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Abstract
In quantum communication with quantum repeaters, multiplexed quantum memory is expected to enhance communication rates. When using an atomic frequency comb (AFC) for on-demand storage, the frequency mode number is often limited by the optical power of the control pulses. Here, using a space-coupled waveguide electro-optic modulator, we increased the output power, allowing us to apply control pulses to multiple modes simultaneously. Further, through enhancement of an experimental setup that increases power density, we increased the number of modes. Consequently, we pioneered, to the best of our knowledge, on-demand storage using five modes of AFC. This technology is a significant achievement toward frequency-multiplexed on-demand quantum memory.
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1. INTRODUCTION
Long-distance quantum communication faces a critical limitation due to photon losses occurring in optical fibers. Even at telecommunication wavelengths, this loss escalates exponentially with distance, reaching approximately 0.2 dB/km. To overcome this challenge, the concept of a quantum repeater has been proposed. Quantum repeaters perform entanglement swapping [1] between distant nodes, which requires synchronizing the arrival times of these probabilistically arriving photons. This synchronization can be realized through quantum memories [2–4], which can store and retrieve the quantum states of photons at theoretically any given time. To enhance entanglement generation, crucial for quantum communication rates, multiplexed quantum memories are employed in quantum repeaters [4]. In recent years, the atomic frequency comb (AFC) [5] has garnered attention as a promising method for multiplexed quantum memories. AFC consists of absorption lines of an ensemble of atoms arranged in a comb structure along the frequency axis, and the frequency interval of the comb is represented by $\Delta$. The quantum state of a photon absorbed in an AFC at $t = 0$ is retrieved as a photon echo at $t = \frac{1}{\Delta}$. The versatility of AFC lies in its ability to multiplex in multiple degrees of freedom, including time [6–11], frequency [12–14], and space [15–17] domains. Among these, frequency multiplexing can be achieved using the inhomogeneous broadening of rare-earth ion-doped material [Fig. 1(a)]. The frequency multiplicity is limited by the number of AFCs that can be generated within the inhomogeneous broadening, depending on the inhomogeneous width and hyperfine-level splitting [17]. In the case of ${\Pr ^{3 +}}{:}{{\rm Y}_2}{{\rm SiO}_5}$, it has succeeded in storing photons from a cavity two-photon source, which features a free spectral range (FSR) of 261 MHz in 15 modes of AFC [13] as well as from a cavity two-photon source, with an FSR of 117.2 MHz in 25 modes of AFC after wavelength conversion [14]. However, in these experiments, AFC functioned only as a fixed-time quantum memory. To achieve on-demand storage in AFC, the concept of spin-wave storage (SW) has been proposed and demonstrated [Fig. 1(b)] [5,18]. On-demand storage is enabled by transferring the quantum state of the absorbed photons to spin wave states. This transfer requires the use of intense light pulses called control pulses (CPs), typically in the order of 10 mW, to induce efficient coherent optical transitions [7,18–21]. Experiments on frequency-multiplexed on-demand AFC using SW have been conducted with two modes separated by 80 MHz [16]. However, when storing multiple modes of photons from sources similar to those reported in the literature [13,14], transferring all modes simultaneously with CPs is essential. Such experiments have not yet been conducted, not even in the case of storing classical light. To apply CPs simultaneously on multiple modes, we propose the utilization of sidebands generated by an electro-optic modulator (EOM) with an applied sinusoidal waveform. However, a major drawback of this approach is the substantial optical power required to apply CPs to multiple modes. Bulk-type EOMs can typically handle a few watts of input optical power. However, they are often unsuitable for increasing modes through sideband generation due to their large half-wave voltage, typically measuring approximately 100 V. In contrast, waveguide-type EOMs, with a relatively small half-wave voltage (a few volts), facilitate the generation of numerous sidebands. Fiber-coupled waveguide EOMs are often limited to an input optical power of below 100 mW and suffer from losses due to fiber coupling, leading to reduced output power. In our experiment, we used space-in and space-out waveguide EOMs, enabling us to achieve high output optical power compared with fiber-coupled waveguide EOMs and a small half-wave voltage ($\sim{6}\;{\rm V}$) compared with bulk-type EOMs. Further, we enhanced the power density by narrowing the beam diameter of CPs, reducing the power required for CPs and thereby increasing the number of modes. In this study, toward multiplexed quantum memory, we demonstrate frequency-multiplexed on-demand AFC by applying CPs simultaneously to five frequency modes of AFC using an experimental setup that incorporates these two enhancements.
Fig. 1. (a) Absorption spectrum with inhomogeneous broadening of ${\Pr ^{3 +}}{:}{{\rm Y}_2}{{\rm SiO}_5}$ (top) and the frequency-multiplexed on-demand AFC generated in it (bottom). (b) Sequence of spin-wave storage (SW).
2. EXPERIMENTAL SETUP
Figure 2(a) illustrates the optical transitions of the ${\Pr ^{3 +}}{:}{{\rm Y}_2}{{\rm SiO}_5}$ crystal used in our experiment. The on-demand AFC has comblike absorption lines in the 1/2g-3/2e transition, with initially no population in the 3/2g-3/2e transition. In the SW technique, we apply an input pulse to the AFC of the 1/2g-3/2e transition and achieve on-demand storage by applying CPs to the 3/2g-3/2e transition, inducing coherent optical transitions before rephasing occurs.
Fig. 2. (a) Hyperfine structure and optical transitions in ${\Pr ^{3 +}}{:}{{\rm Y}_2}{{\rm SiO}_5}$. Yellow and red arrows correspond to Λ-type transitions used in spin-wave storage. (b) Experimental setup. A 606 nm laser, obtained via second-harmonic generation of a 1212 nm external cavity diode laser, serving as the light source. The absolute frequency of this laser was stabilized to an optical frequency comb during the experiment. The linewidth of this laser was approximately 0.1 MHz. The light was split into two beams using a beam splitter (BS), and both beams were subjected to frequency modulation using acousto-optic modulators (AOMs). The first path, referred to as the pump beam or CP beam, was used for generating the AFC and applying the CPs. In this path, the beam entered the sample via a space-coupled waveguide electro-optic modulator (EOM), which divided it into five different frequency modes. Moreover, the second path, referred as the input beam, was used to generate the input pulse. In this path, the light was converted into a single arbitrary frequency mode using a fiber-coupled waveguide EOM, which then entered the sample. These two paths were separated in terms of polarization using a Faraday rotator (FR), a half-wave plate (HWP), and a polarizing beam splitter (PBS). The photon echoes generated from the ${\Pr ^{3 +}}{:}{{\rm Y}_2}{{\rm SiO}_5}$ crystal were detected using a photodetector (PD).
The experimental setup is detailed in Fig. 2(b). The ${\Pr ^{3 +}}{:}{{\rm Y}_2}{{\rm SiO}_5}$ crystal with a doping ratio of 0.05% and dimensions of ${3}\;{\rm mm} \times {3}\;{\rm mm} \times {5}\;{\rm mm}$ was cooled to temperatures below 3.5 K using a cryostat (Fusion, Montana Instrument) during the experiment. Given the 606 nm absorption wavelength of ${\Pr ^{3 +}}{:}{{\rm Y}_2}{{\rm SiO}_5}$, we used a narrow-linewidth 606 nm laser, generated through second-harmonic generation of a 1212 nm external cavity diode laser (TA-SHG pro, TOPTICA). The absolute frequency was stabilized to an optical frequency comb during the experiment. The AFC was generated using a hole-burning technique [22] and a parallel method [9], thereby modulating the pump beam with an acousto-optic modulator (AOM). After creating a pit spanning 18 MHz, we prepared the absorption lines that serve as the AFC in the 1/2g-3/2e transition through a burn-back pulse [23]. Subsequently, the on-demand AFC structure was constructed by alternately applying parallel method pulses to the 1/2g-3/2e transition and clean pulses to the 3/2g-3/2e transition. The pump beam entered a space-coupled waveguide EOM (WPM-K0606-CCUCCU0J0-C-UYN-HP23-CP10-63-06-L1-EPH, AdvR), which was modulated by the 92 MHz sinusoidal wave, before entering the ${\Pr ^{3 +}}{:}{{\rm Y}_2}{{\rm SiO}_5}$. This process enabled us to create five modes of on-demand AFC ($\Delta = 400\,\,{\rm kHz}$) by generating sidebands that were separated by 92 MHz. These five modes are referred to as $-2$, $-1$, 0, 1, and 2 modes, starting from the low-frequency side. The total time required to create the AFC was 706 ms. For the input beam, we generated a Gaussian pulse with ${t_{{\rm FWHM}}} = 283\;{\rm ns}$ using an AOM. This beam underwent frequency conversion to a specific single mode through serrodyne modulation [24] using a fiber-coupled waveguide EOM (PM594, Jenoptik), before entering the ${\Pr ^{3 +}}{:}{{\rm Y}_2}{{\rm SiO}_5}$. The CP used for the SW technique was a complex hyperbolic secant (CHS) pulse [25] with ${t_{{\rm FWHM}}} = 0.5\;\unicode{x00B5}{\rm s}$ and a chirp range of 3 MHz. CP was applied simultaneously to all five modes using the same path as the pump beam. In particular, to ensure spatial overlap, both beams propagated at the same angles, and they are orthogonally polarized and separated using a faraday rotator (FR) and polarizing beam splitter (PBS) before being detected by a photodetector (PD). This approach allowed the pump and input beams to focus to small values, 65 and 50 µm, respectively, at the center of the crystal while maintaining overlap, resulting in a reduction of the optical power required for the CP. The space-coupled waveguide EOM achieved a maximum output power of 50 mW with an approximate coupling efficiency of 40%, resulting in a maximum CP power of 10 mW per mode.
3. EXPERIMENTAL RESULT
A. AFC
In this section, we delve into the experimental results, starting with the description of the generated AFC. Figure 3 represents five frequency modes of the on-demand AFC, with the central 0-mode AFC centered at a relative frequency of 0 MHz. Each enlarged image corresponds to the 1/2g-3/2e transition, featuring a comb structure created with $\Delta = 400\;{\rm kHz}$. Further, the frequency at ${+}{10.2}\;{\rm MHz}$ from the AFC center corresponds to the 3/2g-3/2e transition, left vacant for the SW storage.
B. Photon Echo
We present the results of the photon echo in Fig. 4, along with their respective retrieval efficiencies listed in Table 1. Figure 4(a) represents fixed-time ($\frac{1}{\Delta} = 2.5\;\unicode{x00B5}{\rm s}$) photon echoes. The variation in ${\eta _{{\rm AFC}}}$ across modes is likely due to differences in the finesse of each AFC and variations in the background optical density, as observed in Fig. 3. Figures 4(b) and 4(c) represent on-demand echoes with storage times of (b) $\frac{1}{\Delta} + {T_S} = 6.5\;\;\unicode{x00B5}{\rm s}$ and (c) $\frac{1}{\Delta} + {T_S} = 12.5\;\;\unicode{x00B5}{\rm s}$, respectively. The two preceding peaks between the input pulse and the photon echo are attributed to noise introduced by the CP light reflecting off the cryostat window and reaching the PD. This noise can potentially be eliminated via temporal separation using an AOM shutter [19,26]. To clarify the causes of mode-dependent variations in on-demand echo efficiency, we calculate ${\eta _{{\rm trans}}}$, the transition efficiency of the CP. The efficiency of on-demand echoes is described by Eq. (1), with ${\eta _{{\rm dephase}}}$ accounting for decay due to spin state dephasing, as defined by Eq. (2) [7]:
Fig. 4. Result of photon echo. Photon echoes reproduced from each mode of frequency-multiplexed AFC. Note that only the echoes are plotted with their sizes magnified 20 times. (a) Fixed time echo of $\frac{1}{{\Delta}} = 2.5\;\unicode{x00B5}{\rm s}$. (b) Echo of on-demand storage time with ${T_S} = 4\;\unicode{x00B5}{\rm s}$ ($\frac{1}{{\Delta}} + {T_S} = 6.5\;\unicode{x00B5}{\rm s}$). Note that the signals around $1\;\unicode{x00B5}{\rm s}$ and $5\;\unicode{x00B5}{\rm s}$ are CP noise. (c) Echo of on-demant storage time with ${T_S} = 10\;\unicode{x00B5}{\rm s}$ ($\frac{1}{{\Delta}} + {T_S} = 12.5\;\unicode{x00B5}{\rm s}$). As in (b), the signals around $1\;\unicode{x00B5}{\rm s}$ and $11\;\unicode{x00B5}{\rm s}$ are CP noise.
Table 1. Efficiency of Photon Echo and CP
The parameter ${\gamma _{\textit{IS}}}$ represents a value known as spin inhomogeneity. To determine this value in our setup, we conducted experiments to measure ${\eta _{{\rm SW}}}$ for ${T_S}={6}\sim{35}\;\unicode{x00B5} {\rm s}$. These experiments were conducted using the 0-mode AFC. The results are shown in Fig. 5, and the estimated ${\gamma _{\textit{IS}}}$, obtained from the fitting (shown by the light blue line), is approximately 20.8 kHz. The calculated ${\eta _{{\rm trans}}}$ values are listed in Table 1, using ${\gamma _{\textit{IS}}}$ obtained from Fig. 5 and Eqs. (1) and (2), along with ${\eta _{{\rm AFC}}}$ and ${\eta _{{\rm SW}}}({{T_S} = 4\;\unicode{x00B5}{\rm s}})$ from Table 1. These results reveal mode-dependent variations in ${\eta _{{\rm trans}}}$, with differences of up to 22.5%. The mode-dependent variations in the AFC structure and ${\eta _{{\rm trans}}}$ are attributed to differences in the power of the pump beam and CPs among the modes. In this experiment, we applied a simple 92 MHz sine wave to the space-coupled waveguide EOM for generating sidebands. However, achieving a perfect balance of power among different modes was challenging due to variations in conversion efficiency. A potential improvement involves adjusting the mode power balance by applying multiple harmonic waves to the EOM. These results collectively demonstrate the successful on-demand storage of all five modes using frequency-multiplexed AFC.
Fig. 5. Results of ${\eta _{{\rm SW}}}$ for ${T_S}={6}\sim{35}\;\unicode{x00B5} {\rm s}$. The light blue line was fitted using Eq. (1).
4. DISCUSSION AND CONCLUSION
Taking into consideration the results of the present experiment, our focus shifts to the estimation of the experimentally implementable number of modes in future research. In this experiment, we successfully implemented five modes of on-demand AFC by using two key strategies: minimizing the beam diameter of CP; and increasing the output optical power of the waveguide EOM. Further advancements in the experimental setup are anticipated to result in an augmented number of modes. First, addressing the beam diameter of the CP, our current experimental system achieved a minimized diameter of 65 µm. However, in a previous work [27], an even smaller beam diameter of 18.5 µm was achieved by incorporating a waveguide in the ${\Pr ^{3 +}}{:}{{\rm Y}_2}{{\rm SiO}_5}$ crystal. If a similar waveguide could be implemented in our sample, it would allow for further reduction of the beam diameter to 0.285 times the current size. Considering that power density is inversely proportional to the square of the beam diameter and the Rabi frequency is proportional to the square root of power density, maintaining the same CP as in this experiment could drive the transition with 2.85 mW per mode. Additionally, losses associated with coupling to this waveguide in ${\Pr ^{3 +}}{:}{{\rm Y}_2}{{\rm SiO}_5}$ were reported to be approximately 50%. Subsequently, considering the EOM, the space-coupled waveguide EOM used in this experiment had a coupling efficiency of 40% and a maximum input optical power of 300 mW, which limited the maximum obtainable power to 120 mW. Under these conditions, securing CP power for approximately 21 modes becomes possible. Although we were restricted in our experiment by the laser linewidth of approximately 0.1 MHz, which prevented the creation of AFCs with $\Delta$ less than 400 kHz, a previous study [28] demonstrated the creation of an AFC with $\Delta = 40\;{\rm kHz}$, one-tenth of our current $\Delta$. Thus, the ability to create AFCs with smaller $\Delta$ than the current value may allow for further power savings by extending the ${t_{{\rm FWHM}}}$ of the CP, potentially enabling an increase in the number of modes. Additionally, in this implementation, we used CHS pulses, which are relatively easy to implement; nevertheless, a more efficient and robust pulse, known as the modulated adiabatic pulse, has been proposed in the literature [29]. This pulse is suggested to be capable of achieving high-efficiency transitions at lower power levels compared with CHS pulses, which may also allow for an increase in the number of modes.
Further, in this experiment, we have limited our storage to classical light pulses of approximately 1 mW. However, it should be noted that storing a single photon remains a challenge for future applications in quantum memory. Considering this limitation, we discuss the prospects for frequency-multiplexed on-demand storage at the single-photon level. Regarding experiments with single-frequency modes, on-demand storage at the single-photon level has been reported extensively [19–21,26]. In these experiments, a small angle was made between the CP and the input path as it entered the crystal to prevent noise caused by the CP. On the other hand, in our experimental system, the two beams were not angled to maintain spatial overlap while keeping the beam diameter narrow, so the echoes were buried in the noise, and the experiment could not be performed at the single-photon level. Methods such as the Stark-modulated AFC [30] have been proposed to address coherent noise, including free induction decay and off-resonant echo [26]. This approach utilizes two electrically distinct ion classes that undergo opposite-sign Stark shifts when subjected to an electric field pulse. This is a method of on-demand storage without SW, but it can be applied to SW, and it has been suggested that it can suppress coherent noise due to CP [31]. Additionally, successful embedding of silver wires for applying electric field pulses in an $^{151}{{\rm Eu}^{3 +}}{:}{{\rm Y}_2}{{\rm SiO}_5}$ has been achieved [32], allowing the combination with crystal waveguide technology. In addition, it has been suggested that reducing the power of the CP can contribute to noise reduction [29]. Therefore, implementing the aforementioned methods to diminish the CP power could potentially aid in decreasing noise levels. By integrating these technologies with our current experimental setup, it should be possible to conduct experiments for on-demand storage of frequency-multiplexed modes at the single-photon level.
In conclusion, the enhancements made to our experimental setup have resulted in the successful on-demand storage of five modes of AFC. If successful in the storage of a single photon in the future, the realization of multiplexed quantum memory is expected. Further, this technology holds the promise of increasing the number of frequency modes in the future, rendering it suitable for applications in long-distance quantum communication, leveraging its multiplexing capabilities.
Funding
Ministry of Internal Affairs and Communications (JPMI00316); New Energy and Industrial Technology Development Organization (Deep-Tech Startups Support Program); Secom Science and Technology Foundation; Japan Society for the Promotion of Science (JP20H02652); Moonshot Research and Development Program (JPMJMS226C).
Acknowledgment
We thank K. Minaguchi, K. Mannami, Y. Nodaguchi, T. Tsuno, M. Ichihara, R. Maruyama, and K. Niizeki for their assistance.
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
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