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Optics Letters

Distortion-free gain and noise correlation in sodium vapor with four-wave mixing and coherent population trapping

Timothy T. Grove, M. S. Shahriar, Philip Hemmer, Prem Kumar, Venkatapura S. Sudarshanam, Mark Cronin‐Golomb

Published Jun 1, 1997• 35 citations
Publisher

Abstract

We observed optical gain as great as 30 with nearly distortion-free beam propagation in optically dense sodium vapor, using four-wave mixing. Moreover, 15-dB classical noise correlations were seen in the amplified probe and conjugate beams. To achieve this performance in such a strongly absorbing medium, one must suppress unwanted absorption and self-focusing effects. This is accomplished with coherent population trapping.

DOI
10.1364/ol.22.000769

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 22, 1988•0 citations
We observed optical gain as great as 30 with nearly distortion-free beam propagation in optically dense sodium vapor, using four-wave mixing. Moreover, 15-dB classical noise correlations were seen in the amplified probe and conjugate beams. To achieve this performance in such a strongly absorbing medium, one must suppress unwanted absorption and self-focusing effects. This is accomplished with coherent population trapping.
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.
Summary form only given. Previously, we have used four-wave mixing via coherent population trapping to achieve optical phase conjugation (OPC) with high gain, using two dye lasers and a sodium vapor cell. The /spl Lambda/ transition used involved the two hyperfine ground states and one excited state, so that two different optical frequencies were needed to satisfy the two-photon resonant condition between the probe and one of the pump beams. Later, we demonstrated in rubidium that a single hyperfine transition with Zeeman sublevels is enough to achieve OPC with equally high gain, thus eliminating the need for high-frequency sideband generation. However, in order to guarantee that the diffraction from the grating is primarily dispersive, the backward pump beam had to be detuned by about 60 MHz from the probe and the forward pump. One of the key disadvantages of such a nondegenerate scheme is that applications such as phase-conjugate mirrors are hard to implement. Here, we report the observation of optical phase conjugation in rubidium with equally high gain, but all the frequencies are degenerate.
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.
Two spectral regions of gain exist for a weak probe beam propagating through a medium of two-level-atoms pumped by a strong near-resonance field. Experimentally a cw ring-dye laser is used to explore this gain at the Na D₂ resonance in a vapor. Plane-wave calculations of probe-gain spectra which include the Doppler broadening inherent in a vapor agree well with experimental spectra obtained with a Fabry-Perot interferometer. Such two-beam-coupling gain might have applications as optical pre- or power amplifiers. The gain is also the primary step in four-wave-mixing. Mixing of the pump and sideband which experiences gain produces the medium polarization from which the fourth-wave arises. For phase-matched propagation the fourth-wave, which is at a frequency that experiences little or negative probe-gain (i.e., absorption), grows at nearly the same rate as the primary sideband. Together the two sidebands extract far more than twice as much energy from the pump than does the primary sideband acting alone. Experimentally four-wave-mixing which arises from noise at the gain-sideband-frequency is sometimes accompanied by conical emission at the fourth-wave sideband. Since this sideband is also seen on axis the explanation cannot be simply phase-matching. Simulations which include the full transverse nature of the experiment are currently running on a CRAY supercomputer. These simulations indicate that the radial variation of the medium index of refraction is responsible for conical emission.
Four wave mixing (FWM) performance of sodium vapor was investigated in the strong pump regime (I»I at) necessary to achieve good phase conjugate reflectivity, R. Reflectivities >230% were observed using narrowband CW pump powers less than 1 W. Degenerate FWM spectral response was measured with R as a parameter, and shown to depend on self-focusing effects at higher R. The field of view of the sodium FWM was determined under narrowband high R conditions and found to behave as expected, except for nearly collinear geometries. Faith-ful imaging through a severe optical aberration was demonstrated at moderate R, but experimental observations and analysis indicate potential fidelity problems at large R. Reflect-ivity and field of view were also measured for wideband (2 GHz) laser pumping.