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Physical Review A

Fluctuations and squeezing in resonance fluorescence emitted near a phase conjugator

Henk F. Arnoldus, Thomas F. George

Published Jul 1, 1992• 0 citations
Publisher

Abstract

Atomic resonance fluorescence, emitted near the surface of a four-wave-mixing phase conjugator, exhibits squeezing for certain values of the optical parameters of the incident laser field and for a certain range of the phase-conjugate reflectivity. A condition for the occurrence of squeezing is derived, and it is shown that the presence of the phase-conjugating medium tends to increase the quantum fluctuations, thereby diminishing the squeezing.

DOI
10.1103/physreva.46.679

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Atomic resonance fluorescence, emitted near the surface of a four-wave-mixing phase conjugator, exhibits squeezing for certain values of the optical parameters of the incident laser field and for a certain range of the phase-conjugate reflectivity. A condition for the occurrence of squeezing is derived, and it is shown that the presence of the phase-conjugating medium tends to increase the quantum fluctuations, thereby diminishing the squeezing.
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.
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.
Resonance fluorescence from a two-state atom has been predicted to exhibit quadrature squeezing below the Heisenberg uncertainty limit, provided that the optical parameters (Rabi frequency, detuning, laser linewidth, etc.) are chosen carefully. When the correlation between two quadratures of the radiation field does not vanish, however, the Heisenberg limit for quantum fluctuations might be an unrealistic lower bound. A generalized uncertainty relation, due to Schroedinger, takes into account the possible correlation between the quadrature components of the radiation, and it suggests a modified definition of squeezing. We show that the coherence between the two levels of a laser-driven atom is responsible for the correlation between the quadrature components of the emitted fluorescence, and that the Schrodinger uncertainty limit increases monotonically with the coherence. On the other hand, the fluctuations in the quadrature field diminish with an increasing coherence, and can disappear completely when the coherence reaches 1/2, provided that certain phase relations hold.
We present two approaches to the correlation properties of the fluorescence field emitted by a many-atom source. The first approach is an extension of resonance-fluorescence theory, while the second one is based on scattering theory. Both approaches lead to an understanding of why the ‘anomalous’ correlation properties associated with squeezing and antibunching appear when some phase-matching condition is satisfied and why this condition is the four-wave-mixing one. We show that the effect of atomic motion can be taken into account in the scattering approach and that the many-atom antibunching effect cannot be considered as Doppler-free.
Due to improvements in detector sensitivity, quantum noise is known to be the limiting factor of many lasers and other optical devices. In this work we present a fully quantum mechanical theory of multiwave mixing to study the effects of spontaneous emission noise on three- and four- wave mixing. The foundations of this theory have been presented in a series of papers1-3 demonstrating how such diverse topics as resonance fluorescence, saturation spectroscopy, phase conjugation, and squeezed states of light share a common origin.