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

Transition probabilities of atomic systems between moving walls

Rocío Jáuregui, Carlos Villarreal

Published Oct 1, 1996• 10 citations
Publisher

Abstract

The transition probabilities of a quantum system introduced between parallel conducting walls approaching or receding from each other with arbitrary constant relative speed are evaluated in the dipole approximation. The interaction with the vacuum fluctuations of the quantum electromagnetic field inside the box induces modifications in the spontaneous emission probabilities. While the transition probabilities in free space are recovered in the ultrarelativistic limit, an enhancement or inhibition of the spontaneous emission in the nonrelativistic limit is expected according to the dipole moment orientation of the detector. These results are discussed in the context of photon generation by the moving walls. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.3480

Related papers

Spontaneous emission by moving atoms

Pierre Meystre, Martin Wilkens

It is well known that spontaneous emission is not an intrinsic atomic property, but rather results from the coupling of the atom to the vacuum modes of the electromagnetic field. As such, it can be modified by tailoring the electromagnetic environment into which the atom can radiate. This was already realized by Purcell, who noted that the spontaneous emission rate can be enhanced if the atom placed inside a cavity is resonant with one of the cavity is resonant with one of the cavity modes, and by Kleppner, who discussed the opposite case of inhibited spontaneous emission. It has also been recognized that spontaneous emission need not be an irreversible process. Indeed, a system consisting of a single atom coupled to a single mode of the electromagnetic field undergoes a periodic exchange of excitation between the atom and the field. This periodic exchange remains dominant as long as the strength of the coupling between the atom and a cavity mode is itself dominant. 23 refs., 6 figs.

•Dec 31, 1994•0 citations

Spontaneous emission of a moving atom in vacuum

Wei Guo

Spontaneous emission of an excited two-level nonrelativistic atom is examined in the Schr\"odinger picture by treating the atom's external and internal degrees of freedom on the same quantum footing. After all atomic transitions that lead to the evolution of this atom-vacuum system are analyzed, it is found that the atom's spontaneous emission rate is reduced by its center-of-mass motion. It is also found that, as a result of the entanglement between atomic and photonic states, the spontaneous emission process cannot be explained as a process that takes place in one coordinate system moving with the atom but is observed in another stationary system.

Physical Review A•Jun 23, 2008•8 citations

A Quasi-Probability Approach to the Co-operative Spontaneous Emission

Kensuke S. Ikeda, H. Ito

The dynamics of the co-operative spontaneous emission from many two-level atoms is investigated by introducing a specific form of quasi-probability distribution which apparently excludes the vacuum fluctuation of the radiation field but includes the fluctuation of the atomic dipole moment. It is shown that the equation of motion for the random variables associated with the atom-field coupled system can be written in a quite classical form. As a result, the formula is derived for computing the multi-time correlation functions of the radiation field–essential to its coherence properties–which generalizes Bonifacio, Schwendimann and Haake's adiabatic “corresponding theorem”.

Progress of Theoretical Physics•Sep 1, 1975•7 citations

Induced and Spontaneous Emission in a Coherent Field. II

I. R. Senitzky

The interaction between the electromagnetic field and a number of identical atomic systems, individually characterized by an electric dipole moment and two energy levels, is analyzed for the case where the atomic systems are inside a lossy cavity and exposed to a coherent driving field, resonance being assumed between atomic system, cavity, and driving field.The problem of introducing loss into a quantum-mechanical formalism is treated first. Formal operator expressions are obtained for the field variables which include the absorption and the fluctuation (both thermal and quantum-mechanical) effects of the loss mechanism. Expectation values are then obtained for the field strength and the field energy which are valid for times short compared to the lifetime of the excited state. It is shown that the spontaneous-emission energy in the field increases initially as the square of the time and approaches a steady-state value after a transient period which is of the order of the cavity relaxation time. The induced emission contains two parts: incoherent emission induced by the thermal field, and coherent emission induced by the driving field. The incoherent induced-emission energy has the same time dependence as the spontaneous-emission energy, and the ratio of the former to the latter is the number of photons in the thermal (inducing) field. The coherent induced-emission energy does not approach a steady-state value, but, after a transient period, increases linearly with the time. The ratio of the coherent induced-emission energy to the spontaneous-emission energy is equal, initially, to the number of photons in the driving-field energy, but becomes $\ensuremath{\beta}t$ times as large after the transient period, where $\ensuremath{\beta}$ is the reciprocal of the cavity relaxation time.The expectation value of the rate of energy emission by the atomic systems is also obtained. It is shown that the ratio of the downward to the upward transition probabilities has the well-known value of $\frac{(n+1)}{n}$, where $n$ is the field energy in units of the photon energy, only in the absence of a coherent field.

Physical Review•Jul 15, 1959•45 citations

Spontaneous emission of an atom in the presence of an interface between two dielectrics

A. V. Kozlovskiĭ

The rate of spontaneous emission of an atom in the presence of an interface between two dielectrics was calculated using the quantum theory of electromagnetic radiation. Spatial distribution of the field for quasi-continuous spectrum inside an infinite cavity with ideally conducting walls was determined for multiple values of real refractive indices. Spontaneous emission in the continuous spectrum of the field was calculated using the known spatial Green’s function for a one-dimensional dielectric interface. The rate of spontaneous emission of an atom may either be higher or much lower than that in the free space, depending on the refractive indices and the distance between the atom and the interface between dielectrics.

Optics and Spectroscopy•Dec 1, 2001•0 citations

Quantum electrodynamics in the presence of dielectrics and conductors. III. Relations among one-photon transition probabilities in stationary and nonstationary fields, density of states, the field-correlation functions, and surface-dependent response functions

G. S. Agarwal

In this paper the physical entities such as transition probabilities and the density of states are related to appropriate electromagnetic-field correlation functions and to appropriate response functions. Such response functions have already been computed in a previous paper and therefore these can be used to obtain surface-dependent corrections. It is shown how the density of states and hence Planck's law depends on the presence of surfaces. I explicitly calculate the correction terms for the case of a small blackbody bounded by two plane conducting surfaces. An appreciable correction occurs if the linear dimensions of the blackbody are of the order of a wavelength. Next electric-dipole-type transitions in atomic systems are considered and a straightforward perturbation theory is used to obtain one-photon transition probabilities in terms of the surface-dependent response functions. As an illustration of the surface-dependent terms, the transitions in presence of a conducting surface are considered. The transition probabilities show a marked increase or decrease depending on whether the dipole transition is parallel or perpendicular to the surface. Both stationary and nonstationary fields are considered. As a special case of nonstationary fields, the transitions in a coherent field are considered in detail. It is also shown how the coherent radiation field in presence of dielectrics can be realized. It is found that if the radiation field, in arbitrary geometries, is initially in vacuum state then at later times it would be found in a coherent state if perturbed by an external ($c$-number) electromagnetic field.

Physical Review A•Jan 1, 1975•142 citations
The transition probabilities of a quantum system introduced between parallel conducting walls approaching or receding from each other with arbitrary constant relative speed are evaluated in the dipole approximation. The interaction with the vacuum fluctuations of the quantum electromagnetic field inside the box induces modifications in the spontaneous emission probabilities. While the transition probabilities in free space are recovered in the ultrarelativistic limit, an enhancement or inhibition of the spontaneous emission in the nonrelativistic limit is expected according to the dipole moment orientation of the detector. These results are discussed in the context of photon generation by the moving walls. \textcopyright{} 1996 The American Physical Society.
It is well known that spontaneous emission is not an intrinsic atomic property, but rather results from the coupling of the atom to the vacuum modes of the electromagnetic field. As such, it can be modified by tailoring the electromagnetic environment into which the atom can radiate. This was already realized by Purcell, who noted that the spontaneous emission rate can be enhanced if the atom placed inside a cavity is resonant with one of the cavity is resonant with one of the cavity modes, and by Kleppner, who discussed the opposite case of inhibited spontaneous emission. It has also been recognized that spontaneous emission need not be an irreversible process. Indeed, a system consisting of a single atom coupled to a single mode of the electromagnetic field undergoes a periodic exchange of excitation between the atom and the field. This periodic exchange remains dominant as long as the strength of the coupling between the atom and a cavity mode is itself dominant. 23 refs., 6 figs.
Spontaneous emission of an excited two-level nonrelativistic atom is examined in the Schr\"odinger picture by treating the atom's external and internal degrees of freedom on the same quantum footing. After all atomic transitions that lead to the evolution of this atom-vacuum system are analyzed, it is found that the atom's spontaneous emission rate is reduced by its center-of-mass motion. It is also found that, as a result of the entanglement between atomic and photonic states, the spontaneous emission process cannot be explained as a process that takes place in one coordinate system moving with the atom but is observed in another stationary system.
The dynamics of the co-operative spontaneous emission from many two-level atoms is investigated by introducing a specific form of quasi-probability distribution which apparently excludes the vacuum fluctuation of the radiation field but includes the fluctuation of the atomic dipole moment. It is shown that the equation of motion for the random variables associated with the atom-field coupled system can be written in a quite classical form. As a result, the formula is derived for computing the multi-time correlation functions of the radiation field–essential to its coherence properties–which generalizes Bonifacio, Schwendimann and Haake's adiabatic “corresponding theorem”.
The interaction between the electromagnetic field and a number of identical atomic systems, individually characterized by an electric dipole moment and two energy levels, is analyzed for the case where the atomic systems are inside a lossy cavity and exposed to a coherent driving field, resonance being assumed between atomic system, cavity, and driving field.The problem of introducing loss into a quantum-mechanical formalism is treated first. Formal operator expressions are obtained for the field variables which include the absorption and the fluctuation (both thermal and quantum-mechanical) effects of the loss mechanism. Expectation values are then obtained for the field strength and the field energy which are valid for times short compared to the lifetime of the excited state. It is shown that the spontaneous-emission energy in the field increases initially as the square of the time and approaches a steady-state value after a transient period which is of the order of the cavity relaxation time. The induced emission contains two parts: incoherent emission induced by the thermal field, and coherent emission induced by the driving field. The incoherent induced-emission energy has the same time dependence as the spontaneous-emission energy, and the ratio of the former to the latter is the number of photons in the thermal (inducing) field. The coherent induced-emission energy does not approach a steady-state value, but, after a transient period, increases linearly with the time. The ratio of the coherent induced-emission energy to the spontaneous-emission energy is equal, initially, to the number of photons in the driving-field energy, but becomes $\ensuremath{\beta}t$ times as large after the transient period, where $\ensuremath{\beta}$ is the reciprocal of the cavity relaxation time.The expectation value of the rate of energy emission by the atomic systems is also obtained. It is shown that the ratio of the downward to the upward transition probabilities has the well-known value of (n+1)n\frac{(n+1)}{n}n(n+1)​, where nnn is the field energy in units of the photon energy, only in the absence of a coherent field.
The rate of spontaneous emission of an atom in the presence of an interface between two dielectrics was calculated using the quantum theory of electromagnetic radiation. Spatial distribution of the field for quasi-continuous spectrum inside an infinite cavity with ideally conducting walls was determined for multiple values of real refractive indices. Spontaneous emission in the continuous spectrum of the field was calculated using the known spatial Green’s function for a one-dimensional dielectric interface. The rate of spontaneous emission of an atom may either be higher or much lower than that in the free space, depending on the refractive indices and the distance between the atom and the interface between dielectrics.
In this paper the physical entities such as transition probabilities and the density of states are related to appropriate electromagnetic-field correlation functions and to appropriate response functions. Such response functions have already been computed in a previous paper and therefore these can be used to obtain surface-dependent corrections. It is shown how the density of states and hence Planck's law depends on the presence of surfaces. I explicitly calculate the correction terms for the case of a small blackbody bounded by two plane conducting surfaces. An appreciable correction occurs if the linear dimensions of the blackbody are of the order of a wavelength. Next electric-dipole-type transitions in atomic systems are considered and a straightforward perturbation theory is used to obtain one-photon transition probabilities in terms of the surface-dependent response functions. As an illustration of the surface-dependent terms, the transitions in presence of a conducting surface are considered. The transition probabilities show a marked increase or decrease depending on whether the dipole transition is parallel or perpendicular to the surface. Both stationary and nonstationary fields are considered. As a special case of nonstationary fields, the transitions in a coherent field are considered in detail. It is also shown how the coherent radiation field in presence of dielectrics can be realized. It is found that if the radiation field, in arbitrary geometries, is initially in vacuum state then at later times it would be found in a coherent state if perturbed by an external (ccc-number) electromagnetic field.