Optical Bistability at Low Light Level due to Collective Atomic Recoil

We demonstrate optical nonlinearities due to the interaction of weak optical fields with the collective motion of a strongly dispersive ultracold gas. The combination of a recoil-induced resonance in the high gain regime and optical waveguiding within the dispersive medium enables us to achieve a collective atomic cooperativity of $275\pm 50$ even in the absence of a cavity. As a result, we observe optical bistability at input powers as low as 20 pW. The present scheme allows for dynamic optical control of the dispersive properties of the ultracold gas using very weak pulses of light. The experimental observations are in good agreement with a theoretical model.

Figure 1

(a) Schematic indicating the pump and probe beams used for the RIR, where MOT is the magneto-optic trap. (b) The energy levels relevant to the RIR. (c) Absorption spectrum of a probe beam around the RIR for longitudinal optical depth of $\sim 10$ (i) and $\sim 40$ (ii).

Figure 2

(a) Absorption bistability due to the interaction between the probe and the collective motion of the atomic gas. Depending on the sign of the detuning chirp ($d\delta /dt$), the transmission indicates a shift in both the resonance and the peak amplification ($g_{+}$, $g_{-}$). The dashed arrows indicate the direction in which the detuning is scanned across the RIR. (b) Peak probe amplification indicates a bistable response down to the detection limit of the input probe power.

Figure 3

Numerical simulations based on the theoretical model match the experimental results over a wide range of parameters. Panels on the left show the numerical simulations for the gain coefficient given by $\exp (-2\mathrm{Re}[\alpha ]L)$, where $\alpha$ is the absorption coefficient, and panels on the right show the observed experimental gain of the probe transmission across the RIR, both versus two-photon detuning. Panels (a), (b), and (c) correspond to transmission spectra obtained by chirping the two-photon detuning at scan rates of 0.1, 0.5, and $2.5\mathrm{MHz}/\mathrm{ms}$, respectively.

Figure 4

(a) The ratio of peak gain ($g_{-}/g_{+}$) indicates a limiting scan rate $d\delta /dt\approx 0.5\mathrm{MHz}/\mathrm{ms}$ below which decoherence and thermalization of the momentum distribution suppress optical bistability. The data were obtained at a pump detuning $\Delta \sim -4\Gamma$. (b) Thermalization time (${\gamma }_{\mathrm{pop}}^{-1}$) vs the pump detuning. A fit to the data (dashed line) indicates a power-law dependence ${\gamma }_{\mathrm{pop}}^{-1}\propto {\Delta }^{\alpha }$ with $\alpha =1.57\pm 0.09$.