1. Introduction

Photon sources exploiting atomic media are key components of photonic quantum information technologies based on atom–photon interactions. Such sources can be used to construct quantum information networks consisting of spatially separated nodes to store and process quantum information including quantum repeaters and quantum memory [1–9]. In particular, effective interactions between atomic systems and coherent light are essential for the development of high-quality photon sources based on atomic media [10–17]. Most current experimental setups for photon sources using trapped atoms, such as those based on single atoms, ions, and cold atoms, are complex, bulky, and require high-vacuum conditions; thus, in these setups, it is difficult to manipulate isolated atomic samples [15–19].

Meanwhile, a photon-pair source realized using an alkali atomic vapor cell can afford high device compactness and operational simplicity relative to sources based on cold atomic systems [20–25]. Although warm atomic ensembles are limited by Doppler broadening, this problem of atomic vapor cells has been overcome in the form of a Doppler-free-configuration in a double Λ or cascade type atomic transition. In Cs vapor cell, the twin beam source based on four-wave mixing in a double Λ-scheme has been reported [26]. Recently, bright-photon-pair generation has been experimentally demonstrated using spontaneous four-wave mixing (SFWM) and collective two-photon coherence effects in a cascade-type atomic system [21]. Furthermore, a polarization-entangled photon source from an atomic vapor cell has been experimentally demonstrated using bidirectional counter-propagating pump and coupling lasers [24].

In the atomic-physics community, the chip-scale atomic clock was first fabricated and demonstrated two decades ago using microelectromechanical systems (MEMS) fabrication techniques [27]. Chip-scale atomic devices such as atomic clocks, magnetometers, and gyroscopes continue to open up new possibilities for the development of miniature atom-based instruments [28–35]. In particular, a chip-scale atomic vapor cell combined with fiber array or waveguide optics can potentially be applied in various quantum devices such as single-photon sources and quantum memories based on atomic ensembles.

Here, we experimentally demonstrate the generation of photon pairs via the SFWM process in the 6S1/2–6P3/2–8S1/2 transition from a chip-scale warm atomic ensemble of ¹³³Cs atom. In particular, the optical frequency of the 6P3/2–8S1/2 transition of the ¹³³Cs atom is close to that of the D₁ line of the ⁸⁷Rb atom, which provides a potential resource for hybrid photonic quantum network between the photonic quantum states generated from different atomic systems, such as Rb and Cs atoms [36]. Our chip-scale atomic vapor cell is a simple and small device that is fabricated by the anodic bonding of silicon and glass. Bright photon pairs can be generated from this atomic ensemble with weak laser pumping on the order of tens of microwatts. To characterize the generated photon pairs, we measured the cross-correlation between the signal and idler photons. Furthermore, we investigated the quantum beats of the temporal biphoton waveform of the photon pair generated via SFWM multi-channels relating to the hyperfine states of the intermediate state of the 6P_3/2.

2. Experimental setup for photon-pair generation from warm Cs atomic ensemble

For the Cs vapor cell [ Fig. 1(a)] in our setup, borosilicate wafers on both sides of a through-hole-patterned Si wafer are bonded using anodic bonding. The vapor cell outer dimensions are 2 mm × 3.5 mm × 1.4 mm. This setup also includes a cesium metal dispenser without a buffer gas, as shown in Fig. 1(b). After bonding, the Cs dispenser is activated in situ by a high-power laser, and pure Cs atoms move from the dispenser to the photon-pair chamber for photon-pair generation through a channel. In our experiment, the Cs dispenser is activated in situ by a high-power laser of ∼130 mW during an activation time of ∼30 s. The diameter and thickness of the photon-pair chamber were 1.5 mm and 1 mm, respectively.

 

Fig. 1. Experimental setup for the generation of photon pairs from the Cs atomic cell. (a) Photograph of the chip-scale Cs atomic cell. (b) Structure of the fabricated chip-scale Cs atomic cell (Cs dispenser, channel, and photon-pair chamber). (c) Schematic of the experimental setup for photon-pair generation via spontaneous four-wave mixing (SFWM) (lens focal length = 300 mm).

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Here, we note that the collective two-photon coherence effect is important for the generation of bright photon pairs from Doppler-broadened warm atoms [21]. Two-photon resonance occurs via the application of counter-propagating pump and coupling lasers satisfying the Doppler-free two-photon resonant condition in the warm atomic ensemble. In our setup, as shown in Fig. 1(c), the pump and coupling lasers are counter-propagated, focused, and spatially overlapped in the photon-pair chamber. However, in the co-propagating configuration, we cannot expect the collective two-photon coherence effect, because the two-photon resonance condition is different according to the velocity of the Doppler-broadened atomic ensemble.

The pump and coupling lasers are orthogonally linearly polarized along the horizontal (H) and vertical (V) polarization directions, respectively. Owing to the conservation of angular momentum in the SFWM process, the generated photon pair in the two-photon decay is polarization-correlated with the perpendicular linear-polarized signal/idler (H/V or V/H) photons. However, to minimize laser-scattering noise at the single-photon detectors (SPDs, PerkinElmer SPCM-AQRH-13HC), the polarizations of the signal and idler photons are selected as linear polarizations (V/H) orthogonal to those (H/V) of the pump and coupling lasers. The emitted signal and idler photons are counter-propagated in the phase-matched direction and coupled into two single-mode fibers positioned at a tilt angle of ∼2.3° relative to the propagating directions of the pump and coupling lasers.

Figure 2(a) shows the generation of the photon pair along the cascade decay paths corresponding to the 6S_1/2(F = 4)–6P_3/2(F′ = 3, 4, 5)–8S_1/2(F″ = 4) transition of the ¹³³Cs atom. The wavelengths of the pump and coupling lasers were 852 nm for the 6S_1/2–6P_3/2 transition and 795 nm for the 6P_3/2–8S_1/2 transition. The natural linewidths of the 6P_3/2 and 8S_1/2 states are 5.2 MHz and 1.7 MHz, respectively [37]. To prevent uncorrelated photons due to single-photon resonance, their optical frequencies were detuned beyond the Doppler broadening of the warm Cs ensemble.

 

Fig. 2. Experimental configuration for the generation of photon pairs from Cs atomic ensemble. (a) Cascade emission of signal and idler photons via spontaneous four-wave mixing (SFWM) in the 6S_1/2–6P_3/2–8S_1/2 transition of ¹³³Cs atom. (b) Transmittance spectrum (blue curve) in the atomic vapor cell and saturated absorption spectrum (gray curve) in an ordinary atomic vapor cell of pump laser. (c) Two-photon absorption (TPA) spectrum of the 6S_1/2(F = 4)–6P_3/2(F′ = 3, 4, 5)–8S_1/2(F″ = 3, 4) transition.

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The photon pair generated via the SFWM process in a cascade-type atomic system is strongly correlated with two-photon coherence because of the possibility of nonlinear optical process enhancement via two-photon coherence [23]. In our experiment, we selected the 6S_1/2(F = 4)–8S_1/2(F″ = 4) transition for fulfilling the Doppler-free two-photon resonant condition for photon-pair generation. Therefore, we note here that the two-photon resonance between the 6S_1/2(F = 4)–8S_1/2(F″ = 4) transition should be maintained for the stable operation of the photon pair generated from the Cs cell.

We first investigated the two-photon absorption (TPA) spectrum in the Cs vapor cell. Figure 2(b) shows the transmittance spectrum (blue curve) for the 6S_1/2(F = 4)–6P_3/2(F′ = 3, 4, 5)–8S_1/2(F″ = 3, 4) transition as a function of the detuning frequency of the pumping laser, where the optical frequency of the coupling laser is detuned to ∼1.35 GHz from the 6P_3/2(F′ = 5)–8S_1/2(F″ = 4) transition. The gray-colored curve denotes the saturated absorption spectrum (SAS) of the pump laser for the 6S_1/2(F = 4)–6P_3/2(F′ = 3, 4, 5) transition. From the figure, we can observe the two TPA signals of the F″ = 3 and 4 states of the 8S_1/2 hyperfine states beyond the Doppler broadening of the Cs ensemble.

The temperature of the vapor cell changed the number of atoms, quantified by the optical depth (OD). To obtain the efficient photon-pair source, we investigated the heralding efficiency according to the OD. The temperature of the vapor cell for photon pair generation was set to 75°C, and the optical depth was estimated to be ∼5.4. Usually, the OD on resonance is defined as OD=Nσ₀L, where N denotes the atomic density, σ₀ denotes the resonant absorption cross section, and σ is the effective interaction length. However, in our experiment, we estimated the OD from the transmission spectrum of a weak probe beam of 0.1 µ;W which propagates through the atomic vapor cell. We considered the hyperfine states (F′=3, 4, 5) of the 6P_3/2 state and the Maxwell-Boltzmann velocity distribution in the Cs vapor. The highest achievable OD for photon pair generation is depended on the cell length. Because of the strong absorption of the idler photons of the 6S_1/2–6P_3/2 transition, this OD limitation is primarily due to reabsorption of the idler photons in the atomic ensemble.

When the optical frequency of the pumping laser is scanned around the TPA spectrum, the TPA spectrum is clearly observed in the Cs vapor cell, as shown in Fig. 2(c). The TPA signal of the F″ = 3 state is larger than that of F″ = 4 because the detuning frequency of the F″ = 3 state is smaller than that of F″= 4, corresponding to a frequency difference of ∼877 MHz between the F″ = 3 and 4 hyperfine states.

The TPA spectral width was measured to be ∼28(3) MHz. Here, we note that the TPA spectral width is related to the two-photon coherence length of photon pairs from Doppler-broadened atomic ensembles [23]. However, the measured TPA spectral width is greater than the natural linewidth (1.7 MHz) of the 8S_1/2 state because of two-photon Doppler broadening due to the wavelength difference between the pump and coupling lasers. In our experiment, the two-photon Doppler shift (${\omega _{two}}$) for the 795 nm coupling laser and the 852 nm pump laser in the warm Cs vapor cell can be expressed as ${\omega _{two}} = ({{k_p} - {k_c}} )\cdot v$, where ${k_p}$ and ${k_c}$ are the wave vectors of the pump and coupling lasers, respectively, and v is the atom velocity. The value of ${\omega _{two}}$ was estimated to be ∼18 MHz at a velocity of 210 m/s. Additional causes of spectral broadening such as laser linewidth and transit broadening of the focused beam also need to be considered. The transit time broadening (${\Gamma _t}$) is estimated as ${\Gamma _t} = \frac{v}{{2\Delta w}}$, where the mean velocity ($v$) of atomic ensemble and the beam waist ($\Delta w$) of ∼60 µ;m inside the cell. In our experiment, the transit time broadening is estimated to be ∼1.8 MHz.

3. Experimental results and discussion

We investigated the properties of the temporal correlated photon pairs emitted from the atomic vapor cell. Figure 3(a) shows the temporal biphoton waveform of the photon pair from the ¹³³Cs vapor cell, i.e., the normalized cross-correlation function $g_{SI}^{(2)}(\tau )$ between the signal and idler photons, where τ denotes the time delay between the signal and idler photons. The $g_{SI}^{(2)}(\tau )$ is defined as $g_{SI}^{(2)}(\tau ) = \frac{{G_{SI}^{(2)}(\tau )}}{{{N_S}{N_I}\Delta \tau T}}$, where $G_{SI}^{(2)}(\tau )$ is the second-order cross-correlation function for the paired photon generated from a Doppler-broadened atomic ensemble via SFWM. The N_S and N_I denote the signal and idler single counting rates, respectively, and $G_{SI}^{(2)}(\tau )$ is the measured coincidence histogram. To obtain the $g_{SI}^{(2)}(\tau )$, we measured the coincident detection histogram of the signal and idler photons as a function of τ using a time-correlated single-photon counter (TCSPC) in the start-stop mode with a 88-ps time resolution, and then normalized the measured coincidence histogram to the accidental coincidence count. We averaged the histogram over $\Delta \tau$= 300 ps after measurement for T = 300 s [21]. The $g_{SI}^{(2)}(\tau )$ spectrum exhibits a full-width at half-maximum (FWHM) of ∼4.9(5) ns, which is related to the coherence time of the signal and idler photons. However, the measured FWHM of $g_{SI}^{(2)}(\tau )$ is estimated to be approximately two times greater than the inverse of the Doppler-broadening linewidth of the warm ¹³³Cs atoms. The main cause of the broadened FWHM of $g_{SI}^{(2)}(\tau )$ is the two-photon Doppler shift due to the wavelength difference between the counter-propagating pump and coupling lasers. Therefore, the spectral width of the coherently superposed photons is narrower than the Doppler broadening of the warm Cs ensemble.

 

Fig. 3. Temporal biphoton waveform. (a) Normalized cross-correlation function, $g_{SI}^{(2)}(\tau )$, between signal and idler photons (blue curve). (b) Quantum beats between the three channels of the SFWM process relating to the F′ = 3, 4, and 5 states of 6P_3/2 states in the 6S_1/2(F = 4)–8S_1/2(F″ = 4) transition.

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We estimated the Cauchy-Schwarz inequality from the normalized cross-correlation function $g_{SI}^{(2)}(\tau )$. As is well known, the Cauchy-Schwarz inequality is described as $R = \frac{{{{[{g_{_{SI}}^{(2)}(\tau )} ]}^2}}}{{g_{_{SS}}^{(2)}{{(\tau )}_{}}g_{_{II}}^{(2)}(\tau )}} \le 1$, where $g_{SS}^{(2)}(\tau )$ and $g_{II}^{(2)}(\tau )$ denote the second-order auto-correlation values of signal and idler modes, respectively. We investigated the $g_{SS}^{(2)}(\tau )$ and $g_{II}^{(2)}(\tau )$ for the emitted photons of the idler and signal modes obtained when the coupling laser was activated and both lasers satisfied the two-photon resonance condition. The second-order auto-correlation values of the signal and idler modes for τ = 0 were estimated as $g_{SS}^{(2)}(0)$=∼1.7 and $g_{II}^{(2)}(0)$=∼1.5, respectively. The maximum value of $g_{SI}^{(2)}(\tau )$ was measured to be 622(8), and the Cauchy–Schwarz inequality was estimated to be a factor of ∼100,000, which clearly indicates the quantum nature of the paired photons under a weak pump power of 10 µ;W [38]. The large value of the Cauchy–Schwarz inequality indicates that the SFWM photon-pair flux was enhanced and the uncorrelated single-emission fluorescence from the atomic vapor cell was suppressed [24]. The collective two-photon coherence effect is important cause for the strongly correlated photon pair from Doppler-broadened warm atoms.

From Fig. 3(a), we can observe the quantum beats in the temporal biphoton waveform. Here, we note that quantum beats have also been reported in cascade decay systems of atomic vapors [39–41] and cold atoms [10,42]. The quantum beats are understood as the interference of the signal and idler photon pairs generated via the three decay paths corresponding to the hyperfine states of the 6P_3/2 intermediate level in the 6S_1/2(F = 4)–8S_1/2(F″ = 4) transition, as shown in Fig. 3(b). These three decay paths cannot be distinguished by the SPDs. The beating period corresponds to the hyperfine splitting with frequency differences of 251 MHz (F″ = 4 and 5) and 201 MHz (F″ = 3 and 4) of the 6P_3/2 state. The biphotons demonstrated in this work are multimode frequency. To obtain the single-mode frequency, we can choose the 6S_1/2(F = 4)–6D_5/2(F″ = 6) transition for the generation of photon pairs.

The temperature of the vapor cell is an important experimental parameter for the photonic quantum source based on a warm atomic ensemble. We investigated the heralding efficiency in the cell temperature range from 52°C to 85°C, corresponding to the OD of the medium in the OD range from 1 to 10. In this work, the idler photon was used as heralding arm and the heralding efficiency η_I = N_C / N_I for idler photons was calculated, where N_C denotes a coincidence counting rate of the photon pair [43]. In our experiment, the temperature of the vapor cell was optimized for the heralding efficiency. Figure 4 shows the heralding efficiency (red squares) as a function of OD under the conditions on the pump power of 0.5 mW and the coupling power of 5 mW. The decrease in the heralding efficiency at high OD can be explained by reabsorption of the idler photon in the medium, whereas the optimal OD for high heralding efficiency is explained by the enhancement in the collective emission into the phase-matched direction [44–45].

 

Fig. 4. Single-photon heralding efficiency. Heralding efficiency (red squares) as a function of OD in the OD range from 1 to 10.

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In our photon-pair source from the ¹³³Cs vapor cell, the photon-count rate, photon-pair coincident count rate, and value of $g_{SI}^{(2)}(\tau )$ can be changed by varying the pump and coupling powers as well as the atomic density of the atomic vapor cell. In particular, the photon-pair coincident count rate is an important factor that determines the properties of the photon-pair source from the atomic vapor cell.

Figure 5(a) shows the signal (blue squares) and idler (red circles) single-count rates as functions of the pump power for a coupling power of 5 mW. The coincidence count rate and the maximum value of $g_{SI}^{(2)}(\tau )$ are shown in Fig. 5(b) for the coincidence window of 8.8 ns. The counting rates of the signal and idler photons were measured to be 795 kHz and 446 kHz, respectively, and the coincidence counting rate of the photon pair was obtained to be ∼20 kHz with 0.8 mW of pump power. The difference between the single count rates of signal and idler photons is due to the reabsorption, fiber coupling efficiency, and detection efficiency. First, there is the attenuation effect of the idler photons in the 6S_1/2–6P_3/2 transition due to reabsorption of the idler photons in the dense atomic medium. Second, by coupling to the standard single-mode fiber (HP780) in the signal and idler photons, respectively, the fiber coupling efficiencies of both photons are different due to the wavelength difference. Third, the SPD detection efficiency of the idler photon is lower than that of the signal photon. From the experimental results, the heralding efficiency for idler photons was calculated as 4.5(1)% with OD = 5, for which the fiber coupling efficiency, detection efficiency, and reflection losses of atomic vapor cell windows were not considered. For the case of a maximum normalized cross-correlation value of 622 at 10 µ;W pump power, the counting rates of the signal and idler photons were measured to be 19.7 kHz and 9.3 kHz, respectively, and the coincidence counting rate of the photon pair was obtained to be ∼320 Hz. From the experimental results, the heralding efficiency for idler photons was calculated as 3.4(3)%.

 

Fig. 5. Count rates of photon pair. (a) Single-count rates for signal and idler photons. (b) Maximum value of normalized temporal cross-correlation function and coincidence count rate of photon pairs as functions of pump power for coupling power of 5 mW.

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We note here that in our experiment, the 6S_1/2(F = 4)–8S_1/2(F″ = 4) transition for the generation of photon pairs is not a two-photon cycling transition, which is used to treat the three-level atomic system such as the 5S_1/2(F = 2)–5P_3/2(F′ = 3)–5D_5/2(F″ = 4) transition of ⁸⁷Rb [21]. Therefore, the generation rate of the photon pair may decrease when compared with that for the two-photon cycling transition, because the SFWM process can be significantly enhanced in an atomic medium with pure two-photon coherence in a simple three-level atomic system [36]. Furthermore, in our study, the SPD detection efficiency of the idler photon (852 nm) was ∼9% lower than that of the signal photon (795 nm). Nevertheless, our results confirm that our photon-pair source based on the Cs vapor cell is comparable with previous realized sources based on the ordinary atomic vapor cell [23–24].

From the experimental result with a weak pump power of 10 µ;W, the generation rate of photon pairs R_pair was estimated to be 0.57 MHz (57 MHz/mW) by using the equation R_pair = (N_S × N_I) / N_C, where N_S, N_I, and N_C denote the signal and idler single counting rates and the coincidence counting rate, respectively. For R_pair, we consider the detected pairs without subtracting the background coincidence counts. Figure 6(a) shows the R_pair (open blue circles) as a function of pump power from 0.01 mW to 0.8 mW under the conditions on the coupling power of 5 mW. The trade-off between R_pair and maximum value of $g_{SI}^{(2)}(\tau )$, i.e., between the rate and the SNR, is summarized in Fig. 6(b).

 

Fig. 6. Generation rate of photon pairs. (a) Generation rate (R_pair) of photon pairs from Doppler-broadened warm atoms as a function of pump power. (b) Maximum value of $g_{SI}^{(2)}(\tau )$ versus R_pair.

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To clarify the source of photon pair demonstrated in our work, we have tried to compare to the chip-scale entangled-pair sources of some other works [46–49]. Although the photon-pair generation achieved using our proposed system is due to spontaneous emission from an excited state of the atomic ensemble, the characteristics of our photon pair is comparable to those of SPDC photon-pair sources with a nonlinear crystal waveguide. In particular, the spectral brightness of our system (∼1 × 10⁹ pairs s⁻¹ GHz⁻¹ mW⁻¹) is about more than ∼10³ times higher than that obtained in Ref. [49].

4. Conclusion

In conclusion, we experimentally demonstrated a photon-pair source in the cascade-type 6S_1/2–6P_3/2–8S_1/2 transition of ¹³³Cs realized using a microfabricated Cs vapor cell. Photon pairs could be generated from the atomic ensemble with an interaction length of 1 mm. From the cross-correlation between the signal and idler photons, we found that the Cauchy–Schwarz inequality was violated by a factor of 10⁵. We confirmed that the SFWM photon-pair flux was enhanced, and the photon pair from the atomic vapor cell was strongly temporally correlated. The characteristics of the photon-pair source realized using the Cs vapor cell were comparable with those realized from ordinary atomic vapor cells. Furthermore, we observed the quantum beats of the temporal biphoton waveform of the photon pair due to the multiple channels of the SFWM process relating to the hyperfine states of the intermediate 6P_3/2 state. Although there are many difficulties for chip-scale atomic quantum light source, we can expect to merge the chip-scale atomic vapor cell with the waveguide optic for collection optical systems. It seems to be possible to align the micro lens array block by attaching it to the fiber array with multi-channels. We believe that our approach can be potentially used in future atomic quantum devices such as integrated photonic systems and other related devices. Such devices may enable the construction of practical scalable quantum networks based on atom–photon interactions.