1. Introduction

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 [16]. 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 [17]. Shuker et al. showed that the resolution of the retrieved image was mainly limited by atomic diffusion [18]. 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 [19].

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 [20]. 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 5S_1/2-5P_1/2 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 [21]. 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 (L_P) and coupling (L_C) lasers were used for the 5S_1/2 (F = 1)-5P_1/2 (F′ = 2) and 5S_1/2 (F = 2)-5P_1/2 (F′ = 2) transition, respectively. The frequencies of L_P and L_C were monitored by saturated absorption spectroscopy.

 

Fig. 1 Simple energy levels of Λ-type atomic system in a 5S_1/2-5P_1/2 transition of a ⁸⁷Rb atom.

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Figure 2 shows the detailed experimental setup for light storage using the laser (coherent) L_P light with Poisson statistics and the pseudo-thermal (chaotic) L_C light with Bose-Einstein statistics. To eliminate the relative phase difference between L_P and L_C, we applied the optical injection-locking technique to the independently operated master and slave lasers [4]. The slave (L_P) and master (L_C) 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 L_P and L_C 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 L_P was used to form a propagating Gaussian-shaped pulse. By dividing L_C into writing coupling light (L_W) and reading coupling light (L_R) using a 50:50 beam splitter (BS), we could selectively control the photon bunching characteristics of L_W and L_R to be Poisson or Bose-Einstein distributions. The L_W and L_R light perform different roles for storing and retrieving the L_P 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 L_W and L_R light were successfully generated. The modulators AOM4 for L_W and AOM5 for L_R were controlled according to the timing sequences for the storage and retrieval of L_P. The separately propagated L_W and L_R were merged before passing through the atomic medium.

 

Fig. 2 (a) Detailed experimental setup for the light storage scheme using a probe laser L_P and pseudo-thermal laser L_C. (EOM: electro-optic modulator; AOM: acoustic-optic modulator; ISO: isolator; NF: neutral-density filter; M: mirror; BS: beam splitter; PBS: polarization beam splitter; MS: μ-metal sheet; HT: heating tape; APD: avalanche photodiode; SPC: single-photon counter). (b) Chaotic RF-signal injected into the AOMs to generate the pseudo-thermal light.

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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 L_P, laser L_C, and pseudo-thermal L_C 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 [22]. The measured photon counting was reorganized as a function of counted photon number. The statistical results for the laser L_P and laser L_C correspond to Poisson distributions, which can be expressed as

 

Fig. 3 Experimental result (black bars) and theoretical fit (red bars) of the photon number statistics as a function of the (a) laser L_P, (b) laser L_C, and (c) pseudo-thermal L_C light.

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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 L_C light changed from Poisson to Bose-Einstein distributions, as shown in Fig. 3(c). The measured statistical result for the pseudo-thermal L_C was in good agreement with a fit to the Bose-Einstein function given by

The $\overline{n}$ value in this case was 2.1. We argue that temporal fluctuations in L_C 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) [23] as

The calculated g²(0) values for the L_P, L_C, and pseudo-thermal L_C light were approximately 0.999 ± 0.013, 0.994 ± 0.012, and 1.971 ± 0.025, respectively.

The coherent EIT spectrum obtained with L_P and L_C was compared with the thermal EIT spectrum obtained with L_P and the pseudo-thermal L_C, as shown in Fig. 4 . Figure 4(a) is a typical EIT spectrum for coherent L_P and L_C lasers, where the horizontal axis describes the detuning frequency from the two-photon resonance for the EIT resonance. When the photon bunching characteristics of L_C were changed to those of a Bose-Einstein distribution, the thermal EIT spectral width broadened due to the short coherence time of L_C induced by the strong intensity fluctuations (Fig. 4(b)). The L_P and L_C 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 L_C also induced a reduction in the amplitude of the EIT such that the amplitude of the EIT obtained with the pseudo-thermal L_C before normalization was 3 times smaller than that of the EIT obtained with the L_C laser.

 

Fig. 4 (a) Coherent EIT spectrum obtained with the laser L_C and (b) the thermal EIT spectrum obtained with the pseudo-thermal L_C.

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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 L_P, slow L_P, and retrieved L_P pulses, respectively. There is an apparent difference in the arrival times of the reference L_P and slow L_P pulses. The timing sequences of the L_W and L_R beams for writing and reading are indicated by the solid gray and black lines, respectively, in Fig. 5(a). The photon number statistics of L_W and L_R can be controlled independently by AOM2 and AOM3. The FWHM of the input L_P pulse was 8.6 μs, and the delay time Δt between the reference input L_P and slow L_P pulses was 2 μs. The speed of the L_P pulse using the delay time Δt was derived by v_g = 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 [9]. With a delay time of 2 μs, the speed of the slow L_P pulse was 25000 m/s, or 0.000083c. By controlling the timing sequences of L_W and L_R, we were able to store the L_P pulse for 20 μs, which is referred to as the storage time. We could observe the retrieval of the L_P pulse from the atomic ensemble by switching on L_R. The retrieval efficiency was estimated to be 20% from the ratio of the amplitudes of the slowed and retrieved light pulses.

 

Fig. 5 Light storage and photon number statistics for the retrieved pulses. (a) The transmission of the reference L_P light pulse (black dotted line), slow L_P light pulse (red dashed line), and retrieved L_P pulse (blue solid line) during L_W and L_R switching. The “Write,” “Storage,” and “Read” times of the L_P pulse were controlled by the timing sequences of L_W (gray solid line) and L_R (gray dashed line). (b) The photon number statistics for pulses retrieved during the 3-μs gating time with L_R.

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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 L_R laser. The mean photon number was estimated to be 2.1. With L_W 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 L_P pulses according to the photon number statistics of L_W and L_R. After an L_P pulse was stored with the writing pseudo-thermal L_W and the reading laser L_R, we measured the photon number statistics of the retrieved L_P. Figure 6(a) shows the time sequences of the L_P pulse, the writing pseudo-thermal L_W, and the reading laser L_R. To measure the photon count events only for the retrieved L_P, a 3-μs electronic gating pulse was applied to the SPD immediately after L_R was turned on, as shown in Fig. 6(a). The intensity fluctuations of the pseudo-thermal L_W are faster than those of the original L_P pulse duration. Therefore, the single retrieved pulse has the statistical properties of chaotic intensity fluctuation of the pseudo-thermal coupling light.

 

Fig. 6 Change in the characteristics of the retrieved pulse according to the photon number statistics of the writing coupling light. (a) Time sequences for the stored and retrieved L_P pulses with the writing pseudo-thermal L_W and the reading laser L_R. (b) Photon number statistics of the retrieved L_P pulses during the 3-μs gating time.

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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 L_W light. The g²(0) calculated from the experimental data was 1.853 ± 0.021. When the L_P pulse was stored in the EIT medium, the information of not only the L_P pulse but also that of the pseudo-thermal L_W light was stored in the EIT atomic medium because of the strong correlations between the two [24,25]. Therefore, the randomly fluctuating retrieved L_P pulses indicate the transfer of the random intensity fluctuations of the pseudo-thermal L_W to the retrieved L_P, that is, the non-bunching characteristics of L_P could be changed to strong bunching characteristics.

When the stored light is retrieved from the EIT medium, the properties of the reading L_R light can affect the characteristics of the retrieved L_P pulse. To investigate the effect of the reading L_R, the photon number statistics of the L_R light was changed to those of pseudo-thermal light. Figure 7(a) shows the time sequences of the L_P pulse, the writing laser L_W, and the reading pseudo-thermal L_R. Before L_R is turned on, a typical light storage process is observed and all the properties of L_P are preserved in the EIT medium. However, when the pseudo-thermal L_R is turned on, the properties of the retrieved L_p can change significantly.

 

Fig. 7 Change in the characteristics of the retrieved pulse according to the photon number statistics of the reading coupling light. (a) Time sequences for the stored and retrieved L_P pulses, the writing laser L_W, and the pseudo-thermal L_R. (b) The photon number statistics of the pulses retrieved during the gating time by the reading pseudo-thermal L_R.

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Figure 7(b) shows the experimental result (black bars) and theoretical fit (red bars) of the photon number statistics for the retrieved L_P pulses using the pseudo-thermal L_R. 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 L_R was turned on after the storage time, the retrieved L_P pulses randomly fluctuated during the gating time. The intensity fluctuations in the L_R 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 L_P pulses were quite different from the results seen in Fig. 6. For the previous case, the retrieved L_P 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.

4. Conclusion

We have investigated the influence of the writing and reading coupling light on the light pulse retrieved from an EIT medium consisting of the 5S_1/2-5P_1/2 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 L_W was applied to the atomic ensemble, the retrieved L_P pulses exhibited a Bose-Einstein distribution even though the original input L_P pulses had a Poisson distribution. The random intensity fluctuations in the pseudo-thermal L_W light were transferred to the retrieved L_P light. Both the information of the L_P pulse and also that of the pseudo-thermal L_W light were stored in the EIT atomic medium. Although all the properties of L_P were stored in a typical EIT medium, the photon number statistics of the retrieved L_P was changed when pseudo-thermal coupling light was used as L_R. Therefore, it is possible to distort the retrieved L_P 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.