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

Optics Letters

Enhanced squeezing in a squeezed vacuum

Sunghyuck An, Murray Sargent

Published Jan 15, 1990• 0 citations
Publisher

Abstract

A quantum theory of multiwave mixing based on a combination of a Langevin quantum regression method and a density operator technique is outlined. The approach is simple, yet general, and is particularly valuable for analyzing complicated media such as semiconductors. We apply it to find the quantum multiwave mixing equations in a squeezed vacuum. Comparing squeezing spectra in squeezed and ordinary vacua, we find significantly enhanced squeezing for the appropriate pump-vacuum relative phase.

DOI
10.1364/ol.15.000139

Related papers

Quantum theory of multiwave mixing: Squeezed-vacuum model

Sunghyuck An, Murray Sargent

The present paper combines a Langevin quantum-regression method with a density-operator approach to derive the master equation for the quantum theory of multiwave mixing in a very efficient way. The approach is quite general and is particularly valuable for analyzing complicated media such as semiconductors. It is used in the present paper to derive the quantum multiwave-mixing equations in a squeezed vacuum. We find improved formulas for resonance fluorescence in a squeezed vacuum as well as the squeezing coefficients in a squeezed vacuum. Comparing squeezing spectra in squeezed and ordinary vacua, we find significantly enhanced squeezing for the appropriate pump-vacuum relative phase.

Physical Review A•Dec 1, 1989•2 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

Theory of multiwave mixing in a squeezed vacuum

Sunghyuck An, Murray Sargent

We present a theory of nondegenerate multiwave mixing in a squeezed vacuum. The probe absorption and coupling coefficients are derived using a standard Fourier-series method. We average the coefficients over pump spatial holes and solve the coupled mode equations to find the four-wave-mixing reflection coefficient. Reflectivity peaks and dips are found to be narrower than in an unsqueezed vacuum. Both the absorption and the reflectivity provide sensitive ways to measure the amount of squeezing in the vacuum.

Physical Review A•Apr 1, 1989•23 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

Quantum theory of multiwave mixing. VII. Connection to quantum Langevin theory

David A. Holm, Murray Sargent

We transform our quantum theory of multiwave mixing, which is based on a reduced density operator, to the corresponding nondegenerate quantum-noise Langevin equations. We derive the diffusion coefficients from the drift coefficients using the generalized Einstein relation and illustrate the resulting quantum Langevin theory of multiwave mixing by specializing to the Reid and Walls degenerate theory of squeezed states of light.

Physical Review A•Jun 1, 1986•20 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
A quantum theory of multiwave mixing based on a combination of a Langevin quantum regression method and a density operator technique is outlined. The approach is simple, yet general, and is particularly valuable for analyzing complicated media such as semiconductors. We apply it to find the quantum multiwave mixing equations in a squeezed vacuum. Comparing squeezing spectra in squeezed and ordinary vacua, we find significantly enhanced squeezing for the appropriate pump-vacuum relative phase.
The present paper combines a Langevin quantum-regression method with a density-operator approach to derive the master equation for the quantum theory of multiwave mixing in a very efficient way. The approach is quite general and is particularly valuable for analyzing complicated media such as semiconductors. It is used in the present paper to derive the quantum multiwave-mixing equations in a squeezed vacuum. We find improved formulas for resonance fluorescence in a squeezed vacuum as well as the squeezing coefficients in a squeezed vacuum. Comparing squeezing spectra in squeezed and ordinary vacua, we find significantly enhanced squeezing for the appropriate pump-vacuum relative phase.
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.
We present a theory of nondegenerate multiwave mixing in a squeezed vacuum. The probe absorption and coupling coefficients are derived using a standard Fourier-series method. We average the coefficients over pump spatial holes and solve the coupled mode equations to find the four-wave-mixing reflection coefficient. Reflectivity peaks and dips are found to be narrower than in an unsqueezed vacuum. Both the absorption and the reflectivity provide sensitive ways to measure the amount of squeezing in the vacuum.
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.