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Abstract
We experimentally investigate the frequency down-conversion through the four-wave mixing (FWM) process in a cold 85Rb atomic ensemble, with a diamond-level configuration. An atomic cloud with a high optical depth (OD) of 190 is prepared to achieve a high efficiency frequency conversion. Here, we convert a signal pulse field (795 nm) attenuated to a single-photon level, into a telecom light at 1529.3 nm within near C-band range and the frequency-conversion efficiency can reach up to 32%. We find that the OD is an essential factor affecting conversion efficiency and the efficiency may exceed 32% with an improvement in the OD. Moreover, we note the signal-to-noise ratio of the detected telecom field is higher than 10 while the mean signal count is larger than 0.2. Our work may be combined with quantum memories based on cold 85Rb ensemble at 795 nm and serve for long-distance quantum networks.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
One of the most prominent and interesting phenomena of the interaction between optical fields and a nonlinear medium is the four-wave mixing (FWM) [1] that originates from the third-order nonlinear process. Recently, FWM processes have found various applications in atomic systems, such as the generation of correlated photon pairs [2,3] or squeezed light [4], the storage of coherent light [5], optical frequency conversion [6] and phase-insensitive optical amplification [7], etc. Among them, the long-distance quantum communication processing [8] is an extensively researched topic, which includes generating telecom-wavelength photons [9,10] or converting the frequency of photons into the telecom-wavelength window.
To date, frequency conversion based on FWM in the rubidium atomic system has been widely investigated in various energy-level schemes, such as ladder-type [11–13], double-lambda type [14,15], and diamond-type [16,17]. For example, double-lambda schemes with conversion efficiency up to $91.2\%$ have been reported [18]. Unfortunately, the generated photons are still limited in the visible-wavelength window (from 780 nm to 795 nm wavelengths), which restricts its applications in long-distance communications due to the inevitable high losses in fibre-optical channels. One conventional way towards the conversion between photons in telecom and visible spectrum range is adopted to diamond schemes. Although an E-band [19] frequency conversion with an efficiency as high as 54$\%$ has been realized in the profound work recently [20], the converted photons (1367 nm) are still not in the best wavelength of a telecom-fiber. More specifically, a photon in 1367 nm has a much larger transmission loss of 0.37 dB/km, compared to that of the photon in 1529.3 nm (0.19 dB/km). For instance, when incorporated into a 100 km long-distance communication network, a converter with 1529.3 nm provides an advantage of 18 dB of less loss in the fiber. Until now, the frequency conversion process from 795 nm wavelength to 1529.3 nm (near C-band) wavelengths with a co-linear propagation structure of lights in a cold $^{85}$Rb ensemble has not been reported, and we explored this conversion process in our experiment. As been studied in the pioneering work [21], the attainable conversion efficiency is highly related to the optical depth (OD) of the medium. In this work, we establish a dense cold $^{85}$Rb atomic ensemble, the OD of which is measured to be 190 in an independent experiment, by utilizing a technique called dark-spontaneous emission optical trap [22] and then realize a telecom-wavelength conversion based on nonlinear optical frequency down-conversion process of FWM.
Here, we consider a diamond configuration ($5S_{1/2}-5P_{1/2}-4D_{3/2}-5P_{3/2}-5S_{1/2}$) in cold $^{85}$Rb as it covers resonance frequency of telecom-wavelength (1529.3 nm) and a wavelength (795 nm) that commonly used for atom-based optical memory [23]. The frequency down-conversion process is investigated while the mean photon count of the input signal field is attenuated to the magnitude of a single photon level. As described by the theory in previous work [21], we experimentally verified that the frequency-conversion efficiency increases with the OD. Such frequency converters, operating at the single photon level and high OD, play an important role in atom-based quantum repeater and long-distance quantum communication.
2. Experimental setup
Figure 1(a) shows a four-levels diamond configuration of $^{85}$Rb atomic system, which consists of two intermediate states $\left \lvert 2\right \rangle$ ($\left \lvert 5P_{1/2},F^{\prime }=3\right \rangle$) and $\left \lvert 4\right \rangle$ ($\left \lvert 5P_{3/2},F^{\prime }=4\right \rangle$), one ground state $\left \lvert 1 \right \rangle$ ($\left \lvert 5S_{1/2},F=3\right \rangle$), and one excited state $\left \lvert 3\right \rangle$ ($\left \lvert 4D_{3/2},F^{\prime \prime }=3\right \rangle$). We define the detuning $\Delta _{s}$ ($\Delta _{p2}$) with the form of $\Delta _{s}=\omega _{s}-\omega _{12}$ ($\Delta _{p2}=\omega _{p2}-\omega _{23}$), where $\omega _{s}$ ($\omega _{p2}$) is the frequency of signal (pump2) field and $\omega _{ij}$ is the frequency of the $|i\rangle \leftrightarrow |j\rangle$ transition. The signal (795 nm) and pump1 (1475 nm) fields couple the atomic transition $|1\rangle \rightarrow |2\rangle$ with a detuning of $\Delta _{s}=-2\pi \times 6$ MHz (The negative sign means red detuning.) and the atomic transition $|2\rangle \rightarrow |3\rangle$ under resonance, respectively. The transition between $|1\rangle \leftrightarrow |4\rangle$ is coupled by a pump2 (780 nm) field with a detuning of $\Delta _{p2}=-2\pi \times 36$ MHz. According to the principle of energy conservation, the telecom (FWM) light at 1529.3 nm can be generated through the transition from $|3\rangle$ to $|4\rangle$ in the FWM process, providing the phase-matching condition is satisfied.
Fig. 1. (a) Energy-level diagram of diamond configuration. (b) Schematic diagram of the experimental setup. MOT: magneto-optical trap; PBS: polarizing beam splitter; DM1, DM2: dichroic mirror; IF1, IF2: Interference filter; FC1, FC2: fibre collimator; FF: fibre filter. (c) Time sequence for the frequency down-conversion process.
A simplified schematic of our experiment is depicted in Fig. 1(b). The nonlinear media is a cigar-shaped $^{85}$Rb atomic cloud (with an OD of 190) that is prepared in a dark-line two-dimensional magneto-optical trap (MOT). We focus strong pump1 (1.87 mW) and pump2 (1.4 mW) fields, together with a single-photon-level signal light into the ensemble with different waists of 152 $\mu$m, 117 $\mu$m, and 71 $\mu$m, respectively. The pump fields and signal light propagate collinearly in the $^{85}$Rb atoms with vertical and horizontal polarization. We block the pump2 field with a dichroic mirror (DM2) and use interference filters (IF2) and a polarization beam splitter (PBS) to filter out the generated telecom light with horizontal polarization from the strong pump1 light. The telecom light is collected by a fiber collimator (FC2) and a fiber filter (FF) is used to isolate the background fluorescence and further improve the signal-to-noise ratio (SNR). Finally, we detect the generated telecom photon with an infrared single-photon detector (Qasky WT-SPD100, InGaAs Photon Detector, 10$\%$ detection efficiency) which is connected to the FF. Similarly, we use the IF1 to filter out the signal field and measure the count of input signal photons by an avalanche diode detector (PerkinElmer SPCM-AQR-16-FC, 65$\%$ detection efficiency). The time sequence is shown in Fig. 1(c). Our system is repeated with a period of 10 ms including an 8 ms trapping time and an experimental time of $\Delta T=2$ ms (The MOT magnetic field and MOT beams are turned off.). In each cycle, we modulate the signal light and pump fields with the temporal modes of a Gaussian pulse and square-shaped pulses. The square-shaped pulses of the pump fields are used to keep the instantaneous intensities of the pump fields constant during the FWM process, and the conversion efficiency will decrease when the pump intensities are weak. We have not observed a significant difference between the condition where the signal pulse is Gaussian-shaped and the condition of a square-shaped signal pulse. However, considering the need of transmitting the signal light in an optical fiber for further applications, a temporal mode of Gaussian pulse is chosen in our work. The pulse time width of pump1, pump2, and signal fields are 1 $\mu$s, 5 $\mu$s, and 200 ns respectively. The experimental times for the pumping fields (pump1 and pump2) in our work need to be less than 2 ms (the experimental window in each cycle) and should overlap with the signal pulse. The temporal width of the near-resonance pump2 light should be tailored to be as short as possible to avoid introducing an influence on the effective optical depth.
3. Experimental results and theoretical analysis
In our experiment, the input signal pulse with a temporal width of 200 ns and pulse repetition rate of $R_{p}=100$ Hz, is attenuated to the single-photon level by a neutral density filter. By taking the transmittance (58.5$\%$) of the uncoated glass vacuum cell and various optical components, the coupling efficiency (83.7$\%$) of the FC1, and the detection efficiency (65$\%$) of the detector into consideration, we can obtain the number of input signal photons through dividing the count of detected signal photons ($N_{s}$) by a factor of $T_{s}=0.318$. Similarly, We can calculate the number of converted telecom photons by considering the count of detected telecom photons ($N_{t}$) with the transmission factor $T_{t}=0.0299$, where $T_{t}$ includes the transmittance (54.3$\%$) of the MOT and various optical components, the detection efficiency (10$\%$) of the detector, the transmittance (91.8$\%$) of the FF, and the coupling efficiency (60$\%$) of the FC2. Here, we define the frequency-conversion efficiency as:
In Fig. 2(a), the average counts of input signal photons per pulse is ensured to be $\overline {n}=0.8$ ($\overline {n}=N_{s}/(300R_{p}T_{s})$) by a coincidence count of 300 s. We adjust the signal detuning $\Delta _{s}$ through an acousto-optic modulator (AOM), and the frequency-conversion efficiency $\eta$ is measured while the $\Delta _{s}$ is scanned from $-2\pi \times 40$ MHz to $2\pi \times 40$ MHz. We find that $\eta$ is higher in the case of a near-resonance signal field, and the main reasons include the strong atomic absorption [20] and the phase-matching condition satisfied by the frequencies of the experimental beams in our work. The solid line is fitted by the Lorentzian function $y=y_{0}+2Aw/(\pi (4(x-x_{c})^{2}+w^{2}))$ with fitted values ($y_{0}=-0.306$, $x_{c}=-1.507$, $w=125.9$, $A=119.8$). The fitting curve gives a bandwidth of 70 MHz in FWHM. We find that the frequency-conversion efficiency of our system reaches its maximum value when the signal detuning $\Delta _{s}$ is $-2\pi \times 6$ MHz.
Fig. 2. (a) Measured frequency-conversion efficiency $\eta$ as a function of signal detuning $\Delta _{s}$. Red dot: experimental measurement. Black line: a Lorentzian fit. (b) The relation of frequency-conversion efficiency $\eta$ to pump2 intensity. Red dot: experimental data. Black line: fitted curve.
We study the dependence of frequency-conversion efficiency on the pump2 intensity in Fig. 2(b), where the results are obtained under the optimal detuning conditions of $\Delta _{s}=-2\pi \times 6$ MHz and $\Delta _{p2}=-2\pi \times 36$ MHz, the mean signal photon per pulse is $\overline {n}=0.8$. The power of pump1 $P_{1}$ is fixed at 1.87 mW and the pump2 intensity is calculated by the formula ($I_{p2}=P_{2}/(\pi w^{2}_{p2})$), where $w_{p2}=117~\mu$m and $P_{2}$ are the beam waist and the power of pump2 respectively. Owing to the finite number of atoms and signal photons that interact with optical fields, we observe a tendency of saturation as the pump2 intensity increases. As shown in Fig. 2(b), the $\eta$ grows with the increase of $I_{p2}$ and a trend of saturation can be observed. This result is consistent with the conclusion drawn in the previous work [20]. To visualize the rising trend of the $\eta$, we fit the experimental data with $\eta =\eta _{max}(1-exp(-(I_{p2}-I_{0})/I_{s}))$ as proposed by [20], where $\eta _{max}=0.32$, $I_{0}=0.6$ W/cm$^{2}$ and $I_{s}=0.95$ W/cm$^{2}$. The maximum $\eta$ achieved in our system is $32\%$.
A crucial factor to achieve high frequency-conversion efficiency is the OD of our $^{85}$Rb ensemble. We experimentally investigate the influences of different OD on conversion efficiency $\eta$ at the conditions of $\Delta _{s}=-2\pi \times 6$ MHz, $\Delta _{p2}=-2\pi \times 36$ MHz, $P_{1}=1.87$ mW, $P_{2}=1.4$ mW and $\overline {n}=0.8$, which is illustrated in Fig. 3 (blue dots). The OD is defined as $OD=\rho \sigma L$ [21], where $L$ is the length of atomic cloud, $\rho$ is the number density of atoms, and $\sigma =3\lambda ^{2}/(4\pi )$ is the resonant absorption cross-section. Therefore an increase in OD indicates an increase in the number density of atoms, which implies an enhanced probability of FWM process occurring between optical fields and atoms. We can fetch the information from Fig. 3 (blue dots) that the increase in this probability has a significant influence on the improvement of the $\eta$. Considering the specific relationship between OD and $\eta$, we refer to the theoretical analysis in previous work [21]. The co-moving propagation equation for signal ($E_{s}^{+}$) and telecom ($E_{t}^{+}$) fields under momentum and energy conservation conditions are described as
Fig. 3. Experimental data (blue dot) and theoretical fitting (black curve) of frequency-conversion efficiency $\eta$ with the growth of OD, and all data have the background noise subtracted. The error bar is estimated from Poissonian statistics and using Monte Carlo simulations.
Figure 4 indicates that the frequency-conversion efficiency $\eta$ with different $\overline {n}$ of input signal field. The $\overline {n}$ is scanned from 0.06 to 3.1. We find that the $\eta$ is independent of the $\overline {n}$, and the average $\eta$ is 32$\%$. In addition, due to the noise caused by the dark count of the detector and the unfiltered pump fields, the SNR of the detected telecom fields decreases with the reduction of the $\overline {n}$, and the SNR is higher than 10 when $\overline {n}$ is 0.2 in our experimental system. Our scheme performs well when $\overline {n}$ is at single photon level.
Fig. 4. Measured frequency-conversion efficiency $\eta$ with the growth of $\overline {n}$ and all results have the back-ground noise subtracted.
Compared to the previous work [13] that adopts a ladder configuration, in where exists difficulty filtering out the weak FWM light from the strong homo-chromatic pump light, the proposed converter can operate at single-photon level with a high SNR since the pump and FWM lights are hetero-chromatic. What’s more, in contrast to other works [13,20], our setup with a co-linear structure enhances the probability of FWM process by increasing the overlapped area between optical fields and atomic ensemble.
We can conclude from Fig. 3 that one of the most effective ways to improve conversion efficiency in further is increasing the OD of the ensemble. Fortunately, there are several feasible methods towards this goal such as building a temporal dark spontaneous-force optical trap [24] or placing the atomic ensemble in a ring cavity [25] to increase the interaction length between optical fields and non-linear medium.
4. Conclusion
In conclusion, we report a telecom-wavelength (near C-band) frequency converter in cold $^{85}$Rb ensemble with high OD through the FWM process. The frequency-down conversion at the wavelength from 795 nm to 1529.3 nm is achieved by a diamond-type energy level configuration. What’s more, we experimentally confirm that the $\eta$ improves significantly with the increase of OD, and the experimental data is in reasonable agreement with our theoretical fitting. Besides, we observe that the SNR in our work is well performed when $\overline {n}$ is at single photon level. Our scheme has the potential for applications in atom-based quantum repeater and long-distance quantum networks.
Funding
National Key Research and Development Program of China (2022YFA1404000); National Natural Science Foundation of China (11934013, 61525504, U20A20218); Youth Innovation Promotion Association of the Chinese Academy of Sciences (2018490); Major Science and Technology Projects in Anhui Province (202203a13010001).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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