Mirrorless Optical Parametric Oscillation with Tunable Threshold in Cold Atoms

We report the demonstration of a mirrorless optical parametric oscillator with a tunable threshold in laser-cooled atoms with four-wave mixing (FWM) using electromagnetically induced transparency. Driven by two classical laser beams, the generated Stokes and anti-Stokes fields counterpropagate and build up efficient intrinsic feedback through the nonlinear FWM process. This feedback does not involve any cavity or spatially distributed microstructures. We observe the transition of photon correlation properties from the biphoton quantum regime (below the threshold) to the oscillation regime (above the threshold). The pump threshold can be tuned by varying the operating parameters. We achieve the oscillation with a threshold as low as $15\mu \mathrm{W}$.

Figure 1

Experimental configuration for realizing the MLOPO with FWM in cold atoms. (a) Experimental setup. (b) ${}^{85}\mathrm{Rb}$ atomic energy level diagram and FWM transitions. The atomic hyperfine levels are chosen as $|1⟩=|5S_{1/2},F=2⟩$, $|2⟩=|5S_{1/2},F=3⟩$, $|3⟩=|5P_{1/2},F=3⟩$, and $|4⟩=|5P_{3/2},F=3⟩$. The circularly polarized (${\sigma }^{-}$) pump laser (780 nm) is blue detuned by ${\mathrm{\Delta }}_p$ from the transition $|1⟩\to |4⟩$, and the coupling laser (${\sigma }^{+}$, 795 nm) is on resonance to the transition $|2⟩\leftrightarrow |3⟩$. The generated circularly polarized Stokes (${\sigma }^{-}$) [anti-Stokes (${\sigma }^{+}$)] photons pass through a quarter-wave plate (QWP) and a linear polarizer before they are collected by a SMF. Here the combination of the QWP and polarizer works as a polarization filter. Both Fabry-Perot (FP) filters have the same bandwidth of 500 MHz. (c) Detection setup for measuring the autocorrelation function $g^{(2)}(\tau )$, used for spectrum measurement below the threshold. (d) Detection setup for determining the photon spectrum above the threshold by beating the output with a reference laser beam. The reference laser beam beating with the Stokes emission is phase locked to the pump laser. The reference laser beam beating with the anti-Stokes emission is phase locked to the coupling laser.

Figure 2

(a) Output Stokes and anti-Stokes photon rates as functions of the pump laser power, showing the threshold at $1000\mu \mathrm{W}$. (b) Normalized Stokes–anti-Stokes cross-correlation function under different pump powers. The pump laser detuning is ${\mathrm{\Delta }}_p=2\pi \times 60\mathrm{MHz}$, and the coupling laser power is $1200\mu \mathrm{W}$.

Figure 3

(a) Pump threshold versus pump detuning and coupling power. (b) Pump threshold as a function of the coupling power at different pump detunings. The dots are experimental data, and the solid lines are calculated from the theory.

Figure 4

FWHM spectral widths of the Stokes and anti-Stokes emissions versus the pump power at two different coupling laser powers: (a) 300 and (b) $50\mu \mathrm{W}$. The pump detuning is ${\mathrm{\Delta }}_p=2\pi \times 60\mathrm{MHz}$. The pump thresholds for (a) and (b) are about 350 and $200\mu \mathrm{W}$, respectively.