Triply-resonant Optical Parametric Oscillator by Four-wave Mixing with Rubidium Vapor inside an Optical Cavity Xudong Yu $^{1}$, Min Xiao$^{2}$, and Jing Zhang1 † $^{1}$The State Key Laboratory of Quantum Optics Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, P.R. China and 2 Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA We present an experimental demonstration of simultaneous above-threshold oscillations of the Stokes and anti-Stokes fields together with the single pumping beam with rubidium atoms inside an optical standing-wave cavity. The triple resonant conditions can be achieved easily by making use of the large dispersions due to two-photon transitions in the three-level atomic system. This work provides a way to achieve high efficient nonlinear frequency conversion and the generated bright Stokes and anti-Stokes cavity output beams are potential resource for applications in quantum information science. Various atomic systems have been used as intracavity gain media to realize cavity oscillations [1–7]. Especially, multi-level atomic systems have more interesting charac- teristics and can be more efficient in managing the ab- sorption and dispersion properties of the intracavity gain medium for building up resonance simultaneously of dif- ferent cavity modes. It is easy to have an off-resonant pump beam to make the Stokes or anti-Stakes field be on resonance with one of the cavity modes in a three-level Λ-type atomic system, and get it to oscillate with a large pump power [7]. When the pump beam is tuned near one of the atomic transitions in a three-level Λ system inside an optical cavity, cavity field oscillation (or lasing without population inversion) can occur in the frequency corresponding to the other atomic transition [8]. This system can be considered as an optical parametric oscil- lator (OPO) since the atomic variables can be adiabat- ically eliminated in treating the atom-field interactions [9, 10]. In this Letter, we present our experimental demonstra- tion of a triply-resonant atom-cavity system, as shown in Fig.1. With one pump laser beam (frequency ω$_{p}$ ) tuned to the cavity resonance as the cavity input, two optical fields, both the Stokes field (frequency ω$_{b}$ ) and anti-Stokes field (frequency ω$_{a}$ ), are generated simulta- neously. The frequency of the pump beam is detuned from the atomic resonances | 1 〉 ↔ | 0 〉 and | 2 〉 ↔ | 0 〉 by the amount of Δ$_{b}$ = ω$_{p}$ − ω$_{01}$ and Δ$_{a}$ = ω$_{p}$ − ω$_{02}$ (thus Δ$_{a}$ − Δ$_{b}$ = ω$_{12}$ ), which generates two sidebands at frequencies of ± ω$_{12}$ from the pump beam frequency, respectively. Typically, the generated Stokes and anti- Stokes fields are difficult to be made on resonance with the cavity modes at the same time, since the cavity mode has already been tuned to be on resonance with the pump field. However, since we work with the naturally mixed $^{87}$Rb and $^{85}$Rb vapor cell as the intracavity medium, there are several broad absorption bands in the transmission spectrum, as shown in Fig. 2(a). The weak field cavity transmission spectrum is given in Fig. 2(b), which shows the cavity transmission peaks with modified peak sep- arations caused by the enhanced dispersions associated with the tails of the absorption lineshape at high atomic density [11]. By manipulating the large intracavity dis- persions via pump laser frequency detuning, the Stokes and anti-Stokes fields can be made to be simultaneously on resonance with the modified cavity modes together with the pump field, which is very similar to the case of a triple-resonant OPO with nonlinear crystals [12–19]. The experiment is done by placing a naturally mixed rubidium vapor cell inside an optical standing-wave cav- ity of length 17.7 cm . The cavity is composed of two curved mirrors with the same radius of curvature of 100 mm . The reflectivity is 90% at 780 nm for the input cou- pler M 1 (on right), which is mounted on a PZT to adjust the cavity length. The left mirror M 2 has a reflectivity of arXiv:1001.0291v1 [quant-ph] 2 Jan 2010 ✁ ✂ ✄ ☎ ✆ GLYPH<a0> ✝ ✞ ✟ ✠ ✡ ☛ ☞ ✌ ✍ ✎ ✏ ✑ ✒ ✓ ✔ ✕ ✖ ✗ ✘ ✙ ✚ ✛ ✜ ✢ ✣ ✤ ✥ ✦ / 4 ✧ ★ ✩ ✪ ✫ ✬ ✭ ✮ ✯ ✰ ✱ 1 2 0 p b ✲ ✳ ✴ a b a b p a FIG. 1: (Color online). Schematic of the experimental setup of the coupled three-level atoms-cavity system. λ/ 4: quarter- wave plate; D1, D2: detectors; HV-AMP: high voltage am- plifier; PZT: piezoelectric transducer; PBS: polarized beam splitter; L : optical lens; F-P: Febry-Perot cavity. Bottom: relevant energy levels and field configurations. ω p a = ω p b = ω p is the frequency of the single pump field.