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Observation of atomic relaxation near an interface through detection of emitted fluorescence

Henk F. Arnoldus, Thomas F. George

Published Nov 1, 1989• 1 citation
OpenAlex

Abstract

Abstract : In this Comment we discuss the general features of spontaneous decay of an atom which is close to the surface of a dielectric (or metal) layer, and this is compared to atomic decay near a four-wave mixing phase conjugator. It is pointed out that the decay or relaxation constants can be expressed entirely in terms of the classical Fresnel coefficients for reflection and transmission of a plane wave, independent of what the explicit forms of these coefficients are. For decay near a dielectric the relaxation constants can be measured directly by counting the number of fluorescent photons per unit of time, after excitation by a laser. For relaxation near a phase conjugator this procedure would require a spectral resolution in the photon detection, since there are two distinct contributions to the fluorescent yield of a two-state atom. The two possible decay mechanisms have different relaxation constants and produce radiation with different frequencies. Atomic relaxation, Near an interface, Emitted fluorescence, Classical fresnel coefficients, Phase conjugator, Four-wave mixing. (jes)

Related papers

Spontaneous Decay of an Atom Near a Phase Conjugator

Henk F. Arnoldus, Thomas F. George

Relaxation of the density operator of an atom near a four-wave mixing phase conjugator (PC) is studied. The relaxation operator Tau can be expressed in the Cartesian components of the atomic dipole operator and correlation functions of the vacuum electromagnetic field. We evaluate these correlation functions in terms of the Fresnel coefficients for reflection and transmission of a polarized monochromatic plane wave. Our expression for Tau includes both linear and nonlinear interactions in the medium, and it reduces to well-known results in the limits of a pure dielectric, a mirror, and empty space. The example of a model two-state atom in combination with a model PC is worked out in detail. From the rate equations for the populations of the levels we infer that the relaxation acquires a contribution from both ordinary spontaneous decay and stimulated transitions which are induced by the PC. It is shown that an atom in its ground state has a finite probability of being excited, and that the excited state has a finite population in the long-time limit. We also work out the case of a degenerate two-level atom in combination with a realistic model of a transparent PC, and it is shown that our present results for the transition rates are consistent with earlier calculations of the fluorescence yield.

Unknow•Mar 1, 1992•0 citations

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

Phase-conjugated fluorescence

Henk F. Arnoldus, Thomas F. George

Fluorescent emission by an atom near a phase conjugator (PC) based on four-wave mixing is studied from first principles. The Maxwell-Heisenberg equations are solved for the radiation field, and with an asymptotic expansion an expression is derived for the field in the far zone. The total emitted power that can be measured by a detector in this region is evaluated, and it is found that this power acquires three distinct contributions. First, there are photons that are emitted by the atom directly towards the detector, and without any interaction with the medium. Second, there are photons that first travel towards the surface of the PC, and they have a certain probability of being reflected in the specular direction and towards the detector. The third kind of radiation consists of phase-conjugated photons, which are emitted independently of the previous ones. It is shown that the first two processes are a result of simple atomic spontaneous decay, but that the emission of a phase-conjugated fluorescent photon involves a three-photon process. The latter process has a probability proportional to the population of the atomic ground state. It is pointed out that an atom in its ground state polarizes the nonlinear medium of the PC, which subsequently can emit spontaneously two photons. An absorption-emission-absorption process by the atom then produces a fluorescent photon, together with a spontaneous excitation of the atom.

Physical Review A•Apr 1, 1991•21 citations

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

Henk F. Arnoldus, Thomas F. George

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

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

Quantum electrodynamics near an interface

J. M. Wylie, John E. Sipe

A quantum-mechanical linear-response formalism is used to calculate the frequency shift and lifetime of an excited atom near an arbitrary flat interface. The results depend on the frequency-dependent atom and field susceptibilities, and in the vicinity of an interface can be expressed in terms of the appropriate Fresnel reflection coefficients; the contributions from surface excitations are easily identified. As examples, we consider an atom above a metal and a dielectric waveguide.

Physical Review A•Sep 1, 1984•482 citations
Abstract : In this Comment we discuss the general features of spontaneous decay of an atom which is close to the surface of a dielectric (or metal) layer, and this is compared to atomic decay near a four-wave mixing phase conjugator. It is pointed out that the decay or relaxation constants can be expressed entirely in terms of the classical Fresnel coefficients for reflection and transmission of a plane wave, independent of what the explicit forms of these coefficients are. For decay near a dielectric the relaxation constants can be measured directly by counting the number of fluorescent photons per unit of time, after excitation by a laser. For relaxation near a phase conjugator this procedure would require a spectral resolution in the photon detection, since there are two distinct contributions to the fluorescent yield of a two-state atom. The two possible decay mechanisms have different relaxation constants and produce radiation with different frequencies. Atomic relaxation, Near an interface, Emitted fluorescence, Classical fresnel coefficients, Phase conjugator, Four-wave mixing. (jes)
Relaxation of the density operator of an atom near a four-wave mixing phase conjugator (PC) is studied. The relaxation operator Tau can be expressed in the Cartesian components of the atomic dipole operator and correlation functions of the vacuum electromagnetic field. We evaluate these correlation functions in terms of the Fresnel coefficients for reflection and transmission of a polarized monochromatic plane wave. Our expression for Tau includes both linear and nonlinear interactions in the medium, and it reduces to well-known results in the limits of a pure dielectric, a mirror, and empty space. The example of a model two-state atom in combination with a model PC is worked out in detail. From the rate equations for the populations of the levels we infer that the relaxation acquires a contribution from both ordinary spontaneous decay and stimulated transitions which are induced by the PC. It is shown that an atom in its ground state has a finite probability of being excited, and that the excited state has a finite population in the long-time limit. We also work out the case of a degenerate two-level atom in combination with a realistic model of a transparent PC, and it is shown that our present results for the transition rates are consistent with earlier calculations of the fluorescence yield.
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.
Fluorescent emission by an atom near a phase conjugator (PC) based on four-wave mixing is studied from first principles. The Maxwell-Heisenberg equations are solved for the radiation field, and with an asymptotic expansion an expression is derived for the field in the far zone. The total emitted power that can be measured by a detector in this region is evaluated, and it is found that this power acquires three distinct contributions. First, there are photons that are emitted by the atom directly towards the detector, and without any interaction with the medium. Second, there are photons that first travel towards the surface of the PC, and they have a certain probability of being reflected in the specular direction and towards the detector. The third kind of radiation consists of phase-conjugated photons, which are emitted independently of the previous ones. It is shown that the first two processes are a result of simple atomic spontaneous decay, but that the emission of a phase-conjugated fluorescent photon involves a three-photon process. The latter process has a probability proportional to the population of the atomic ground state. It is pointed out that an atom in its ground state polarizes the nonlinear medium of the PC, which subsequently can emit spontaneously two photons. An absorption-emission-absorption process by the atom then produces a fluorescent photon, together with a spontaneous excitation of the atom.
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.
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.