Quantum statistics of degenerate four wave mixing

József Janszky, Yu. Ya. Yushin

Roy S. Bondurant, Mari W. Maeda, Prem Kumar +1 more

J. Bajer, Jan Peřina

Pierre Villain, Patrik Öhberg, Luis Santos +2 more

We study the process of four-wave mixing (FWM) in ultracold degenerate atomic gases. In particular, we address the problem of FWM in boson-fermion mixtures. We develop an approximate description of such processes using asymptotic analysis of high-order perturbation theory taking into account quantum statistics. We perform also numerical simulations of FWM in boson-fermion mixtures and obtain an analytic and numerical estimate of the efficiency of the process.

Roy S. Bondurant, Prem Kumar, Jeffrey H. Shapiro +1 more

The suitability of degenerate four-wave mixing (DFWM) as a source of squeezed-state (two-photon coherent state) light is investigated, both theoretically and experimentally. In previous semiclassical theory, which neglected pump quantization and loss in the nonlinear medium, Yuen and Shapiro [Opt. Lett. 4, 334 (1979)] showed that such states would be generated by 50%-50% combination of the transmitted probe (TP) and the phase-conjugate (PC) output beams of DFWM. Here the effects of quantum fluctuations in the amplitudes and phases of the pump beams are calculated in a traveling-wave finite-interaction-length DFWM configuration. It is shown that in the limit of strong pump beams and weak nonlinear coupling, the classical-pumps assumption of Yuen and Shapiro is valid. With use of this assumption, loss in the nonlinear medium is incorporated into the model by coupling the interacting modes to a set of reservoir modes. It is shown that loss presents an absolute limit on the degree of squeezing that can be achieved with DFWM. Also, for comparison with experimental work, the photoelectron statistics of the TP, PC, and 50%-50% combination modes are calculated for lossy DFWM; significant deviations are found from the predictions for lossless operation. Quantum-noise measurements on the PC and TP beams generated in sodiumvapor DFWM are described. The mixer is pumped and probed by the nearly transform-limited pulses produced by a continuous-wave-oscillator-pulse-amplifier chain dye laser at 589 nm wave-length. The normalized second-factorial moment ${g}_{2}$ of the PC and TP beams is determined from photoelectron-counting measurements. Inability to simultaneously achieve high DFWM reflectivity and acceptably low scattered-plus-fluorescent background, coupled with low photomultiplier quantum efficiency, restrict the experiment to a DFWM regime wherein theory predicts Poisson statistics. Experimental ${g}_{2}$ values corroborate this prediction, indicating that systematic and excess noises have been eliminated. No attempt was made to measure the quantum statistics of the 50%-50% combination mode.

Jan Peřina, Vlasta Peřinová, C. Sibilia +1 more