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

Annual Meeting Optical Society of America

Wave packet analysis of the multimode Jaynes-Cummings model

Jonathan S. Parker, Carlos R. Stroud

Published Jan 1, 1986• 0 citations
Publisher

Abstract

A spontaneously decaying two-level atom in an evacuated high-Q cavity undergoes Rabi oscillations. This phenomenon has been observed experimentally as enhanced or inhibited spontaneous emission. In the standard Jaynes-Cummings model the atom is assumed to interact with only a single cavity mode. By retaining the infinite set of cavity modes the propagation of the spontaneously emitted radiation may be calculated. Such an analysis yields a clear physical picture of Rabi oscillations. These vacuum-field Rabi oscillations are compared with Rabi oscillations of a one-electron atom induced by coherent radiation. We show that the same wave packet analysis explains both types of Rabi oscillation. The limit in which a multimode cavity may be approximated as a single-mode cavity is discussed.

DOI
10.1364/oam.1986.thj8

Related papers

Transient theory of cavity-modified spontaneous emission

Jonathan S. Parker, Carlos R. Stroud

We present a numerical and analytical study of a multimode Jaynes-Cummings model describing the spontaneous decay of a single atom in a high-Q cavity. The theory of cavity-modified spontaneous emission is discussed in terms of quantities that have clear physical interpretations: the photon wave packet radiated by the atom, its reflection by the cavity boundaries, and its reabsorption by the atom. Multimode corrections to the single-mode Jaynes-Cummings model are calculated. The multimode corrections are formulated in terms of quantities that may be calculated by solving the single-mode equations of motion.

Physical Review A•May 1, 1987•49 citations

Quantum Rabi oscillations of a qubit strongly coupled to a one-dimensional waveguide

Ya. S. Greenberg, A. A. Shtygashev, O. A. Chuikin +2 more

We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. We show that for a strongly interacting qubit-photon system, the dynamics are captured by a reduced two-level model. In this framework, each level is defined as the product of the atomic excited state and a specific field mode, which takes the form of a multiphoton Fock-like state. In this picture, the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a coherent state with a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.

quant-pharXiv:2608.16077•Aug 18, 2026•0 citations

Cavity-modified spontaneous emission: From Rabi oscillations to exponential decay

H. Gie\Sen, Jill D. Berger, Georg Mohs +2 more

We revisit the problem of spontaneous emission by a two-level system in a cavity, concentrating in particular on those aspects associated with the finite propagation time of light between the atom and the cavity boundaries. We find that spontaneous emission always occurs first at the free space rate and there is then an abrupt change in these dynamics when light reflected by the cavity mirrors returns to the atom, leading to interference effects that result either in an enhancement or a reduction of this rate or in a periodic exchange of excitation between the atom and the cavity field. From this point of view, reversible spontaneous emission in terms of single-mode ``vacuum Rabi oscillations'' can be interpreted as resulting from the interference between the multimode partial waves reflected at the cavity mirrors and the instantaneously radiated light. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Apr 1, 1996•49 citations

Vacuum-field Rabi oscillations in a bimodal cavity

Ho Trung Dung, A.S. Shumovsky

Examining the spontaneous emission of a two-level atom interacting at the same time with two modes of the cavity radiation field the authors show that such multimode coupling may lead to irregular patterns in the vacuum-field Rabi oscillations. It also leads to the appearance of a new line in the spontaneous emission spectra in comparison with the case of single-mode single-atom coupling.

Quantum Optics Journal of the European Optical Society Part B•Apr 1, 1992•5 citations

Theoretical aspects of the quantum electrodynamics of two-level atoms in high-Q cavities

Amitabh Joshi, S. V. Lawande

The Jaynes-Cummings model provides a useful means of studying several quantum electrodynamic effects in matter-radiation interaction. One such effect is the phenomenon of collapses and revivals of Rabi oscillations. Various aspects of this phenomenon are studied in terms of the dynamical evolution of the atom as well as the statistical properties of the field. In particular, the sensitivity of collapses and revivals on the initial photon statistics, the cavity field damping mechanism is highlighted. For this purpose the basic model of Jaynes and Cummings has been extended and modified. Some multiatom effects are also discussed.

Optical Engineering•Jun 1, 1994•1 citation

Emission spectra for the Jaynes-Cummings model with intensity-dependent coupling

Vladimír Bužek, Igor Jex

The authors have investigated the spectrum of the emitted light by a single atom interacting with a single mode of the radiation in an ideal cavity via the intensity-dependent coupling (the Jaynes-Cummings model with intensity-dependent coupling see B. Buck, Phys. Lett., vol.A81, p.132 (1981)). From the authors' results it follows that in the resonant case the two-peaked structure of the spectrum associated with the vacuum-field Rabi splitting is preserved for any initial state of the radiation field (e.g. number state, thermal state, coherent state and the squeezed vacuum) with an arbitrary average number of photons.

Quantum Optics Journal of the European Optical Society Part B•Apr 1, 1990•29 citations
A spontaneously decaying two-level atom in an evacuated high-Q cavity undergoes Rabi oscillations. This phenomenon has been observed experimentally as enhanced or inhibited spontaneous emission. In the standard Jaynes-Cummings model the atom is assumed to interact with only a single cavity mode. By retaining the infinite set of cavity modes the propagation of the spontaneously emitted radiation may be calculated. Such an analysis yields a clear physical picture of Rabi oscillations. These vacuum-field Rabi oscillations are compared with Rabi oscillations of a one-electron atom induced by coherent radiation. We show that the same wave packet analysis explains both types of Rabi oscillation. The limit in which a multimode cavity may be approximated as a single-mode cavity is discussed.
We present a numerical and analytical study of a multimode Jaynes-Cummings model describing the spontaneous decay of a single atom in a high-Q cavity. The theory of cavity-modified spontaneous emission is discussed in terms of quantities that have clear physical interpretations: the photon wave packet radiated by the atom, its reflection by the cavity boundaries, and its reabsorption by the atom. Multimode corrections to the single-mode Jaynes-Cummings model are calculated. The multimode corrections are formulated in terms of quantities that may be calculated by solving the single-mode equations of motion.
We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. We show that for a strongly interacting qubit-photon system, the dynamics are captured by a reduced two-level model. In this framework, each level is defined as the product of the atomic excited state and a specific field mode, which takes the form of a multiphoton Fock-like state. In this picture, the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a coherent state with a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.
We revisit the problem of spontaneous emission by a two-level system in a cavity, concentrating in particular on those aspects associated with the finite propagation time of light between the atom and the cavity boundaries. We find that spontaneous emission always occurs first at the free space rate and there is then an abrupt change in these dynamics when light reflected by the cavity mirrors returns to the atom, leading to interference effects that result either in an enhancement or a reduction of this rate or in a periodic exchange of excitation between the atom and the cavity field. From this point of view, reversible spontaneous emission in terms of single-mode ``vacuum Rabi oscillations'' can be interpreted as resulting from the interference between the multimode partial waves reflected at the cavity mirrors and the instantaneously radiated light. \textcopyright{} 1996 The American Physical Society.
The Jaynes-Cummings model provides a useful means of studying several quantum electrodynamic effects in matter-radiation interaction. One such effect is the phenomenon of collapses and revivals of Rabi oscillations. Various aspects of this phenomenon are studied in terms of the dynamical evolution of the atom as well as the statistical properties of the field. In particular, the sensitivity of collapses and revivals on the initial photon statistics, the cavity field damping mechanism is highlighted. For this purpose the basic model of Jaynes and Cummings has been extended and modified. Some multiatom effects are also discussed.
The authors have investigated the spectrum of the emitted light by a single atom interacting with a single mode of the radiation in an ideal cavity via the intensity-dependent coupling (the Jaynes-Cummings model with intensity-dependent coupling see B. Buck, Phys. Lett., vol.A81, p.132 (1981)). From the authors' results it follows that in the resonant case the two-peaked structure of the spectrum associated with the vacuum-field Rabi splitting is preserved for any initial state of the radiation field (e.g. number state, thermal state, coherent state and the squeezed vacuum) with an arbitrary average number of photons.