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

Journal of Physics A Mathematical and General

Quantum revivals in the Jaynes-Cummings model

P. Filipowicz

Published Dec 21, 1986• 45 citations
Publisher

Abstract

The author obtains an exact integral representation of the sum describing the evolution of the inversion of the two-level atom in the Jaynes-Cummings model when the field is initially prepared in a coherent state or a state generated by classical sources at non-zero temperature. The author uses the saddle point method to estimate the integrals.

DOI
10.1088/0305-4470/19/18/024

Related papers

Inside the Jaynes–Cummings sum

S. I. Pavlik

Abstract It is shown that the atomic inversion in the Jaynes–Cummings model has an exact representation as an integral over the Hankel contour. For a field in a coherent state, the integral is evaluated using the saddle point method. The trajectories of saddle points as a function of time are on the branches of the multi-valued Lambert function. All of them start at the initial moment of time, but make the maximum contribution to the inversion at different times. If the collapse and the first revival are clearly distinguished, then subsequent revivals are determined by the comparable contributions of several trajectories.

arXiv:2307.07838•Physica Scripta•Dec 13, 2023•1 citation

The Jaynes-Cummings model thermal revivals

Gabriel Arroyo-Correa, J. J. Sánchez-Mondragón

Consistent with the standard interpretation of the revivals in the Jaynes-Cummings models the time evolution interference among the quantized field states, the authors have developed an exact mathematical analysis of the series describing the evolution of the atomic inversion when the quantum electrodynamic field is initially prepared in a thermal state. A complete and exact functional analysis to isolate the revivals is carried out.

Quantum Optics Journal of the European Optical Society Part B•Dec 1, 1990•22 citations

Mixed thermal-coherent revivals in the Jaynes-Cummings model

Evguenii V. Kurmyshev, J. J. Sánchez-Mondragón, Gabriel Arroyo-Correa

The existence of revivals in the atomic inversion of the Jaynes-Cummings model (JCM) has been pinpointed on the numerical display of its expectation value. However, until recently its individual identification, isolation, and analytical representation was successful if the initial photon statistics allowed the use of saddle point techniques. 1 The recent introduction of a new analytical method,2 free of such restriction, and its successful use with thermal JCM revivals allows us to study the mixed thermal coherent JCM revivals, drawing a direct relation to the saddle point technique. We compare our results with previous ones of the pure thermal case,2 and the coherent limiting cases, in particular with the systematic technique proposed by Fleischhauer and Schleich.

Annual Meeting Optical Society of America•Jan 1, 1991•0 citations

Analytic approximation for Jaynes-Cummings revivals

H. J. Carmichael

Recent interest in the collapse and revival of Rabi oscillations in the Jaynes-Cummings model was stimulated by a paper in 1980 by Eberly et al.1 These authors presented an analytic expression for the inversion of a two-level atom interacting with a single mode of the radiation field taken to be initially in a coherent state. Their analytic expression agreed well with a numerical evaluation of the standard summation formula for the inversion. Since the publication of this analytic result various discussions of its proof have appeared. Existing versions of the proof all convert the summation formula into an integral and evaluate this integral using the method of stationary phase.2 This approach is mathematically intricate and leaves one with little physical intuition for the approximations that are made. I offer an alternative proof, which, in compact form, takes only a few lines. The proof is built up in a series of approximations based on an expansion of the troublesome square root (n) in the Jaynes-Cummings summation formula in a Taylor series about the mean photon number: n=n¯[1+12n−n¯n¯−18(n−n¯n¯)2+…]. The analytical expression of Eberly ef al. is recovered using standard sums and integrals and this Taylor expansion to second order.

Annual Meeting Optical Society of America•Jan 1, 1988•0 citations

Thermal QED revivals in the Jaynes-Cummings model

Gabriel Arroyo-Correa, J. J. Sánchez-Mondragón

We develop an exact mathematical analysis of the time evolution of the atomic inversion in the Jaynes-Cummings model when the field is initially prepared in a thermal state, where the initial state of the TLA is the ground or excited state m = ∓1.

Annual Meeting Optical Society of America•Jan 1, 1989•0 citations

Time-averaged properties of the Jaynes-Cummings model

James D. Cresser, Mark S. Hillery

Exact solutions in the form of infinite series are well known for the Jaynes-Cummings model describing the interaction of a two-level atom with a single-mode field prepared in a coherent state. While these solutions have led to the discovery of many interesting properties of the Jaynes-Cummings model as a function of time, the nature of the solutions is such that it is not a simple matter to make statements of a general nature about the properties of the system. In this paper it is shown that by taking infinite time averages of the series expressions for the atomic inversion and inversion correlation, squeezing, and antibunching, simple closed-form expressions are obtained from which general properties of the Jaynes-Cummings model can be readily inferred. In particular, new conditions are obtained under which the field is significantly squeezed on average, and further information is obtained on the long-time behavior of the revivals in the atomic inversion.

Physical Review A•Aug 1, 1989•12 citations
The author obtains an exact integral representation of the sum describing the evolution of the inversion of the two-level atom in the Jaynes-Cummings model when the field is initially prepared in a coherent state or a state generated by classical sources at non-zero temperature. The author uses the saddle point method to estimate the integrals.
Abstract It is shown that the atomic inversion in the Jaynes–Cummings model has an exact representation as an integral over the Hankel contour. For a field in a coherent state, the integral is evaluated using the saddle point method. The trajectories of saddle points as a function of time are on the branches of the multi-valued Lambert function. All of them start at the initial moment of time, but make the maximum contribution to the inversion at different times. If the collapse and the first revival are clearly distinguished, then subsequent revivals are determined by the comparable contributions of several trajectories.
The existence of revivals in the atomic inversion of the Jaynes-Cummings model (JCM) has been pinpointed on the numerical display of its expectation value. However, until recently its individual identification, isolation, and analytical representation was successful if the initial photon statistics allowed the use of saddle point techniques. 1 The recent introduction of a new analytical method,2 free of such restriction, and its successful use with thermal JCM revivals allows us to study the mixed thermal coherent JCM revivals, drawing a direct relation to the saddle point technique. We compare our results with previous ones of the pure thermal case,2 and the coherent limiting cases, in particular with the systematic technique proposed by Fleischhauer and Schleich.
Recent interest in the collapse and revival of Rabi oscillations in the Jaynes-Cummings model was stimulated by a paper in 1980 by Eberly et al.1 These authors presented an analytic expression for the inversion of a two-level atom interacting with a single mode of the radiation field taken to be initially in a coherent state. Their analytic expression agreed well with a numerical evaluation of the standard summation formula for the inversion. Since the publication of this analytic result various discussions of its proof have appeared. Existing versions of the proof all convert the summation formula into an integral and evaluate this integral using the method of stationary phase.2 This approach is mathematically intricate and leaves one with little physical intuition for the approximations that are made. I offer an alternative proof, which, in compact form, takes only a few lines. The proof is built up in a series of approximations based on an expansion of the troublesome square root (n) in the Jaynes-Cummings summation formula in a Taylor series about the mean photon number: n=n¯[1+12n−n¯n¯−18(n−n¯n¯)2+…]. The analytical expression of Eberly ef al. is recovered using standard sums and integrals and this Taylor expansion to second order.
Exact solutions in the form of infinite series are well known for the Jaynes-Cummings model describing the interaction of a two-level atom with a single-mode field prepared in a coherent state. While these solutions have led to the discovery of many interesting properties of the Jaynes-Cummings model as a function of time, the nature of the solutions is such that it is not a simple matter to make statements of a general nature about the properties of the system. In this paper it is shown that by taking infinite time averages of the series expressions for the atomic inversion and inversion correlation, squeezing, and antibunching, simple closed-form expressions are obtained from which general properties of the Jaynes-Cummings model can be readily inferred. In particular, new conditions are obtained under which the field is significantly squeezed on average, and further information is obtained on the long-time behavior of the revivals in the atomic inversion.