Photon-Pair Generation from Chip-Scale Cs Atomic Vapor Cell

The realization of a narrowband photonic quantum source based on a chip-scale atomic device is considered essential in the practical development of photonic quantum information science and technology. In this study, we present the rst step toward the development of a photon-pair source based on a microfabricated chip-scale Cs atomic vapor cell. Time-correlated photon pairs from the millimeter-scale Cs vapor cell are emitted via the spontaneous four-wave mixing process of the cascade-type 6S 1/2 – 6P 3/2 –8S 1/2 transition of 133 Cs. The maximum normalized cross-correlation value between the signal and idler photons is measured as 622(8) under a weak pump power of 10 mW. Our photon source violates the Cauchy–Schwartz inequality by a factor of >10 5 . We believe that our approach has very important applications in the context of realizing practical scalable quantum networks based on atom– photon interactions.


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][2][3][4][5][6][7][8][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][11][12][13][14][15][16][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 highvacuum conditions; thus, in these setups, it is di cult to manipulate isolated atomic samples [15][16][17][18][19].
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-con guration 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 rst 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][29][30][31][32]. In particular, a chip-scale atomic vapor cell combined with silicon waveguides or waveguide optics can potentially be applied in various quantum devices such as single-photon sources and quantum memories based on atomic ensembles. However, to the best of our knowledge, photon-pair generation from chip-scale atomic vapor cells has not thus been reported.
Here, we experimentally demonstrate the generation of photon pairs via the SFWM process from a chipscale warm atomic ensemble of 133 Cs atoms for the rst time. 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 chip-scale 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 observed the quantum beats of the temporal biphoton waveform of the photon pair generated via SFWM multi-channels relating to the hyper ne states of the 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. The diameter and thickness of the photon-pair chamber were 1.5 mm and 1 mm, respectively.
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.   [33]. To prevent uncorrelated photons due to single-photon resonance, their optical frequencies were detuned beyond the Doppler broadening of the warm Cs ensemble.
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 twophoton coherence [23]. In our experiment, we selected the 6S 1/2 (F = 4)-8S 1/2 (F″ = 4) transition for ful lling 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 chip-scale Cs cell.
We rst investigated the two-photon absorption (TPA) spectrum in the chip-scale Cs vapor cell. Figure   2 When the optical frequency of the pumping laser is scanned around the TPA spectrum, the TPA spectrum is clearly observed in the chip-scale 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 hyper ne states.

Experimental Results
We investigated the heralding e ciency according to the OD. In our experiment, the temperature of the vapor cell was optimized for the heralding e ciency. Figure 4 shows the heralding e ciency (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 e ciency at high OD can be explained by reabsorption of the idler photon in the medium, whereas the optimal OD for high heralding e ciency is explained by the enhancement in the collective emission into the phase-matched direction [40][41].
We note here that in our experiment, the 6S 1/2 (F = 4)-8S 1/2 (F² = 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 (F² = 4) transition of 87 Rb [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 signi cantly enhanced in an atomic medium with pure two-photon coherence in a simple three-level atomic system. Furthermore, in our study, the SPD detection e ciency of the idler photon (852 nm) was ~9% lower than that of the signal photon (795 nm). Nevertheless, our results con rm that our photon-pair source based on the chip-scale Cs vapor cell is comparable with previous realized sources based on the ordinary atomic vapor cell [23][24].

Conclusion
In conclusion, we experimentally demonstrated a photon-pair source realized using a microfabricated chip-scale Cs vapor cell. Bright photon pairs could be generated from the chip-scale 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 10 5 . We con rmed that the SFWM photon-pair ux was enhanced, and the photon pair from the chip-scale atomic vapor cell was strongly temporally correlated. The characteristics of the photon-pair source realized using the chip-scale 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 hyper ne states of the intermediate 6P 3/2 state. We believe that our approach can be potentially used in future chip-scale 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.     Signal photon heralding e ciency. Heralding e ciency (red squares) as a function of OD in the OD range from 1 to 10.