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Squeezing in phase-conjugated resonance fluorescence

Henk F. Arnoldus

Published Jan 1, 1993• 0 citations
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Abstract

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.

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Journal of Physics B Atomic Molecular and Optical Physics•Jun 14, 1991•1 citation
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.
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.
An expression for the emitted fluorescence radiation by an atom near a phase conjugator is derived from a plane-wave expansion of the electric-field operator and Heisenberg's equation of motion for the annihilation operator. The result is compared to a solution that was found previously, based on the classical Maxwell equations. It is shown that both theories yield the same expression for the field in the radiation zone, in the limit of a transparent medium. This confirms the correctness of either approach to the problem of optical phase conjugation of atomic radiation.
An expression for the emitted fluorescence radiation by an atom near a phase conjugator is derived from a plane-wave expansion of the electric field operator and Heisenberg's equation of motion for the annihilation operator. The result is compared to a solution which was found previously, based on the classical Maxwell equations, where it is shown that both theories yield the same expression for the field in the radiation zone, in the limit of a transparent medium, which confirms the correctness of either approach to the problem of optical phase conjugation of atomic radiation.
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.
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.