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 propagation of nonclassical radiation in a near-resonant medium

P. D. Drummond, M. G. Raymer

Published Aug 1, 1991• 49 citations
Publisher

Abstract

We develop the quantum theory of the propagation of nonclassical radiation in a nearly resonant medium. The medium is taken to have two levels, which are coupled by the radiation field. Heisenberg equations of motion are developed and compared with stochastic equations in a positive P representation. Initial conditions for absorbers and amplifiers are calculated, so that, for example, superfluorescence or self-induced transparency can be treated. The theoretical methods introduced here allow nonclassical statistics of the radiation field to be calculated such as photon antibunching or squeezing. Both radiative and collisional damping are included.

DOI
10.1103/physreva.44.2072

Related papers

Superradiant Effects on Pulse Propagation in Resonant Media

Antonio M. Ponte Goncalves, Andree A. Tallet, R. Lefèbvre

A theoretical model for the propagation of coherent light pulses in resonant media where a large number of atoms cooperate in spontaneous emission (superradiance) is discussed. The medium is supposedly free of inhomogeneous broadening, and no lossy relaxation mechanisms are taken into account. The conditions for the emission of all spontaneous radiation in the direction of pulse propagation are described. A semi-classical model is used and, at each point in the medium, the propagation field and the spontaneous damping field are considered separately. The equation governing the evolution of a superradiant system in the presence of an applied pulse is derived. A mechanism of energy transfer from the traveling pulse to the medium is described which includes superradiant spontaneous emission effects. As a result of the neglect of all lossy relaxation processes, all energy stored in the medium is eventually returned to the pulse by coherent spontaneous emission. Therefore, in this theory, all pulses travel through the medium without energy loss. Numerical results for square input pulses are discussed which show two possible types of propagation behavior: (a) Low input intensities produce a negative tail to the input (positive) pulse and sharpening of the tail with the advance in the medium; (b) higher input intensities produce, after sufficient penetration, a steady-state pulse envelope somewhat similar to the $2\ensuremath{\pi}$ pulses of self-induced transparency. The steady-state solutions of the equations of motion are found numerically and the pulse shapes are computed for different degrees of superradiance. In the limit of strong superradiance, very asymmetric pulse envelopes of large area are found. For negligible superradiance, approximately $2\ensuremath{\pi}$ hyperbolic-secant pulses are obtained. The effects of inhomogeneous broadening are briefly considered, and the consequences of important superradiant damping in photon-echo experiments are qualitatively discussed.

Physical Review•Dec 10, 1969•17 citations

Quantum theory of optical bistability. II. Atomic fluorescence in a high- Q cavity

P. D. Drummond, Daniel F. Walls

A quantum treatment of a coherently driven cavity with a medium of two-level atoms is given. The system displays both absorptive and dispersive bistability. Quantum fluctuations are included via a Fokker-Planck equation in a generalized $P$ representation, after adiabatic elimination of the atomic variables. The transmitted spectrum and correlation function is calculated in a linearized (Gaussian) approximation. In the limit of large detuning and radiative damping, the quantum fluctuations are identical to those of a simple nonlinear polarizability theory. An analysis is given of the nonclassical statistical properties of the intensity-correlation spectrum.

Physical Review A•May 1, 1981•194 citations

Simple atomic systems in resonant laser fields

Mikhail L. Ter-Mikhaelyan

The interaction of simple, two- and three-level atomic systems with monochromatic and nonmonochromatic laser radiation near resonance transitions is discussed based on the Schroedinger equation with radiation decay and no collisional relaxation, outside the framework of the usual perturbation theory. The mathematical schemes employed include the resonance approximation, exact methods, the quasi-energy method, the adiabatic approximation, etc. A large number of physical phenomena, such as oscillating and inverted populations, self-induced resonances, processes of first order in the weak field, Raman scattering, coherent population transfer, etc. are considered. The review is intended for a broad readership.

Physics-Uspekhi•Dec 31, 1997•42 citations

Propagation of nonclassical optical radiation through a semiconductor slab

Dmytro Vasylyev, W. Vogel, K. Henneberger +2 more

Based on a microscopic derivation of the emission spectra of a bulk semiconductor, we arrive at a clear physical interpretation of the noise current operators in macroscopic quantum electrodynamics. This opens the possibility to study medium effects on nonclassical radiation propagating through an absorbing or amplifying semiconductor. As an example, the propagation of an incident squeezed vacuum is analyzed.

arXiv:0802.2777•Physical Review A•Sep 29, 2008•9 citations

Quantum theory of light in nonlinear media with dispersion and absorption

Eduard Schmidt, John Jeffers, Stephen Mark Barnett +2 more

We present a canonical quantum theory of radiation in nonlinear media taking into account the effects of linear dispersion and absorption in a consistent way. We start from a microscopic model and apply recently developed concepts of the quantization of radiation in dispersive and absorbing linear media and extend the theory in order to include nonlinear optical processes. We derive propagation equations in space and time for the quantized radiation field, with special emphasis on the propagation of quantum-light pulses in Kerr media. In particular, the method enables us to derive systematically the noise sources that arise naturally in the nonlinear terms.

Journal of Modern Optics•Feb 1, 1998•16 citations

Propagation of quantum fluctuations through passive optical systems

Xiao Min, H. J. Kimble

By employing the input-output theory of damped quantum systems developed by Gardiner and Collett,1 we discuss the propagation of nonclassical fields through optical systems containing frequency selective elements such as Fabry-Perot interferometers. Our results are of general applicability and are expressed in terms of the linearized drift and diffusion coefficients of the generalized Fokker-Planck equation describing the intracavity field of the nonlinear source. The two nonclassical effects of photon antibunching and squeezing are treated in detail with reference to the examples of intracavity harmonic conversion and optical bistability. Not surprisingly photon antibunching can be enhanced by the suppression of the coherent part of the spectrum of intensity fluctuations with a narrow bandwidth cavity. However the enhancement is ultimately limited and the antibunching lost altogether as the amplitude of the coherent carrier is reduced to a level comparable to that of the field fluctuations (which are set by the system size). Following the suggestion of Levenson et al., 2 we investigate the use of auxiliary cavities for the control of phase and amplitude in the propagation and detection of squeezed states of light. While for a small degree of squeezing such filter cavities operate in a straightforward fashion, a mixing of field quadratures can occur as the degree of squeezing increases leading to a loss of nonclassical behavior.

Annual Meeting Optical Society of America•Jan 1, 1986•1 citation
We develop the quantum theory of the propagation of nonclassical radiation in a nearly resonant medium. The medium is taken to have two levels, which are coupled by the radiation field. Heisenberg equations of motion are developed and compared with stochastic equations in a positive P representation. Initial conditions for absorbers and amplifiers are calculated, so that, for example, superfluorescence or self-induced transparency can be treated. The theoretical methods introduced here allow nonclassical statistics of the radiation field to be calculated such as photon antibunching or squeezing. Both radiative and collisional damping are included.
A theoretical model for the propagation of coherent light pulses in resonant media where a large number of atoms cooperate in spontaneous emission (superradiance) is discussed. The medium is supposedly free of inhomogeneous broadening, and no lossy relaxation mechanisms are taken into account. The conditions for the emission of all spontaneous radiation in the direction of pulse propagation are described. A semi-classical model is used and, at each point in the medium, the propagation field and the spontaneous damping field are considered separately. The equation governing the evolution of a superradiant system in the presence of an applied pulse is derived. A mechanism of energy transfer from the traveling pulse to the medium is described which includes superradiant spontaneous emission effects. As a result of the neglect of all lossy relaxation processes, all energy stored in the medium is eventually returned to the pulse by coherent spontaneous emission. Therefore, in this theory, all pulses travel through the medium without energy loss. Numerical results for square input pulses are discussed which show two possible types of propagation behavior: (a) Low input intensities produce a negative tail to the input (positive) pulse and sharpening of the tail with the advance in the medium; (b) higher input intensities produce, after sufficient penetration, a steady-state pulse envelope somewhat similar to the $2\ensuremath{\pi}$ pulses of self-induced transparency. The steady-state solutions of the equations of motion are found numerically and the pulse shapes are computed for different degrees of superradiance. In the limit of strong superradiance, very asymmetric pulse envelopes of large area are found. For negligible superradiance, approximately $2\ensuremath{\pi}$ hyperbolic-secant pulses are obtained. The effects of inhomogeneous broadening are briefly considered, and the consequences of important superradiant damping in photon-echo experiments are qualitatively discussed.
A quantum treatment of a coherently driven cavity with a medium of two-level atoms is given. The system displays both absorptive and dispersive bistability. Quantum fluctuations are included via a Fokker-Planck equation in a generalized PPP representation, after adiabatic elimination of the atomic variables. The transmitted spectrum and correlation function is calculated in a linearized (Gaussian) approximation. In the limit of large detuning and radiative damping, the quantum fluctuations are identical to those of a simple nonlinear polarizability theory. An analysis is given of the nonclassical statistical properties of the intensity-correlation spectrum.
The interaction of simple, two- and three-level atomic systems with monochromatic and nonmonochromatic laser radiation near resonance transitions is discussed based on the Schroedinger equation with radiation decay and no collisional relaxation, outside the framework of the usual perturbation theory. The mathematical schemes employed include the resonance approximation, exact methods, the quasi-energy method, the adiabatic approximation, etc. A large number of physical phenomena, such as oscillating and inverted populations, self-induced resonances, processes of first order in the weak field, Raman scattering, coherent population transfer, etc. are considered. The review is intended for a broad readership.
We present a canonical quantum theory of radiation in nonlinear media taking into account the effects of linear dispersion and absorption in a consistent way. We start from a microscopic model and apply recently developed concepts of the quantization of radiation in dispersive and absorbing linear media and extend the theory in order to include nonlinear optical processes. We derive propagation equations in space and time for the quantized radiation field, with special emphasis on the propagation of quantum-light pulses in Kerr media. In particular, the method enables us to derive systematically the noise sources that arise naturally in the nonlinear terms.
By employing the input-output theory of damped quantum systems developed by Gardiner and Collett,1 we discuss the propagation of nonclassical fields through optical systems containing frequency selective elements such as Fabry-Perot interferometers. Our results are of general applicability and are expressed in terms of the linearized drift and diffusion coefficients of the generalized Fokker-Planck equation describing the intracavity field of the nonlinear source. The two nonclassical effects of photon antibunching and squeezing are treated in detail with reference to the examples of intracavity harmonic conversion and optical bistability. Not surprisingly photon antibunching can be enhanced by the suppression of the coherent part of the spectrum of intensity fluctuations with a narrow bandwidth cavity. However the enhancement is ultimately limited and the antibunching lost altogether as the amplitude of the coherent carrier is reduced to a level comparable to that of the field fluctuations (which are set by the system size). Following the suggestion of Levenson et al., 2 we investigate the use of auxiliary cavities for the control of phase and amplitude in the propagation and detection of squeezed states of light. While for a small degree of squeezing such filter cavities operate in a straightforward fashion, a mixing of field quadratures can occur as the degree of squeezing increases leading to a loss of nonclassical behavior.