We report on the transfer of statistical characteristics from writing and reading coupling light to stored and retrieved probe light pulses in a Λ-type electromagnetically induced transparency (EIT) scheme based on the 5S1/2-5P1/2 transition of 87Rb atoms. When the coherent probe laser pulse was stored in the EIT medium using the pseudo-thermal coupling light, the characteristics of the pseudo-thermal writing coupling light were transferred to the stored probe laser pulse because of the strong correlation between the probe and coupling light in the EIT medium. The photon number statistics of the retrieved probe light changed from Poisson distribution to Bose-Einstein distribution. Additionally, we measured the change in the properties of the retrieved light pulse due to the photon number statistics of the pseudo-thermal reading coupling light.
©2012 Optical Society of America
Due to the narrow transparency window and steep dispersion, the electromagnetically induced transparency (EIT) of novel devices such as optical magnetometers and atomic clocks [1–4] is widely studied, and the EIT is in the spotlight as a good optical buffer, a device for light storage and slow light propagation [5–11]. In particular, light storage in an atomic ensemble has attracted attention because coherent control using the interactions between optical fields and coherently prepared media can realize quantum memory for the manipulation of photonic quantum states in quantum communication and quantum networks [12–15].
To investigate the potential of quantum memory in an atomic ensemble, various studies on the EIT and light storage has been completed [16–19]. Gao et al. investigated the storage and retrieval of arbitrary polarized light in a Rb vapor as a function of linear, elliptical and circular polarized lights uisng an all-optical technique . Measurement of the beat-note signal after light storage and retrieval was shown to reveal by Chen et al., no significant phase shift induced by the switching of the coupling field . Shuker et al. showed that the resolution of the retrieved image was mainly limited by atomic diffusion . Cho and Kim studied the preservation of statistical properties of a retrieved light pulse in an atomic ensemble by using a pseudo-thermal probe light and a coherent coupling light after the light passed through an EIT medium .
The storage properties in the EIT medium is related to experimental parameters such as the transit time, atomic density, laser linewidth, and Rabi frequency of the coupling light. In particular, the properties of the coupling light significantly affect the stored and retrieved probe light in a Λ-type EIT medium because of the strong correlation between the probe and coupling light. In the light storage regime, the storage and retrieval of probe pulse based on EIT is interpreted as the dark-state polariton. The dark-state polariton is generated with both the probe and coupling light. So, there is the information of the coupling light in the dark-state polariton. According to the change of Rabi-frequency of the coupling light, the group velocity of dark-state polariton could be controlled to decelerate, stop and reaccelerate . In spite of the important role of the coupling light in light storage, the majority of research has focused on the preservation of the properties of the probe light in the EIT medium [16–19]. However, how the properties of the probe light change during the storage and retrieval processes according to the properties of the coupling light is an interesting problem.
In this paper, we present the photon bunching characteristics of the light storage and retrieval in the 5S1/2-5P1/2 transition of the Λ-type system of the 87Rb atom according to the statistical properties of the coupling light, such as the Poisson and Bose-Einstein distributions. Pseudo-thermal coupling light with a Bose-Einstein distribution can be generated by a randomly modulated acoustic-optic modulator through the injection of a chaotic RF-signal . By measuring the photon bunching characteristics of the probe light pulse before and after storage in the EIT medium, we investigate the effects of the writing and reading coupling light in the storage and retrieval of the probe light pulse. In the view of the symmetry between probe and coupling light, the role of the coupling light is very important for not only the conservation of the stored probe light but also transformation of the coupling optical information. Particularly, this paper shows that the chaotic property of the coupling light can be transferred to the retrieved probe light through the EIT medium.
2. Experimental setup
Figure 1 shows the simple energy levels of the Λ-type EIT system based on the 87Rb D1-line, which consists of two adjacent hyperfine ground states and one common excited state. The probe (LP) and coupling (LC) lasers were used for the 5S1/2 (F = 1)-5P1/2 (F′ = 2) and 5S1/2 (F = 2)-5P1/2 (F′ = 2) transition, respectively. The frequencies of LP and LC were monitored by saturated absorption spectroscopy.
Figure 2 shows the detailed experimental setup for light storage using the laser (coherent) LP light with Poisson statistics and the pseudo-thermal (chaotic) LC light with Bose-Einstein statistics. To eliminate the relative phase difference between LP and LC, we applied the optical injection-locking technique to the independently operated master and slave lasers . The slave (LP) and master (LC) lasers corresponding to a Fabry–Perot laser diode of 100 mW and a single-mode grating-feedback external-cavity diode, respectively. After the master laser passed through a 6.8-GHz electro-optic modulator (EOM), the slave laser mode was injection-locked to one of the sidebands of the modulated master laser frequency. The powers of LP and LC were controlled by neutral-density (ND) filters. To avoid any unwanted optical feedback to the laser diodes, we installed isolators (ISOs) in front of both the master and slave lasers. The acoustic-optic modulator (AOM1) for LP was used to form a propagating Gaussian-shaped pulse. By dividing LC into writing coupling light (LW) and reading coupling light (LR) using a 50:50 beam splitter (BS), we could selectively control the photon bunching characteristics of LW and LR to be Poisson or Bose-Einstein distributions. The LW and LR light perform different roles for storing and retrieving the LP pulse. With the injection of chaotic RF-signals such as the random intensity fluctuations, shown in Fig. 2(b), into AOM2 and AOM3, pseudo-thermal LW and LR light were successfully generated. The modulators AOM4 for LW and AOM5 for LR were controlled according to the timing sequences for the storage and retrieval of LP. The separately propagated LW and LR were merged before passing through the atomic medium.
To form the Λ-type EIT and light storage scheme, we used an atomic vapor cell containing 72% of 85Rb and 28% of 87Rb with a neon buffer gas at 6.67 kPa. The vapor cell was 50 mm long and 25 mm in diameter. To prevent the effect of the Earth’s magnetic field, the cell was magnetically shielded using three sheets of μ-metal. To increase atomic evaporation, heating tapes were wound around the μ-metal sheets and were stabilized at a temperature of 90 °C using a temperature controller (TZ4ST, Autonics) with ± 0.1 °C accuracy. The EIT spectrum and photon numbers of the probe light were detected using an Silicon avalanche photodiode (APD) module (C5460, Hamamatsu Photonics) and recorded on a single-photon counter (SPC) module (SPCM-AQRH-13FC, Perkinelmer Optoelectronics) with which has dead time of 35 ns and 250 dark counts per second, respectively.
3. Experimental results
Figure 3 shows the experimental result (black bars) and theoretical fit (red bars) of the photon number statistics for the laser LP, laser LC, and pseudo-thermal LC light. To achieve reasonable photon number statistics, the gating time (25 ns) of SPD was much shorter than the coherence time of the probe and coupling light. The photon counting was measured within finite measurement time (3 μs) and obtained by averaging 20000 times. Finite detector efficiency does not affect the photon number statistics for coherent and thermal lights . The measured photon counting was reorganized as a function of counted photon number. The statistical results for the laser LP and laser LC correspond to Poisson distributions, which can be expressed as
After injecting the white noise RF-signal (Fig. 2(b)) into AOM2 and AOM3, pseudo-thermal light was generated, and the statistical properties of the LC light changed from Poisson to Bose-Einstein distributions, as shown in Fig. 3(c). The measured statistical result for the pseudo-thermal LC was in good agreement with a fit to the Bose-Einstein function given by
The value in this case was 2.1. We argue that temporal fluctuations in LC were successfully induced by AOM2 and AOM3 with the injection of the white noise signal. From the measured statistical data, we can calculate the second-order coherence g2(0)  as
The calculated g2(0) values for the LP, LC, and pseudo-thermal LC light were approximately 0.999 ± 0.013, 0.994 ± 0.012, and 1.971 ± 0.025, respectively.
The coherent EIT spectrum obtained with LP and LC was compared with the thermal EIT spectrum obtained with LP and the pseudo-thermal LC, as shown in Fig. 4 . Figure 4(a) is a typical EIT spectrum for coherent LP and LC lasers, where the horizontal axis describes the detuning frequency from the two-photon resonance for the EIT resonance. When the photon bunching characteristics of LC were changed to those of a Bose-Einstein distribution, the thermal EIT spectral width broadened due to the short coherence time of LC induced by the strong intensity fluctuations (Fig. 4(b)). The LP and LC powers were 50 μW and 0.55 mW, respectively. During the experiments, the vapor cell temperature was maintained at 90 °C. The full width at half maximum (FWHM) of the peaks in the coherent and thermal EIT spectra were measured to be 60 and 120 kHz, respectively. The short coherence time of the pseudo-thermal LC also induced a reduction in the amplitude of the EIT such that the amplitude of the EIT obtained with the pseudo-thermal LC before normalization was 3 times smaller than that of the EIT obtained with the LC laser.
Figure 5(a) shows a typical experimental result for light storage in the Rb vapor cell using the probe pulse and coupling lasers. The black dotted, red dashed, and blue solid lines represent the reference LP, slow LP, and retrieved LP pulses, respectively. There is an apparent difference in the arrival times of the reference LP and slow LP pulses. The timing sequences of the LW and LR beams for writing and reading are indicated by the solid gray and black lines, respectively, in Fig. 5(a). The photon number statistics of LW and LR can be controlled independently by AOM2 and AOM3. The FWHM of the input LP pulse was 8.6 μs, and the delay time Δt between the reference input LP and slow LP pulses was 2 μs. The speed of the LP pulse using the delay time Δt was derived by vg = d/(Δt − d/c), where c is the speed of light in vacuum, and d is the length of the Rb vapor cell, which corresponds to the thickness of the atomic medium . With a delay time of 2 μs, the speed of the slow LP pulse was 25000 m/s, or 0.000083c. By controlling the timing sequences of LW and LR, we were able to store the LP pulse for 20 μs, which is referred to as the storage time. We could observe the retrieval of the LP pulse from the atomic ensemble by switching on LR. The retrieval efficiency was estimated to be 20% from the ratio of the amplitudes of the slowed and retrieved light pulses.
Figure 5(b) shows the experimental result (black bars) and theoretical fit (red bars) of the photon number statistics of the pulses retrieved during the gating time (3 μs) with the LR laser. The mean photon number was estimated to be 2.1. With LW operating under the conditions in Fig. 4(b), the experimental results for the retrieved light pulse were in good agreement with the Poisson distribution. The g2(0) value calculated from the experimental data was 0.997 ± 0.018. This shows that the photon count distribution of the probe pulse was preserved during the storage and retrieval processes in the EIT medium.
We investigated the statistical characteristics of the retrieval LP pulses according to the photon number statistics of LW and LR. After an LP pulse was stored with the writing pseudo-thermal LW and the reading laser LR, we measured the photon number statistics of the retrieved LP. Figure 6(a) shows the time sequences of the LP pulse, the writing pseudo-thermal LW, and the reading laser LR. To measure the photon count events only for the retrieved LP, a 3-μs electronic gating pulse was applied to the SPD immediately after LR was turned on, as shown in Fig. 6(a). The intensity fluctuations of the pseudo-thermal LW are faster than those of the original LP pulse duration. Therefore, the single retrieved pulse has the statistical properties of chaotic intensity fluctuation of the pseudo-thermal coupling light.
Figure 6(b) shows the experimental result (black bars) and theoretical fit (red bars) of the photon number statistics for the pulses retrieved during the 3-μs gating time. The mean photon number in this case was estimated to be 1.4. The statistical results in Fig. 6(b) are in good agreement with the Bose-Einstein distribution, which indicates that random retrievals of light pulses outside the gating time were induced by the pseudo-thermal LW light. The g2(0) calculated from the experimental data was 1.853 ± 0.021. When the LP pulse was stored in the EIT medium, the information of not only the LP pulse but also that of the pseudo-thermal LW light was stored in the EIT atomic medium because of the strong correlations between the two [24,25]. Therefore, the randomly fluctuating retrieved LP pulses indicate the transfer of the random intensity fluctuations of the pseudo-thermal LW to the retrieved LP, that is, the non-bunching characteristics of LP could be changed to strong bunching characteristics.
When the stored light is retrieved from the EIT medium, the properties of the reading LR light can affect the characteristics of the retrieved LP pulse. To investigate the effect of the reading LR, the photon number statistics of the LR light was changed to those of pseudo-thermal light. Figure 7(a) shows the time sequences of the LP pulse, the writing laser LW, and the reading pseudo-thermal LR. Before LR is turned on, a typical light storage process is observed and all the properties of LP are preserved in the EIT medium. However, when the pseudo-thermal LR is turned on, the properties of the retrieved Lp can change significantly.
Figure 7(b) shows the experimental result (black bars) and theoretical fit (red bars) of the photon number statistics for the retrieved LP pulses using the pseudo-thermal LR. The mean photon number was estimated to be 1.9. The photon number statistics of the retrieved light pulse were analyzed to be not those of a Poisson distribution but nearer those of a Bose-Einstein distribution. When the pseudo-thermal LR was turned on after the storage time, the retrieved LP pulses randomly fluctuated during the gating time. The intensity fluctuations in the LR light are reflected in the random retrieval time. This means that the stored light pulses were randomly retrieved inside or outside the gating time interval according to the randomly fluctuating intensity of the pseudo-thermal coupling light. The random fluctuations of the retrieved LP pulses were quite different from the results seen in Fig. 6. For the previous case, the retrieved LP pulses fluctuated with the gating time, but in Fig. 7, the retrieval time was seen to occur randomly. We can see strong bunching characteristics corresponding to the high counting rate at zero photon number, as shown in Fig. 7(b). Therefore, the properties of the writing and reading coupling light significantly affect the properties of the light retrieved from an EIT medium.
We have investigated the influence of the writing and reading coupling light on the light pulse retrieved from an EIT medium consisting of the 5S1/2-5P1/2 transition of 87Rb atoms. Controlling the photon number statistics of the writing and reading coupling light independently, we studied the statistical characteristics of the retrieved light pulse according to the photon number statistics of the writing and reading coupling light. When the pseudo-thermal LW was applied to the atomic ensemble, the retrieved LP pulses exhibited a Bose-Einstein distribution even though the original input LP pulses had a Poisson distribution. The random intensity fluctuations in the pseudo-thermal LW light were transferred to the retrieved LP light. Both the information of the LP pulse and also that of the pseudo-thermal LW light were stored in the EIT atomic medium. Although all the properties of LP were stored in a typical EIT medium, the photon number statistics of the retrieved LP was changed when pseudo-thermal coupling light was used as LR. Therefore, it is possible to distort the retrieved LP light according to the optical properties of the reading coupling light. In the opposite view, the coupling light property may be stored by EIT medium. We believe that our results will assist in the realization of quantum memory based on light storage mechanisms using various light sources such as Poisson and Bose-Einstein distributed photons and involving information transfer via an EIT medium.
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).
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