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Annual Meeting Optical Society of America

Observation of phase-sensitive noise in sodium vapor

Mari W. Maeda, Prem Kumar, Jeffrey H. Shapiro

Published Jan 1, 1985• 0 citations
Publisher

Abstract

Squeezed states of light exhibit phase-sensitive quantum noise measurable via optical homodyne detection. They have been predicted to be generated via degenerate four-wave mixing, resonance fluorescence, and nonlinear propagation.1 We report observing phase-sensitive noise via optical homodyning on a cw dye laser beam which has propagated through sodium vapor near the D lines. A p-polarized dye laser beam of ~5-W/cm2 intensity was passed through sodium vapor near its D lines. Homodyne measurements were made on both the s- and the p-polarized components of the transmitted beam using the dual-detector subtraction scheme.2 A spectrum analyzer monitored the noise in a 6–15-MHz band. In the absence of sodium, the noise in this band was vacuum-state quantum noise limited and was insensitive to the relative local-oscillator beam/transmitted laser beam phase θ. In the presence of sodium, the noise was sensitive to θ, with dependence of the form As,p + Bs,p cos2(θ − ϕs,p), where ϕs = 0 for s polarization and ϕp = π/2 for p polarization. For one set of data we measured As = 2 dB, Bs = 3 dB, Ap = 3 dB, and Bp = 2.5 dB above the noise levels in the absence of sodium. The s-poiarization data were collected with the local-oscillator power PLO far in excess of the s component of the transmitted pump power PTP; for p polarization, PLO ~ PTP prevailed. The measurement uncertainty in the spectrum analyzer data is ±0.5 dB. Possible physical mechanisms to explain these results are discussed.

DOI
10.1364/oam.1985.fm4

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•Apr 26, 1987•0 citations
Squeezed states of light exhibit phase-sensitive quantum noise measurable via optical homodyne detection. They have been predicted to be generated via degenerate four-wave mixing, resonance fluorescence, and nonlinear propagation.1 We report observing phase-sensitive noise via optical homodyning on a cw dye laser beam which has propagated through sodium vapor near the D lines. A p-polarized dye laser beam of ~5-W/cm2 intensity was passed through sodium vapor near its D lines. Homodyne measurements were made on both the s- and the p-polarized components of the transmitted beam using the dual-detector subtraction scheme.2 A spectrum analyzer monitored the noise in a 6–15-MHz band. In the absence of sodium, the noise in this band was vacuum-state quantum noise limited and was insensitive to the relative local-oscillator beam/transmitted laser beam phase θ. In the presence of sodium, the noise was sensitive to θ, with dependence of the form As,p + Bs,p cos2(θ − ϕs,p), where ϕs = 0 for s polarization and ϕp = π/2 for p polarization. For one set of data we measured As = 2 dB, Bs = 3 dB, Ap = 3 dB, and Bp = 2.5 dB above the noise levels in the absence of sodium. The s-poiarization data were collected with the local-oscillator power PLO far in excess of the s component of the transmitted pump power PTP; for p polarization, PLO ~ PTP prevailed. The measurement uncertainty in the spectrum analyzer data is ±0.5 dB. Possible physical mechanisms to explain these results are discussed.
We have observed optical phase-sensitive noise in homodyne detection of a cw light beam which has propagated through sodium vapor near the D lines. Although at present the minimum noise is at or above the vacuum-state quantum limit due to zero-point fluctuations, nevertheless its phase behavior is like that of a squeezed state. Our observations are consistent both with the predictions of the quantum-mechanical theory of degenerate four-wave mixing and the theory of multiatom resonance fluorescence in the forward direction.
Squeezed states of light exhibit phase-sensitive quantum noise which falls below the semiclassical shot noise limit. We report results from experiments in sodium vapor to observe squeezed light. In a single-beam experiment, a dye laser beam transmitted through sodium vapor was homodyned. Phase-sensitive noise on the radio frequency off­set modes was observed at or above the semiclassical limit.1 In a two-beam correlation experiment, the transmitted probe and the reflected con­jugate beams in forward four-wave mixing were direct detected. Although this configuration does not generate squeezed light, the subtracted photo­current exhibits subshot noise fluctuations.2 Phase-insensitive noise above the semiclassical limit was observed with a strong positive correlation between the probe and the conjugate photo­currents. In a squeezed state experiment, a probe-conjugate combination mode of forward four-wave mixing was homodyned.3 With the input beam blocked, the noise showed nonclassical phase-sensitivity with a minimum of 0.2 dB below the vacuum state limit. When only the probe or the conjugate beam was homodyned, the noise remained phase-insensitive near the vacuum state level.
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 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.
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.