ECAMP 15

Four-wave mixing (FWM) is a nonlinear optical process in which two (or three) interacting optical fields generate two (or one) new fields via the medium’s nonlinearity of third order $\chi^{(3)}$. Alkali vapors, especially those of Rb and Cs, exhibit exceptionally high nonlinear optical responses. Under near-resonant conditions, the third-order nonlinear susceptibility of these atomic vapors can exceed that of typical bulk nonlinear media by factors of $10^{6}$ to $10^{10}$.
Recently, silicon micromachining has revolutionized alkali vapor cell production, yielding chip-scale devices that are mass-producible, cost-effective, and multifunctional. These cells have already enabled high-performance atomic magnetometers [5,6], compact gradiometers [7], and chip-scale clocks [8,9], while offering exceptional miniaturization, stability, and seamless integration with on-chip photonic circuitry [10–12].
Traditionally, continuous-wave (CW) FWM has been realized in centimeter-scale vapor cells, where the extended interaction length facilitates efficient nonlinear conversion. In our work, we demonstrate for the first time that efficient CW FWM can be achieved in chip-scale micromachined Rb vapor cells, marking a significant step toward compact nonlinear optical platforms.
We employed resonant four-wave mixing (FWM) in millimeter-scale rubidium vapor cells to generate continuous-wave coherent emission at both blue and mid-infrared wavelengths. Under optimized conditions, the blue output reached 17 $\mu$W of continuous coherent power. Remarkably, replacing the anodically bonded Pyrex window with an anodically bonded silicon window enabled mid-infrared emission with powers up to 50 nW. We further characterized the temperature dependence and input-power scaling of the blue emission, confirming efficient nonlinear conversion within these compact vapor cells.
Incorporating injection-locking techniques can significantly boost the CBL and CMIRL output into the high-power regime, paving the way for compact, high-power sources suited for various applications. Our results underscore the potential of micromachined Rb FWM to serve as a compact, manufacturable platform for next-generation quantum devices.

\href{https://drive.google.com/file/d/1hHLiduWByTjphtVPuplYa3tW8DsRebYy/view?usp=sharing}
{Fig. 1. Concept of continuous-wave four-wave mixing process in chip-scale Rb vapor cell. (a) Energy levels of $^{85}$Rb illustrating the transitions involved in generating coherent blue light (CBL) and coherent mid-infrared light (CMIRL). The diagram highlights the excitation processes using the 780 nm and 776 nm lasers, leading to production of the 420 nm and 5.2 $\mu$m emissions. (b) Photo of generated light through FWM in micromachined Rb vapor cell. For clarity, the captions were added to the photo. By choosing the type of the cell, we may detect both CBL and CMIRL. (c) Schematic view on the chip-scale Rb cells used in this work. One has Pyrex backside (left), which absorbs 5.2 $\mu$m emission and transmits another three wavelengths involved in the process; another has Si backside (right) and transmits 5.2 {$\mu$}m emission only. (d) The number of photons per second as function of detuning of laser 780 nm for measured CBL (blue curve) and CMIRL (purple curve) with shown Rb reference (gray curve). Factor of 55 for CMIRL compared to CBL caused by losses.}

References
1 S. Wang, J. Yuan, L. Wang, et al., “Measurement of the Kerr nonlinear refractive index of the Rb vapor based on an optical frequency comb using the z-scan method,” Opt. Express 28, 38334–38342 (2020).
[2] B. Ding, X. Yu, H. Lu, et al., “Third-order optical nonlinearity in silicon nitride films prepared using magnetron sputtering and application for optical bistability,” J. Appl. Phys. 125, 113102 (2019).
[3] K. Zhang, G. Böhm, and M. A. Belkin, “Kerr nonlinearity and group velocity dispersion of InGaAs/InP and GaAsSb/InP waveguides in the mid-infrared,” APL Photonics 8, 066107 (2023).
[4] R. Schiek, “Nonlinear refractive index in silica glass,” Opt. Mater. Express 13, 066107 (2023).
[5] K. Levi, A. Giat, L. Golan, et al., “Remote chip-scale quantum sensing of magnetic fields,” Opt. Quantum 3, 84–92 (2025).
[6] R. Mhaskar, S. Knappe, and J. Kitching, “A low-power, high-sensitivity micromachined optical magnetometer,” Appl. Phys. Lett. 101, 241105 (2012).
[7] J. Zhang and J. Shang, “Miniature quantum gradiometer using 3D interconnected atomic vapor cells,” 2025 IEEE 38th Int. Conf. on Micro Electro Mech. Syst. (MEMS) pp. 589–591 (2025).
[8] M. Pellaton, C. Affolderbach, Y. Pétremand, et al., “Study of laser-pumped double-resonance clock signals using a microfabricated cell,” Phys. Scr. 2012, 014013 (2012).
[9] S. Knappe, V. Shah, P. D. D. Schwindt, et al., “A microfabricated atomic clock,” Appl. Phys. Lett. 85, 1460–1462 (2004).
[10] H. Schmidt and A. R. Hawkins, “Electromagnetically induced transparency in alkali atoms integrated on a semiconductor chip,” Appl. Phys. Lett. 86, 032106 (2005).
[11] A. Goban, C.-L. Hung, S.-P. Yu, et al., “Atom–light interactions in photonic crystals,” Nat. Commun. 5, 3808 (2014).
[12] P. Londero, V. Venkataraman, A. R. Bhagwat, et al., “Ultralow-power four-wave mixing with Rb in a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. 103, 043602 (2009).