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Journal of Modern Optics

Spectral and Temporal Distribution of Phase-conjugated Fluorescent Photons

Henk F. Arnoldus, Thomas F. George

Published Aug 1, 1991• 2 citations
Publisher

Abstract

Spontaneous emission of fluorescence radiation by an atom near the surface of a four-wave mixing phase conjugator is considered. It is shown that the spectral photon distribution consists of two Lorentzians, which have their peaks symmetrically located at the two sides of the pump frequency ¯ω of the nonlinear crystal. With ω0 the atomic resonance, the line at 2¯ω−ω0 is more than twice as strong as the line at ω0. When the phase-conjugate reflectivity exceeds unity, the temporal photon distribution exhibits nonclassical behaviour. Then, antibunching of photons prevails, and the photon statistics are sub-Poissonian.

DOI
10.1080/09500349114551601

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Statistics of Fluorescent Photons Emitted Near a Phase Conjugator.

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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 Journal of Physical Chemistry•Jan 1, 1996•0 citations
Spontaneous emission of fluorescence radiation by an atom near the surface of a four-wave mixing phase conjugator is considered. It is shown that the spectral photon distribution consists of two Lorentzians, which have their peaks symmetrically located at the two sides of the pump frequency ¯ω of the nonlinear crystal. With ω0 the atomic resonance, the line at 2¯ω−ω0 is more than twice as strong as the line at ω0. When the phase-conjugate reflectivity exceeds unity, the temporal photon distribution exhibits nonclassical behaviour. Then, antibunching of photons prevails, and the photon statistics are sub-Poissonian.
Abstract : Temporal photon correlations and photon count statistics of fluorescence radiation, emitted by an atom in the vicinity of a phase conjugator, are considered. The fluorescent intensity and the two-photon correlation function are expressed in terms of photon emission operators. An explicit evaluation shows their dependence on the phase-conjugate reflectivity of the surface. The variance of the photon count distribution for long counting times is expressed in terms of the Q-factor, which is evaluated as a function of the reflectivity. It appears that for a reflectivity larger than unity, the photon correlation displays antibunching and the statistics is sub-poissonian.
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.
Emission of resonance fluorescence by an atom near the surface of a four-wave mixing phase conjugator is considered. The dipole radiation field, regarded as a Heisenberg-operator field, is decomposed into plane waves with the aid of Weyl's representation of the Green's function for the wave equation. Each plane-wave component which is incident on the surface of the nonlinear medium, is reflected as its phase-conjugate image. Summation of all reflected plane waves then yields the phase conjugate replica of the incident dipole radiation. This field adds to the radiation which is emitted by the atom into the direction away from the medium. The condition under which squeezing occurs in the emitted resonance fluorescence is investigated.
Resonance fluorescence by an atom near the surface of a phase conjugator is studied. The atom is irradiated by a finite-linewidth laser beam, and the bandwidth is modelled by a randomly fluctuating phase. Expressions for the steady-state atomic density operator and the resonance fluorescence spectrum are obtained. For a small laser linewidth the spectrum contains two delta peaks: the usual peak at the laser frequency and its phase-conjugate image. In the limit of separated lines the spectrum consists of the Mollow triplet and its phase-conjugate replica. In the image triplet the positions of the fluorescence line and the three-photon line are reversed, as compared with the original triplet. Also, the intensity of the image spectrum is distributed differently over the three lines.
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.