2 two-photon transition in rubidium using femtosecond frequency comb

Measurement 144 (2019) 83–87

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Absolute frequency measurement of the hyperfine structure of the 5S1/2 – 5D3/2 two-photon transition in rubidium using femtosecond frequency comb Osama Terra National Institute of Standards (NIS), Tersa St. Haram, Code:12211, P.O. Box: 136, Giza, Egypt

a r t i c l e

i n f o

Article history: Received 24 November 2018 Received in revised form 20 March 2019 Accepted 12 April 2019 Available online 18 April 2019 Keywords: Optical frequency standards Two-photon transition in rubidium Femtosecond frequency comb

a b s t r a c t In this paper, the absolute optical frequencies of the hyperfine components of the 5S1/2 – 5D3/2 twophoton transition in rubidium is measured using a femtosecond frequency comb (OFC). In order to Interrogate this transition, a laser light at a wavelength of 778.2 nm is used. This wavelength is obtained from the frequency doubling of a telecom wavelength at 1556.4 nm emitted from a narrow linewidth fiber laser. The absolute frequency measurement with OFC is performed while the laser frequency is locked to each hyperfine component of the transition. The measurement uncertainty is estimated to be as low as ±3.4 kHz at 2 r after correcting the main systematic shifts. The stability of the 85Rb 5S1/2(Fg = 3) 5D3/2 (Fe = 4) hyperfine component shows a Standard Allan Deviation of 3  10 12 at 1 s, which reaches 7  10 13 at 1000 s. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction With the advent of narrow linewidth lasers at different wavelength regions, it was possible to observe extremely narrow transitions in cold atoms or trapped ions which facilitate the redefinition of the second and the determination of the fundamental constants [1,2]. Furthermore, it endorses the development of Doppler-free based optical frequency standards (OFS), which opens the door for different applications such as length metrology and optical telecommunications [1,2]. Optical telecommunications are rapidly developing with the continual introduction of newer technologies to increase the communication bandwidth. The most promising new technologies are the Wavelength Division Multiplexing and the coherent communication [3,4]. Both technologies require the measurement of wavelength accuracy and stability of telecommunication lasers. Wavemeters and optical spectrum analyzers (OSA) are used to measure the wavelength of these lasers. Therefore, the calibration of wavemeters and OSAs is crucial to assure the accuracy of the measured wavelengths which facilitates the development of such new technologies. For the calibration of grating based OSAs with accuracies as low as few picometers, Hydrogen cyanide (H13C14N) gas cell with accurately determined molecular energy level transitions in the range from 1530 nm to 1560 nm is commonly used [5].

E-mail addresses: [email protected], [email protected] https://doi.org/10.1016/j.measurement.2019.04.042 0263-2241/Ó 2019 Elsevier Ltd. All rights reserved.

However, for the calibration of wavemeters with accuracies down to the sub-picometer (typically ± 0.2 pm), the frequency accuracy of the hydrogen cyanide cell is not sufficient. Therefore, OFS with better accuracy than that of the hydrogen cyanide cell is required. Iodine stabilized He-Ne lasers at 633 nm are commonly used for the wavemeter calibration since they usually exists as a primary length standard in many metrology institutes [6]; however, nonlinearities in the wavemeter promotes the need for OFS in the telecommunication wavelength. Optical clocks based on cold atoms and ion traps provides ultraprecise frequency values, however, they are still so complicated to build, expensive, not portable and also not operating in the telecommunication range [2,7]. In addition, their superior accuracy is not required for such calibration. Therefore, several relatively simple OFSs that span the telecommunication wavelength range are of great importance to complete the chain of traceability for the telecommunication devices. The Consultative Committee for Length (CCL) recommended the use of the absorption line P (16) in acetylene (13C2H2) near 1542.38 nm with an uncertainty of 5 kHz or (2.6  10 11) for the practical realization of meter [8]. In addition, the absolute frequencies in the telecommunication range of twophoton transition (TPT) 5S1/2 – 5D5/2 in Rb are accurately measured [9]. Another promising transition with slightly better uncertainty is the TPT (5S1/2 – 5D3/2) in rubidium. Unfortunately, the absolute frequency of this transition was measured only once using an optical frequency chain by Nez et al. in 1993 [10]. Based only on this

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O. Terra / Measurement 144 (2019) 83–87

measurement, the CIPM adopted their absolute frequency values [11]. Optical frequency chains provide a complicated means for absolute optical frequency measurement [12]. It involves several frequency multiplications and intermediate oscillators to close the gap between the optical frequencies and the SI unit of time. Such complicated procedure can be susceptible to different sources of errors. Therefore, the need for additional reliable measurement for the absolute frequencies of this transition is a perquisite. Recently, with the advent of femtosecond frequency comb, the direct link between optical and microwave frequencies become possible [13]. Therefore, frequency combs not only can provide full characterization of the stabilized lasers in terms of stability but they can also facilitate the direct traceability of optical frequencies to the SI unit of time. In this work, a fiber laser near 1556 nm is frequency doubled to 778 nm to interrogate the hyperfine components of the TPT (5S1/2 – 5D3/2) in a vapor cell of rubidium with natural abundance of 28% for 87Rb and 72% for 85Rb. Subsequently, the frequency of fiber laser is locked to each hyperfine component of this transition. A femtosecond frequency comb is used then to measure the absolute frequency of each hyperfine component of this transition. The uncertainty in the measured frequencies and the correction factors is then estimated. Finally, the measured optical frequency values are compared to the only known values published by Nez et al. in 1993 for the same transition measured using an optical frequency chain.

3. Experimental setup In this section, a setup is introduced to lock the laser frequency to each hyperfine component of the TPT while measuring the absolute frequency of that component using a femtosecond frequency comb, see Fig. 2. The setup comprises a fiber laser from NKTphotonics (Adjustik-E15) which operates at 1556.4 nm with output power of 43 mW. The laser has a thermal wavelength tuning range of 2 nm and Piezo wavelength tuning range of 22 pm with 20 kHz bandwidth. Part of the laser beam is sent to another laboratory where the femtosecond frequency comb is located through 30 m of standard single mode fiber. The other part is directed to an Erbium-doped fiber amplifier (Pritel-FA30) to amplify the laser power to be sufficient for the frequency doubling process. The amplified light is directed to a waveguide crystal of PeriodicallyPoled Lithium-Niobate (WG-PPLN) (HC-Photonics), where the frequency doubling process occurs. The WG-PPLN crystal which has a poling period of approximately 20 mm and 40 mm length is maintained at 48.5 °C to enable the second-harmonic generation process. Since the frequency doubling process is polarization sensitive, an active polarization controller (General Photonics PCDM02-3X) is introduced before the WG-PPLN crystal to actively control the fundamental light polarization. Since the active control is based on detecting the change in optical power out of the crystal

2. The two-photon transition Hyperfine structures in any transition are often concealed by the Doppler broadening of spectral lines. Different techniques have been introduced to eliminate the Doppler broadening from atomic and molecular transitions. Among these techniques, the saturated absorption (SA) and two-photon absorption (TPA) are the most commonly-known. The TPA in rubidium atom takes place by simultaneously absorbing two photons from opposite directions. In this way, the Doppler shifts due to the motion of atoms during the absorption will be cancelled since photons from opposite directions will have opposite signs [14]. Therefore, unlike the SA where only the atoms at rest contribute to the absorption, in the TPA, all atoms contribute to the absorption independent of their velocities and will produce a Doppler-free absorption linewidth. Consequently, the signal-to-noise ratio (SNR) of the TPA is superior to that of the SA. When a laser wavelength is tuned to this transition, fluorescence light at 420 nm will be detected from the spontaneous decay 5D-6P-5S. Fig. 1 demonstrates the two-photon process together with the hyperfine levels for the 5S1/2–5D3/2 TPT in natural rubidium measured here and elsewhere [11].

Fig. 2. Absolute frequency measurement setup of the 5S1/2 – 5D3/2 TPT in rubidium. WGPPLN: waveguide periodically-poled Lithium-Niobate crystal, APC: Active polarization controller, EDFA: Erbium-doped fiber amplifier, C: triplet collimator, L: Convex Lens, M: flat sliver mirror, F: filter, PC: polarization controller, BS: beam splitter, fr: repetition rate, fo: offset frequency, PD: photodetector, TEC: Thermoelectric element.

Fig. 1. Hyperfine levels for the 5S1/2–5D3/2 TPT in natural rubidium measured here and elsewhere [11].

O. Terra / Measurement 144 (2019) 83–87

to stabilize the light polarization, a fixed power level for the twophoton process is insured. A collimator (Thorlabs-TC12FC780) is used to collimate the light exiting the fiber. The light is then filtered using a 780 nm optical filter to eliminate the fundamental wavelength at 1556 nm. The pure 778 nm light is then focused at the center of a natural rubidium gas cell (Thorlabs-CQ19075RB) using 260 mm convex lens. The beam radius at focus is measured using a beam profiler (Thorlabs-BP209VIS) to be 100 mm. A reflecting mirror and another focusing lens are used to align the counterpropagating beam back exactly at the same focus. The rubidium cell is sustained in a thermally-conducting box in such a way that permits heating the cell with flat thermoelectric elements. Two thermoelectric elements, a thermocouple and a temperature control circuit are used to keep cell temperature at 95 ± 1 °C. A photomultiplier detector (PMT) (Thorlabs-PMM01) is used to detect the fluorescence signal at 420 nm. A 420 nm interference filter and a 50 mm collimating lens are used to filter and focus the fluorescence signal at the PMT detector. Since earth’s magnetic field can cause shift in the transition frequencies, the Rb cell together with the PMT are placed in a magnetic shield. The shield which is made from m-metal helps to isolate the magnetic field of earth to less than 10 mG (limited by the measurement device). Although room light is kept off during the measurement, an extra light-isolation is applied to PMT detector to obtain high detection SNR. The output of the PMT is directed to the frequency locking electronics, which consists of a lock-in amplifier (SRS-SR850), a highspeed PID controller (Newport-LB1005), a waveform generator (SRS-DS345) and an Oscilloscope. The lock-in amplifier applies a modulation signal to the fiber laser with frequency of 16 kHz and amplitude of 200 mV, which was sufficient to dither the laser frequency over a hyperfine component of the TPT. Consequently, the output of the lock-in amplifier represents a derivative-like signal which is used to lock the laser to the hyperfine component of interest. Afterwards, the fundamental wavelength (1556.4 nm) is transferred through 30 m of single-mode fiber to the femtosecond frequency comb laboratory to measure transition frequencies, see Fig. 3. The femtosecond frequency comb (Menlo systemsFC1500250WG) is a mode-locked fiber laser which emits a train of femtosecond pulses (90 fs) with repetition-rate of 250 MHz and spectral bandwidth of 34 nm that is centered at a wavelength of 1567 nm. In order to have well-known frequencies for the comb modes, the repetition rate and the offset frequency are locked to a GPS-disciplined quartz oscillator. The oscillator has a short-term

Fluorescence signal (Arb. Unit)

85

Rb (Fg=2)

1.0

0.8

85

Rb (Fg=3)

0.6 87

Rb (Fg=1)

87

Rb (Fg=2)

0.4

0.2

0.0 0

20

40

600

2120

3440 3460

Frequency (MHz) Fig. 3. Fluorescence spectrum of the hyperfine structure of the TPT (5S1/2-5D3/2) in rubidium.

85

stability of 5  10–12 at 1 s that reaches 5  10–13 at 400 s. Therefore, all comb modes are expected to have the same stability as the reference oscillator. A beat between the laser and the nearest comb mode of number N is counted using a zero dead-time frequency counter (FXM50). The number of the comb mode N is obtained by measuring the change in the beat frequency between the laser and the N-th mode as the repetition rate changes [15]. 4. Results and discussion 4.1. Hyperfine structure of the transition The fluorescence spectrum of the hyperfine component of the TPT (5S1/2-5D3/2) is obtained by sweeping the frequency of a fiber laser over each group of hyperfine components with the same ground transition. The laser is swept by applying a suitable voltage to the piezo tuning port of the fiber laser. The laser linewidth is found to be 3.4 kHz, from a measurement using the selfheterodyne technique in a previous work by the author [9]. The laser’s linewidth was sufficient to resolve the narrow hyperfine levels of this transition, as shown in Fig. 3. 4.2. Frequency measurement Some parameters have to be considered before locking the laser frequency to the TPT. First, and foremost, laser power has to be stable enough and measured precisely since it greatly affects the absolute value and the stability of the laser frequency due to the AC Stark shift. Laser power change originates mainly from the dependence of the frequency doubling efficiency on the polarization of the input light. Therefore, by using active polarization controller to fix the polarization of the input light will keep the output power from the PPLN crystal stable; especially, since the active polarization control technique depends on detecting the power change on a portion of the output power from the WG-PPLN crystal. The modulation frequency and depth has to be selected carefully, since they affect the attained accuracy and stability. Based on a previous work by the author, the second harmonic power is chosen to be 5 mW while the modulation frequency is chosen to be 16 kHz, and the modulation depth is chosen to be 0.75 MHz [9]. The Rb cell temperature is maintained at 95 °C during the measurement (except for the 85Rb (2 ? 1) hyperfine component where it is kept at 135 °C to allow sufficient SNR of the detected fluorescence signal for laser stabilization). The frequency stability of the laser, which is stabilized to the 85Rb 5S1/2 (Fg = 3)-5D3/2 (Fe = 4) hyperfine component, is measured with the femtosecond frequency comb. The Allan Standard Deviation (ADEV) of the beat signal between the comb and the laser is found to be around 3  10 12 at 1 s (most probably limited by comb stability), reaching 7  10 13 at 1000 s, see Fig. 4. Table 1 depicts the result of the absolute frequency measurement on the hyperfine component of the TPT (5S1/2-5D3/2) using a femtosecond frequency comb, which was the only measurement on this transition with the femtosecond comb. Although, there was one old measurement on this transition back to 1993, it was made using a Cs-linked frequency chain [12]. The values reported by the old measurement are also placed in Table 1 for comparison. The results from the current measurement show a great match to the old results. The frequency differences between both measurements are ranging from 0 to 4.2 kHz, which lies in the uncertainty budget from both measurements. 4.3. Systematic shifts and uncertainty evaluation The effect of the various systematic shifts on the measured absolute frequency of the hyperfine components should be consid-

O. Terra / Measurement 144 (2019) 83–87

1E-11

4

(a)

3

(b)

2

Relative ADEV

Frequency (kHz) - 385 240 698 496 kHz

86

1

1E-12

0 -1 -2 -3

1E-13

-4 0

1

3

4

6

1

7

10

100

1000

Averaging time (seconds)

Time (Hours)

Fig. 4. Measured frequency of the laser locked to the 85Rb 5S1/2 (Fg = 3)-5D3/2 (Fe = 4) (frequency = 385 240 698 496 kHz) hyperfine component (a) Frequency versus time and (b) Relative ADEV.

Table 1 The results from the current absolute frequency measurement on the hyperfine components of the TPT (5S1/2-5D3/2) in rubidium (after correction of systematic shifts) together with the results from the old measurement [11]. STD: Standard deviation. Isotope

Component Fg ? Fe

Ref. [11] (kHz)

Measured frequency (kHz)

STD (kHz)

Frequency difference (kHz)

85

3?1 3?2 3?3 3?4 2?1 2?2 2?3 2?4

385 385 385 385 385 385 385 385

240 240 240 240 242 242 242 242

679 683 689 698 197 201 207 216

712.0 216.5 192.1 496.0 577.5 083.9 058.8 362.9

(5.0) (5.0) (5.0) (5.0) (5.0) (5.0) (5.0) (5.0)

385 385 385 385 385 385 385 385

240 240 240 240 242 242 242 242

679 683 689 698 197 201 207 216

711.8 216.6 193.2 496.0 573.3 081.2 056.9 363.7

3.5 2.9 2.3 2.8 3.7 1.4 3.3 2.8

0.2 0.1 1.1 0.0 4.2 2.7 1.9 0.8

87

2?0 2?1 2?2 2?3 1?3 1?2 1?1

385 385 385 385 385 385 385

240 240 240 240 243 243 243

094 101 115 137 519 533 555

977.7 727.6 692.6 803.8 070.2 031.8 144.5

(5.0) (5.0) (5.0) (5.0) (5.0) (5.0) (5.0)

385 385 385 385 385 385 385

240 240 240 240 243 243 243

094 101 115 137 519 533 555

975.3 726.6 693.9 803.5 073.4 032.4 142.3

2.6 1.7 1.2 1.4 2.2 2.6 3.4

2.4 1.0 1.3 0.3 3.2 0.6 2.2

Rb

ered before reporting the measurement results. Among those shifts, the ‘‘AC Stark shift” (called also the ‘‘Light shift”) is found to be the dominant one. Light shift must be determined at each measurement since it is sensitive to mirrors alignment. The absolute frequency of each hyperfine component is measured at two different powers, namely 5 and 10 mW to enable the accurate evaluation of the light shift. For the 85Rb (Fg = 3 ? Fe = 1), (Fg = 2 ? Fe = 1) hyperfine components the power is changed from 8 mW to 12 mW to allow sufficient SNR of the fluorescence signal for laser stabilization. The average light shift is found to be 6.8 ± 0.2 kHz/mW. Since the laser is operating at 5 mW, the average shift is found to be 34 ± 1 kHz, which is varied slightly for each transition component. The second contribution comes from the ‘‘Pressure shift”. The pressure shift is evaluated by increasing the Rb cell temperature from 75 °C to 150 °C, which corresponds to a pressure change of 533 mPa. As a result, a shift in the optical frequency of the 85Rb (Fg = 3 ? Fe = 4) hyperfine component is measured to be 38.3 ± 1 kHz, see Fig. 5, which corresponds to 72 ± 2 Hz/mPa. Since the cell is operating at 95 °C (17 mPa), the pressure shift is calculated to be 1224 ± 34 Hz. The electronics that stabilizes the laser to the TPT can introduce also an optical frequency shift. This shift is measured by introducing an offset in the electronics while measuring the absolute frequency of the 85Rb 5S1/2 (Fg = 2)-5D3/2 (Fe = 4) hyperfine component, which results 723 Hz/mV. Since this offset is set

0

Frequency shift (kHz)

Rb

-10

-20

-30

-40

70

80

90

100

110

120

130

Temperature (oC)

140

150

Fig. 5. Frequency shift of the 85Rb (Fg = 3-Fe = 4) hyperfine component as a result of Rb cell temperature increase.

to zero during the stabilization, only a possible uncertainty in the offset of 1 mV is considered, which can result from the slope of the error signal or the electronics. A l-metal sheet is used to shield the earth magnetic field, which is measured after shielding to be

O. Terra / Measurement 144 (2019) 83–87 Table 2 Uncertainty budget and corrections for the 5S1/2-5D3/2 transition in natural rubidium. Systematic effect AC Stark shift Pressure shift Electronics Error Zeeman shift Blackbody radiation shift Second-order Doppler shift Total *

Correction 34 kHz 1224 Hz 0 0 209 Hz 229 Hz 35.662 kHz

Uncertainty 1 kHz 34 Hz 723 Hz 0 13 Hz 1 Hz ±1235 Hz*

The uncertainties are summed in quadrature.

<10 mG (limited by the measurement device), which is not believed to cause a considerable shift. Therefore, it will be neglected from the calculation. There are some other nonsignificant contributions which can be considered also in the calculations. Black-body radiation shifts are calculated for rubidium at 300 K by Farely and Wing [16]. These calculations are extrapolated for 95 ± 1 °C, which results a shift of 6 Hz for 5S1/2 and 423 Hz for 5D3/2. Therefore, for 5S1/2 – 5D3/2 transition, the shift will be 209 ± 13 Hz. Although the two-photon effect succeeds to suppress the first-order Doppler shift, it doesn’t eliminate the second-order Doppler shift. If the transition frequency is (to ), this   to V 2 shift can be calculated from 2c , where V is the speed of the 2 atom [17]. For a temperature of 95 ± 1 °C, we obtain a shift of 229 ± 1 Hz. The systematic sources of uncertainty together with the applied corrections are summarized in Table 2. The uncertainty in the measured frequency values is calculated based on the contributions from the systematic shift and the standard deviation of the measurement to range from ±3.4 kHz to ±7.8 kHz at 2r (confidence of 95%) depending on the standard deviation of the hyperfine component of the TPT. 5. Conclusion An absolute frequency measurement on the hyperfine components of the 5S1/2 – 5D3/2 two-photon transition in rubidium using an optical frequency comb is performed. In order to do so, a double optical frequency standard near 1556 nm and 778 nm is developed, which is based on the 5S1/2 – 5D3/2 two-photon transition in rubidium. The frequency doubled light is generated through a PPLN waveguide crystal. This enables the interrogation of the hyperfine components of this transition at the 778 nm wavelength.

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Frequency locking electronics are used to stabilize the frequency of the fiber laser to each component of the transition. Afterwards, the absolute frequency of the hyperfine components of this transition is measured with femtosecond frequency comb. The measured frequency values are stated after the correction for the light shift as the most dominant systematic effect to the measurement uncertainty. The stability of the 85Rb 5S1/2 (Fg = 3)-5D3/2 (Fe = 4) hyperfine component shows an Allan Deviation of 3  10 12 at 1 s, reaching 7  10 13 at 1000 s. The measurement uncertainty is found to range from ±3.4 kHz to ±7.8 kHz at 2r (confidence of 95%) depending on the standard deviation of the hyperfine component of the two-photon transition. References [1] T. Udem et al., Optical frequency metrology, Nature 416 (2002) 233. [2] S.B. Koller et al., A transportable optical lattice clock with 7  10–17 uncertainty, Phys. Rev. Lett. 118 (2017) 073601. [3] R. Antil, Pinki, S. Beniwal, An overview of DWDM technology & network, Int. J. Sci. Technol. Res. 1 (11) (2012). [4] K. Kikuchi, Fundamentals of coherent optical fiber communications, J. Lightw. Technol. 34 (1) (2016) 157–179. [5] O. Terra, H. Hussein, Calibration of grating-based optical spectrum analyzers, J. Opt. 44 (4) (2015) 366–372. [6] L. Robertsson et al., Results from the CI-2004 campaign at the BIPM of the BIPM.L-K11 ongoing key comparison, Metrologia 42 (2005) 1–22. [7] U. Sterr et al., Ultrastable lasers: new developments and applications, Proc. SPIE 7431 (2009) 74310A. [8] T.J. Quinn, Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2001), Metrologia 40 (2003) 103–133. [9] O. Terra, H. Hussein, An ultra-stable optical frequency standard for telecommunication purposes based upon the 5S1/2 ? 5D5/2 two-photon transition in rubidium, Appl. Phys. B 122 (2) (2016) 27. [10] F. Nez, F. Biraben, R. Felder, Y. Millerioux, Optical frequency determination of the hyperfine components of the 5S1/2 – 5D3/2 two-photon transitions in rubidium, Opt. Commun. 102 (1993) 432–438. [11] BIPM documents, ‘‘rubidium (k778 nm)” MEP (2005). [12] H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, G. Zinner, First phase-coherent frequency measurement of visible radiation, Phys. Rev. Lett. 76 (1996) 18. [13] T. Udem, J. Reichert, R. Holzwarth, T.W. Hänsch, Accurate measurement of large optical frequency differences with a mode-locked laser, Opt. Lett. 24 (1999) 881–883. [14] J.M. Hollas, Modern Spectroscopy, fourth ed., John Wiley, 2004, p. 371. [15] L.S. Ma et al., A new method to determine the absolute mode number of a mode-locked femtosecond-laser comb used for absolute optical frequency measurements, IEEE J. Sel. Top. Quant. Elec. 9 (2003) 1066. [16] J. Farley, W. Wing, Accurate calculation of dynamic Stark shifts and depopulation rates of Rydberg energy levels induced by blackbody radiation. Hydrogen, helium, and alkali-metal atoms, Phys. Rev. A 23 (1981) 2397. [17] B. Cagnac, G. Grynberg, F. Biraben, Spectroscopie d’absorption multiphotonique sans effet Doppler, J. Phys. Frac. 34 (1973) 845–858.