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GENERATION OF SQEEZING IN TWO-PHOTON THREE-LEVEL MEDIA

Sunghyuck An, Murray Sargent

Published Jul 18, 1988• 0 citations
OpenAlex

Abstract

In this summary we extend the quantum theory of multiwave mixing by Holm and Sargent1,2 to a three-level cascade model with a two-photos pump and apply the results to the generation of squeezed states. The experimental observation of the suppresion of amplified spontaneous emission by the four-wave mixing process in this model has been reported by Malcuit, Gauthier, and Boyd.3 This experiment has been interpreted semiclassically by the same authors4 and quantum mechanically by Agarwal.5 Agarwal also has shown the generation of squeezed states in this model, but simplified his treatment by ignoring the spontaneous emission to and from the intermediate level. In contrast our treatment allows for arbitrary detunings of a classical pump and quantized sidemode fields, and includes a complete treatment of spontaneous emission.

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In this summary we extend the quantum theory of multiwave mixing by Holm and Sargent1,2 to a three-level cascade model with a two-photos pump and apply the results to the generation of squeezed states. The experimental observation of the suppresion of amplified spontaneous emission by the four-wave mixing process in this model has been reported by Malcuit, Gauthier, and Boyd.3 This experiment has been interpreted semiclassically by the same authors4 and quantum mechanically by Agarwal.5 Agarwal also has shown the generation of squeezed states in this model, but simplified his treatment by ignoring the spontaneous emission to and from the intermediate level. In contrast our treatment allows for arbitrary detunings of a classical pump and quantized sidemode fields, and includes a complete treatment of spontaneous emission.
We present a fully quantum-mechanical theory of nondegenerate multiwave mixing processes in three-level cascades with a two-photon pump. The explicit formulas for the resonance fluorescence spectrum and the quantum combination-tone source term are derived. The theory is applied to the generation of squeezed states of light. We find almost perfect squeezing for some strong-pump intensities and tunings within the Rabi sidebands. We find good broadband squeezing for low-pump intensities and tunings outside a small region around central tuning. Both cases avoid regions of significant spontaneous emission.
This dissertation presents theories of multiwave mixing in two- and three-level media. The first part of the dissertation treats the semiclassical theories in two-level media. Chapter 2 gives the simple semiclassical theory of four-wave mixing when the two pump frequences differ by more than the reciprocal of the population-difference lifetime. This difference washes out the pump spatial holes as well as one of the two reflection gratings. We compare the results to the degenerate treatment of Abrams and Lind and find significant differences in the reflection coefficient spectra. Chapter 3 presents the semiclassical theory of multiwave in a squeezed vacuum characterized by unequal in-phase and in-quadrature dipole decay times. For a highly squeezed vacuum, we find sharp resonances in both probe absorption and reflection coefficients, which provide sensitive ways to measure the amount of squeezing in the vacuum. The second part of the dissertation treats the quantum theories in two- and three-level media. Chapter 4 develops the fourth-order quantum theory of multiwave mixing to describe the effects of sidemode saturation in two-level media. We derive explicit formulas for the fourth-order quantum coefficients and show that the fourth-order quantum theory reproduces the third-order semiclassical coefficient obtained by truncating a continued fraction. We apply the results to cavity problems and find significant differences in the sideband spectra given by the second- and fourth-order treatments, particularly as the sidemode approaches the laser threshold. The final chapter presents a quantum theory of multiwave mixing in three-level cascades with a two-photon pump. The explicit formulas for the resonance fluorescence spectrum and the quantum combination-tone source term are derived. The theory is applied to the generation of squeezed states of light. We find almost perfect squeezing for some strong pump intensities and good broad-band squeezing for low pump intensities.
Over the past three years we have developed a quantum theory of multiwave mixing designed to determine effects of quantum noise on laser and optical bistability instabilities, pump/probe saturation spectroscopy, AM and FM modulation spectroscopy, and phase conjugation. The theory treats a classical pump field and one or two quantum-mechanical sidemode fields interacting with one- or two-photon, two-level media. The theory1 produces a master equation for the reduced sidemode density operator able to describe all of the above phenomena in a uniform way closely related to the corresponding semiclassical theories. It has led to a number of significant predictions about the effects of spontaneous emission on laser spectroscopy and optical instabilities.
Multiphoton transitions are of great interest in laser spectroscopy because they permit the study of new physical phenomena and because of their potential applications. Malcuit et al.1 studied two-photon transitions in atomic sodium and showed that for appropriate phase-matching four-wave mixing can overcome the usual spontaneous decay processes. We have recently developed a quantum theory2 to treat such multiwave mixing processes in two-photon media. Because of the greater complexity of two-photon transitions, many effects arise that are absent in the one-photon case, some of which have important consequences in the generation of squeezed states. For the two-photon two-level model, the field modes have frequencies approximately one-half the frequency difference between the levels. We find that our coefficients differ from the corresponding one-photon theory in that dynamic Stark shifts have a major effect and that the pump-induced coherence between the two levels has a new term in the conjugate coupling terms, which leads to improved squeezing.