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Journal of physics. A, Proceedings of the Physical Society. General

An exact analysis of spontaneous emission by a single two level atom in the rotating wave approximation. I. Analytic results

S. Swain

Published Nov 1, 1972• 36 citations
Publisher

Abstract

The problem of a single two level atom in its excited state, placed in a cavity in which no photons are present initially, and interacting with N modes of the electromagnetic field is solved exactly in the electric dipole, rotating wave approximation. Expressions for the energy eigenvalues and eigenvectors are derived, and an exact representation for the time dependent wavefunction of the system is given. These quantities are evaluated analytically for N=1,2 and 3, and the time dependent properties of the system for these values of N are investigated and discussed.

DOI
10.1088/0305-4470/5/11/007

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An exact analysis of spontaneous emission by a single two level atom in the rotating wave approximation II. Numerical results

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For Pt. I see ibid. vol.5, p.1587(1972). The problem considered is that of spontaneous emission by a single, two level atom which interacts with N modes of the electromagnetic field in the electric dipole, rotating wave approximation. The equations derived in Pt. I are solved numerically for N = 4,5,10,11,20,21 and 201 to find the eigenvalues and various time dependent properties of the system. The connection between this approach and conventional Wigner-Weisskopf theory is discussed.

Journal of physics. A, Proceedings of the Physical Society. General•Nov 1, 1972•12 citations

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On the Theory of Spontaneous Emission by a Single Atom Located in an Ideal Cavity

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Abstract With the help of the well‐known eigenfunctions for a two‐level system coupled to a single mode of the radiation field, the correlation functions for both the atomic dipole and the electric field oscillation are calculated, in rotating‐wave approximation, for an atom emitting spontaneously into an ideal cavity. Using the Eberly‐Wódkiewicz formalism, the corresponding spectra are evaluated in the long‐time, narrow‐band detection limit. The two spectra exhibit the same Rabi splitting, but the ratio of the strengths of the two lines is significantly different, in the off‐resonance case, for the dipole and the field oscillation.

Annalen der Physik•Jan 1, 1986•1 citation

Spontaneous emission of light from atoms: the model

P. Marecki, Nikodem Szpak

Abstract We investigate (non‐relativistic) atomic systems interacting with quantum electromagnetic field (QEF). The resulting model describes spontaneous emission of light from a two‐level atom surrounded by various initial states of the QEF. We assume that the quantum field interacts with the atom via the standard, minimal‐coupling Hamiltonian, with the A2 term neglected. We also assume that there will appear at most single excitations (photons). By conducting the analysis on a general level we allow for an arbitrary initial state of the QEF (which can be for instance: the vacuum, the ground state in a cavity, or the squeezed state). We derive a Volterra‐type equation which governs the time evolution of the amplitude of the excited state. The two‐point function of the initial state of the QEF, integrated with a combination of atomic wavefunctions, forms the kernel of this equation.

Annalen der Physik•Jun 21, 2005•2 citations
The problem of a single two level atom in its excited state, placed in a cavity in which no photons are present initially, and interacting with N modes of the electromagnetic field is solved exactly in the electric dipole, rotating wave approximation. Expressions for the energy eigenvalues and eigenvectors are derived, and an exact representation for the time dependent wavefunction of the system is given. These quantities are evaluated analytically for N=1,2 and 3, and the time dependent properties of the system for these values of N are investigated and discussed.
We present an analysis of the spontaneous emission by two identical two-level atoms a distance R apart, both of which are initially in the upper state. This analysis applies for two interacting atoms emitting both in a free space and in a cavity structure. In this paper we use the Heisenberg picture. We work under the dipole approximation and the rotating-wave approximation. We assume that all the field modes are initially in the vacuum state and the two atoms A and B are in the upper state. We will concentrate on the motion of the product of the dipole operators of two atoms. Because we have two excitations at t=0, and because we work under rotating-wave approximation, we will always have two excitations, i.e., two excited atoms, or one excited atom plus one photon, or two unexcited atoms with two photons.
A quantum model of N two-level atoms coupled by a single-mode radiation field under a restricted rotating-wave approximation is studied, assuming a dipole-interaction approximation and that the total number of excitations of the system is conserved. A solution is found for the case of spontaneous emission when the atoms are initially prepared in the state of complete inversion. This solution is valid for all times. A general solution of the model is also found for any initial configuration of the system, in the cases of both spontaneous and stimulated emission. This solution is in a closed form and valid for times tau < tau max .
We investigate (non-relativistic) atomic systems interacting with quantum electromagnetic field (QEF). The resulting model describes spontaneous emission of light from a two-level atom surrounded by various initial states of the QEF. We assume that the quantum field interacts with the atom via the standard, minimal-coupling Hamiltonian, with the A2 term neglected. We also assume that there will appear at most single excitations (photons). By conducting the analysis on a general level we allow for an arbitrary initial state of the QEF (which can be for instance: the vacuum, the ground state in a cavity, or the squeezed state). We derive a Volterra-type equation which governs the time evolution of the amplitude of the excited state. The two-point function of the initial state of the QEF, integrated with a combination of atomic wavefunctions, forms the kernel of this equation.
Abstract With the help of the well‐known eigenfunctions for a two‐level system coupled to a single mode of the radiation field, the correlation functions for both the atomic dipole and the electric field oscillation are calculated, in rotating‐wave approximation, for an atom emitting spontaneously into an ideal cavity. Using the Eberly‐Wódkiewicz formalism, the corresponding spectra are evaluated in the long‐time, narrow‐band detection limit. The two spectra exhibit the same Rabi splitting, but the ratio of the strengths of the two lines is significantly different, in the off‐resonance case, for the dipole and the field oscillation.
Abstract We investigate (non‐relativistic) atomic systems interacting with quantum electromagnetic field (QEF). The resulting model describes spontaneous emission of light from a two‐level atom surrounded by various initial states of the QEF. We assume that the quantum field interacts with the atom via the standard, minimal‐coupling Hamiltonian, with the A2 term neglected. We also assume that there will appear at most single excitations (photons). By conducting the analysis on a general level we allow for an arbitrary initial state of the QEF (which can be for instance: the vacuum, the ground state in a cavity, or the squeezed state). We derive a Volterra‐type equation which governs the time evolution of the amplitude of the excited state. The two‐point function of the initial state of the QEF, integrated with a combination of atomic wavefunctions, forms the kernel of this equation.