1. INTRODUCTION

Future development of quantum communication networks requires novel methods to manipulate quantum information. In recent years, electromagnetically induced transparency (EIT) has attracted much attention because of its applications in quantum information processing [1]. One very promising application of the EIT effect is that a probe light pulse can be slowed and even stored using dynamical EIT [2]. This EIT-based light storage enables us to transfer quantum states between light field and the medium and has potential applications in quantum memory and quantum repeater [3 –6]. In order to perform multiple information processing, the coherent manipulation of double light pulses is also developed. The slowing and storage of double light pulses have been achieved in an EIT tripod-type atomic system [7 –10]. Using cold rubidium atoms with EIT lambda-type system, the storage of two signal pulses with transverse images has been implemented experimentally [11]. Nonlinear coupling of storing double light pulses has been investigated experimentally in lambda-type cold cesium atoms [12].

Coherent storage of optical images in a coherently driven medium plays a significant role in many fields with possible applications [13]. In these applications, the amplitude and phase of images are expected to be preserved. Because of unique properties of the EIT effect, it is used as an important candidate for storing optical images. Recently, there has been some interest in using EIT techniques to store transverse spatial images. Some experimental progress on EIT-based image storage has been reported [13 –19]. Image storage provides large information capacity and can be used to perform multiple information processing. Quantum storage needs to preserve transverse spatial coherence and longitudinal phase coherence of light pulses. The preservation of longitudinal phase coherence has been investigated by a beat interferometer in light storage with cold atoms [20]. A direct demonstration of the preservation of transverse spatial coherence has been performed by the interference of a retrieved pulse and a fiber-delayed pulse in atomic vapor [21]. Storage of spatially structured light pulses such as an optical vortex [22] or optical topological charge [23] in EIT media also demonstrated that the transverse spatial coherence of light pulse was preserved.

In this paper, we experimentally demonstrate the preservation of transverse spatial coherence in the storage of double light pulses by using an EIT-driven solid. An EIT three-level lambda-type atomic system is used to perform the experiments rather than the four-level tripod-type atomic system in [9]. Two frequency-degenerate optical pulses with different propagation directions are used as input probe pulses. Due to the steep dispersion induced by EIT, two input probe pulses are slowed in the crystal. By manipulating the intensity of the control field, two probe pulses are stored into atomic coherence and later retrieved in the opposite process. By analyzing the Young-type spatial interference of two probe pulses before and after the storage, it is clearly demonstrated that transverse spatial coherence of light pulses are preserved in the storage process. Also, high interference visibility is well maintained for different storage times. This demonstration has important applications for image and information processing.

The present experiment is related to the first direct demonstration of the preservation of spatial coherence in atomic vapor quantum memory [21]. Here, we demonstrate the preservation of transverse spatial coherence in the storage of double light pulses by using a doped solid rather than atomic vapor. The solid mediums without atomic diffusion provide spatially fixed interaction units and have important applications for information processing. We perform the storage of double light pulses compared with the storage of a single pulse in [21], and the transverse spatial coherence of two probe pulses are investigated. Due to the limited length of the fiber delay line, the experimental data of [21] are limited to a storage time of 8.3 μs. In our case, the transverse spatial coherence can be investigated in the whole decay time scale.

2. EXPERIMENTAL CONFIGURATION

We perform the storage of double light pulses in ${\mathrm{Pr}}^{+3}\text{:}{\mathrm{Y}}_2{\mathrm{SiO}}_5$ (Pr:YSO) crystal. Figure 1 shows the level coupling of Pr ions for the storage of double light pulses. Compared with atomic gases, rare-earth-doped solids provide narrow spectrum lines and long decoherence time [24,25] and can be used to perform efficient information processing [26,27]. The laser beams drive optical transitions involving hyperfine levels of the ground state (${}^3{H}_4$) and the excited state (${}^1{D}_2$). Both states consist of three doubly degenerate hyperfine levels. The center wavelength of ${}^3{H}_4\to {}^1{D}_2$ transition is about 605.977 nm. Two lower levels (${}^3{H}_4(\pm 1/2)$ and ${}^3{H}_4(\pm 3/2)$) and one upper level (${}^1{D}_2(\pm 3/2)$) are chosen to form an EIT lambda-type system. The strong control field ${\omega }_c$ couples the transition of ${}^3{H}_4(\pm 1/2)\to {}^1{D}_2(\pm 3/2)$. Two weak probe fields ${\omega }_{p1}$ and ${\omega }_{p2}$ couple the transition of ${}^3{H}_4(\pm 3/2)\to {}^1{D}_2(\pm 3/2)$. These two probe fields have different propagation directions with the same frequency. The repump field is used to pump the populations to the levels ${}^3{H}_4(\pm 1/2)$ and ${}^3{H}_4(\pm 3/2)$ by the optical pump effect.

 

Fig. 1. Coupling scheme of Pr ions. Powers of the control, probe-1 and probe-2 fields are 14 mW, 0.5 mW and 0.5 mW, respectively.

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Figure 2 shows the experimental setup of light storage. The Pr:YSO crystal of 0.05% dopant concentration is cooled to 3.5 K temperature by using a cryostat. Its length along the crystal B axis is 3 mm. A frequency-stabilized dye laser (R6G) provides the laser radiation, and its linewidth is about 1 MHz. The initial laser is split into three laser beams (the control, probe field, and repump field). Each laser beam is guided to an acousto-optical modulator to control its intensity and frequency. The probe field is further divided into two probe fields (${\omega }_{p1}$ and ${\omega }_{p2}$) by beam splitter. These two probe fields propagate through the crystal along different directions. Two probe fields are spatially overlapped with the control field in the crystal. The noncollinear configuration significantly reduces noise from the scattering of the control field. The angle between the two probe beams is about 4°, and the beam waist in the crystal is about 300 μm. The input probe pulses are Gauss-shaped, and their temporal length is about 43 μs. After passing through the crystal, two probes fields are partially directed to photodiodes (PD) for the pulse intensity measurement and partially sent to the CCD camera to monitor the patterns of Young-type spatial interference induced by these two probe fields.

 

Fig. 2. Experimental setup of the storage of double light pulses. L, lens; PD, photodiode; BS, beam splitter.

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3. EXPERIMENTAL RESULTS AND DISCUSSION

In order to select single ensembles of Pr ions to perform slow light and storage, we apply the preparation process of [28]. Through preparation pulses, Pr ions shown in Fig. 1 are selected, and the populations are prepared to ${}^3{H}_4(\pm 3/2)$ level. Subsequently, the control field and two probe pulses are applied to form the EIT lambda-type system. Under the EIT condition, the opaque medium becomes transparent due to quantum interference. Steep dispersion can be obtained in the transparency windows, which induces the slowing and storage of the light pulse. Figure 3(a) shows the slowing of two input probe pulses recorded by PD. It is seen that two probe pulses experience the same time delay of 40 μs. To investigate transverse spatial coherence, we establish Young-type two-beam interferometer by making two output probe pulses interfere at the CCD position. The transverse spatial interference patterns are directly recorded by CCD. In order to obtain Young’s interference patterns before the storage, CCD is triggered after input probe pulses completely enter the crystal. Figure 3(b) shows Young’s spatial interference image recorded by CCD. We further use image-processing software to deal with the interference image and obtain the intensity distribution of the interference image in the horizontal direction, as shown in Fig. 3(c). From [21] and [29], the fitting curves of the Young-type interference are Gaussian envelops multiplied by a sine curve. So the fitting interference intensity $I_{\text{in}}$ can be written as $I_{\text{in}}=A{\sin }^2(fx+\varphi )\exp [-{(x-\mathrm{\Delta })}^2/2{\sigma }^2]$, where $x$ is the horizontal coordinate, $A$ is the modulated amplitude, $f$ is the frequency of the sine function, $\varphi$ is the phase of the sine function, $\sigma$ is the standard deviation parameter of the Gaussian function, and $\mathrm{\Delta }$ is the position parameter of the Gaussian function. In experiments, two probe intensities have small differences; thus, the interference signal has a small background. Because the laser beam has a Gaussian-shaped intensity distribution, the background signal $I_b$ is a Gaussian function $I_b=B\exp [-{(x-\mathrm{\Delta })}^2/2{\sigma }^2]$. After considering small mismatch of two probe intensities, the fitting intensity can be further written as $I=[A{\sin }^2(fx+\varphi )+B]\exp [-{(x-\mathrm{\Delta })}^2/2{\sigma }^2]$. Using the above equation, we fit the experimental data. The interference visibility V is 0.85, which is calculated from the offset and amplitude of the sinusoidal modulation [29]. The visibility is limited by the dark noise of CCD and small mismatch in two probe intensities.

 

Fig. 3. (a) Experimental demonstration of the slowing of two probe pulses. (b) Young’s spatial interference patterns of two probe pulses before the storage. (c) Intensity distribution of the interference patterns.

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Next, we further perform the storage of two probe pulses by manipulating the control field. EIT storage is based on coherent conversion between light fields and atomic coherence. Under the EIT condition, the probe pulses are stored into atomic coherence between two lower levels by switching off the control field. After a given storage time, the stored atomic coherence is retrieved into the probe pulses by switching back on the control field. Figure 4(a) shows the storage and retrieval of two probe pulses for several different storage times. The front edges of probe pulses do not experience the storage operation and leave the EIT medium before the control field is switched off. The back edges of probe pulses experience the storage and later retrieval, and their reduced intensity is due to the dephasing of atomic coherence during the storage. To record Young’s spatial interference patterns of two retrieved pulses, CCD is triggered after the control field is switched back on. Figure 4(b) shows Young’s spatial interference patterns and their associated intensity distribution. In order to obtain the clear interference patterns compared to Fig. 3(b), we increase the CCD gain for different storage times to compensate the reduced intensities of the retrieved pulses. It is clearly seen that the interference patterns of the retrieved probe pulses are the same as that before the storage shown in Fig. 3(b). The spatial interference patterns do not change before and after the storage, which is a direct demonstration that the transverse spatial coherence of light pulses are preserved in the storage process. From the intensity distribution of the interference patterns, it is found that high interference visibility is well maintained during the storage and retrieval process.

 

Fig. 4. (a) Storage and retrieval of two probe pulses for a storage time of 6 μs, 12 μs and 18 μs. (b) Young’s spatial interference patterns of two retrieved pulses after the storage and their associated intensity distribution for three different storage times.

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In light storage of atomic gases, atomic diffusion causes the spreading of the retrieved light field as the storage time increases, which results in the distortion of the retrieved image for image storage. The solid-state mediums, without atomic diffusion, provide the spatially fixed interaction units and can be used as an excellent candidate for light and image storage. In our case, a doped solid is used as the experimental medium, and the Young’s spatial interference patterns are preserved for different storage times. Figure 5(a) shows the retrieved intensities of two probe pulses versus the storage time. It is seen that the retrieved intensities decrease with the storage time, which is due to the dephasing of stored atomic coherence caused by the spin inhomogeneous broadening [14]. The coherence time of ground-state spin transition of Pr ions is about 500 μs [30]. In our case, the measured maximum storage time is about 30 μs, which is far below the coherence time but similar to that of [31]. All Pr ions in the spin inhomogeneous bandwidth contribute to the preparation of the coherence [31], and the storage time is not determined by the spin decoherence but the dephasing of spin coherence. If the external magnetic field and dynamical decoupling technique are applied, the storage time can be remarkably increased. The interference visibilities for different storage times are further investigated in Fig. 5(b). It is seen that all interference visibilities are above 0.84 for different storage times and are almost kept constant. Even for 30 μs storage time, the interference visibility is still 0.85, although the retrieved probe pulses have very weak intensities. High interference visibility is well maintained in EIT-based light storage. Through the above demonstration, it is directly shown that the transverse spatial coherence of light pulses is preserved in the storage process.

 

Fig. 5. (a) Retrieved intensity of two probe pulses versus the storage time. (b) Interference visibility versus the storage time.

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4. CONCLUSION

Using an EIT-driven solid, we experimentally report on the preservation of transverse spatial coherence in the storage of double light pulses. In an EIT lambda-type system, two probe pulses with different propagation directions are slowed and stored in the crystal. By investigating Young’s interference patterns of two probe pulses before and after the storage, we give a direct demonstration of the preservation of transverse spatial coherence of light pulses in the storage process. High interference visibility is well maintained for different storage times. The obtained results are believed to be useful for further image processing and light manipulation.