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Journal of Modern Optics

Photon Statistics of Atomic Fluorescence Near a Phase-conjugate Mirror or a Degenerate Parametric Amplifier

Benno H. W. Hendriks, Gerard Nienhuis

Published Oct 1, 1989• 7 citations
Publisher

Abstract

We have studied the modification of the photon statistics of the resonance fluorescence of a coherently driven two-state atom due to the presence of a phase-conjugate mirror (PCM) or a degenerate parametric amplifier (DPA). In both cases, we give explicit expressions for the n-fold intensity correlation function. We find that the photon statistics depends on the relative phase of the PCM or DPA and the driving field. The non-classical properties of the photon statistics can be enhanced because of the presence of the PCM or of the DPA, when the decay of the coherences is obstructed.

DOI
10.1080/09500348914551341

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We have studied the modification of the photon statistics of the resonance fluorescence of a coherently driven two-state atom due to the presence of a phase-conjugate mirror (PCM) or a degenerate parametric amplifier (DPA). In both cases, we give explicit expressions for the n-fold intensity correlation function. We find that the photon statistics depends on the relative phase of the PCM or DPA and the driving field. The non-classical properties of the photon statistics can be enhanced because of the presence of the PCM or of the DPA, when the decay of the coherences is obstructed.
Resonance fluorescence from a single two-level atom driven by a beam of squeezed light is studied in the weak field limit. We consider the situation where the atom is coupled to the ordinary vacuum and only a few field modes corresponding to the driving field are squeezed. The field produced by the degenerate optical parametric oscillator is used as the driving field. This driving field can be described in terms of two real independent Gaussian processes. Heisenberg equations of motion are solved in the steady-state, and analytic expressions for the fluorescent light intensity and the spectrum of fluorescent light are derived. We also consider photon statistics of fluorescent light. In particular, squeezing, antibunching, and sub-Poissonian statistics of fluorescent photons are discussed and analytic expressions for the quadrature variance and the two-time intensity correlation function are presented. Contrary to the case of coherent excitation the second-order intensity correlation function does not factorize.
Resonance fluorescence from a single two-level atom driven by a beam of squeezed light is studied in the weak-field limit. We consider the situation where the atom is coupled to the ordinary vacuum and only a few field modes corresponding to the driving field are squeezed. The field produced by the degenerate optical parametric oscillator is used as the driving field. Heisenberg equations of motion are solved in the steady-state and analytic expressions for the fluorescent-light intensity and the spectrum of fluorescent light are derived. We also consider photon statistics of fluorescent light. In particular, squeezing, antibunching, and sub-Poissonian statistics of fluorescent photons are discussed, and analytic expressions for the quadrature variance and the two-time intensity correlation function are presented. Contrary to the case of coherent excitation, the second-order intensity correlation function does not factorize. This and other differences are discussed, and curves are presented to illustrate the behavior of various quantities. We also present results for thermal excitation of the atom.
We present some effects of a squeezed vacuum on the photon statistics of a coherently driven two-level atom. The intensity-intensity correlation function g(2){\mathit{g}}^{(2)}g(2)(\ensuremath{\tau}), Mandel's response function Q(T), and the photon-counting distribution P(0,T) show the manifestation of the inhibition of atomic phase decay in the presence of a squeezed vacuum.
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.
Using the quantum theory of a non-degenerate parametric amplifier, we discuss the phase correlations between signal and idler modes well above threshold. Particular attention is paid to the influence which fluctuation of the driving laser has on these correlations. We point out that the signal and idler mode phase correlation may be tuned by control of the driving laser field intensity and linewidth. For coherent driving, the mode phases are negatively cross-correlated. We stress the qualitative importance of these mode correlations for a class of two-photon resonant excitation experiments in atoms. In particular, the non-degenerate parametric oscillator represents a concrete model of a source with negatively cross-correlated phase fluctuations.