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Enhanced effects of subluminal and superluminal propagation
Physics Letters A 327 (2004) 15–20 www.elsevier.com/locate/pla
Enhanced effects of subluminal and superluminal propagation Feng Xiao, Hong Guo ∗ , Luming Li, Cheng Liu, Xuzong Chen QO01 Group, Key Laboratory for Quantum Information and Measurements, Ministry of Education, and School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, PR China Received 18 November 2003; received in revised form 7 April 2004; accepted 16 April 2004 Available online 27 April 2004 Communicated by P.R. Holland
Abstract We have experimentally investigated the enhanced effects of subluminal and superluminal propagation, based on electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA), respectively. By adding only an incoherently pumping laser to each case, the slower subluminal group velocity, and the faster superluminal pulse propagation are, respectively, observed. By only changing the intensity of the incoherent pumping beam, we are able to control, respectively, the subluminal group velocity continuously from vg = c/20000 to vg = c/8300, and superluminal group velocity from vg = −c/1667 to vg = −c/3030. Qualitative explanations for the two cases are given. 2004 Elsevier B.V. All rights reserved. PACS: 42.50.Gy; 42.50.Hz; 42.62.Fi Keywords: Subluminal; Superluminal; Electromagnetically induced transparency; Electromagnetically induced absorption
1. Introduction Coherence between alternative pathways in quantum-mechanical processes have led to many interesting consequences. Among them, electromagnetically induced transparency (EIT) that was observed in 1991 for the first time [1], has attracted a great deal of recent interest in experimental and theoretical fields [2]. EIT is a technique for eliminating the absorbing effect of a medium on a propagating weak probe field in resonance of an atomic transition, with a strong coupling
* Corresponding author.
E-mail address: [email protected] (H. Guo). 0375-9601/$ – see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2004.04.032
field on another linked transition. One of the important applications of EIT is used to slow and stop light, due to its highly normal dispersion in the center of the transparent window [3]. In 1999, the light was slowed down to vg = 17 m/s by Hau et al. [4], and soon, storage of light in cold atoms [5], hot atomic vapor [6] and solid [7] have been achieved. These studies have made a great progress to push this effect to applications. Another important consequence of quantum coherence, electromagnetically induced absorption (EIA) that was firstly observed by Akulshin et al. [8] in 1998, has also been studied extensively recently both in experimental and theoretical fields [9,10], owing to its potential application to superluminal pulse propagation, which is a highlight since Wang et al. reported the
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F. Xiao et al. / Physics Letters A 327 (2004) 15–20
experiment in 2000 [11]. As an absorption enhancement effect opposite to EIT, EIA arises from the spontaneous transfer of the atomic coherence among the degenerated states from the excited level to the ground level. EIA effect, which has not been explored in a great depth, however, has been applied to the propagation with a superluminal group velocity, due to the highly anomalous dispersion where the enhanced absorption occurs [12]. In 2003, Akulshin et al. [13] and Kim et al. [14], respectively, reported the experiments, where the negative group velocities of vg = −c/5100 and vg = −c/14400 were achieved in Cs vapor cells, based on the mechanism of EIA. The above-mentioned experiments of positive and negative group velocity propagations are performed in the EIT and the EIA systems, and have some limits, such as their dispersions cannot be changed easily. A recent paper has reported that the AWI system has many advantages to slow light compared with the EIT system [15], for example, the slower and controllable group velocity can be achieved in the AWI system. In Ref. [15], the AWI system results from applying an incoherent pumping beam into the EIT system, and the polarization of the pumping beam is the same as that of the probe beam (σ − ), while it is arbitrary in this Letter with the similarly experimental results achieved. In addition, we carry out a new experimental study on the enhanced effect of the superluminal propagation by introducing an incoherent pumping into the EIA system. In the following, two experiments are performed to investigate the propagations of slow light and negative group velocity, based on the EIT and the EIA systems, respectively. Through introducing an incoherent pumping laser into each system, the slower group velocity in the first case, and the faster in the second are observed. When we change the intensities of the incoherent pumping beams, the group velocities can be controlled smoothly.
2. Experiments and results For slowing light, the energy-level scheme, which consists of two parts including the elemental EIT configuration and the incoherent pumping system, is shown in Fig. 1. We employ two lasers to couple the same transition 6S1/2(F = |3) → 6P3/2 (F = |2) with left and right circular polarizations for the cou-
Fig. 1. Schematic diagram of the atomic levels for slowing light. 6S1/2 , F = |3 and 6P3/2 , F = |2 contribute to the EIT configuration, for which ωp driving the transition 6S1/2 (F = |4) → 6P3/2 (F = |4) serves for incoherent pumping.
Fig. 2. Schematic diagram of the atomic levels for negative group velocity propagation. 6S1/2 , F = |4 and 6P3/2 , F = |5 contribute to the EIA configuration, for which ωp driving the transition 6S1/2 (F = |3) → 6P3/2 (F = |4) serves for incoherent pumping.
pling and the probe, respectively, and 6S1/2(F = |4) → 6P3/2(F = |4) for incoherent pumping, as shown in Fig. 1, where ωc , ωb , and ωp are, respectively, the coupling, the probe, and the pumping laser frequency. If the pumping laser with right circular polarization is added to the EIT configuration, it will work as an AWI system, as discussed in Ref. [15]. In our experiments, the polarization of the pumping laser can be left circular and linear. For the negative group velocity propagation, Fig. 2 shows the energy scheme, which also consists of two parts, the elemental EIA system that involves the levels of 6S1/2 (F = |4) and 6P3/2 (F = |5), and the incoherent pumping system including the levels of 6S1/2 (F = |3) and 6P3/2 (F = |4). Two left and right circularly polarized laser beams driving the transition of 6S1/2 (F = |4) → 6P3/2(F = |5) serve
F. Xiao et al. / Physics Letters A 327 (2004) 15–20
Fig. 3. The schematic experimental set-up for the two experiments. Laser1 is prepared for the coupling laser and the probe laser, and Laser2 for the incoherent pumping laser. HWP: half-wave plate; PBS: polarized beamsplitter; BS: beam splitter; QWP: quarter-wave plate; APD: avalanche photodiode.
for the coupling and the probe, respectively, and the incoherent pumping laser beam drives the transition of 6S1/2 (F = |3) → 6P3/2 (F = |4). The reason why the above two pumping beams are incoherent arises from their processes after they are applied. The first pumping beam is resonantly tuned to the transition 6S1/2 (F = |4) → 6P3/2 (F = |4), therefore, atoms excited from the ground state 6S1/2 (F = |4) by the pump beam, via the excited state 6P3/2 (F = |4), can be moved into the ground state 6S1/2 (F = |3) by spontaneous transition, which is so-called optical pumping. This process is incoherent because the optically pumped atoms have not been interacting with coupling or probe fields that produce atomic coherence until they are moved into the state 6S1/2 (F = |3). The similar process happens when the pumping beam is added in the second case. The pulse propagation experiments is carried out in cesium vapor at room temperature. A detail schematic diagram for the experimental set-up is shown in Fig. 3. Both the coupling and the probe laser beams come from Laser1, an external-cavity diode laser (Toptica DL-100) that can be tuned to the D2 line of cesium atom with the linewidth of 1 MHz, and the incoherent pumping laser beam come from Laser2, another external-cavity diode laser (Newfocus Vortex6000) with the same frequency range and linewidth. A Gaussian probe pulse is generated through slightly rotating the polarization angle of the linearly polarized coupling laser by the Pockels cell, which is controlled by a high-voltage converter amplifying the electrical signal of the Gaussian shape saved in an arbitrary
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function generator (AFG, Sony-Tektronics AFG320). The Gaussian pulse is programmed by a computer and transmitted to the AFG. The rotated polarization component perpendicular to the polarization of the coupling field serves for the probe field, where the temporal shape of the probe pulse is decided by the time-dependent voltage applied to the Pockels cell. The coupling and the probe fields overlaps. QWP1 (quarter-wave plate) converts the two linearly and orthogonally polarized fields into counter rotating circularly polarized fields, and QWP2 turns the beams, which have passed through the 5 cm long no-buffergas cesium vapor cell, again to linearly and orthogonally polarized fields. The probe field is separated from the coupling one by a Glan prism, and detected by APD1, an avalanche photodiode. The cesium vapor cell is shielded by a µ-metal sheet to protect from the earth magnetic field, so all the magnetic sub-levels in the hyperfine structures are approximately degenerate. The pumping beam has nearly the same propagating direction as the coupling beam, while the spatial angle between them is responsible for the pumping efficiency. The two experiments are performed in the same set-up, as mentioned above and shown in Fig. 3. The digital oscilloscope is triggered by the AFG, which in the same time sends an electronical Gaussian pulse to Pockels cell to generate a Gaussian probe pulse. The Gaussian probe field is splitted into two parts by BS, a beam splitter. One passes through the cesium vapor cell and propagates with subluminal (or superluminal) speed corresponding to EIT (or EIA) configuration, and the other propagates with nearly c, the vacuum speed of light. The two paths of probe pulses are, respectively, detected by APD1 and APD2, two same avalanche photodiodes (Hamamatsu APD module C5460), and compared in the digital oscilloscope. In the two experiments, firstly we block the pumping beam and obtain the pulse propagation in the EIT (or EIA) configuration, then add the pumping beam to investigate the enhanced effect on the pulse propagation. The results of subluminal propagation are shown in Fig. 4. The probe pulse is delayed by 1.3 µs in the EIT medium, where the intensity of the coupling laser is 3.28 mW/cm2 , corresponding to the Rabi frequency Ωc ≈ 6.4 MHz, and that of the probe laser 50 µW. When we add the incoherent pumping beam, with the
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Fig. 4. Pulse delay in the cases with and without pumping beam. (a) The solid curve corresponds to the reference travelling with vacuum speed c, the dotted one corresponds to travel in the EIT condition, and the dashed one with the pumping beam with left circular polarization added. (b) Normalized pulses. All pulses in the figure are the average of 32 pulses.
Fig. 5. Subluminal group velocity vs. intensity of the pumping beam.
left circular polarization and the intensity of 8 mW corresponding to the Rabi frequency Ωp ≈ 6.5 MHz, the pulse is delayed by 2.8 µs, which has an increased delay time of 1.5 µs compared with that of the former case. We find that the polarization of the pumping beam has much influence on the amplitude of the
Fig. 6. Pulse delay (advancement) in the cases with and without pumping beam. (a) The solid curve corresponds to the reference travelling with vacuum speed c, the dotted one corresponds to travel in the EIA condition, and the dashed one with the pumping beam with left circular polarization added. (b) Normalized pulses. All pulses in the figure are the average of 32 pulses.
probe pulse, but little on the delay time. The right circularly polarized pumping beam, which corresponds to an AWI system that is a special case for our experiments, leads to an amplified amplitude [15], and the other polarized ones often lead to the smaller amplitude, but the slowed group velocity is nearly same. Fig. 5 shows the dependence of the subluminal group velocity on the intensity of the incoherent pumping beam. The group velocity decreases nonlinearly, which is in accordance with a saturated tendency, with the pumping intensity. The results of the superluminal propagation are shown in Fig. 6. The probe pulse is advanced by 0.28 µs in the EIA medium, where the intensity of the coupling laser is 110 µW/cm2 , corresponding to the Rabi frequency Ωc ≈ 1.2 MHz, and that of the probe laser 50 µW. When we add the incoherent pumping beam, with the left circular polarization and the in-
F. Xiao et al. / Physics Letters A 327 (2004) 15–20
Fig. 7. Superluminal group velocity vs. intensity of the pumping beam.
tensity of 1 mW corresponding to the Rabi frequency Ωp ≈ 3.5 MHz, the advance time become 0.6 µs, 0.32 µs more than that of the former case. The polarization of the pumping beam is able to influence both the pulse amplitude and the advanced time, especially the linear one. Fig. 7 shows the superluminal group velocity versus the pumping intensity. The group velocity increases nonlinearly, which is also in accordance with a saturated tendency, with the pumping intensity.
3. Discussion and conclusion In an EIT system, the control and the probe fields drive the atoms into the coherent population trapping (CPT), the so-called “dark state”. As a result, the atomic population is “trapped” in a coherent superposition of the sub-levels in the ground states 6S1/2 (F = |3), and no population in the state 6P3/2 (F = |2). In the classic explanation [2], the probability amplitude of absorption lies on two driving terms of equal magnitude and opposite sign. One driven by the probe field, the other driven by the coupling field, and the two terms balance so that EIT occurs. When the incoherent pumping laser is added, many atoms are pumped from the state 6S1/2 (F = |4) to 6S1/2 (F = |3). So the former balance between the two terms is destroyed, while a part of the control and the probe field is absorbed and then some atoms populate the state 6P3/2 (F = |2). On the other hand, the adiabatically attenuated control field narrows the transparent window of the medium and increases coherence between the sub-levels in the ground state 6S1/2 (F = |3) [16]. Therefore, the
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probe field will be increased by the population of the state 6P3/2 (F = |2), and decreased by the narrowed transparent windows, however, more slowed due to the enhanced coherence between the sub-levels in the ground state 6S1/2 (F = |3). So, through introducing a suitable incoherent pumping, dn/dω will be larger than that in the original EIT medium. EIA occurs due to spontaneous transfer of atomic coherence between degenerate excited states (herein the sub-levels in the excited state 6P3/2 (F = |5)) to atomic coherence between degenerate ground states (herein the sub-levels in the ground state 6S1/2 (F = |4)). By introducing an incoherent optical pumping, the EIA signal is able to be amplified [17], and the spectral linewidth be narrowed due to the enhanced coherence. So, |dn/dω| will be larger than that in the EIA medium without incoherent pumping. To summarize, an incoherent pumping added to an EIT (or EIA) configuration will increase the population that take part in the interference, which makes the EIT (or EIA [17]) more efficient. In other words, adding an incoherent pumping beam will enhance the interference and coherence between the corresponding states that is responsible for the slow light (or negative group velocity) propagation, and then the normal (or anomalous) dispersion, dn/dω, which leads to a slower subluminal (or faster superluminal) group velocity. If the intensity of the added pumping changes, the dispersion of medium will follow. This is useful to change the subluminal (or superluminal) group velocity. In conclusion, by applying an incoherent pumping to an EIT (or EIA) scheme, we can obtain the enhanced coherence that lead to the slower subluminal (or faster superluminal) group velocity. Besides, we can conveniently adjust the light speed by changing only the intensity of pumping laser. It will contribute to the applications for adjusting coherence and the speed of light.
Acknowledgements This work is partially supported by the state Key Development Program for Basic Research of China (Grant No. 2001CB309308), the Key Project of National Natural Science Foundation of China (Grant No. 69789801), the National Hi-Tech ICF program, and
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the Key Project of Natural Science Foundation of the Ministry of Education of China (Grant No. 00-09).
References [1] K.J. Boller, A. Imamoglu, S.E. Harris, Phys. Rev. Lett. 66 (1991) 2593. [2] S.E. Harris, Phys. Today 50 (1997) 36. [3] L.V. Hau, S.E. Harris, Z. Duton, C.H. Behroozi, Nature 397 (1999) 594. [4] M. Xiao, Y. Li, S. Jin, J. Gea-Banacloche, Phys. Rev. Lett. 74 (1995) 666. [5] C. Liu, Z. Dutton, C.H. Behroozi, L.V. Hau, Nature 409 (2001) 490. [6] D.F. Phillips, A. Fleischhauer, A. Mair, R.L. Walsworth, M.D. Lukin, Phys. Rev. Lett. 86 (2001) 783. [7] A.V. Turukhin, V.S. Sudarshanam, M.S. Shahriar, J.A. Musser, B.S. Ham, P.R. Hemmer, Phys. Rev. Lett. 88 (2002) 023602.
[8] A.M. Akulshin, S. Barreiro, A. Lezama, Phys. Rev. A 57 (1998) 2996. [9] A.V. Taichenachev, A.M. Tumaikin, V.I. Yudin, Phys. Rev. A 61 (1999) 011802-1. [10] A. Lezama, S. Barreiro, A.M. Akulshin, Phys. Rev. A 59 (1999) 4732. [11] L.J. Wang, A. Kuzmich, A. Digariu, Nature 406 (2000) 277. [12] A.M. Akulshin, S. Barreiro, A. Lezama, Phys. Rev. Lett. 83 (1999) 4277. [13] A.M. Akulshin, A. Cimmino, A.I. Sidorov, P. Hannaford, G.I. Opat, Phys. Rev. A 67 (2003) 011801. [14] K. Kim, H.S. Moon, C. Lee, S.K. Kim, J.B. Kim, Phys. Rev. A 68 (2003) 013810. [15] K. Kim, F. Xiao, C.H. Lee, S.K. Kim, X.Z. Cheng, J.B. Kim, J. Phys. B: At. Mol. Opt. Phys. 36 (2003) 2671. [16] M. Fleichhauer, M.D. Lukin, Phys. Rev. A 65 (2002) 022314. [17] J.B. Kim, K. Kim, H.S. Moon, M. Kwon, H.D. Park, J. Korea Phys. Soc. 39 (2001) 859.
Enhanced effects of subluminal and superluminal propagation Feng Xiao, Hong Guo ∗ , Luming Li, Cheng Liu, Xuzong Chen QO01 Group, Key Laboratory for Quantum Information and Measurements, Ministry of Education, and School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, PR China Received 18 November 2003; received in revised form 7 April 2004; accepted 16 April 2004 Available online 27 April 2004 Communicated by P.R. Holland
Abstract We have experimentally investigated the enhanced effects of subluminal and superluminal propagation, based on electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA), respectively. By adding only an incoherently pumping laser to each case, the slower subluminal group velocity, and the faster superluminal pulse propagation are, respectively, observed. By only changing the intensity of the incoherent pumping beam, we are able to control, respectively, the subluminal group velocity continuously from vg = c/20000 to vg = c/8300, and superluminal group velocity from vg = −c/1667 to vg = −c/3030. Qualitative explanations for the two cases are given. 2004 Elsevier B.V. All rights reserved. PACS: 42.50.Gy; 42.50.Hz; 42.62.Fi Keywords: Subluminal; Superluminal; Electromagnetically induced transparency; Electromagnetically induced absorption
1. Introduction Coherence between alternative pathways in quantum-mechanical processes have led to many interesting consequences. Among them, electromagnetically induced transparency (EIT) that was observed in 1991 for the first time [1], has attracted a great deal of recent interest in experimental and theoretical fields [2]. EIT is a technique for eliminating the absorbing effect of a medium on a propagating weak probe field in resonance of an atomic transition, with a strong coupling
* Corresponding author.
E-mail address: [email protected] (H. Guo). 0375-9601/$ – see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2004.04.032
field on another linked transition. One of the important applications of EIT is used to slow and stop light, due to its highly normal dispersion in the center of the transparent window [3]. In 1999, the light was slowed down to vg = 17 m/s by Hau et al. [4], and soon, storage of light in cold atoms [5], hot atomic vapor [6] and solid [7] have been achieved. These studies have made a great progress to push this effect to applications. Another important consequence of quantum coherence, electromagnetically induced absorption (EIA) that was firstly observed by Akulshin et al. [8] in 1998, has also been studied extensively recently both in experimental and theoretical fields [9,10], owing to its potential application to superluminal pulse propagation, which is a highlight since Wang et al. reported the
16
F. Xiao et al. / Physics Letters A 327 (2004) 15–20
experiment in 2000 [11]. As an absorption enhancement effect opposite to EIT, EIA arises from the spontaneous transfer of the atomic coherence among the degenerated states from the excited level to the ground level. EIA effect, which has not been explored in a great depth, however, has been applied to the propagation with a superluminal group velocity, due to the highly anomalous dispersion where the enhanced absorption occurs [12]. In 2003, Akulshin et al. [13] and Kim et al. [14], respectively, reported the experiments, where the negative group velocities of vg = −c/5100 and vg = −c/14400 were achieved in Cs vapor cells, based on the mechanism of EIA. The above-mentioned experiments of positive and negative group velocity propagations are performed in the EIT and the EIA systems, and have some limits, such as their dispersions cannot be changed easily. A recent paper has reported that the AWI system has many advantages to slow light compared with the EIT system [15], for example, the slower and controllable group velocity can be achieved in the AWI system. In Ref. [15], the AWI system results from applying an incoherent pumping beam into the EIT system, and the polarization of the pumping beam is the same as that of the probe beam (σ − ), while it is arbitrary in this Letter with the similarly experimental results achieved. In addition, we carry out a new experimental study on the enhanced effect of the superluminal propagation by introducing an incoherent pumping into the EIA system. In the following, two experiments are performed to investigate the propagations of slow light and negative group velocity, based on the EIT and the EIA systems, respectively. Through introducing an incoherent pumping laser into each system, the slower group velocity in the first case, and the faster in the second are observed. When we change the intensities of the incoherent pumping beams, the group velocities can be controlled smoothly.
2. Experiments and results For slowing light, the energy-level scheme, which consists of two parts including the elemental EIT configuration and the incoherent pumping system, is shown in Fig. 1. We employ two lasers to couple the same transition 6S1/2(F = |3) → 6P3/2 (F = |2) with left and right circular polarizations for the cou-
Fig. 1. Schematic diagram of the atomic levels for slowing light. 6S1/2 , F = |3 and 6P3/2 , F = |2 contribute to the EIT configuration, for which ωp driving the transition 6S1/2 (F = |4) → 6P3/2 (F = |4) serves for incoherent pumping.
Fig. 2. Schematic diagram of the atomic levels for negative group velocity propagation. 6S1/2 , F = |4 and 6P3/2 , F = |5 contribute to the EIA configuration, for which ωp driving the transition 6S1/2 (F = |3) → 6P3/2 (F = |4) serves for incoherent pumping.
pling and the probe, respectively, and 6S1/2(F = |4) → 6P3/2(F = |4) for incoherent pumping, as shown in Fig. 1, where ωc , ωb , and ωp are, respectively, the coupling, the probe, and the pumping laser frequency. If the pumping laser with right circular polarization is added to the EIT configuration, it will work as an AWI system, as discussed in Ref. [15]. In our experiments, the polarization of the pumping laser can be left circular and linear. For the negative group velocity propagation, Fig. 2 shows the energy scheme, which also consists of two parts, the elemental EIA system that involves the levels of 6S1/2 (F = |4) and 6P3/2 (F = |5), and the incoherent pumping system including the levels of 6S1/2 (F = |3) and 6P3/2 (F = |4). Two left and right circularly polarized laser beams driving the transition of 6S1/2 (F = |4) → 6P3/2(F = |5) serve
F. Xiao et al. / Physics Letters A 327 (2004) 15–20
Fig. 3. The schematic experimental set-up for the two experiments. Laser1 is prepared for the coupling laser and the probe laser, and Laser2 for the incoherent pumping laser. HWP: half-wave plate; PBS: polarized beamsplitter; BS: beam splitter; QWP: quarter-wave plate; APD: avalanche photodiode.
for the coupling and the probe, respectively, and the incoherent pumping laser beam drives the transition of 6S1/2 (F = |3) → 6P3/2 (F = |4). The reason why the above two pumping beams are incoherent arises from their processes after they are applied. The first pumping beam is resonantly tuned to the transition 6S1/2 (F = |4) → 6P3/2 (F = |4), therefore, atoms excited from the ground state 6S1/2 (F = |4) by the pump beam, via the excited state 6P3/2 (F = |4), can be moved into the ground state 6S1/2 (F = |3) by spontaneous transition, which is so-called optical pumping. This process is incoherent because the optically pumped atoms have not been interacting with coupling or probe fields that produce atomic coherence until they are moved into the state 6S1/2 (F = |3). The similar process happens when the pumping beam is added in the second case. The pulse propagation experiments is carried out in cesium vapor at room temperature. A detail schematic diagram for the experimental set-up is shown in Fig. 3. Both the coupling and the probe laser beams come from Laser1, an external-cavity diode laser (Toptica DL-100) that can be tuned to the D2 line of cesium atom with the linewidth of 1 MHz, and the incoherent pumping laser beam come from Laser2, another external-cavity diode laser (Newfocus Vortex6000) with the same frequency range and linewidth. A Gaussian probe pulse is generated through slightly rotating the polarization angle of the linearly polarized coupling laser by the Pockels cell, which is controlled by a high-voltage converter amplifying the electrical signal of the Gaussian shape saved in an arbitrary
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function generator (AFG, Sony-Tektronics AFG320). The Gaussian pulse is programmed by a computer and transmitted to the AFG. The rotated polarization component perpendicular to the polarization of the coupling field serves for the probe field, where the temporal shape of the probe pulse is decided by the time-dependent voltage applied to the Pockels cell. The coupling and the probe fields overlaps. QWP1 (quarter-wave plate) converts the two linearly and orthogonally polarized fields into counter rotating circularly polarized fields, and QWP2 turns the beams, which have passed through the 5 cm long no-buffergas cesium vapor cell, again to linearly and orthogonally polarized fields. The probe field is separated from the coupling one by a Glan prism, and detected by APD1, an avalanche photodiode. The cesium vapor cell is shielded by a µ-metal sheet to protect from the earth magnetic field, so all the magnetic sub-levels in the hyperfine structures are approximately degenerate. The pumping beam has nearly the same propagating direction as the coupling beam, while the spatial angle between them is responsible for the pumping efficiency. The two experiments are performed in the same set-up, as mentioned above and shown in Fig. 3. The digital oscilloscope is triggered by the AFG, which in the same time sends an electronical Gaussian pulse to Pockels cell to generate a Gaussian probe pulse. The Gaussian probe field is splitted into two parts by BS, a beam splitter. One passes through the cesium vapor cell and propagates with subluminal (or superluminal) speed corresponding to EIT (or EIA) configuration, and the other propagates with nearly c, the vacuum speed of light. The two paths of probe pulses are, respectively, detected by APD1 and APD2, two same avalanche photodiodes (Hamamatsu APD module C5460), and compared in the digital oscilloscope. In the two experiments, firstly we block the pumping beam and obtain the pulse propagation in the EIT (or EIA) configuration, then add the pumping beam to investigate the enhanced effect on the pulse propagation. The results of subluminal propagation are shown in Fig. 4. The probe pulse is delayed by 1.3 µs in the EIT medium, where the intensity of the coupling laser is 3.28 mW/cm2 , corresponding to the Rabi frequency Ωc ≈ 6.4 MHz, and that of the probe laser 50 µW. When we add the incoherent pumping beam, with the
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Fig. 4. Pulse delay in the cases with and without pumping beam. (a) The solid curve corresponds to the reference travelling with vacuum speed c, the dotted one corresponds to travel in the EIT condition, and the dashed one with the pumping beam with left circular polarization added. (b) Normalized pulses. All pulses in the figure are the average of 32 pulses.
Fig. 5. Subluminal group velocity vs. intensity of the pumping beam.
left circular polarization and the intensity of 8 mW corresponding to the Rabi frequency Ωp ≈ 6.5 MHz, the pulse is delayed by 2.8 µs, which has an increased delay time of 1.5 µs compared with that of the former case. We find that the polarization of the pumping beam has much influence on the amplitude of the
Fig. 6. Pulse delay (advancement) in the cases with and without pumping beam. (a) The solid curve corresponds to the reference travelling with vacuum speed c, the dotted one corresponds to travel in the EIA condition, and the dashed one with the pumping beam with left circular polarization added. (b) Normalized pulses. All pulses in the figure are the average of 32 pulses.
probe pulse, but little on the delay time. The right circularly polarized pumping beam, which corresponds to an AWI system that is a special case for our experiments, leads to an amplified amplitude [15], and the other polarized ones often lead to the smaller amplitude, but the slowed group velocity is nearly same. Fig. 5 shows the dependence of the subluminal group velocity on the intensity of the incoherent pumping beam. The group velocity decreases nonlinearly, which is in accordance with a saturated tendency, with the pumping intensity. The results of the superluminal propagation are shown in Fig. 6. The probe pulse is advanced by 0.28 µs in the EIA medium, where the intensity of the coupling laser is 110 µW/cm2 , corresponding to the Rabi frequency Ωc ≈ 1.2 MHz, and that of the probe laser 50 µW. When we add the incoherent pumping beam, with the left circular polarization and the in-
F. Xiao et al. / Physics Letters A 327 (2004) 15–20
Fig. 7. Superluminal group velocity vs. intensity of the pumping beam.
tensity of 1 mW corresponding to the Rabi frequency Ωp ≈ 3.5 MHz, the advance time become 0.6 µs, 0.32 µs more than that of the former case. The polarization of the pumping beam is able to influence both the pulse amplitude and the advanced time, especially the linear one. Fig. 7 shows the superluminal group velocity versus the pumping intensity. The group velocity increases nonlinearly, which is also in accordance with a saturated tendency, with the pumping intensity.
3. Discussion and conclusion In an EIT system, the control and the probe fields drive the atoms into the coherent population trapping (CPT), the so-called “dark state”. As a result, the atomic population is “trapped” in a coherent superposition of the sub-levels in the ground states 6S1/2 (F = |3), and no population in the state 6P3/2 (F = |2). In the classic explanation [2], the probability amplitude of absorption lies on two driving terms of equal magnitude and opposite sign. One driven by the probe field, the other driven by the coupling field, and the two terms balance so that EIT occurs. When the incoherent pumping laser is added, many atoms are pumped from the state 6S1/2 (F = |4) to 6S1/2 (F = |3). So the former balance between the two terms is destroyed, while a part of the control and the probe field is absorbed and then some atoms populate the state 6P3/2 (F = |2). On the other hand, the adiabatically attenuated control field narrows the transparent window of the medium and increases coherence between the sub-levels in the ground state 6S1/2 (F = |3) [16]. Therefore, the
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probe field will be increased by the population of the state 6P3/2 (F = |2), and decreased by the narrowed transparent windows, however, more slowed due to the enhanced coherence between the sub-levels in the ground state 6S1/2 (F = |3). So, through introducing a suitable incoherent pumping, dn/dω will be larger than that in the original EIT medium. EIA occurs due to spontaneous transfer of atomic coherence between degenerate excited states (herein the sub-levels in the excited state 6P3/2 (F = |5)) to atomic coherence between degenerate ground states (herein the sub-levels in the ground state 6S1/2 (F = |4)). By introducing an incoherent optical pumping, the EIA signal is able to be amplified [17], and the spectral linewidth be narrowed due to the enhanced coherence. So, |dn/dω| will be larger than that in the EIA medium without incoherent pumping. To summarize, an incoherent pumping added to an EIT (or EIA) configuration will increase the population that take part in the interference, which makes the EIT (or EIA [17]) more efficient. In other words, adding an incoherent pumping beam will enhance the interference and coherence between the corresponding states that is responsible for the slow light (or negative group velocity) propagation, and then the normal (or anomalous) dispersion, dn/dω, which leads to a slower subluminal (or faster superluminal) group velocity. If the intensity of the added pumping changes, the dispersion of medium will follow. This is useful to change the subluminal (or superluminal) group velocity. In conclusion, by applying an incoherent pumping to an EIT (or EIA) scheme, we can obtain the enhanced coherence that lead to the slower subluminal (or faster superluminal) group velocity. Besides, we can conveniently adjust the light speed by changing only the intensity of pumping laser. It will contribute to the applications for adjusting coherence and the speed of light.
Acknowledgements This work is partially supported by the state Key Development Program for Basic Research of China (Grant No. 2001CB309308), the Key Project of National Natural Science Foundation of China (Grant No. 69789801), the National Hi-Tech ICF program, and
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F. Xiao et al. / Physics Letters A 327 (2004) 15–20
the Key Project of Natural Science Foundation of the Ministry of Education of China (Grant No. 00-09).
References [1] K.J. Boller, A. Imamoglu, S.E. Harris, Phys. Rev. Lett. 66 (1991) 2593. [2] S.E. Harris, Phys. Today 50 (1997) 36. [3] L.V. Hau, S.E. Harris, Z. Duton, C.H. Behroozi, Nature 397 (1999) 594. [4] M. Xiao, Y. Li, S. Jin, J. Gea-Banacloche, Phys. Rev. Lett. 74 (1995) 666. [5] C. Liu, Z. Dutton, C.H. Behroozi, L.V. Hau, Nature 409 (2001) 490. [6] D.F. Phillips, A. Fleischhauer, A. Mair, R.L. Walsworth, M.D. Lukin, Phys. Rev. Lett. 86 (2001) 783. [7] A.V. Turukhin, V.S. Sudarshanam, M.S. Shahriar, J.A. Musser, B.S. Ham, P.R. Hemmer, Phys. Rev. Lett. 88 (2002) 023602.
[8] A.M. Akulshin, S. Barreiro, A. Lezama, Phys. Rev. A 57 (1998) 2996. [9] A.V. Taichenachev, A.M. Tumaikin, V.I. Yudin, Phys. Rev. A 61 (1999) 011802-1. [10] A. Lezama, S. Barreiro, A.M. Akulshin, Phys. Rev. A 59 (1999) 4732. [11] L.J. Wang, A. Kuzmich, A. Digariu, Nature 406 (2000) 277. [12] A.M. Akulshin, S. Barreiro, A. Lezama, Phys. Rev. Lett. 83 (1999) 4277. [13] A.M. Akulshin, A. Cimmino, A.I. Sidorov, P. Hannaford, G.I. Opat, Phys. Rev. A 67 (2003) 011801. [14] K. Kim, H.S. Moon, C. Lee, S.K. Kim, J.B. Kim, Phys. Rev. A 68 (2003) 013810. [15] K. Kim, F. Xiao, C.H. Lee, S.K. Kim, X.Z. Cheng, J.B. Kim, J. Phys. B: At. Mol. Opt. Phys. 36 (2003) 2671. [16] M. Fleichhauer, M.D. Lukin, Phys. Rev. A 65 (2002) 022314. [17] J.B. Kim, K. Kim, H.S. Moon, M. Kwon, H.D. Park, J. Korea Phys. Soc. 39 (2001) 859.