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Optics Letters

Single-beam squeezed-state generation in sodium vapor and its self-focusing limitations

Seng‐Tiong Ho, N. C. Wong, Jeffrey H. Shapiro

Published Jun 1, 1991• 11 citations
Publisher

Abstract

We describe an experiment that generates squeezed states by means of forward four-wave mixing in sodium vapor with a single optical beam. The single-beam arrangement maximizes the pump-probe spatial overlap in the nonlinear medium. Self-focusing (or self-defocusing) is found to be the major limiting factor in achieving optimal squeezing.
DOI
10.1364/ol.16.000840

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Conference on Lasers and Electro-Optics•Aug 29, 2005•0 citations
We have generated squeezed states of light with a single pump beam propagating through Doppler broadened sodium vapor via forward four-wave mixing (FWM) with spatially degenerate pump and probe modes. The two probe-mode inputs are vacuum states at nondegenerate frequencies, which are transformed to squeezed vacuum by the FWM interaction. Compared with previous FWM configurations,1 this single-pass single-pump-beam configuration ensures maximal overlap of the four interacting beams, thus maximizing the squeezing nonlinearity and improving the overall efficiency. The transmitted pump has the wrong phase to act as the local oscillator for detecting the squeezed spectrum.1 Therefore, a cavity is used to filter out most of the transmitted pump intensity, and the squeezed vacuum is detected with another local oscillator using the standard dual-detector scheme. The residual pump beam provides a reference to monitor the phase between the pump and squeezed vacuum. The observed 0.8-dB reduction in the shot noise corresponds to an inferred 50% squeezing of the light at the exit of the vapor medium, which is in reasonable agreement with the theory given by Ho et al. 2 A linearly polarized pump is found to give less squeezing than a circularly polarized pump, possibly due to optical pumping.
We describe our efforts to observe squeezing, and related nonclassical effects, in three forward four-wave mixing experiments using sodium vapor as a nonlinear medium. In a single-beam experiment with homodyne detection, we found optically phase-sensitive noise, which was radio-frequency phase insensitive, in a cw dye-laser beam that had propagated through sodium vapor. The minima of the phase-sensitive noise were always at or above the coherent-state value. In our forward four-wave mixing experiment with probe–conjugate-beam direct detection and correlation, we found that the sodium-vapor interaction produced positive noise correlation between the probe and conjugate beams. The correlation, however, did not exceed the excess noises on these beams, so that a nonclassical behavior was not demonstrated. Finally, our forward four-wave mixing experiment with probe–conjugate-beam combination and homodyne detection did demonstrate the generation of squeezed-state light in our setup. Optically phase-sensitive noise with a minimum falling 4% below the coherent-state level was observed.
We apply our quantum theory of nondegenerate multiwave mixing [ Phys. Rev. A37, 2017 ( 1988)] to squeezed-state generation experiments with two-level atoms. Our main interest is to predict the amount of squeezing achievable with a Doppler-broadened two-level medium. We are particularly interested in the single-beam configuration, in which all four interacting beams are spatially degenerate. We analytically solve the coupled-mode quantum Langevin equations for nondegenerate four-wave mixing. The solutions are used to compute the amount of squeezing. In the computation the effects of pump–probe phase mismatch, collisions, Doppler broadening, and Gaussian-intensity variation are comprehensively taken into account for the first time to our knowledge. Simple rules of thumb as to where one can see squeezing in both degenerate- and nondegenerate-frequency cases are derived by examining the limit of a short medium. We then present the case of an infinitely long medium, in which maximum squeezing is achieved when there is no pump–probe phase mismatch. With the inclusion of pump–probe phase mismatch, however, the maximum amount of squeezing is obtained with a finite-length medium instead. This prompts us to investigate in detail the finite-length medium case. Our results show that the effects of Doppler broadening and Gaussian-intensity variation can be largely circumvented by detuning the pump frequency more than three Doppler half-widths from resonance and that good broadband squeezing can be achieved even with a Doppler-broadened medium that has a moderate amount of collision broadening. Under these circumstances it is found that the effect of pump self-focusing or defocusing will be the major factor that limits the amount of achievable squeezing. In particular, the spatially varying nonlinear refractive indices seen by the pump and the probe modes are quite different, which causes the former to become spatially mismatched with the latter in the region in which strong squeezing is otherwise expected.
There is presently a growing interest in nearly degenerate four-wave mixing, both for application in optical phase conjugation and the generation of squeezed states. In particular, the self-oscillation of a system interacting with one or two pump beams has been investigated in great detail in the case of photorefractive materials, but very few experiments have been done in vapors in the cw regime. The results that we obtained using sodium are presented here. They are strikingly different from the results obtained with photorefractive materials. For example, the oscillating beam and pump beam frequencies coincide with a precision better than 10−2 Hz. Another interesting aspect of this oscillating beam is that it exhibits a phase sensitive noise: just above threshold, the noise on one quadrature of the field can be 10−2 times smaller than the noise on the other quadrature.
Summary form only given. The interaction between an intense pump beam and a weak probe beam in an atomic vapor has been the subject of numerous investigations. Besides the well-known features in the frequency spectrum of the light, interesting spatial phenomena are observed. They are due to the inhomogeneous intensity distribution of a laser beam, coupled to propagation, and range from self-focusing or defocusing effects to the generation of localized distributions of light that propagate self-similarly (bright or dark solitons). We investigate the reshaping of a probe beam due to the interaction with a pump in sodium vapor, a problem that is important in many different contexts.