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Spontaneous Decay of an Atom Near a Phase Conjugator

Henk F. Arnoldus, Thomas F. George

Published Mar 1, 1992• 0 citations
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Abstract

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.

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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

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

Henk F. Arnoldus, Thomas F. George

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)

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Permanent Electronic Excitation of a Molecular Layer on a Surface through Phase Conjugation

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Polarisation theory of phase conjugation in resonant non-degenerate four-wave mixing

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The theory of polarised light phase conjugation (PC) in non-degenerate four-wave mixing in a resonant medium has been developed in the irreducible tensorial formalism. The theory is applied to a wave with any polarisation in a resonant medium with levels of arbitrary momentum in the absence of pump-induced saturation effects. The formula for the non-linear susceptibility of the medium has been found and it is shown that the change of the polarisation at PC is essentially connected with the relaxation of the atomic multipole momenta (population, orientation and alignment). Wave equations were investigated for different pump-wave polarisations and three different physical mechanisms of the PC are discussed. The influence of the different relaxation rates of the atomic multipole momenta on the PC reflectivity has been investigated. The spectral dependence of the reflectivity and the spectral ranges which depend on the wave polarisation are found. For motionless atoms with small momenta (J 1 = 1 / 2 to J 2 = 1 / 2 , J 1 =1 to J 2 =0), exact formulae for the non-linear susceptibility of the medium as a function of pump intensity were found. The spontaneous decay of higher level to the lower one was taken into account. Because of optical pumping, saturation effects can be shown at considerably smaller intensities than in the usual two-level system. The exact expressions for the PC reflectivity at different polarisations of the pump waves are given.

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Peter W. Milonni, Erik J. Bochove, Richard J. Cook

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Journal of the Optical Society of America B•Oct 1, 1989•15 citations

Theoretical description of two-photon phase conjugation in polar molecules

Claudine Katan, J. P. Lavoine, A. A. Villaeys

Degenerate four-wave-mixing phase conjugation is analyzed in the case of two-photon transitions between levels having unequal dipole moments. The theoretical treatment is based upon a nonperturbative solution of the density matrix and does not require the rotating-wave approximation. We give an analytical expression for the polarization component oscillating at the field frequency for a medium excited by stationary waves. In the weak-probe-beam limit, the contributions in the direction of the probe and conjugated beams are evaluated. For instance, by using this two-photon process, instead of the usual single-photon one which is independent of the permanent dipole moments even in the strong-field limit, it is shown that lower intensities are sufficient to reach higher reflectivities. The influences of the permanent dipole moments, relaxation rates, and field frequency are also discussed.

Physical Review A•Aug 1, 1993•18 citations
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.
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.
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)
The dynamics of an atom (or molecule) located near the surface of a four-wave mixing phase conjugator is studied. This device consists of a slab of nonlinear material, which is illuminated by two strong counterpropagating laser beams. The atomic dipole field induces a polarization in the nonlinear material, and as a result, a phase-conjugated replica is emitted toward the atom. This effectively leads to a four-wave mixing process at the site of the atom, during which two pump photons are annihilated in favor of an electronic excitation of the atom. The mismatch in energy is emitted as a single fluorescent photon. In the steady state the atom acquires a finite population of the excited level, although there is no direct optical pumping of the atomic transition. It is shown that this population is determined entirely by the Fresnel reflection coefficients of the medium. In case of magnetic degeneracy of the levels, the distribution over the sublevels is furthermore determined by geometrical Clebsch−Gordan coefficients. Three cases of low angular momentum are worked out in detail, as examples.
The theory of polarised light phase conjugation (PC) in non-degenerate four-wave mixing in a resonant medium has been developed in the irreducible tensorial formalism. The theory is applied to a wave with any polarisation in a resonant medium with levels of arbitrary momentum in the absence of pump-induced saturation effects. The formula for the non-linear susceptibility of the medium has been found and it is shown that the change of the polarisation at PC is essentially connected with the relaxation of the atomic multipole momenta (population, orientation and alignment). Wave equations were investigated for different pump-wave polarisations and three different physical mechanisms of the PC are discussed. The influence of the different relaxation rates of the atomic multipole momenta on the PC reflectivity has been investigated. The spectral dependence of the reflectivity and the spectral ranges which depend on the wave polarisation are found. For motionless atoms with small momenta (J 1 = 1 / 2 to J 2 = 1 / 2 , J 1 =1 to J 2 =0), exact formulae for the non-linear susceptibility of the medium as a function of pump intensity were found. The spontaneous decay of higher level to the lower one was taken into account. Because of optical pumping, saturation effects can be shown at considerably smaller intensities than in the usual two-level system. The exact expressions for the PC reflectivity at different polarisations of the pump waves are given.
We present a quantum-electrodynamic theory of spontaneous emission in the presence of a phase-conjugating mirror (PCM) and show that the radiative relaxation rate is increased owing to the amplification of quantum noise by the PCM. For any finite value of the PCM reflectivity an atom in any initial state will relax to a steady state with a finite probability of being excited. In particular, there is a finite probability of spontaneous excitation of a ground-state atom placed near the PCM. The fluorescence spectrum of an atom near a PCM is generally described by two Lorentzian functions.
Degenerate four-wave-mixing phase conjugation is analyzed in the case of two-photon transitions between levels having unequal dipole moments. The theoretical treatment is based upon a nonperturbative solution of the density matrix and does not require the rotating-wave approximation. We give an analytical expression for the polarization component oscillating at the field frequency for a medium excited by stationary waves. In the weak-probe-beam limit, the contributions in the direction of the probe and conjugated beams are evaluated. For instance, by using this two-photon process, instead of the usual single-photon one which is independent of the permanent dipole moments even in the strong-field limit, it is shown that lower intensities are sufficient to reach higher reflectivities. The influences of the permanent dipole moments, relaxation rates, and field frequency are also discussed.