Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

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

Sunghyuck An, Murray Sargent

Published Feb 1, 1989• 19 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.39.1841

Related papers

Generation of squeezing in two-photon three-level media

Sunghyuck An, Murray Sargent

We present a fully quantum-mechanical theory of nondegenerate four-wave mixing processes in three-level cascades with a two-photon pump. The results are 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.

Optics Letters•Jun 1, 1988•10 citations

Quantum theory of multiwave mixing. IX. Squeezed states in two-photon media

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

We apply our quantum theory of multiwave mixing for the two-photon two-level model to the generation of squeezed states of light. Because of the two-photon transition, a larger number of interaction potentials are present compared to one-photon models, leading to effects absent in the one-photon case. The two most significant of these are the appearance of dynamic Stark shifts and conjugate scattering off the pump induced two-photon coherence. We show that this can lead to almost perfect squeezing, even for low pump intensities and low detunings from the two-photon resonance.

Physical Review A•Apr 1, 1987•26 citations

Theory of multiwave mixing in two- and three-level media.

Sunghyuck An

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.

•Jan 1, 1988•0 citations

GENERATION OF SQEEZING IN TWO-PHOTON THREE-LEVEL MEDIA

Sunghyuck An, Murray Sargent

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.

•Jul 18, 1988•0 citations

Quantum theory of multiwave mixing. VIII. Squeezed states

David A. Holm, M. Sargent

We apply our quantum theory of multiwave mixing to the generation of squeezed states of light via three- and four-wave mixing in cavities and in propagation. We compare the cavity predictions to the experimental results of Slusher et al. [Phys. Rev. Lett. 55, 2409 (1985)], finding reasonably good agreement. The squeezing found there is due to the fact that the number operators are driven by resonance fluorescence, which nearly vanishes for the large detunings chosen, while the combination tone operators are driven by relatively large source terms. We give a physical discussion as to why the spectral quantities outside the cavity are given by those inside multiplied by the cavity linewidth. We have found analytic formulas for the variances for arbitrary propagation distances, detunings, and pump intensities. We derive these formulas both from the density operator and from the Langevin methods. To obtain significant squeezing, the propagation distances must be large compared with the resonant Beer's law length.

Physical Review A•Mar 1, 1987•55 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
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.
We apply our quantum theory of multiwave mixing for the two-photon two-level model to the generation of squeezed states of light. Because of the two-photon transition, a larger number of interaction potentials are present compared to one-photon models, leading to effects absent in the one-photon case. The two most significant of these are the appearance of dynamic Stark shifts and conjugate scattering off the pump induced two-photon coherence. We show that this can lead to almost perfect squeezing, even for low pump intensities and low detunings from the two-photon resonance.
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.
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 apply our quantum theory of multiwave mixing to the generation of squeezed states of light via three- and four-wave mixing in cavities and in propagation. We compare the cavity predictions to the experimental results of Slusher et al. [Phys. Rev. Lett. 55, 2409 (1985)], finding reasonably good agreement. The squeezing found there is due to the fact that the number operators are driven by resonance fluorescence, which nearly vanishes for the large detunings chosen, while the combination tone operators are driven by relatively large source terms. We give a physical discussion as to why the spectral quantities outside the cavity are given by those inside multiplied by the cavity linewidth. We have found analytic formulas for the variances for arbitrary propagation distances, detunings, and pump intensities. We derive these formulas both from the density operator and from the Langevin methods. To obtain significant squeezing, the propagation distances must be large compared with the resonant Beer's law length.