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Applied Physics Letters

Multidimensional four-wave-mixing spectroscopy with squeezed light

Zhenquan Yang, Prasoon Saurabh, Frank Schlawin, Shaul Mukamel, Konstantin E. Dorfman

Published Jun 15, 2020• 20 citations
Publisher

Abstract

A set of nonlinear spectroscopic measurements with quantum light is presented. It involves a strong pump with frequency ωpu and a weak probe at ωpr interacting with a solid state target to generate a conjugated beam ωc=2ωpu−ωpr via nondegenerate four-wave mixing. The χ(3) susceptibility can be measured by the noise spectra of the intensity difference of the squeezed beams. We discuss three spectroscopic setups based on squeezed light: first, single four-wave mixing in a single crystal; second, cascading scheme involving two crystals; third, an SU(1, 1) interferometer based on two separate four-wave mixing processes. We further investigate the microscopic noise and optical losses in all three setups. Simulations are presented for silicon-vacancy color centers in diamond.

DOI
10.1063/5.0009575

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A set of nonlinear spectroscopic measurements with quantum light is presented. It involves a strong pump with frequency ωpu and a weak probe at ωpr interacting with a solid state target to generate a conjugated beam ωc=2ωpu−ωpr via nondegenerate four-wave mixing. The χ(3) susceptibility can be measured by the noise spectra of the intensity difference of the squeezed beams. We discuss three spectroscopic setups based on squeezed light: first, single four-wave mixing in a single crystal; second, cascading scheme involving two crystals; third, an SU(1, 1) interferometer based on two separate four-wave mixing processes. We further investigate the microscopic noise and optical losses in all three setups. Simulations are presented for silicon-vacancy color centers in diamond.
Four-wave mixing (FWM) of optical fields has been extensively used in quantum information processing, sensing, and memories. It also forms a basis for nonlinear spectroscopies such as transient grating, stimulated Raman, and photon echo where phase matching is used to select desired components of the third-order response of matter. Here we report an experimental study of the two-dimensional quantum noise intensity difference spectra of a pair of squeezed beams generated by FWM in hot Rb vapor. The measurement reveals details of the [Formula: see text] susceptibility dressed by the strong pump field which induces an AC Stark shift, with higher spectral resolution compared to classical measurements of probe and conjugate beam intensities. We demonstrate how quantum correlations of squeezed light can be utilized as a spectroscopic tool which unlike their classical counterparts are robust to external noise.
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 g2{g}_{2}g2​ 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 g2{g}_{2}g2​ 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.
We have measured -3.5 dB (-8.1 dB corrected for losses) relative intensity squeezing between probe and conjugate beams generated by stimulated, nondegenerate four-wave mixing in hot rubidium vapor. Unlike early observations of squeezing in atomic vapors based on saturation of a two-level system, our scheme uses a resonant nonlinearity based on ground-state coherences in a three-level system. Since this scheme produces narrowband, squeezed light near an atomic resonance, it is of interest for experiments involving cold atoms or atomic ensembles.
We report the measurement of the intensity difference squeezing via the non-degenerate four-wave mixing process in a rubidium atomic vapor medium. Two pairs of balanced detection systems are employed to measure the probe and the conjugate beams, respectively. It is convenient to get the quantum shot noise limit, the squeezed and the amplified noise power spectra. We also investigate the influence of the input extra quadrature amplitude noise of the probe beam. The influence of the extra noise can be minimized and the squeezing can be optimized under the proper parameter condition. We measure the −3.7-dB intensity difference squeezing when the probe beam has a 3-dB extra quadrature amplitude noise. This result is slightly smaller than −4.1 dB when the ideal coherent light (no extra noise) for the probe beam is used.