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Symmetries of spontaneous decay for atoms near any surface. Technical report

Henk F. Arnoldus, Thomas F. George

Published Jun 1, 1988• 0 citations
OpenAlex

Abstract

The structure of spontaneous decay of atoms in the vicinity of a surface is shown to be determined by spatial symmetries. The spontaneous-decay operator for a degenerate two level atom is derived, and with symmetry considerations the number of free parameters is reduced to two. Only the dimensionless and normalized inverse lifetimes b-parallel and b-perpendicular for a parallel and perpendicular dipole moment with respect to the surface, respectively, enter the expression for the relaxation operator for any atom near any surface. These two parameters incorporate the atom-surface-distance dependence of all Einstein coefficients for spontaneous decay, and all optical properties of the substrate material. It is shown that the specific features of spontaneous decay are mainly geometrical, and a consequence of symmetries of the vacuum radiation field, irrespective of the presence of the atom. With an example, it is shown how the parameters b-parallel and b-perpendicular can be calculated in a particular case. It is also pointed out that an explicit quantization of the radiation field can be avoided, even though the process of spontaneous emission is purely quantum mechanical.

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Spontaneous decay and atomic fluorescence near a metal surface of an absorbing dielectric

Henk F. Arnoldus, Thomas F. George

Abstract : Optical properties of an atom in the vicinity of a metal or dielectric are different from those in free space. The spontaneous decay of an atom with two degenerate levels is studied, where the relaxation operator is obtained as a function of the atom-surface separation and the complex bulk dielectric constant epsilon(omega). The Einstein coefficient A(m)(e) of an excited state jeme appears to depend on the magnetic quantum number me. A sum rule for A(m)(e) is derived, and from the rotational symmetry with respect to the surface normal it is found that A(m)(e) = A(-m)(e). A general expression for the fluorescent radiation field in the far zone is then derived, which incorporates the polarization properties of the fluorescence, as they are modified by the presence of the dielectric. It is shown that the angular distribution of the emitted intensity depends strongly on epsilon(omega), and it is pointed out how information about the substrate, e.g., epsilon(omega), can be extracted from the temporal statistical behavior of the emitted photons. It is emphasized that the major surface effects are purely geometrical, despite the essential quantum nature of the problem. Keywords: Spontaneous decay, Atomic fluorescence, Atom near metal surface, Absorbing dielectric, Einstein coefficient, Magnetic quantum number.

•Oct 1, 1987•0 citations

Spontaneous decay and atomic fluorescence near a metal surface or an absorbing dielectric

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Optical properties of an atom in the vicinity of a metal or dielectric are different from those in free space. The spontaneous decay of an atom with two degenerate levels is studied, where the relaxation operator is obtained as a function of the atom-surface separation and the complex bulk dielectric of an excited state \ensuremath{\Vert}${j}_{e}$${m}_{e}$〉 appears to depend on the magnetic is derived, and from the rotational symmetry with respect to the surface normal it is found . A general expression for the fluorescent radiation field in the far zone is then derived, which incorporates the polarization properties of the fluorescence, as they are modified by the presence of the dielectric. It is shown that the angular distribution of the emitted intensity depends strongly on \ensuremath{\epsilon}(\ensuremath{\omega}), and it is pointed out how information about the substrate, e.g., \ensuremath{\epsilon}(\ensuremath{\omega}), can be extracted from the temporal statistical behavior of the emitted photons. It is emphasized that the major surface effects are purely geometrical, despite the essential quantum nature of the problem.

Physical Review A•Feb 1, 1988•22 citations

Correlations between photons in resonance fluorescence emitted by an atom near a metal surface. Technical report

Henk F. Arnoldus, Thomas F. George

The photon correlations of resonance fluorescence emitted by a degenerate two-level atom near a metal surface are studied. An intense non-monochromatic optical laser drives a low-lying atomic transition, and the emitted fluorescence is detected by a photon counter. An expression for the spontaneous decay operator is derived, and it appears that the various substates of the upper level have a different lifetime due to the presence of the surface, or equivalently, due to the loss of spherical symmetry. The temporal photon correlation function is then evaluated in terms of a photon-emission operator and the time evolution operator for the atomic density matrix. The general theory is exemplified with a detailed elaboration of the j/sub g/ = 0 yields j/sub e/ = 1 transition, for which the two-photon correlation is obtained explicitly as a function of the lifetime A(h), depending on the atom surface distance h, the laser linewidth, the detuning from resonance, and the dipole-coupling strength with the external field.

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Correlations between photons in resonance fluorescence emitted by an atom near a metal surface

Henk F. Arnoldus, Thomas F. George

Abstract : The photon correlations of resonance fluorescence emitted by a degenerate two-level atom near a metal surface are studied. An intense non monochromatic optical laser drives a low lying atomic transition, and the emitted fluorescence is detected by a photon counter. An expression for the spontaneous decay operator is derived, and it appears that the various substates of the upper level have a different lifetime due to the presence of the surface, or equivalently, due to the loss of spherical symmetry. The temporal photon correlation function is then evaluated in terms of a photon-emission operator and the time evolution operator for the atomic density matrix. The general theory is exemplified with a detailed elaboration of the j sub g = 0 yields j sub e = 1 transition, for which the two-photon correlation is obtained explicitly as a function of the lifetime A(h), depending on the atom surface distance h, the laser linewidth, the detuning from resonance, and the dipole-coupling strength with the external field. Keywords: Photon correlations; Resonance fluorescence; Atom near metal surface; Loss of spherical symmetry; Substates; Different lifetimes.

•Oct 1, 1987•0 citations

Atomic multipole relaxation rates near surfaces

J. A. Crosse, Stefan Scheel

The spontaneous relaxation rates for an atom in free space and close to an absorbing surface are calculated to various orders of the electromagnetic multipole expansion. The spontaneous decay rates for dipole, quadrupole, and octupole transitions are calculated in terms of their respective primitive electric multipole moments and the magnetic relaxation rate is calculated for the dipole and quadrupole transitions in terms of their respective primitive magnetic multipole moments. The theory of electromagnetic-field quantization in magnetoelectric materials is used to derive general expressions for the decay rates in terms of the dyadic Green's function. We focus on the decay rates in free space and near an infinite half space. For the decay of atoms near to an absorbing dielectric surface, we find a hierarchy of scaling laws depending on the atom-surface distance $z$.

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Correlations between photons in resonance fluorescence emitted by an atom near a metal surface

Henk F. Arnoldus, Thomas F. George

The photon correlations of resonance fluorescence emitted by a degenerate two-level atom near a metal surface are studied. An intense nonmonochromatic optical laser drives a low-lying atomic transition, and the emitted fluorescence is detected by a photon counter. An expression for the spontaneous-decay operator is derived, and it appears that the various substates of the upper level have a different lifetime due to the presence of the surface, or equivalently, due to the loss of spherical symmetry. The temporal photon correlation function is then evaluated in terms of a photon-emission operator and the time-evolution operator for the atomic density matrix. The general theory is exemplified with a detailed elaboration of the ${j}_{g}$=0\ensuremath{\rightarrow}${j}_{e}$=1 transition, for which the two-photon correlation is obtained explicitly as a function of the inverse lifetime A(h), depending on the atom-surface distance h, the laser linewidth, the detuning from resonance, and the dipole-coupling strength with the external field.

Physical Review A•Feb 1, 1988•5 citations
The structure of spontaneous decay of atoms in the vicinity of a surface is shown to be determined by spatial symmetries. The spontaneous-decay operator for a degenerate two level atom is derived, and with symmetry considerations the number of free parameters is reduced to two. Only the dimensionless and normalized inverse lifetimes b-parallel and b-perpendicular for a parallel and perpendicular dipole moment with respect to the surface, respectively, enter the expression for the relaxation operator for any atom near any surface. These two parameters incorporate the atom-surface-distance dependence of all Einstein coefficients for spontaneous decay, and all optical properties of the substrate material. It is shown that the specific features of spontaneous decay are mainly geometrical, and a consequence of symmetries of the vacuum radiation field, irrespective of the presence of the atom. With an example, it is shown how the parameters b-parallel and b-perpendicular can be calculated in a particular case. It is also pointed out that an explicit quantization of the radiation field can be avoided, even though the process of spontaneous emission is purely quantum mechanical.
Abstract : Optical properties of an atom in the vicinity of a metal or dielectric are different from those in free space. The spontaneous decay of an atom with two degenerate levels is studied, where the relaxation operator is obtained as a function of the atom-surface separation and the complex bulk dielectric constant epsilon(omega). The Einstein coefficient A(m)(e) of an excited state jeme appears to depend on the magnetic quantum number me. A sum rule for A(m)(e) is derived, and from the rotational symmetry with respect to the surface normal it is found that A(m)(e) = A(-m)(e). A general expression for the fluorescent radiation field in the far zone is then derived, which incorporates the polarization properties of the fluorescence, as they are modified by the presence of the dielectric. It is shown that the angular distribution of the emitted intensity depends strongly on epsilon(omega), and it is pointed out how information about the substrate, e.g., epsilon(omega), can be extracted from the temporal statistical behavior of the emitted photons. It is emphasized that the major surface effects are purely geometrical, despite the essential quantum nature of the problem. Keywords: Spontaneous decay, Atomic fluorescence, Atom near metal surface, Absorbing dielectric, Einstein coefficient, Magnetic quantum number.
Optical properties of an atom in the vicinity of a metal or dielectric are different from those in free space. The spontaneous decay of an atom with two degenerate levels is studied, where the relaxation operator is obtained as a function of the atom-surface separation and the complex bulk dielectric of an excited state \ensuremath{\Vert}je{j}_{e}je​me{m}_{e}me​〉 appears to depend on the magnetic is derived, and from the rotational symmetry with respect to the surface normal it is found . A general expression for the fluorescent radiation field in the far zone is then derived, which incorporates the polarization properties of the fluorescence, as they are modified by the presence of the dielectric. It is shown that the angular distribution of the emitted intensity depends strongly on \ensuremath{\epsilon}(\ensuremath{\omega}), and it is pointed out how information about the substrate, e.g., \ensuremath{\epsilon}(\ensuremath{\omega}), can be extracted from the temporal statistical behavior of the emitted photons. It is emphasized that the major surface effects are purely geometrical, despite the essential quantum nature of the problem.
The photon correlations of resonance fluorescence emitted by a degenerate two-level atom near a metal surface are studied. An intense non-monochromatic optical laser drives a low-lying atomic transition, and the emitted fluorescence is detected by a photon counter. An expression for the spontaneous decay operator is derived, and it appears that the various substates of the upper level have a different lifetime due to the presence of the surface, or equivalently, due to the loss of spherical symmetry. The temporal photon correlation function is then evaluated in terms of a photon-emission operator and the time evolution operator for the atomic density matrix. The general theory is exemplified with a detailed elaboration of the j/sub g/ = 0 yields j/sub e/ = 1 transition, for which the two-photon correlation is obtained explicitly as a function of the lifetime A(h), depending on the atom surface distance h, the laser linewidth, the detuning from resonance, and the dipole-coupling strength with the external field.
Abstract : The photon correlations of resonance fluorescence emitted by a degenerate two-level atom near a metal surface are studied. An intense non monochromatic optical laser drives a low lying atomic transition, and the emitted fluorescence is detected by a photon counter. An expression for the spontaneous decay operator is derived, and it appears that the various substates of the upper level have a different lifetime due to the presence of the surface, or equivalently, due to the loss of spherical symmetry. The temporal photon correlation function is then evaluated in terms of a photon-emission operator and the time evolution operator for the atomic density matrix. The general theory is exemplified with a detailed elaboration of the j sub g = 0 yields j sub e = 1 transition, for which the two-photon correlation is obtained explicitly as a function of the lifetime A(h), depending on the atom surface distance h, the laser linewidth, the detuning from resonance, and the dipole-coupling strength with the external field. Keywords: Photon correlations; Resonance fluorescence; Atom near metal surface; Loss of spherical symmetry; Substates; Different lifetimes.
The spontaneous relaxation rates for an atom in free space and close to an absorbing surface are calculated to various orders of the electromagnetic multipole expansion. The spontaneous decay rates for dipole, quadrupole, and octupole transitions are calculated in terms of their respective primitive electric multipole moments and the magnetic relaxation rate is calculated for the dipole and quadrupole transitions in terms of their respective primitive magnetic multipole moments. The theory of electromagnetic-field quantization in magnetoelectric materials is used to derive general expressions for the decay rates in terms of the dyadic Green's function. We focus on the decay rates in free space and near an infinite half space. For the decay of atoms near to an absorbing dielectric surface, we find a hierarchy of scaling laws depending on the atom-surface distance zzz.
The photon correlations of resonance fluorescence emitted by a degenerate two-level atom near a metal surface are studied. An intense nonmonochromatic optical laser drives a low-lying atomic transition, and the emitted fluorescence is detected by a photon counter. An expression for the spontaneous-decay operator is derived, and it appears that the various substates of the upper level have a different lifetime due to the presence of the surface, or equivalently, due to the loss of spherical symmetry. The temporal photon correlation function is then evaluated in terms of a photon-emission operator and the time-evolution operator for the atomic density matrix. The general theory is exemplified with a detailed elaboration of the jg{j}_{g}jg​=0\ensuremath{\rightarrow}je{j}_{e}je​=1 transition, for which the two-photon correlation is obtained explicitly as a function of the inverse lifetime A(h), depending on the atom-surface distance h, the laser linewidth, the detuning from resonance, and the dipole-coupling strength with the external field.