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Journal of the Optical Society of America B

Effects of quantum noise on phase conjugation

David A. Holm, Murray Sargent

Published Jan 1, 1987• 0 citations
OpenAlex

Abstract

Due to improvements in detector sensitivity, quantum noise is known to be the limiting factor of many lasers and other optical devices. In this work we present a fully quantum mechanical theory of multiwave mixing to study the effects of spontaneous emission noise on three- and four- wave mixing. The foundations of this theory have been presented in a series of papers1-3 demonstrating how such diverse topics as resonance fluorescence, saturation spectroscopy, phase conjugation, and squeezed states of light share a common origin.

Related papers

Quantum theory of multiwave mixing IV Effects of cavities on the spectrum of resonance fluorescence

David A. Holm, Stig Stenholm, M. Sargent

In the presence of a high-finesse cavity, the resonance fluorescence spectrum can be altered by stimulated emission and multiwave mixing processes. We show that under some conditions it is possible for spontaneous emission to induce conjugate fields similar to semiclassical phase conjugation, requiring the use of the multiwave quantum theory described in earlier papers in this series. The theory is applicable to laser spectroscopy and optical bistability. We present explicit spectra and suggest possible experimental tests. In particular we find a quantum limit for FM spectroscopy that shows that even if the medium under study leaves the FM phase and amplitude relationships intact according to semiclassical theory, spontaneous emission can create an AM component detectable in a square-law detector.

Journal of the Optical Society of America B•Sep 1, 1985•30 citations

Generation of Squeezed States in Optical Bistability

David A. Holm, M. Sargent, Barbara A. Capron

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.

Topical Meeting on Optical Bistability (OB)•Jan 1, 1985•0 citations

QUANTUM THEORY OF MULTIWAVE MIXING (RESONANCE FLUORESCENCE, SATURATION SPECTROSCOPY, MODULATION, PHASE CONJUGATION, QUANTUM NOISE).

David A. Holm

This dissertation formulates and applies a theory describing how one or two strong classical waves and one or two weak quantum mechanical waves interact in a two-level medium. The theory unifies many topics in quantum optics, such as resonance fluorescence, saturation spectroscopy, modulation spectroscopy, the build up of laser and optical bistability instabilities, and phase conjugation. The theory is based on a quantum population pulsation approach that resembles the semiclassical theories, but is substantially more detailed. Calculations are performed to include the effects of inhomogeneous broadening, spatial hole burning, and Gaussian transverse variations. The resonance fluorescence spectrum in a high finesse optical cavity is analyzed in detail, demonstrating how stimulated emission and multiwave processes alter the spectrum from the usual three peaks. The effects of quantum noise during the propagation of weak signal and conjugate fields in phase conjugation and modulation spectroscopy are studied. Our analysis demonstrates that quantum noise affects not only the intensities of the signal and conjugate, but also their relative phase, and in particular we determine a quantum limit to the semiclassical theory of FM modulation spectroscopy. Finally, we derive the corresponding theory for the two-photon, two-level medium. This yields the first calculation of the two-photon resonance fluorescence spectrum. Because of the greater number of possible interactions in the two-photon two-level model, the theoretical formalism is considerably more complex, and many effects arise that are absent in the one-photon problem. We discuss the role of the Stark shifts on the emission spectrum and show how the Rayleigh scattering is markedly different.

•Jan 1, 1985•0 citations

Squeezed states in nondegenerate four-wave mixing

David A. Holm, Murray Sargent

Our quantum theory of multiwave mixing1 treats the interactions between one or two classical pump fields with one or two quantized fields in two-level media. It unifies a number of areas of quantum optics, such as resonance fluorescence, saturation spectroscopy, laser instabilities, and phase conjugation. This paper applies the theory to the generation of squeezed states of light.

•Jun 9, 1986•0 citations

Quantum theory of multiwave mixing. X. Two-photon three-level model

Sunghyuck An, Murray Sargent

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.

Physical Review A•Feb 1, 1989•19 citations

Quantum theory of multiwave mixing in two-photon two-level media

David A. Holm, Murray Sargent

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.

Annual Meeting Optical Society of America•Jan 1, 1986•0 citations
Due to improvements in detector sensitivity, quantum noise is known to be the limiting factor of many lasers and other optical devices. In this work we present a fully quantum mechanical theory of multiwave mixing to study the effects of spontaneous emission noise on three- and four- wave mixing. The foundations of this theory have been presented in a series of papers1-3 demonstrating how such diverse topics as resonance fluorescence, saturation spectroscopy, phase conjugation, and squeezed states of light share a common origin.
In the presence of a high-finesse cavity, the resonance fluorescence spectrum can be altered by stimulated emission and multiwave mixing processes. We show that under some conditions it is possible for spontaneous emission to induce conjugate fields similar to semiclassical phase conjugation, requiring the use of the multiwave quantum theory described in earlier papers in this series. The theory is applicable to laser spectroscopy and optical bistability. We present explicit spectra and suggest possible experimental tests. In particular we find a quantum limit for FM spectroscopy that shows that even if the medium under study leaves the FM phase and amplitude relationships intact according to semiclassical theory, spontaneous emission can create an AM component detectable in a square-law detector.
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.
This dissertation formulates and applies a theory describing how one or two strong classical waves and one or two weak quantum mechanical waves interact in a two-level medium. The theory unifies many topics in quantum optics, such as resonance fluorescence, saturation spectroscopy, modulation spectroscopy, the build up of laser and optical bistability instabilities, and phase conjugation. The theory is based on a quantum population pulsation approach that resembles the semiclassical theories, but is substantially more detailed. Calculations are performed to include the effects of inhomogeneous broadening, spatial hole burning, and Gaussian transverse variations. The resonance fluorescence spectrum in a high finesse optical cavity is analyzed in detail, demonstrating how stimulated emission and multiwave processes alter the spectrum from the usual three peaks. The effects of quantum noise during the propagation of weak signal and conjugate fields in phase conjugation and modulation spectroscopy are studied. Our analysis demonstrates that quantum noise affects not only the intensities of the signal and conjugate, but also their relative phase, and in particular we determine a quantum limit to the semiclassical theory of FM modulation spectroscopy. Finally, we derive the corresponding theory for the two-photon, two-level medium. This yields the first calculation of the two-photon resonance fluorescence spectrum. Because of the greater number of possible interactions in the two-photon two-level model, the theoretical formalism is considerably more complex, and many effects arise that are absent in the one-photon problem. We discuss the role of the Stark shifts on the emission spectrum and show how the Rayleigh scattering is markedly different.
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.
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.