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Abstract
We report on the dynamic manipulation of light in a warm 87Rb atomic ensemble using light storage based on the atomic spin coherence arising from the electromagnetically induced transparency (EIT) and spontaneous four-wave mixing (FWM) processes. We demonstrate that, subsequent to the generation of atomic spin coherence between two hyperfine ground states via the EIT storage process, it is possible to control the delay time, direction, and optical frequency of the retrieved light according to the timing sequence and powers of the coupling, probe, and driving lasers used for atomic-spin-coherence generation and the spontaneous FWM process. We believe that our results provide useful ideas in photon frequency conversion and photon control in connection with the quantum memories that is essential in the quantum communications technology.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Photon manipulation via atom–photon interactions is widely regarded important as it finds its applications in various branches of quantum optics research such as quantum communication [1], quantum memory [2–4], and quantum repeaters [5–7]. In particular, quantum memory is a key technology for long-distance quantum communication, photonic quantum information networks, and on-demand single-photon sources. The quantum memory of the photonic quantum state has been intensively studied in atomic media with atomic coherence. Quantum memory is based on preservation of quantum properties such as entanglement, qubits, and photon statistics of the stored light [8–11]. In the view of the photon manipulation, quantum memory technologies are used to control the arrival time of photons with high-efficiency and high-fidelity of photonic quantum states [4]. However, the optical manipulation of photon properties such as the optical frequency, spatial mode, and polarization, via interactions with an atomic medium, can be extremely useful for the maintenance and operation of photonic quantum states. In this regard, previous studies have reported on photon manipulation in warm [12–14] and cold [15–17] atomic ensembles.
In the abovementioned atomic ensembles, if light can be split into two different paths and its optical frequency can be converted via atom–photon interactions, the photons can be coherently and dynamically manipulated. In a warm atomic ensemble, light beam splitting via the spatial transport of atomic coherence has been demonstrated via the electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) effects [13–14]. Despite the random atomic motion of the Doppler-broadened atoms, changes of the relative magnitude, delay time, and width of the spatially transported light pulse have been observed as functions of the distance between two spatially separated paths [14]. As this method relies on two spatially separated channels, it is difficult to dynamically manipulate the relative magnitude and delay time of the spatially transported light pulses. On the contrary, coherent and dynamic beam splitting has been demonstrated in cold atomic ensembles by using light storage based on the EIT and four-wave mixing (FWM) processes [15].
The FWM process in a double-Λ configuration may be useful for the manipulation of light from an atomic medium with atomic coherence; this is because the driving laser can induce FWM light from the coherent atomic medium under the phase-matching condition [18–19]. Although the EIT and FWM processes have been used to improve the efficiency of quantum memory in an optically thick atomic ensemble of warm Rb atoms via the collective ground-state spin coherence [17], the coherent and dynamic light manipulation in warm ensembles, via the EIT and FWM processes, has not thus far been reported to the best of our knowledge.
This work shows the coherent and dynamic light manipulation in a Doppler-broadened warm atomic vapor cell, for the first time. We experimentally demonstrate the optical manipulation of light retrieved from a quantum memory by exploiting the EIT and FWM processes in the double-Λ-type atomic system of a warm 87Rb atomic ensemble. Through the optical control of the coupling and driving lasers in the EIT and FWM processes, our approach allows us to control the time, direction, and optical frequency of the retrieved light from the atomic spin coherence generated between two hyperfine ground states. Moreover, we theoretically address the enhancement of the atomic spin coherence via the FWM process using a simple four-level atomic model of the double-Λ system.
2. Experimental setup
Figure 1(a) shows the energy-level diagram of the 5S1/2–5P1/2 transition of 87Rb atoms for the FWM process with coupling, probe, and driving lasers. The double-Λ atomic system consists of two Λ-type atomic systems: one Λ-type configuration originates from coupling laser Ωc and probe laser Ωp, where the frequencies of ΩC and Ωp are on-resonance with respect to the 5S1/2 (F = 1)–5P1/2(F′ = 2) and 5S1/2(F = 2)–5P1/2(F′ = 2) transitions, respectively. A second Λ-type configuration is formed by driving laser Ωd and the FWM light. In the first Λ-type configuration, the atomic spin coherence between the two hyperfine ground states of 5S1/2 (F = 1 and 2) is generated using Ωc and Ωp. In the second Λ-type configuration, we can understand the generation of Stokes photon ωs via the following FWM process: the role of Ωd is to induce generation of the ωs-photons from the atomic medium in the presence of Λ-type two-photon coherence due to Ωc and Ωp.
Fig. 1. Energy-level diagram and experimental configuration for the manipulation of Stokes and anti-Stokes signals based on quantum memory in Rb atomic vapor. (a) Energy-level diagram of the 5S1/2–5P1/2 transition of 87Rb atoms for the four-wave mixing (FWM) process with probe (Ωp), coupling (Ωc), and driving (Ωd) lasers. (b) Timing sequence of Ωc, Ωp, and Ωd with time delay (τ), generation of atomic spin coherence between two hyperfine ground states via the electromagnetically induced transparency (EIT) storage process, and retrieval of the Stokes (ωs) and anti-Stokes (ωas) signals directionally separated by an angle θ.
Let us briefly illustrate the light manipulation based on the quantum memory via the spontaneous FWM process due to Ωc and Ωd. Figure 1(b) shows the timing sequence of Ωc, Ωp, and Ωd with time delay τ, the generation of the atomic spin coherence between two hyperfine ground states via the EIT storage process, and the retrieval of the Stokes (ωs) and anti-Stokes (ωas) light signals directionally separated by an angle θ. The retrieved ωs and ωas signals are generated from the atomic spin coherence via the spontaneous FWM process due to Ωc and Ωd. We can control the retrieval time (τ) and the propagation directions of both ωs and ωas. The angle between ωs and ωas is determined along the phase-matched direction under the Doppler-free condition for Λ-type two-photon resonance in the Doppler-broadened double-Λ-type atomic system.
The schematic of the experimental apparatus used to manipulate the retrieved signals from the quantum memory is shown in Fig. 2. In our setup, two external-cavity diode lasers (ECDLs, ECDL1 for coupling and ECDL2 for the probe and driving lasers) are electrically phase-locked to 6.8 GHz, corresponding to the hyperfine splitting frequency of the 5S1/2 ground state of the 87Rb atom. The spectral widths of the ECDLs are estimated to be less than 1 MHz and the relative frequency jitter of the two locked lasers is measured to be smaller than 2 Hz, corresponding to the measurement limitation of the radio frequency (RF) spectrum analyzer. The coupling laser, controlled by a fiber electro-optic modulator (EOM1), is used for the generation of atomic spin coherence and the manipulation of the retrieved light via the EIT and FWM processes. The ECDL2, used for the driving and probe lights, is first split into two. One beam is assigned as the driving laser, which is used for the manipulation of the retrieved light via fiber EOM2, whereas the other is treated as the probe light pulse with a half-Gaussian shape with use of fiber EOM3. In this study, the lasers are linearly polarized in the perpendicular directions, and the optical powers of the probe, coupling, and driving lasers were 10 µW, 5.0 mW, and 2.5 mW, respectively.
Fig. 2. Schematic of experimental apparatus for the manipulation of Stokes and anti-Stokes light signals based on the quantum memory in an 87Rb atomic vapor cell (ECDL: external-cavity diode laser; FC: fiber collimator; QWP: quarter-wave plate; HWP: half-wave plate; M: mirror; PBS: polarizing beam splitter; APD: avalanche photodiode; EF: solid fused-silica etalon filter).
In the setup, the Ωp laser pulse is combined with the copropagating ΩC laser at a polarizing beam splitter (PBS). The Ωd laser is aligned with a small tilt angle of 2.4° relative to the propagation directions of the ΩC and Ωp lasers. For the storage medium, we used an 87Rb vapor cell with a diameter of 2.5 cm and length of 5 cm, which also contained 4-Torr Ne buffer gas. To shield the vapor cell from the Earth’s magnetic field, the cell was wrapped with three layers of µ-metal sheets. The temperature of the vapor cell was controlled at 45°C, which corresponded to the atomic number density of 1.5 × 1011/cm3. To remove the residual ΩC and Ωd lasers, we used etalon filters (EFs) with a full-width-at-half-maximum (FWHM) bandwidth of 950 MHz and peak transmission of 85%. Following the generation of atomic spin coherence in the vapor cell, the retrieved ωs and ωas signals were measured by two avalanche photodiodes (APDs).
3. Experimental results and discussion
We first investigate the slow light pulse in the coherent atomic medium via EIT and FWM processes. Figure 3(a) shows the input probe pulse (gray curve) with a pulse width of 2 µs, the slow light (red curve) in the EIT medium (obtained with the ΩC and Ωp lasers), and the slow light (blue curve) in the FWM medium (obtained with the ΩC, Ωp, and Ωd lasers). In our experiment, the EIT slow-light pulse was measured with the delay time of 0.54 µs and transmittance of 27% under the conditions of the optical depth of 10, ΩC power of 5.0 mW, and Ωp power of 10 µW. In the case of the FWM slow light with the addition of the 2.5 mW Ωd laser, the delay time and the transmittance were measured to be 0.91 µs and 43%, respectively. Here, we note that the delay times of 0.54 µs and 0.91 µs correspond to approximately quarter and half of the pulse width 2 µs, respectively. From the results in Fig. 3(a), we note that the slow light pulse under the FWM condition is more efficient than that under the EIT condition because the added Ωd enhances the ground-state spin coherence (${\rho _{12}}$) with the generated FWM light (ΩFWM).
Fig. 3. Atomic spin coherence obtained via electronically induced transparency (EIT) and four-wave mixing (FWM) processes. (a) Slow-light pulses under EIT and FWM conditions. (b) Storage of probe (Ωp) and FWM (ΩFWM) pulses and retrieval of Stokes (ωs) and anti-Stokes (ωas) light signals under the FWM condition; (top panel) timing sequence of the Ωc, Ωp, and Ωd lasers with the time delay of 7.2 µs; (middle and bottom panels) relative amplitudes of the probe (red curve) and FWM (blue curve) pulses, respectively.
To further understand the enhancement of ${\rho _{12}}$ via the FWM process, we can treat the experimental atomic system as a simple four-level atomic model of the double-Λ configuration. The four-level atomic model is composed of two ground states ($|1 \rangle$, $|2 \rangle$) and two excited states ($|3 \rangle$, $|4 \rangle$). Moreover, ΩC, Ωp, and Ωd denote the Rabi frequencies of the coupling, probe, and driving lasers coupled to the $|1 \rangle$–$|3 \rangle$, $|2 \rangle$–$|3 \rangle$, and $|2 \rangle$–$|4 \rangle$ transitions, respectively. Parameter ${\rho _{12}}$ is directly related to the generated FWM light (ΩFWM). It is convenient to transform the system into a co-rotating frame to eliminate the fast rotations. Thus we can transform the density-matrix elements into the rotating frame of a slowly varying density operator. Subsequently, the atomic spin coherence (${\rho _{12}}$) can be expressed as [18]
Figure 3(b) shows the storage of Ωp and ΩFWM pulses under the FWM condition and the subsequent retrieval of ωs and ωas signals. When ΩC and Ωd lasers are simultaneously turned off at 0 and turned on at 7.2 µs, the storage process involves the generation of atomic spin coherence, whereas the retrieval process corresponds to the regeneration of ωs and ωas signals from the atomic spin coherence via the spontaneous FWM process due to ΩC and Ωd lasers. Particularly, we remark that the only ΩC and Ωd lasers are necessary for the spontaneous FWM process. In the retrieval process, when the both ΩC and Ωd lasers are turned on, two spontaneous Raman processes occur in the double-Λ system consisting of two Λ-type atomic systems along with a spontaneous FWM process due to the retrieved ωs and ωas signals.
Let us discuss the dynamics of the probe and FWM pulses in the 5 cm-long atomic vapor cell. Figure 4 shows the simulation results of the relative amplitudes of the probe and FWM pulses as temporal and spatial functions during the storage and retrieval processes under the FWM condition. We numerically calculated the probe and FWM pulse propagations using the coupled Maxwell–Bloch equations in the double-Λ-type four-level atomic model. In our calculations, we considered the phase-mismatch factor, Doppler shift, and averaging over the atomic motion in the Doppler-broadened ensemble of atoms. The atomic density matrix elements were averaged over the Maxwellian velocity distribution. Considering the broadening effect of the 4-Torr Ne buffer gas, the decay rates were set to Γ/2π = 46 MHz and γ/2π = 0.1 MHz, and the optical depth was set to 10. Moreover, the Rabi frequencies ΩC and Ωd were set to 8 MHz and 4 MHz, respectively.
Fig. 4. Calculated probe and four-wave mixing (FWM) pulse propagations in the double-Λ-type four-level atomic model; dynamics of the probe and FWM pulses in the atomic vapor cell.
The simulation results in Fig. 4 reveal the behavior of a Gaussian probe pulse and generated FWM signal on the space–time plane. It is noteworthy that the atomic medium of the vapor cell spans the length from 0 to 5 cm. The ΩC and Ωd lasers are turned off at t = 0 and turned on at t = 7.2 µs. The FWM generation and probe absorption in the storage process are suitably calculated from 0 to 5 cm in the atomic medium. The results show that the storage of the Ωp and ΩFWM pulses is established at around t = 0, and the ωs and ωas signals are retrieved at t = 7.2 µs.
Figure 5 shows the manipulation of the ωs and ωas signals under the experimental conditions corresponding to Fig. 1(b). The atomic spin coherence is generated in the EIT storage process, and the ωs and ωas signals are generated via the spontaneous FWM (Fig. 5(a)) and enhanced Raman (Fig. 5(b)) processes, respectively. The enhanced Raman process means that the Raman field is generated from the atomic spin coherence [20–21]. Although atomic spin coherence is generated due to Ωc and Ωp, the properties of the generated ωas signals are different from those of the Ωp pulse in terms of the tilt angle (θ) and the optical frequency conversion.
Fig. 5. (a) Generation of ωs and ωas signals via electronically induced transparency (EIT) storage and spontaneous four-wave mixing (FWM) retrieval and (b) generation of ωas light via EIT storage and enhanced Raman retrieval.
In Fig. 5(a), it appears that the Ωp pulse is separated into the ωs and ωas signals at 7.2 µs. Here, we note that we can control the amplitude ratio between ωs and ωas by adjusting the powers of Ωc and Ωd in the retrieval process. When the powers of ΩC, Ωp, and Ωd are set to 5.0 mW, 10 µW, and 2.5 mW, respectively, the relative amplitude of the ωs signal is ∼6 times larger than that of the ωas signal.
However, from Fig. 5(b), we note that the Ωp pulse is converted into only ωas light via the enhanced Raman process. When the laser powers are the same as the counterparts corresponding to Fig. 5(a), the relative amplitude of the ωas signal is identical with the corresponding results shown in Fig. 3(b) and Fig. 5(a); however, the temporal shape of the ωas signal is significantly different from the corresponding results in the presence of Ωc. This discrepancy in the temporal shape of the ωas signal arises because the ωas signal in Fig. 5(b) is generated via the enhanced Raman process, whereas the other signals are due to the spontaneous FWM process.
Interestingly, the temporal shape of the ωas signal generated via the spontaneous FWM process is identical to that of ωs because ωas is induced by the retrieved ωs signal. The temporal shape of the retrieved ωs is determined by that of the retrieved light corresponding to the typical EIT-quantum memory without the Ωd laser. Therefore, the ωas signal is strongly correlated with the ωs signal via the spontaneous FWM process in the double-Λ-type atomic system.
To further understand the result of Fig. 5(b), we can numerically calculate the pulse propagations in the Stokes (probe) and anti-Stokes channels using the coupled Maxwell–Bloch equations in the simple four-level atomic model of the double-Λ configuration. Figure 6 shows that the storage of the probe field with the coupling field is established at around t = 0, and the only ωas light due to the Ωd is retrieved at t = 7.2 µs. In the storage process, the atomic spin coherence between the two ground states is generated by the Ωc and Ωp. In the retrieval process, we can understand the generation of anti-Stokes photon ωas via the enhanced Raman process: the role of Ωd is to generate the ωas-photons from the atomic medium in the presence of Λ-type two-photon coherence due to Ωc and Ωp. Although the simple atomic model in this study differs from a real atomic system with hyperfine structures and Zeeman sublevels, the calculated results for generation of ωas light via EIT storage and enhanced Raman retrieval are in a good agreement with the experimental result shown in Fig. 5(b).
Fig. 6. Calculated pulse propagations of the Stokes and anti-Stokes channels via the enhanced Raman process in the double-Λ-type four-level atomic model.
4. Conclusion
We experimentally demonstrated the manipulation of the Stokes and anti-Stokes signals retrieved from the atomic spin coherence via the spontaneous FWM process in the Doppler-broadened double-Λ-type atomic ensemble of a warm 87Rb vapor cell with a 4-Torr Ne buffer gas. We investigated the slow light pulses in the coherent atomic medium with atomic spin coherence. The slow light pulse under the FWM condition was more efficient than that under the EIT condition because of the enhancement of the ground-state spin coherence in the FWM process. After the generation of the atomic spin coherence between two hyperfine ground states via the EIT storage process, we could manipulate the Stokes and anti-Stokes signals retrieved from the atomic spin coherence via the spontaneous FWM process. Numerically calculating the probe and FWM pulse propagations using the coupled Maxwell–Bloch equations for the double-Λ-type four-level atomic model, we confirmed the retrieval of the ωs and ωas signals via the spontaneous FWM process with a time delay. The amplitude ratio of the generated ωs and ωas signals could be controlled by adjusting the laser powers in the storage and retrieval processes. Furthermore, we could split the stored probe pulse via EIT memory into the two ωs and ωas signals via the spontaneous FWM process. The ωas signal was strongly correlated with the ωs signal via spontaneous FWM in the double-Λ-type atomic system. We believe that presented results may suggest a novel method for photon-pair generation via spontaneous FWM in the double-Λ-type atomic systems.
Funding
National Research Foundation of Korea (2018R1A2A1A19019181, 2020M3E4A1080030); Ministry of Science and ICT, South Korea (IITP-2020-0-01606).
Disclosures
The authors declare no conflicts of interest.
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