effective areas can be transferred from 0.50 to 0.10 m2 with some losses. The soliton signals in R3 is entered in the add/drop filter, where the dark–bright soliton conversion can be performed by using Eqs. (4) and (5). Results obtained when a dark soliton pulse is input into a MRR and NRR system as shown in Fig. 1. The add/drop filter is formed by using two couplers and a ring with radius (Rd ) of 10 m,
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Fig. 13. The dynamic optical tweezers output within the add/drop filter, when the bright soliton input with the central wavelength 0 = 1.5 m, where (a) add/drop signal, (b) dark–bright soliton collision, (c) optical tweezers at throughput port, and (d) optical tweezers at drop port.
Fig. 12. Results of the soliton signals within the ring resonator system, where (a) ring R1 , (b) ring R2 , (c) and (d) ring R3 , and (d) and (e) dark–bright solitons conversion at the add/drop filter. The input dark soliton power is 2 W.
the coupling constants (41 and 42 ) are the same values (0.50). When the add/drop filter is connected to the third ring (R3 ), the dark–bright soliton conversion can be seen. The bright and dark solitons are detected by the through (throughput) and drop ports as shown in Fig. 12(d) and (e), respectively. In application, the dynamic optical tweezers is occurred, when we added bright soliton input at the add port with shown in Fig. 1, the parameters of system are set the same as the previous section. The bright soliton was generated at the central wavelength 0 = 1.5 m, when the bright soliton propagating into the add/drop system, the occurrence of dark-bright soliton collision in add/drop system is shown in Fig. 13(a) and (b). The tunable dark soliton is as shown in Fig. 14, whereas the smallest dark soliton width of 16 nm is obtained as shown in Fig. 14(d). The output soliton can be configured as the dynamic tweezers, where the use of such tweezers for trapping and transportation is possible, which will be discussed in the next section.
Fig. 14. The tuned dynamic optical tweezers output within the add/drop filter, when the bright soliton input with the central wavelength 0 = 1.5 m, where (a) the add/drop signal, (b) dark–bright soliton collision, (c) optical tweezers at throughput port, and (d) optical tweezers at drop port.
tal polarization states corresponds to an optical switch between the short and the long pulses. We assume those horizontally polarized pulses with a temporal separation of t. The coherence time of the consecutive pulses is larger than (t. Then the following state
5. Quantum tweezers and transportation Let us consider that the case when the dark soliton output is partially input into the quantum processor unit. Generally, there are two pairs of possible polarization entangled photons forming within the ring device, which are represented by the four polarization orientation angles as [0◦ , 90◦ ], [135◦ and 180◦ ]. These can be formed by using the optical component called the polarization rotatable device and a polarizing beam splitter (PBS). In this concept, we assume that the polarized photon can be performed by using the proposed arrangement. Where each pair of the transmitted qubits can be randomly formed the entangled photon pairs. To begin this concept, we introduce the technique that can be used to create the entangled photon pair (qubits) as shown in Fig. 15, a polarization coupler that separates the basic vertical and horizon-
Fig. 15. A schematic of an entangled photon pair manipulation within a ring resonator. The Bell’s state is propagating to a rotatable polarizer and then is split by a beam splitter (PBS) flying to detector D1 and D2 .
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Fig. 16. A schematic of atomic/molecular router and network system, where Ri , Rj : ring radii and is , js are the coupling coefficients.
is created by Eq. (6) [16].
˚ = 1, H 1, H + 2, H 2, H (6) p s i s i
In the expression k, H , k is the number of time slots (1 or 2),
where denotes the state of polarization [horizontal H or vertical
V ], and the subscript identifies whether the state is the signal (s) or the idler (i) state. In Eq. (6), for simplicity, we have omitted an amplitude term that is common to all product states. We employ subsequent equations in this paper. This the same simplification in
two-photon state with H polarization shown by Eq. (6) is input into the orthogonal polarization-delay circuit shown schematically. The delay circuit consists of a coupler and the difference between the round-trip times of the micro ring resonator, which is equal to t. The micro ring is tilted by changing the round trip of the ring is converted into V at the delay circuit output. That is the delay
circuits convert k, H to be
r k, H + t2 exp(i) k + 1, V + rt2 exp(i3 ) k + 2, V
+r2 t2 exp(i3 ) k + 3, V . Where t and r is the amplitude transmittances to cross and bar ports in a coupler. Then Eq. (6) is converted into the polarized state by the delay circuit as
˚ = [1, H + exp(is )2, V ] × [1, H + exp(ii )2, V ] s s i i
+ [2, H + exp(is )3, V ] × [2, H + exp(ii )2, V ] s s i i
= [1, H 1, H + exp(ii )1, H 2, V ] s i s i
(7) + exp(is ) 2, V s 1, H + exp[i(s i
+ i )]2, V 2, V + 2, H 2, H s i s i
+ exp (ii ) 2, H 3, V + exp (is ) 3, V 2, H s i s i
+ exp[i (s + i )]3, V 3, V s
i
By the coincidence counts in the second time slot, we can extract the fourth and fifth terms. As a result, we can obtain the following polarization entangled state as
˚ = 2, H 2, H + exp[i(s + i )]2, V 2, V s i s i
(8)
We assume that the response time of the Kerr effect is much less than the cavity round-trip time. Because of the Kerr nonlinearity of the optical device, the strong pulses acquire an intensity dependent phase shift during propagation. The interference of light pulses at a coupler introduces the output beam, which is entangled. Due to the polarization states of light pulses are changed and converted while circulating in the delay circuit, where the polarization entangled photon pairs can be generated. The entangled photons of the nonlinear ring resonator are separated to be the signal and idler photon probability. The polarization angle adjustment device is applied to investigate the orientation and optical output intensity, this concept is well described by the published work [17]. By using the reasonable dark–bright soliton input power, the tunable optical tweezer can be controlled, which can be used as the dynamic optical tweezer probe. The smallest tweezer width of 16 nm is generated and achieved. In application, such a behavior can be used to confine the suitable size of light pulse or molecule, which can be employed in the same way of the optical tweezer. But in this case the terms dynamic probing is come to be a realistic function, therefore, the transportation of the trapped atom/molecule/photon is plausible. Moreover, the trapped states of the transported atom/molecule can be configured by using the quantum processor as shown in Fig. 15. Thus, the transported atom with long distance link via quantum tweezer is realized. From the above reasons, the transmission of atoms/molecules from dark soliton pulses via a wavelength router is plausible, which can be described by the following reasons: (i) a dark soliton pulse can propagate into the optical device/media, (ii) atom/molecule being trapped by tweezers force during the movement, the atom/molecule recovery can be realized by using the optical detection scheme, where the dark–bright soliton conversion technique is also available [18]. From Fig. 16, the transmission atoms/molecules can be performed by the dark soliton pulse, the atoms/molecules recovery can be taken by using the add/drop filter incorporating in the wavelength router, i.e. optical network. However, the separation of atoms/molecules from light pulse is required to have the specific environment, which becomes the interesting research area, where light with the specific wavelength (i ) is detected by a detector, while the required molecule is absorbed by the specific environment. The atom/molecule states can be allocated by using the quantum processing unit as shown in Fig. 16, where the corresponding states of the transmitted atom/molecule between input and output states can be recognized and formed the
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Fig. 17. Laser tool mechanism diagram, where Rs : ring radii, s : coupling coefficients, Rd : an add/drop ring radius, Aeff s: effective areas.
secret information. Therefore, in practice, the quantum processing unit is required to connect into the system, where the input and output states can be linked and obtained the required information. 6. Trapping forces In operation, the trapping forces are exerted by the intensity gradients in the strongly focused beams of light to trap and move the microscopic volumes of matters, in which the optical forces are customarily defined by the relationship [19]. F=
Qnm P c
(9)
where Q is a dimensionless efficiency, nm is the index of refraction of the suspending medium, c is the speed of light, and P is the incident laser power, measured at the specimen. Q represents the fraction of power utilized to exert force. For incident plane wave on a perfectly absorbing particle, Q is equal to 1. To achieve stable trapping, the radiation pressure must create a stable, threedimensional equilibrium. Because biological specimens are usually contained in aqueous medium, the dependence of F on nm can rarely be exploited to achieve higher trapping forces. Increasing the laser power is possible, but only over a limited range due to the possibility of optical damage. Q itself is therefore the main determinant of trapping force. It depends upon the NA (numerical aperture), laser wavelength, light polarization state, laser mode structure, relative index of refraction, and geometry of the particle. Furthermore, in the Rayleigh regime, trapping forces decompose naturally into two components. Since, in this limit, the electromagnetic field is uniform across the dielectric, particles can be treated as induced point dipoles. The scattering force is given by
Fscatt = nm
S
c
where
=
8 4 (kr) r 2 3
,
(10)
m2 − 1 m2 + 2
2 (11)
is the scattering cross section of a Rayleigh sphere with radius r. S is the time averaged Poynting vector, n is the index of refraction of the particle, m = n/nm is the relative index, and k = 2nm / is the wave number of the light. Scattering force is proportional to the energy flux and points along the direction of propagation of the incident light. The gradient field (Fgrad ) is the Lorentz force acting on the dipole induced by the light field. It is given by Fgrad =
˛ 2
∇ E , 2
where ˛ = n2m r 3
m2 − 1 m2 + 2
(12)
(13)
is the polarizability of the particle. The gradient force is proportional and parallel to the gradient in energy density (for m > 1). The large gradient force is formed by the large depth of the laser
beam, in which the stable trapping requires that the gradient force in the −ˆz direction, which is against the direction of incident light (dark soliton valley), and it is greater than the scattering force. By increasing the NA, when the focal spot size is decreased, the gradient strength is increased [19], which can be formed within the tiny system, for instance, nanoscale device (nanoring resonator). 7. An atomic collision concept A model of an atomic collision system is as shown in Fig. 17. The generated dark soliton pulse from the experiment can be amplified and tuned dynamically from both ends, whereas the analytical details are shown in the previous section. Here, after the input dark soliton pulse is amplified and reached the desired value, the optical energy can be storage within a ring resonator R3 , which has been designed and well described by Refs. [19,20]. The controlled parameters are the coupling coefficients, (31 , 3 and 32 ) that can be chosen to control the output energy. However, the other source is required to obtain the dynamic tunable tweezers, therefore, the other soliton pulse is input into the add port of the add/drop filter as shown in Fig. 1. To operate the system, we can explain the atomic collision system as the following details. The resonant dark soliton output from the throughput port is entered into the atomic chamber, where in some ways there are some atoms trapped by the dark soliton, i.e. optical tweezers, which is become the output trapping atom, while the another system is also performed. The collision is perform in the collision/atomic chamber, which the high protection and shield are required. 8. Dual mode atomic-laser tools operation A model of a dual mode atomic-laser gun is as shown in Fig. 18. The generated dark soliton pulse from the experiment can be amplified and tuned dynamically, which is shown in details in the previous section. In principle, the dual mode atom-laser gun functions can operate by using the dark–bright soliton conversion and collision control, which is analyzed and discussed in the previous section. Here, each part of the system as shown in Fig. 18 can be described as following details. After the input dark soliton pulse is amplified and reached the desired value, the optical energy can be storage within a ring resonator R3 which has been designed and well described by Refs. [19,20]. The controlled parameters are the coupling coefficients, (31 , 3 and 32 ) that can be chosen to control the output energy. However, the other source is required to obtain the dynamic tunable tweezers, therefore, the other soliton pulse is input into the add port of the add/drop filter as shown in Fig. 1. To operate the system, we can explain the dual mode function as the following details. The resonant dark soliton output from the throughput port is entered into the atomic chamber, where in some ways there are some atoms trapped by the dark soliton, i.e. optical tweezers, which is become the output bullet, while, the bright soliton output become a laser output for the laser gun at the drop port, which is controlled by the alternative switch and absorber. This function is well described by the dark–bright soliton conversion.
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Fig. 18. Atomic tool mechanism diagram, where Rs : ring radii, s : coupling coefficients, Rd : an add/drop ring radius, Aeff s: effective areas.
9. Conclusion We have successfully generated the multi-dark soliton using forward and backward pumping of the S-band erbium doped fiber, where the Stimulated Brillouin Scattering (SBS) is a nonlinear interaction between pump fields with Stokes field through the acoustic wave. The pumping power generated an acoustic wave and caused perturbation to the refractive index of the fiber which functions as a grating and scatters light into the lower frequency. Results obtained have shown that the stable multi dark soliton can be generated. The use of muti-dark soliton pulses to form the optical and quantum tweezers are described, the atoms/molecules trapping and transportation using quantum tweezers via a wavelength router is discussed, where in this case the quantum states of the transported atoms/molecules are specified, which is allowed to use in quantum information applications. We have shown that the propagating dark soliton within the MRR and NRR system can be converted to be a bright soliton by using the ring resonator system, incorporating the add/drop multiplexer, moreover, the amplification and tenability of the dark soliton pulse can be obtained. By using the reasonable dark–bright soliton input power, the tunable optical tweezers can be controlled, which can be used as the dynamic optical tweezers probe. In application, such a behavior can be used to confine the suitable size of light pulse or molecule, which can be employed in the same way of the optical tweezers. But in this case the terms dynamic probing is come to be a realistic function. Moreover, the transportation of the trapped pulse or molecule is plausible. Finally, we have shown that the use of the tunable dynamic tweezers for the atomic collision investigation is also plausible. We have also shown that the use of the tunable dynamic tweezers for a dual mode atomic and laser gun is also plausible. References [1] D. Jaksch, H.-J. Briegel, J.I. Cirac, C.W. Gardiner, P. Zoller, Entanglement of atoms via cold controlled collisions, Phys. Rev. Lett. 82 (1999) 1975–1978.
[2] T. Calarco, H.-J. Briegel, D. Jakch, J.I. Cirac, P. Zoller, Quantum computing with neutral atoms, J. Mod. Optic. 47 (2007) 2137–2142. [3] M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, England, 2000. [4] P.W.H. Pinkse, T. Fischer, P. Maunz, G. Rempe, Trapping an atom with single photons, Nature 404 (2000) 365–368. [5] S.M. Block, Making light work with optical tweezers, Nature 360 (1992) 493–495. [6] A. Ashkin, J.M. Dziedzic, T. Yamane, Optical trapping and manipulation of single cells using infrared laser beams, Nature 330 (1987) 769–771. [7] K. Svoboda, S.M. Block, Biological applications of optical forces, Annu. Rev. Biophys. Biomol. Struct. 23 (1994) 247–285. [8] J. Conia, B.S. Edwards, S. Voelkel, The micro-robotic laboratory: optical trapping and scissing for the biologist, J. Clin. Lab. Anal. 11 (1997) 28– 38. [9] R.B. Diener, B. Wu, M.G. Raizen, Q. Niu, Quantum Tweezer for Atoms, Phys. Rev. Lett. 89 (2002) 070401. [10] S. Mitatha, N. Pornsuwancharoen, P.P. Yupapin, A simultaneous short-wave and millimeter-wave generation using a soliton pulse within a nano-waveguide, IEEE Photon. Technol. Lett. 21 (2009) 932–934. [11] G.P. Agarwal, Nonlinear Fiber Optics, 4th edition, Academic Press, New York, 2007. [12] C. Fietz, G. Shvets, Nonlinear polarization conversion using microring resonators, Opt. Lett. 32 (2007) 1683–1685. [13] Y. Kokubun, Y. Hatakeyama, M. Ogata, S. Suzuki, N. Zaizen, Fabrication technologies for vertically coupled microring resonator with multilevel crossing busline and ultracompact-ring radius, IEEE J. Sel. Top. Quantum Electron. 11 (2005) 4–10. [14] P.P. Yupapin, P. Saeung, C. Li, Characteristics of complementary ring-resonator add/drop filters modeling by using graphical approach, Opt. Commun. 272 (2007) 81–86. [15] P.P. Yupapin, W. Suwancharoen, Chaotic signal generation and cancellation using a micro ring resonator incorporating an optical add/drop multiplexer, Opt. Commun. 280/2 (2007) 343–350. [16] S. Suchat, W. Khannam, P.P. Yupapin, Quantum key distribution via an optical wireless communication link for telephone network, Opt. Eng. Lett. 46 (10) (2007) 100502. [17] P.P. Yupapin, S. Suchat, Entangle photon generation using fiber optic MachZehnder interferometer incorporating nonlinear effect in a fiber ring resonator, Nanophotonics (JNP) 1 (2007) 13504. [18] K. Sarapat, N. Sangwara, K. Srinuanjan, P.P. Yupapin, N. Pornsuwancharoen, Novel dark–bright optical soliton conversion system and power amplification, Opt. Eng. 48 (2009) 0450041. [19] K. Svoboda, S.M. Block, Biological applications of optical forces, Annu. Rev. Biophys. Biomol. Struct. (1994) 247–282. [20] P.P. Yupapin, N. Pornsuwancharoen, Proposed nonlinear micro ring resonator arrangement for stopping and storing light, IEEE Photon. Technol. Lett. 21 (2009) 404–406.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Multitweezers generation using dark soliton pulses and applications B. Jukgoljun a,b , S. Pipatsart b , M.A. Jalil c,d , P.P. Yupapin b,∗ , J. Ali d a
Department of Physics, Faculty of Science, Burapha University, Bangsaen, Cholburi 20131, Thailand Nanoscale Science and Engineering Research Alliance, Advanced Research Center for Photonics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand c Ibnu Sina Institute for Fundamental Science Studies (IIS), Universiti Teknologi Malaysia (UTM), 81300 Johor Bahru, Malaysia d Institute of Advanced Photonics Science, Nanotechnology Research Alliance, Universiti Teknologi Malaysia (UTM), 81300 Johor Bahru, Malaysia b
a r t i c l e
i n f o
Article history: Received 25 July 2010 Accepted 8 October 2010
Keywords: Quantum tweezers Dynamic tweezers Tweezers transportation Multi-tweezers
a b s t r a c t Multi-dark soliton pulses have been successfully generated by using forward and backward pumping of the S-band erbium doped fiber in the fiber optic loop, where the Stimulated Brillouin Scattering (SBS) is a nonlinear interaction between pump fields with Stokes field through acoustic wave. Results obtained have shown that the dark soliton trains can be generated and configured as the multi-optical tweezers. The advantage is that the generated tweezers are in the form of dynamic tweezers, where they can transmit/transport via the soliton communication link. The single dark soliton is also experimentally generated by using the different fiber optic scheme. We have also theoretically shown that the dynamic tweezers can be controlled and tuned, which is available for trapping and transportation in the communication link via a wavelength router. The quantum states of the transported atoms/molecules by the dynamic tweezers can be performed by using the quantum processing unit incorporating in the system. © 2010 Elsevier GmbH. All rights reserved.
1. Introduction Atom trapping tool is likely to be one of the key components of future information technology. The envisioned quantum computer and network consist of major components such as quantum information processor, quantum memory and quantum channel for communication between nodes. In order to realize these components, active research work has been going on to identify suitable candidates for fundamental building blocks – quantum states to realize logic states (qubits), quantum processors to realize logic processing and quantum carrier to realize logic transport. Many earlier works with different trapping techniques have been reported, where the creation of a photon–atom bound state was first envisaged for the case of an atom in a long-lived excited state inside a high-quality microwave cavity [1,2], In practice, however, light forces in the microwave domain are insufficient to support an atom against gravity. Although optical photons can provide forces of the required magnitude, atomic decay rates and cavity losses are larger too, and so the atom–cavity system must be continually excited by an external laser [3,4]. Optical tweezer is a powerful tool in the three-dimensional rotation of and translation (location manipulation) of nano-structures such as micro- and nano-particles as well as living micro-organisms [5]. The benefit offered by optical tweezer is the ability to interact
with nano-scaled objects in a non-invasive manner, i.e. there is no physical contact with the sample, thus preserving many important characteristics of the sample, such as the manipulation of a cell with no harm to the cell. Optical tweezers are now widely used and they are particularly powerful in the field of microbiology to study cell–cell interactions [6–8], manipulate organelles without breaking the cell membrane and to measure adhesion forces between cells. However, the dynamic tweezer is needed instead of the static one. Recently, quantum tweezer has been proposed as the interesting tool in the trapping atom research areas, where the motion of atom for long distance flight can be realized, which can provide many aspects of applications, especially, in the quantum information processing [9]. Therefore, in this paper, the quantum tweezer generation scheme is proposed, where the dark soliton pulse can be experimentally generated by using a pumped laser in a fiber optic system. The obtained dark soliton can be amplified and tuned by using the nonlinear ring resonator system analytically. The dynamic behavior of soliton conversion, i.e. tunable optical tweezer within an add/drop filter is analyzed. A concept of quantum tweezer using the entangled photon (dark soliton pulse) to trap atom is also discussed for long distance atom trapping transportation. Finally, the concept of the atomic collision is also plausible by using two systems of dark soliton generation. 2. Operating principle
∗ Corresponding author. Fax: +66 2 3264 354. E-mail address: [email protected] (P.P. Yupapin). 0030-4026/$ – see front matter © 2010 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2010.10.003
We assume that the experimentally generated dark soliton pulse (even a Gaussian pulse) can be amplified and formed the soliton propagation within a nonlinear media. Therefore, we are looking for
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as shown in Fig. 1, which consists of a series MRRs. The resonant output is formed, thus, the normalized output of the light field is the ratio between the output and input fields [Eout (t) and Ein (t)] in each roundtrip, which is given by[14]
Eout (t) 2 = (1 − ) Ein (t)
1− (1 − x
(1 − (1 − )x2 )
2 √ √ 2 1 − 1 − ) + 4x 1 − 1 − sin (/2) (3)
Fig. 1. Schematic of a dark–bright soliton conversion system, where Rs is the ring radii, s is the coupling coefficient, and 41 and 42 are the add/drop coupling coefficients.
a stationary dark soliton pulse, which is introduced into the multistage micro-ring resonators as shown in Fig. 1. The input optical field (Ein ) of the dark soliton pulse input is given by [10,11] Ein (t) = A tanh
T T0
exp
z 2LD
− iω0 t
(1)
where A and z are the optical field amplitude and propagation distance, respectively. T is a soliton pulse propagation time in a frame moving at the group velocity, T = t − ˇ1 z, where ˇ1 and ˇ2 are the coefficients of the linear and second-order terms of Taylor expansion of the propagation constant. LD = T02 /|ˇ2 | is the dispersion length of the soliton pulse. T0 in equation is a soliton pulse propagation time at initial input (or soliton pulse width), where t is the soliton phase shift time, and the frequency shift of the soliton is ω0 . This solution describes a pulse that keeps its temporal width invariance as it propagates, and thus is called a temporal soliton. When a soliton peak intensity (|ˇ2 /T02 |) is given, then T0 is known. For the soliton pulse in the microring device, a balance should be achieved between the dispersion length (LD ) and the nonlinear length (LNL = 1/NL ), where = n2 k0 , is the length scale over which dispersive or nonlinear effects makes the beam become wider or narrower. For a soliton pulse, there is a balance between dispersion and nonlinear lengths, hence LD = LNL . When light propagates within the nonlinear material (medium), the refractive index (n) of light within the medium is given by n = n0 + n2 I = n0 +
n2 P, Aeff
(2)
where n0 and n2 are the linear and nonlinear refractive indexes, respectively. I and P are the optical intensity and optical power, respectively. The effective mode core area of the device is given by Aeff . For the microring resonator (MRR) and nanoring resonator (NRR), the effective mode core areas range from 0.50 to 0.10 m2 [12,13]. When a soliton pulse is input and propagated within a MRR,
The close form of Eq. (3) indicates that a ring resonator in this particular case is very similar to a Fabry–Perot cavity, which has an input and output mirror with a field reflectivity, (1 − ), and a fully reflecting mirror. is the coupling coefficient, and x = exp(−˛L/2) represents a roundtrip loss coefficient, 0 = kLn0 and NL = kLn2 |Ein |2 are the linear and nonlinear phase shifts, k = 2/ is the wave propagation number in a vacuum, where L and ˛ are waveguide length and linear absorption coefficient, respectively. In this work, the iterative method is introduced to obtain the results as shown in Eq. (3), and similarly, when the output field is connected and input into the other ring resonators. To retrieve the signals from the chaotic noise, we propose to use the add/drop device with the appropriate parameters. This is given in the following details. The optical circuits of ring-resonator add/drop filters for the throughput and drop port can be given by Eqs. (4) and (5), respectively [15].
2 Et = Ein
(1 − 1 ) − 2
1 − 1 ·
1 − 2 e−(˛/2)L cos (kn L) + (1 − 2 )e−˛L
1 + (1 − 1 )(1 − 2 )e−˛L − 2
1 − 1 ·
(4)
1 − 2 e−(˛/2)L cos (kn L)
and
2 Ed = Ein
1 2 e−(˛/2)L 1 + (1 − 1 )(1 − 2
)e−˛L
−2
1 − 1 ·
(5) 1 − 2 e−(˛/2)L cos (kn L)
where Et and Ed represent the optical fields of the throughput and drop ports, respectively. ˇ = kneff is the propagation constant, neff is the effective refractive index of the waveguide, and the circumference of the ring is L = 2R, with R as the radius of the ring. In the following, new parameters is used for simplification with = ˇL as the phase constant. The chaotic noise cancellation can be managed by using the specific parameters of the add/drop device, and the required signals can be retrieved by the specific users. 1 and 2 are the coupling coefficient of the add/drop filters, kn = 2/ is the wave propagation number for in a vacuum, and where the waveguide (ring resonator) loss is ˛ = 0.5 dB mm−1 . The fractional coupler intensity loss is = 0.1. In the case of the add/drop device, the nonlinear refractive index is neglected.
a 7.7 km DCF
1400nm RP
30 m DC-EDF 10%
3
2
50%
OC1
1400/1500nm WSC
980/1500nm WSC
980/1500nm WSC
2
50%
1
980nm LD
9.4dBm BP
980nm LD
3
OC2
90%
1
b 1400nm RP
7.7 km DCF
30 m DC-EDF
10% 90%
OC2
3
2 1
50%
OC1
1400/1500nm WSC
980/1500nm WSC
980/1500nm WSC
2
3
50%
9.4dBm BP
980nm LD
980nm LD
1
Fig. 2. The experimental set up for (a) forward pumping and (b) backward pumping, where OSA: optical spectrum analyzer, OCs: optical circulators, BP: Brillouin pumping, RP: Raman pumping, WDM: wavelength division multiplexing, DCF: dispersion compensated fiber, LDs: laser diodes. DC: depressed cladding, EDF: erbium doped fiber.
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Fig. 3. Result of ASE of the bi-directional pump in the depressed cladding fiber.
Fig. 5. Results of the multi-Brillouin lasing spectrum with BP wavelength set at 1500 nm.
3. Optical tweezers generation Fig. 2(a) and (b) shows the experimental setup for multiwavelength BEFL in the forward and backward pumping configuration respectively. Both the setup consists of a Brillouin pump (BP) with a 9.4 dBm output power, a Raman pump (RP) with a 296 mW output power that pumps the 7.7 km dispersion compensated fiber (DCF) and two laser diodes (LDs) with an output power of 48 mW and 121 mW respectively. These LDs were bi-directionally pumped a 30 m length depressed cladding fiber with a spooling diameter of 7 cm. A linear resonator consisting of two optical circulators (OC) at both ends of the setup is used. These two optical circulators also create a double pass configuration inside the cavity. Three wavelength division multiplexers (WDM) are used to combine the different wavelength inside the cavity. A 3 dB OC1 couples the signal from the BP into the cavity. A 90:10 output coupler that is being placed at different locations as shown in Fig. 2(a) and (b) is tapped 10% of this signal. This output signal is directly observed using an optical spectrum analyzer (OSA) with a resolution of 0.02 nm. The amplified spontaneous emission (ASE) of the DC-EDF fiber was pumped bi-directionally by the two LDs as shown in Fig. 3. This scheme gives efficient amplification resulting in a higher ASE spectrum being obtained. The fundamental cut-off wavelength of the fiber is dependent on the spooling diameter of the fiber. It must be between the S-band and the longer wavelength bands of the Cband and the L-band region. Thus from Fig. 3, it can be observed that the 7 cm spooling diameter of the DC-EDF used in this experiment has a cut-off wavelength between 1490 nm and 1510 nm. The ASE shows that the emission is suppressed in the c-band region, which it is at a wavelength of 1510 nm. This suppression gives a significant gain in the S-band region. Fig. 4 shows the tunable multiple-Brillouin lasing at different settings of wavelengths at BP. Note that this multi-wavelength Brillouin lasing are obtained from the experimental setup in Fig. 1(a). The power setting of the BP is kept constant at 9.4 dBm but the wavelength of the signal is varied at 1500 nm, 1502 nm and 1504 nm. From the output spectrum of 13, 12 and 11 peaks are obtained at 1500 nm, 1502 nm and 1504 nm respectively. The lasing peaks at 1500 nm are more stable and fluctuates less as compared to 1502 nm and 1504 nm lasing. Due to the less numbers of fluctuations of the lasing spectrum and the highest number of peaks obtained at 1500 nm, the multi-
Fig. 4. The tunable multiple-Brillouin lasing peaks at different wavelengths of Brillouin pumping.
Fig. 6. The stability of the multi-Brillouin lasing spectrum at 1500 nm.
Brillouin lasing at this wavelength is chosen for close scrutiny. Fig. 5 shows the 13 Brillouin peaks generated with a constant spacing of 0.08 nm. The peak power of this multiple Brillouin pulses is stable at a power of 46 mW with about 1 dB fluctuation in each peak except for the second peak on the left hand side of the spectrum and the last peak at the right hand side of the lasing spectrum. The highest output power of the second peak is due to the first Stokes. The high power value of the first Stoke is essential for the generation of the multi-Brillouin peaks. In order to ensure the stability of the multi-Brillouin lasing, the results are repeated a number of times from 00 to 04 ns. Fig. 6 shows the stability and evolution of the lasing spectrum. It can be seen that the same spectrum is almost reproducible. The time interval between two spectrums is 60 s. The generation of multi-Brillouin lasing is much dependent on the pumping power that interacts with the acoustic wave. Fig. 7 shows the changes in the multi-Brillouin lasing spectrum obtained when the power of RP is varied between 296 mW and 225 mW. It can be observed that the numbers of multiBrillouin peaks obtained varies from 13 peaks to 6 peaks when the RP power is decreased. These results indicate that the number of Brillouin peaks and anti-stokes are also reduced when RP power is decreased. The generation of multi-Brillouin lasing is much dependent on the pumping power that interacts with the acoustic wave. Fig. 8 shows the changes in the multi-Brillouin lasing spectrum obtained when the power of RP is varied between 296 mW and 225 mW. It can be observed that the numbers of multi-Brillouin
Fig. 7. Multi-Brillouin lasing spectrum at different Raman pump power.
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Fig. 8. The multi-Brillouin peaks obtained at different wavelength setting of Brillouin pumping.
Fig. 9. Multi-Brillouin lasing spectrum with BP wavelength set at 1504 nm.
peaks obtained varies from 13 peaks to 6 peaks when the RP power is decreased. Fig. 1(b) shows the multi-wavelength BEFL setup for the backward pumping configuration. The 90:10 output coupling is placed after the OC2 coupler in this configuration. In the forward pumping configuration, the highest numbers of multi-Brillouin peaks are obtained at the 1500 nm BP wavelength. In the backward pumping scheme, the numbers of multi-Brillouin peaks are obtained when the setting wavelengths of BP are at 1502 nm and 1504 nm as compared to the number of peaks when the BP wavelength are set at 1500 nm wavelength. Fig. 9 shows, 8 number of peak obtained at the wavelength of 1500 nm, where 10 peaks are observed when the wavelength of the BP is set at 1502 nm and 1504 nm. From Fig. 10, an optical spectrum analyzer (OSA) with a resolution of 0.07 nm is used to analyze the output of the proposed setup. The operation of the experimental setup is also follows; the BP generates a 1500 nm signal at 1.96 dBm, where it enters Port 1 of the first OC. The signal then travels onward to the DCF, where the nonlinear interaction provides the first Stokes wavelength. The BP and Stokes then travels onwards to the second OC where it is reflected back to the DCF and again to Port 2 of the first OC, where it will now exit via Port 3 which is connected to the OSA. The experimental setup is shown in Fig. 10. The dark soliton generator consists of a fiber laser based on a non-linear gain medium that is placed in a linear cavity. The non-linear gain medium is a 7.7 km dispersion compensating fiber (DCF) which is pumped by a 1500 nm Brillouin pump (BP) at 1.96 dBm. An optical circulator
Fig. 10. Shows an experimental setup.
Fig. 11. Shows dark soliton propagation over time, which is similar to a potential well, where (a) a dark soliton train and (b) a modulated soliton train.
(OC) is used at one end of the setup to act as a fiber based mirror, with Port 3 connected to Port 1 while Port 2 is connected to the rest of the experimental setup. Another OC is also used in the experimental setup to guide the incoming and outgoing signals. From Fig. 11, the soliton propagation over time can be obtained. As can be seen in the figure, the soliton pulse maintains its shape through the time of testing with no observable fluctuation in the power or wavelength. This is critical as any slight fluctuation cause the beam to lose its hold over the transported atom or molecule, effectively dropping it. 4. Dynamic tweezers In operation, the generated dark soliton pulse, for instance, with 50-ns pulse width, and a maximum power of 0.65 W is input into the dark–bright soliton conversion system as shown in Fig. 1. The suitable ring parameters are used, such as ring radii where R1 = 10.0 m, R2 = 7.0 m, and R3 = 5.0 m. In order to make the system associate with the practical device [12,13], whereas the selected parameters of the system are fixed to 0 = 1.50 m, n0 = 3.34 (InGaAsP/InP). The effective core areas are Aeff = 0.50, 0.25, and 0.10 m2 for a MRR and NRR, respectively. The waveguide and coupling loses are ˛ = 0.5 dB mm−1 and = 0.1, respectively, and the coupling coefficients s of the MRR are ranged from 0.05 to 0.90. However, more parameters are used as shown in Fig. 1. The nonlinear refractive index is n2 = 2.2 × 10−13 m2 /W. In this case, the waveguide loss used is 0.5 dB mm−1 . The input dark soliton pulse is chopped (sliced) into the smaller signals, where the filtering signals within the rings R2 and R3 are seen. We find that the output signals from R3 are smaller than from R1 , which is more difficult to detect when it is used in the link. In fact, the multistage ring system is proposed due to the different core effective areas of the rings in the system, where the effective areas can be transferred from 0.50 to 0.10 m2 with some losses. The soliton signals in R3 is entered in the add/drop filter, where the dark–bright soliton conversion can be performed by using Eqs. (4) and (5). Results obtained when a dark soliton pulse is input into a MRR and NRR system as shown in Fig. 1. The add/drop filter is formed by using two couplers and a ring with radius (Rd ) of 10 m,
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Fig. 13. The dynamic optical tweezers output within the add/drop filter, when the bright soliton input with the central wavelength 0 = 1.5 m, where (a) add/drop signal, (b) dark–bright soliton collision, (c) optical tweezers at throughput port, and (d) optical tweezers at drop port.
Fig. 12. Results of the soliton signals within the ring resonator system, where (a) ring R1 , (b) ring R2 , (c) and (d) ring R3 , and (d) and (e) dark–bright solitons conversion at the add/drop filter. The input dark soliton power is 2 W.
the coupling constants (41 and 42 ) are the same values (0.50). When the add/drop filter is connected to the third ring (R3 ), the dark–bright soliton conversion can be seen. The bright and dark solitons are detected by the through (throughput) and drop ports as shown in Fig. 12(d) and (e), respectively. In application, the dynamic optical tweezers is occurred, when we added bright soliton input at the add port with shown in Fig. 1, the parameters of system are set the same as the previous section. The bright soliton was generated at the central wavelength 0 = 1.5 m, when the bright soliton propagating into the add/drop system, the occurrence of dark-bright soliton collision in add/drop system is shown in Fig. 13(a) and (b). The tunable dark soliton is as shown in Fig. 14, whereas the smallest dark soliton width of 16 nm is obtained as shown in Fig. 14(d). The output soliton can be configured as the dynamic tweezers, where the use of such tweezers for trapping and transportation is possible, which will be discussed in the next section.
Fig. 14. The tuned dynamic optical tweezers output within the add/drop filter, when the bright soliton input with the central wavelength 0 = 1.5 m, where (a) the add/drop signal, (b) dark–bright soliton collision, (c) optical tweezers at throughput port, and (d) optical tweezers at drop port.
tal polarization states corresponds to an optical switch between the short and the long pulses. We assume those horizontally polarized pulses with a temporal separation of t. The coherence time of the consecutive pulses is larger than (t. Then the following state
5. Quantum tweezers and transportation Let us consider that the case when the dark soliton output is partially input into the quantum processor unit. Generally, there are two pairs of possible polarization entangled photons forming within the ring device, which are represented by the four polarization orientation angles as [0◦ , 90◦ ], [135◦ and 180◦ ]. These can be formed by using the optical component called the polarization rotatable device and a polarizing beam splitter (PBS). In this concept, we assume that the polarized photon can be performed by using the proposed arrangement. Where each pair of the transmitted qubits can be randomly formed the entangled photon pairs. To begin this concept, we introduce the technique that can be used to create the entangled photon pair (qubits) as shown in Fig. 15, a polarization coupler that separates the basic vertical and horizon-
Fig. 15. A schematic of an entangled photon pair manipulation within a ring resonator. The Bell’s state is propagating to a rotatable polarizer and then is split by a beam splitter (PBS) flying to detector D1 and D2 .
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Fig. 16. A schematic of atomic/molecular router and network system, where Ri , Rj : ring radii and is , js are the coupling coefficients.
is created by Eq. (6) [16].
˚ = 1, H 1, H + 2, H 2, H (6) p s i s i
In the expression k, H , k is the number of time slots (1 or 2),
where denotes the state of polarization [horizontal H or vertical
V ], and the subscript identifies whether the state is the signal (s) or the idler (i) state. In Eq. (6), for simplicity, we have omitted an amplitude term that is common to all product states. We employ subsequent equations in this paper. This the same simplification in
two-photon state with H polarization shown by Eq. (6) is input into the orthogonal polarization-delay circuit shown schematically. The delay circuit consists of a coupler and the difference between the round-trip times of the micro ring resonator, which is equal to t. The micro ring is tilted by changing the round trip of the ring is converted into V at the delay circuit output. That is the delay
circuits convert k, H to be
r k, H + t2 exp(i) k + 1, V + rt2 exp(i3 ) k + 2, V
+r2 t2 exp(i3 ) k + 3, V . Where t and r is the amplitude transmittances to cross and bar ports in a coupler. Then Eq. (6) is converted into the polarized state by the delay circuit as
˚ = [1, H + exp(is )2, V ] × [1, H + exp(ii )2, V ] s s i i
+ [2, H + exp(is )3, V ] × [2, H + exp(ii )2, V ] s s i i
= [1, H 1, H + exp(ii )1, H 2, V ] s i s i
(7) + exp(is ) 2, V s 1, H + exp[i(s i
+ i )]2, V 2, V + 2, H 2, H s i s i
+ exp (ii ) 2, H 3, V + exp (is ) 3, V 2, H s i s i
+ exp[i (s + i )]3, V 3, V s
i
By the coincidence counts in the second time slot, we can extract the fourth and fifth terms. As a result, we can obtain the following polarization entangled state as
˚ = 2, H 2, H + exp[i(s + i )]2, V 2, V s i s i
(8)
We assume that the response time of the Kerr effect is much less than the cavity round-trip time. Because of the Kerr nonlinearity of the optical device, the strong pulses acquire an intensity dependent phase shift during propagation. The interference of light pulses at a coupler introduces the output beam, which is entangled. Due to the polarization states of light pulses are changed and converted while circulating in the delay circuit, where the polarization entangled photon pairs can be generated. The entangled photons of the nonlinear ring resonator are separated to be the signal and idler photon probability. The polarization angle adjustment device is applied to investigate the orientation and optical output intensity, this concept is well described by the published work [17]. By using the reasonable dark–bright soliton input power, the tunable optical tweezer can be controlled, which can be used as the dynamic optical tweezer probe. The smallest tweezer width of 16 nm is generated and achieved. In application, such a behavior can be used to confine the suitable size of light pulse or molecule, which can be employed in the same way of the optical tweezer. But in this case the terms dynamic probing is come to be a realistic function, therefore, the transportation of the trapped atom/molecule/photon is plausible. Moreover, the trapped states of the transported atom/molecule can be configured by using the quantum processor as shown in Fig. 15. Thus, the transported atom with long distance link via quantum tweezer is realized. From the above reasons, the transmission of atoms/molecules from dark soliton pulses via a wavelength router is plausible, which can be described by the following reasons: (i) a dark soliton pulse can propagate into the optical device/media, (ii) atom/molecule being trapped by tweezers force during the movement, the atom/molecule recovery can be realized by using the optical detection scheme, where the dark–bright soliton conversion technique is also available [18]. From Fig. 16, the transmission atoms/molecules can be performed by the dark soliton pulse, the atoms/molecules recovery can be taken by using the add/drop filter incorporating in the wavelength router, i.e. optical network. However, the separation of atoms/molecules from light pulse is required to have the specific environment, which becomes the interesting research area, where light with the specific wavelength (i ) is detected by a detector, while the required molecule is absorbed by the specific environment. The atom/molecule states can be allocated by using the quantum processing unit as shown in Fig. 16, where the corresponding states of the transmitted atom/molecule between input and output states can be recognized and formed the
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Fig. 17. Laser tool mechanism diagram, where Rs : ring radii, s : coupling coefficients, Rd : an add/drop ring radius, Aeff s: effective areas.
secret information. Therefore, in practice, the quantum processing unit is required to connect into the system, where the input and output states can be linked and obtained the required information. 6. Trapping forces In operation, the trapping forces are exerted by the intensity gradients in the strongly focused beams of light to trap and move the microscopic volumes of matters, in which the optical forces are customarily defined by the relationship [19]. F=
Qnm P c
(9)
where Q is a dimensionless efficiency, nm is the index of refraction of the suspending medium, c is the speed of light, and P is the incident laser power, measured at the specimen. Q represents the fraction of power utilized to exert force. For incident plane wave on a perfectly absorbing particle, Q is equal to 1. To achieve stable trapping, the radiation pressure must create a stable, threedimensional equilibrium. Because biological specimens are usually contained in aqueous medium, the dependence of F on nm can rarely be exploited to achieve higher trapping forces. Increasing the laser power is possible, but only over a limited range due to the possibility of optical damage. Q itself is therefore the main determinant of trapping force. It depends upon the NA (numerical aperture), laser wavelength, light polarization state, laser mode structure, relative index of refraction, and geometry of the particle. Furthermore, in the Rayleigh regime, trapping forces decompose naturally into two components. Since, in this limit, the electromagnetic field is uniform across the dielectric, particles can be treated as induced point dipoles. The scattering force is given by
Fscatt = nm
S
c
where
=
8 4 (kr) r 2 3
,
(10)
m2 − 1 m2 + 2
2 (11)
is the scattering cross section of a Rayleigh sphere with radius r. S is the time averaged Poynting vector, n is the index of refraction of the particle, m = n/nm is the relative index, and k = 2nm / is the wave number of the light. Scattering force is proportional to the energy flux and points along the direction of propagation of the incident light. The gradient field (Fgrad ) is the Lorentz force acting on the dipole induced by the light field. It is given by Fgrad =
˛ 2
∇ E , 2
where ˛ = n2m r 3
m2 − 1 m2 + 2
(12)
(13)
is the polarizability of the particle. The gradient force is proportional and parallel to the gradient in energy density (for m > 1). The large gradient force is formed by the large depth of the laser
beam, in which the stable trapping requires that the gradient force in the −ˆz direction, which is against the direction of incident light (dark soliton valley), and it is greater than the scattering force. By increasing the NA, when the focal spot size is decreased, the gradient strength is increased [19], which can be formed within the tiny system, for instance, nanoscale device (nanoring resonator). 7. An atomic collision concept A model of an atomic collision system is as shown in Fig. 17. The generated dark soliton pulse from the experiment can be amplified and tuned dynamically from both ends, whereas the analytical details are shown in the previous section. Here, after the input dark soliton pulse is amplified and reached the desired value, the optical energy can be storage within a ring resonator R3 , which has been designed and well described by Refs. [19,20]. The controlled parameters are the coupling coefficients, (31 , 3 and 32 ) that can be chosen to control the output energy. However, the other source is required to obtain the dynamic tunable tweezers, therefore, the other soliton pulse is input into the add port of the add/drop filter as shown in Fig. 1. To operate the system, we can explain the atomic collision system as the following details. The resonant dark soliton output from the throughput port is entered into the atomic chamber, where in some ways there are some atoms trapped by the dark soliton, i.e. optical tweezers, which is become the output trapping atom, while the another system is also performed. The collision is perform in the collision/atomic chamber, which the high protection and shield are required. 8. Dual mode atomic-laser tools operation A model of a dual mode atomic-laser gun is as shown in Fig. 18. The generated dark soliton pulse from the experiment can be amplified and tuned dynamically, which is shown in details in the previous section. In principle, the dual mode atom-laser gun functions can operate by using the dark–bright soliton conversion and collision control, which is analyzed and discussed in the previous section. Here, each part of the system as shown in Fig. 18 can be described as following details. After the input dark soliton pulse is amplified and reached the desired value, the optical energy can be storage within a ring resonator R3 which has been designed and well described by Refs. [19,20]. The controlled parameters are the coupling coefficients, (31 , 3 and 32 ) that can be chosen to control the output energy. However, the other source is required to obtain the dynamic tunable tweezers, therefore, the other soliton pulse is input into the add port of the add/drop filter as shown in Fig. 1. To operate the system, we can explain the dual mode function as the following details. The resonant dark soliton output from the throughput port is entered into the atomic chamber, where in some ways there are some atoms trapped by the dark soliton, i.e. optical tweezers, which is become the output bullet, while, the bright soliton output become a laser output for the laser gun at the drop port, which is controlled by the alternative switch and absorber. This function is well described by the dark–bright soliton conversion.
B. Jukgoljun et al. / Optik 122 (2011) 1492–1499
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Fig. 18. Atomic tool mechanism diagram, where Rs : ring radii, s : coupling coefficients, Rd : an add/drop ring radius, Aeff s: effective areas.
9. Conclusion We have successfully generated the multi-dark soliton using forward and backward pumping of the S-band erbium doped fiber, where the Stimulated Brillouin Scattering (SBS) is a nonlinear interaction between pump fields with Stokes field through the acoustic wave. The pumping power generated an acoustic wave and caused perturbation to the refractive index of the fiber which functions as a grating and scatters light into the lower frequency. Results obtained have shown that the stable multi dark soliton can be generated. The use of muti-dark soliton pulses to form the optical and quantum tweezers are described, the atoms/molecules trapping and transportation using quantum tweezers via a wavelength router is discussed, where in this case the quantum states of the transported atoms/molecules are specified, which is allowed to use in quantum information applications. We have shown that the propagating dark soliton within the MRR and NRR system can be converted to be a bright soliton by using the ring resonator system, incorporating the add/drop multiplexer, moreover, the amplification and tenability of the dark soliton pulse can be obtained. By using the reasonable dark–bright soliton input power, the tunable optical tweezers can be controlled, which can be used as the dynamic optical tweezers probe. In application, such a behavior can be used to confine the suitable size of light pulse or molecule, which can be employed in the same way of the optical tweezers. But in this case the terms dynamic probing is come to be a realistic function. Moreover, the transportation of the trapped pulse or molecule is plausible. Finally, we have shown that the use of the tunable dynamic tweezers for the atomic collision investigation is also plausible. We have also shown that the use of the tunable dynamic tweezers for a dual mode atomic and laser gun is also plausible. References [1] D. Jaksch, H.-J. Briegel, J.I. Cirac, C.W. Gardiner, P. Zoller, Entanglement of atoms via cold controlled collisions, Phys. Rev. Lett. 82 (1999) 1975–1978.
[2] T. Calarco, H.-J. Briegel, D. Jakch, J.I. Cirac, P. Zoller, Quantum computing with neutral atoms, J. Mod. Optic. 47 (2007) 2137–2142. [3] M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, England, 2000. [4] P.W.H. Pinkse, T. Fischer, P. Maunz, G. Rempe, Trapping an atom with single photons, Nature 404 (2000) 365–368. [5] S.M. Block, Making light work with optical tweezers, Nature 360 (1992) 493–495. [6] A. Ashkin, J.M. Dziedzic, T. Yamane, Optical trapping and manipulation of single cells using infrared laser beams, Nature 330 (1987) 769–771. [7] K. Svoboda, S.M. Block, Biological applications of optical forces, Annu. Rev. Biophys. Biomol. Struct. 23 (1994) 247–285. [8] J. Conia, B.S. Edwards, S. Voelkel, The micro-robotic laboratory: optical trapping and scissing for the biologist, J. Clin. Lab. Anal. 11 (1997) 28– 38. [9] R.B. Diener, B. Wu, M.G. Raizen, Q. Niu, Quantum Tweezer for Atoms, Phys. Rev. Lett. 89 (2002) 070401. [10] S. Mitatha, N. Pornsuwancharoen, P.P. Yupapin, A simultaneous short-wave and millimeter-wave generation using a soliton pulse within a nano-waveguide, IEEE Photon. Technol. Lett. 21 (2009) 932–934. [11] G.P. Agarwal, Nonlinear Fiber Optics, 4th edition, Academic Press, New York, 2007. [12] C. Fietz, G. Shvets, Nonlinear polarization conversion using microring resonators, Opt. Lett. 32 (2007) 1683–1685. [13] Y. Kokubun, Y. Hatakeyama, M. Ogata, S. Suzuki, N. Zaizen, Fabrication technologies for vertically coupled microring resonator with multilevel crossing busline and ultracompact-ring radius, IEEE J. Sel. Top. Quantum Electron. 11 (2005) 4–10. [14] P.P. Yupapin, P. Saeung, C. Li, Characteristics of complementary ring-resonator add/drop filters modeling by using graphical approach, Opt. Commun. 272 (2007) 81–86. [15] P.P. Yupapin, W. Suwancharoen, Chaotic signal generation and cancellation using a micro ring resonator incorporating an optical add/drop multiplexer, Opt. Commun. 280/2 (2007) 343–350. [16] S. Suchat, W. Khannam, P.P. Yupapin, Quantum key distribution via an optical wireless communication link for telephone network, Opt. Eng. Lett. 46 (10) (2007) 100502. [17] P.P. Yupapin, S. Suchat, Entangle photon generation using fiber optic MachZehnder interferometer incorporating nonlinear effect in a fiber ring resonator, Nanophotonics (JNP) 1 (2007) 13504. [18] K. Sarapat, N. Sangwara, K. Srinuanjan, P.P. Yupapin, N. Pornsuwancharoen, Novel dark–bright optical soliton conversion system and power amplification, Opt. Eng. 48 (2009) 0450041. [19] K. Svoboda, S.M. Block, Biological applications of optical forces, Annu. Rev. Biophys. Biomol. Struct. (1994) 247–282. [20] P.P. Yupapin, N. Pornsuwancharoen, Proposed nonlinear micro ring resonator arrangement for stopping and storing light, IEEE Photon. Technol. Lett. 21 (2009) 404–406.