We report the spatial transport of spontaneously transferred atomic coherence (STAC) in electromagnetically induced absorption (EIA), which resulted from moving atoms with the STAC of the 5S1/2 (F = 2)-5P3/2 (F′ = 3) transition of 87Rb in a paraffin-coated vapor cell. In our experiment, two channels were spatially separate; the writing channel (WC) generated STAC in the EIA configuration, and the reading channel (RC) retrieved the optical field from the spatially transported STAC. Transported between the spatially separated positions, the fast light pulse of EIA in the WC and the delayed light pulse in the RC were observed. When the laser direction of the RC was counter-propagated in the direction of the WC, we observed direction reversal of the transported light pulse in the EIA medium. Furthermore, the delay time, the magnitude, and the width of the spatially transported light pulse were investigated with respect to the distance between the two channels.
© 2014 Optical Society of America
Atomic coherence may be interpreted as the superposition of atomic states interacting with coherent light fields. Representative atomic media with atomic coherence include coherently driven atomic ensembles, which are based on electromagnetically induced transparency (EIT) [1, 2] and electromagnetically induced absorption (EIA) effects [3, 4]. These atomic media have been used for storage and manipulation of the quantum state of an optical light pulse [5–16]. Many studies on quantum memory have been successfully conducted in an atomic medium with atomic coherence [5–14]. Interestingly, control of optical pulses stored in an atomic system and transport of optical information have been reported [17–19].
However, after the information of an optical pulse is mapped into the coherent atomic states of atoms, the mapped atoms in a vapor cell move with a Boltzmann distribution because of the thermal motion of the atoms. In an atomic system governed by thermal motion, the optical pulse information at the initial storage position is dispersed in the vapor cell with the randomly moving atoms. However, Zibrov et al. have demonstrated the possibility of transporting the light’s state between different spatial points in an EIT medium . In their study, they obtained the transported light pulse at a spatial position different from the initial position in an EIT medium with a buffer gas. Furthermore, Xiao et al. reported atomic coherence transport in the EIT medium of a wall-coated atomic vapor cell .
To date, studies on the spatial transport of atomic coherence have been conducted in a Λ-type EIT medium [20, 21]. It is commonly known that the physical origin of atomic coherence in EIA differs from the origin in EIT [3, 4]. EIA is attractive because of information velocity and causality of fast light [22–25]. Also, it is important to understand the two-photon quantum interference phenomena, because the physical origin of atomic coherence in EIA differs from the origin in EIT. Other applications of EIA are tunable optical delay line and group velocity control of light pulse [26, 27]. Although the atomic coherence transport in an EIT medium has been studied, the spatial transport of the spontaneously transferred atomic coherence (STAC) in an EIA medium has not yet been investigated.
In this paper, we demonstrate both the spatial transport and direction reversal of STAC in the EIA medium of a paraffin-coated 87Rb vapor cell. We investigate the signal spatially transported by moving atoms with the STAC of the 5S1/2 (F = 2)-5P3/2 (F′ = 3) transition of 87Rb. Moving atoms with decoherence-free wall collisions could transport the light field information from the writing position to the reading position. The magnitude, delay time, width of the spatially transported light pulse resulting from the EIA effect were investigated according to the distance between the writing and reading positions.
2. Experimental setup
To optimize the EIA effect, we used the closed atomic system of the 5S1/2 (F = 2)-5P3/2 (F′ = 3) transition of 87Rb. When the longitudinal magnetic field parallel to the laser’s propagation was used for the Hanle configuration, the W-type configuration was generated between the Zeeman sublevels of the 5S1/2 (F = 2)-5P3/2 (F′ = 3) transition of 87Rb, as shown in Fig. 1(a).The laser could induce σ+ (Δm = + 1) and σ− (Δm = −1) transitions between the Zeeman sublevels, which are considered as the coupling (ΩC) and probe light (Ωp), respectively.
Figure 1(b) shows the two spatially separated channels, which are called a writing channel (WC) and a reading channel (RC). The WC laser is the linearly polarized laser, which is decomposed into left-circularly polarized (σ−) and the right-circularly polarized (σ+) components. As mentioned previously, the two circularly polarized orthogonal components generated the W-type configuration for EIA in the WC. However, the RC laser is the right-circularly polarized laser (σ+), which induces the only optical pumping effect due to the σ+ (Δm = + 1) transition. Therefore, in the RC region, we cannot consider the EIA effect, which is the spontaneous transfer of atomic coherence from the excited states to the ground states. Moving atoms experienced the following: the STAC effect in the WC interaction, flight without decoherence of the wall collisions, and interaction with the RC. The preserved STAC, which is carried by the moving atoms with wall collisions, transports the light’s information in the WC. Therefore, in the RC region, a fraction of the initial optical pulse may be retrieved from atoms moving with STAC.
To demonstrate the spatial transport of STAC in the EIA medium, the two spatially separated channels were positioned in a paraffin-coated Rb vapor cell, as shown in Fig. 2.One channel (called the WC) was used for typical EIA composed of the probe and coupling lasers. The only coupling laser component was located in another channel (called the RC). All laser fields used in our experiment were generated from an external-cavity diode laser (ECDL). The frequency of the ECDL was locked to the 5S1/2 (F = 2)-5P3/2 (F′ = 3) transition of 87Rb. The output of the ECDL was split into two parts for the WC and RC. One of the ECDL outputs is linearly polarized light composed of the coupling and probe components for the WC. Another output is circularly polarized light, which is used as the only coupling component for the RC. The EIA signal of the Hanle configuration was observed by scanning the longitudinal magnetic field in the zero-value region. To detect the only probe component in the WC, a quarter-wave plate (QWP) and a polarized beam splitter (PBS) were used to select the circularly polarized laser component for the WC. However, the circularly polarized laser component of the RC was blocked by the QWP and PBS because of the coupling laser component. The laser of the WC was designed to produce a Gaussian pulse by passing the beam through two acousto-optic modulators (AOM1 and 2). The paraffin-coated Rb cell was installed inside a solenoid coil for longitudinal magnetic field (B-field) scanning and inside a heating oven for temperature control. To investigate the delay time and magnitude of the spatially transported light pulse with respect to the distance between the two channels, a translation mirror (MT) was used to induce parallel translation for the RC path. Although the co-propagating RC was described in Fig. 2, we could install the counter-propagating RC in our experimental setup to observe the direction reversal of stored light in the EIA medium. The linearly polarized light pulse of the WC passed through the EIA medium and was detected by the first avalanche photodiode (APD1), whereas the retrieval light from the circularly polarized continuous-wave (cw) laser of the RC was detected by APD2.
3. Experimental results and discussion
When the B-field was scanned over the range between –75 and + 75 mG in only the WC (in the absence of the RC), we observed the double-structure EIA spectrum composed of the transit-broadened EIA and the narrow EIA resulting from the Ramsey interference effect, as shown by the red solid curve in Fig. 3.Here, the horizontal axis of Fig. 3 is the B-field parallel to the laser’s propagation. The laser power in the WC was 43 μW, and the laser beam diameter was approximately 2 mm. The temperature of the Rb vapor cell was maintained at 60 °C. The spectral width of the narrow Ramsey EIA spectrum was measured to be 0.5 mG in the Hanle configuration. The narrow EIA resonance means that STAC between degenerate magnetic sublevels could be maintained even after many collisions of atoms with the paraffin-coated wall. The narrow EIA resonance resulted from the constructive effect of the EIA Ramsey interference fringes, based on the velocities of atoms moving with the Maxwell-Boltzmann distribution [28, 29]. Therefore, the STAC of EIA spread throughout the entire paraffin-coated Rb vapor cell.
The right-circularly polarized light of the RC (in the absence of the WC) was not detected in APD2, because of blocking by the QWP and PBS, as shown by the blue solid curve in Fig. 3. The right-circularly polarized light of the RC optically pumps the atomic population into a Zeeman sublevel of 5S1/2 (F = 2) but does not contribute to the generation of atomic coherence.
Figure 4 shows the two spectra in the WC (red solid curve) and RC (blue solid curve) measured by APD1 and 2, respectively, when the linearly polarized laser of the WC was on and the circularly polarized laser of the RC was added at 8 mm separation from the WC position. The added laser of the RC had a power of 25 μW and a beam diameter of 2 mm. Interestingly, we observed a narrow transmittance signal in the RC, as shown by the blue solid curve in Fig. 4. Although the circularly polarized light of the RC could not contribute to the generation of the STAC of EIA, the transmittance signal of the RC was the optical field retrieved from the STAC among the degenerate states from the excited levels to the ground levels. This indicates that, because of atomic movements, the STAC generated in the WC affected the transmittance signal of the RC. In the paraffin-coated atomic vapor cell, the STAC of EIA between the ground states generated in the WC was maintained, despite wall collisions, but was removed by the interaction of the atoms with the circularly polarized light of the RC. However, the broad EIA component was not detected in the transmittance signal of the RC depicted in Fig. 4(a), and the transmittance signal of the RC corresponded to only the Ramsey EIA part. Because the broad EIA part has the decoherence of atoms after a single interaction between atoms and the laser, only the moving atoms with a cylindrical solid angle matching the laser beam diameter of the RC could reach the STAC at the RC. On the other hand, because the narrow Ramsey EIA part retained atomic coherence after several tens of wall collisions, the moving atoms with STAC could reach the RC. In our experiment, the diameter of the vapor cell was 25 mm, and the mean velocity of the Rb atoms was assumed to be 287 m/s at a cell temperature of 60 °C. The mean number of collisions with the paraffin-coated vapor wall to retain the atomic coherence was estimated to be approximately 30.
To clearly observe the transmittance signal of the RC, the narrow Ramsey EIA part of Fig. 4(a) was magnified in the range of –1.5 to + 1.5 mG, as shown in Fig. 4(b). The magnitude of the transmittance signal of the RC was estimated to be approximately 8% of the narrow Ramsey EIA signal. In the figure, we can see the weak asymmetry and shift of the narrow Ramsey EIA spectrum of the WC. This change in the narrow Ramsey EIA of the WC was illustrated as the optical pumping effect by the circularly polarized light of the RC. The time sequence for the transmittance signal of the RC was as follows: the first interaction for the STAC generation in the WC, then the random movements of atoms with STAC, and finally the second interaction in the RC. However, there were also counter-propagated atoms with the time sequence for the transmittance signal of the RC. The counter-moving atoms were optically pumped among the magnetic sublevels in the RC of the first interaction region, and these atoms generated the STAC for EIA in the WC of the second interaction. Therefore, the two spatially separate interactions in both the RC and WC affected each other because of randomly moving atoms.
To demonstrate the spatial transport of the STAC in the EIA medium, after the WC laser was operated with a Gaussian pulse mode, we investigated the optical signal delivered from the WC to the RC by the moving atoms in the paraffin-coated Rb vapor cell. When the circularly polarized laser of the RC was operated in the cw mode, we could first observe the spatially transported optical pulse (blue solid curve) in the EIA medium, as shown in Fig. 5(a).Here, the pulse signals shown in Fig. 5(a) represent the reference pulse (gray dashed curve) and the transmittance pulse (red solid curve) of the EIA medium in the WC and the generated pulse (blue solid curve) in the RC, respectively. To minimize the optical pulse shape distortion resulting from the EIA dispersion medium, the Gaussian-shaped pulse of the WC was set to a full width at half maximum (FWHM) of 3.2 ms, which is considered the narrow Ramsey EIA spectral width (estimated to be 354 Hz). The information of the optical fields in the WC was stored in the moving atoms with the STAC of EIA; the atoms evolved without decoherence between ground states, and the stored optical fields were retrieved using the interaction between the atoms and the circularly polarized laser of RC. Therefore, when the moving atoms with STAC interacted with the circularly polarized light of the RC, it is possible to read out the information of the optical fields of WC from the maintained STAC of the EIA medium.
Figure 5(a) shows that the fast light pulse (red solid curve) in the WC resulted from the anomalous dispersion of the EIA; conversely, the delayed light pulse (blue solid curve) in the RC resulted from the delivery time of the moving atoms. The advancement time of the fast light pulse and the delay time (τd) of the transported light pulse were measured to be 125 μs and 750 μs, respectively. Although the advancement of the fast light pulse was not large, because of the low contrast of the Ramsey EIA resonance, the simultaneous observation of both the fast and delayed light pulses is an interesting phenomenon. As mentioned previously, our experiment was conducted for up to 8 mm separation between laser beams with 2.0 mm diameter. With 8 mm separation between the two laser beams and 287 m/s mean velocity of the Rb atoms, the delivery time of the moving atoms between the two laser beams was measured to be approximately 28 μs. However, the arrival time of the retrieved pulse of RC corresponded to 26 times of the direct delivery time between the two laser beams. This result means that the routes for the retrieved pulse of RC after several collisions with the wall were more dominant than the direct route between the WC and the RC. Considering the 25 mm diameter of the vapor cell, the average number of collisions with the paraffin-coated vapor wall during transit from the WC to the RC was estimated to be approximately 12.
We investigated direction reversal of the transported light pulse in the EIA medium. When the RC laser was counter-propagated into the direction of the WC, we observed the transported counter-propagating light pulse in the EIA medium, as shown in Fig. 5(b). When the transported light underwent direction reversal, the advancement of the fast light pulse and the delay of the transported light pulse were similar to the advancement and delay obtained in Fig. 5(a). Because atomic motion in the paraffin-coated cell is random, the physical origin of the spatial transport of the atomic coherence in the hot vapor cell is independent of the direction of the RC laser. Therefore, this phenomenon may be understood as follows: the information of the photon momentum was not stored in the atomic coherence of the magnetic sublevels of the ground state of the transition.
We investigated the efficiency and delay time of the transported light pulse with respect to the distance between the WC and RC. Figure 6(a) shows the relative magnitude (red squares; left axis) and the delay time (blue circles; right axis) of the spatially transported light pulse as functions of the distance between the WC and RC. If the STAC was spatially transported after the average number 12 of wall collisions, we expect that the relative magnitude and delay time of the transported light pulse would be constant. However, as the distance between the two channels increased, the relative magnitude quickly decreased, and the delay time slightly increased. To understand the results of Fig. 6(a), we must consider the atomic motions in the paraffin-coated cylindrical vapor cell of 25 mm diameter and 50 mm length. The number and route of atoms traveling from the WC to the RC may depend on the positions of the two channels and the shape of the vapor cell. As shown in the cross-section of the paraffin-coated vapor cell and the two laser beams in Fig. 6(b), the position of the WC was fixed at approximately 6 mm from the left wall of the paraffin-coated cell, and the distance (d) between the WC and the RC was varied by moving the position of the RC. The routes of atoms moving from the WC to the RC were necessarily different, depending on d. From the results in Fig. 6(a), under the conditions in our experiment, we inferred that the average length of the route from the WC to the RC was shorter for a small d than for a large d.
However, we guess that the width of the retrieved pulse in the RC would be spreader than the original pulse at the WC, because not all atoms will make the same number of collisions before entering the RC. Under the condition of Fig. 6, the retrieved pulse in the RC was measured to be 3.4 ± 0.1 ms, where the width of the input light pulse in the WC was set to 3.2 ms. Because of the shape and anti-relaxation coating quality of the vapor cell, the relaxation-free collisions number before interacting with the RC has a distribution. The wall collision free number distribution is assumed to be a Poisson distribution . The number statistics are given by the Poisson distribution as
We have experimentally demonstrated the spatial transport of STAC in the EIA medium of the 5S1/2 (F = 2)-5P3/2 (F′ = 3) transition of 87Rb in the paraffin-coated vapor cell. The STAC between magnetic sublevels generated by the EIA mechanism was spatially transported by moving atoms. The optical field from the transported STAC was retrieved at a different position. The spatial transport of STAC mainly resulted from atoms retaining STAC after several collisions with walls in the paraffin-coated vapor cell. Both the fast light pulse in the WC (caused by the anomalous dispersion of EIA) and the delayed light pulse in the RC (caused by the delivery time of the moving atoms) were observed. For atoms traversing the 8 mm separation between the two channels, the delivery time was measured to be approximately 28 μs, and the average number of collisions with the paraffin-coated vapor wall was estimated to be approximately 12. Furthermore, when the RC laser was counter-propagated into the direction of the WC, we observed the transported counter-propagating light pulse in the EIA medium. Despite the random atomic motion in the paraffin-coated vapor cell, the changes of the relative magnitude, delay time, width of the spatially transported light pulse were observed as functions of the distance between the two channels because of the positions of the two channels as well as the shape of the vapor cell. On the basis of our results, we were able to verify that the STAC in EIA was spatially transported in the paraffin-coated vapor cell.
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant#2012R1A2A1A01006579).
References and links
2. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005). [CrossRef]
3. A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor,” Phys. Rev. A 57(4), 2996–3002 (1998). [CrossRef]
4. A. M. Akulshin and R. J. McLean, “Fast light in atomic media,” J. Opt. 12(10), 104001 (2010). [CrossRef]
5. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001). [CrossRef] [PubMed]
6. A. V. Gorshkov, A. André, M. Fleischhauer, A. S. Sørensen, and M. D. Lukin, “Universal Approach to Optimal Photon Storage in Atomic Media,” Phys. Rev. Lett. 98(12), 123601 (2007). [CrossRef] [PubMed]
7. I. Novikova, A. V. Gorshkov, D. F. Phillips, A. S. Sørensen, M. D. Lukin, and R. L. Walsworth, “Optimal control of light pulse storage and retrieval,” Phys. Rev. Lett. 98(24), 243602 (2007). [CrossRef] [PubMed]
10. A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photonics 3(12), 706–714 (2009). [CrossRef]
11. K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik, “Quantum memory for entangled continuous-variable states,” Nat. Phys. 7(1), 13–16 (2011). [CrossRef]
13. Y.-H. Chen, M.-J. Lee, I.-C. Wang, S. Du, Y.-F. Chen, Y.-C. Chen, and I. A. Yu, “Coherent optical memory with high storage efficiency and large fractional delay,” Phys. Rev. Lett. 110(8), 083601 (2013). [CrossRef] [PubMed]
14. O. Firstenberg, M. Shuker, A. Ron, and N. Davidson, “Colloquium: Coherent diffusion of polaritons in atomic media,” Rev. Mod. Phys. 85(3), 941–960 (2013). [CrossRef]
15. A. M. Akulshin, A. Lezama, A. I. Sidorov, R. J. McLean, and P. Hannaford, “Storage of light in an atomic medium using electromagnetically induced absorption,” J. Phys. At. Mol. Opt. Phys. 38(23), L365–L374 (2005). [CrossRef]
16. A. Lezama, A. M. Akulshin, A. I. Sidorov, and P. Hannaford, “Storage and retrieval of light pulses in atomic media with “slow” and “fast” light,” Phys. Rev. A 73(3), 033806 (2006). [CrossRef]
18. B. Wang, S. Li, H. Wu, H. Chang, H. Wang, and M. Xiao, “Controlled release of stored optical pulses in an atomic ensemble into two separate photonic channels,” Phys. Rev. A 72(4), 043801 (2005). [CrossRef]
20. A. S. Zibrov, A. B. Matsko, O. Kocharovskaya, Y. V. Rostovtsev, G. R. Welch, and M. O. Scully, “Transporting and Time Reversing Light via Atomic Coherence,” Phys. Rev. Lett. 88(10), 103601 (2002). [CrossRef] [PubMed]
22. A. Kuzmich, A. Dogariu, L. J. Wang, P. W. Milonni, and R. Y. Chiao, “Signal velocity, causality, and quantum noise in superluminal light pulse propagation,” Phys. Rev. Lett. 86(18), 3925–3929 (2001). [CrossRef] [PubMed]
25. U. Vogl, R. T. Glasser, and P. D. Lett, “Advanced detection of information in optical pulses with negative group velocity,” Phys. Rev. A 86(3), 031806 (2012). [CrossRef]
26. K. Kim, H. S. Moon, C. Lee, S. K. Kim, and J. B. Kim, “Observation of arbitrary group velocities of light from superluminal to subluminal on a single atomic transition line,” Phys. Rev. A 68(1), 013810 (2003). [CrossRef]
27. C.-L. Cui, J.-K. Jia, J.-W. Gao, Y. Xue, G. Wang, and J.-H. Wu, “Ultraslow and superluminal light propagation in a four-level atomic system,” Phys. Rev. A 76(3), 033815 (2007). [CrossRef]