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The Journal of Chemical Physics

Quantum theory of atomic fluorescence near a metal surface

Henk F. Arnoldus, Thomas F. George

Published Oct 15, 1987• 9 citations
Publisher

Abstract

Quantum electrodynamics of an atom near a surface is a timely problem in current theoretical research. It appears, however, that a full dynamical theory, which includes both the time evolution of the atomic density operator and the details of the fluorescence radiation (temporal photon distribution) has never been formulated. In this paper the quantum theory of an atom near a perfect conductor is presented, and it is indicated how the formalism can be modified to account for more realistic optically active substrates. An expression is derived for the atomic spontaneous-decay Liouville operator from the Hamiltonian, which recovers the familiar results for the lifetimes and energy shifts. Furthermore, the emitted power is calculated as a function of time from the explicit expression for the radiation field. Comparison of the atomic-decay rates with the power of the emitted radiation shows the consistency of the theory, as far as the properties of the fluoresence are concerned. An unusual energy interference in the fluorescence, which is emitted by a multilevel atom, is predicted. Similarities and discrepancies with other theories are pointed out, and it is shown that especially the mirror theory has a very restricted applicability.

DOI
10.1063/1.452884

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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.

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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

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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

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

Quantum electrodynamics in the presence of dielectrics and conductors. IV. General theory for spontaneous emission in finite geometries

G. S. Agarwal

A quantum-electrodynamic theory of spontaneous emission in presence of dielectrics and conductors is developed. The theory makes use of the master-equation techniques and the response-function formalism of part I of this series of papers. Various observable entities such as damping coefficients (lifetimes), Lamb shifts, and frequency shifts are related to the appropriate surface-dependent response functions. The results are valid for arbitrary geometries (involving linear dielectrics) and naturally contain, as a special case, the usual results of spontaneous emission in free space. As explicit examples we consider a two-level atom (also the multilevel atom) in presence of a plane dielectric interface and between two conducting plates. Formulas for the shifts and widths are given and their asymptotic behavior for large and short distances is discussed. The behavior when the atom is embedded inside the dielectric is different than when the atom is outside the dielectric. The origin of coherence in the present model is discussed and the coherence effects in this model are contrasted with those in Dicke's model. The results are also compared with those obtained by the image method. Exact expressions for the operator radiation-reaction fields are obtained in terms of the atomic polarization operators and response functions. Approximate results for such fields are also given. The far-zone behavior of the radiation fields is obtained in terms of response functions and the polarization operators. Some of the normally ordered correlation functions are also calculated. The connection of some of the theoretical results with a recent experimental work of Carniglia, Mandel, and Drexhage is discussed. The effect of anisotropy of the dielectric function on the lifetimes as well as on the far-field correlation functions is also considered. Finally the contribution to the shifts and widths due to the excitation of surface polariton modes is computed and the results are compared with those obtained by the quantization of surface polariton field. It is found that such surface modes contribute significantly to widths.

Physical Review A•Oct 1, 1975•224 citations
Quantum electrodynamics of an atom near a surface is a timely problem in current theoretical research. It appears, however, that a full dynamical theory, which includes both the time evolution of the atomic density operator and the details of the fluorescence radiation (temporal photon distribution) has never been formulated. In this paper the quantum theory of an atom near a perfect conductor is presented, and it is indicated how the formalism can be modified to account for more realistic optically active substrates. An expression is derived for the atomic spontaneous-decay Liouville operator from the Hamiltonian, which recovers the familiar results for the lifetimes and energy shifts. Furthermore, the emitted power is calculated as a function of time from the explicit expression for the radiation field. Comparison of the atomic-decay rates with the power of the emitted radiation shows the consistency of the theory, as far as the properties of the fluoresence are concerned. An unusual energy interference in the fluorescence, which is emitted by a multilevel atom, is predicted. Similarities and discrepancies with other theories are pointed out, and it is shown that especially the mirror theory has a very restricted applicability.
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 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.
A quantum-electrodynamic theory of spontaneous emission in presence of dielectrics and conductors is developed. The theory makes use of the master-equation techniques and the response-function formalism of part I of this series of papers. Various observable entities such as damping coefficients (lifetimes), Lamb shifts, and frequency shifts are related to the appropriate surface-dependent response functions. The results are valid for arbitrary geometries (involving linear dielectrics) and naturally contain, as a special case, the usual results of spontaneous emission in free space. As explicit examples we consider a two-level atom (also the multilevel atom) in presence of a plane dielectric interface and between two conducting plates. Formulas for the shifts and widths are given and their asymptotic behavior for large and short distances is discussed. The behavior when the atom is embedded inside the dielectric is different than when the atom is outside the dielectric. The origin of coherence in the present model is discussed and the coherence effects in this model are contrasted with those in Dicke's model. The results are also compared with those obtained by the image method. Exact expressions for the operator radiation-reaction fields are obtained in terms of the atomic polarization operators and response functions. Approximate results for such fields are also given. The far-zone behavior of the radiation fields is obtained in terms of response functions and the polarization operators. Some of the normally ordered correlation functions are also calculated. The connection of some of the theoretical results with a recent experimental work of Carniglia, Mandel, and Drexhage is discussed. The effect of anisotropy of the dielectric function on the lifetimes as well as on the far-field correlation functions is also considered. Finally the contribution to the shifts and widths due to the excitation of surface polariton modes is computed and the results are compared with those obtained by the quantization of surface polariton field. It is found that such surface modes contribute significantly to widths.