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Journal of Optics B Quantum and Semiclassical Optics

Conditioned photon statistics of an optical parametric oscillator

Mambwe Mumba, Perry R. Rice

Published Jul 28, 2004• 0 citations
Publisher

Abstract

The output of a degenerate optical parametric oscillator (DOPO), for weak driving fields, is highly bunched. The photons tend to come out in pairs. Nonclassical behaviour is evident in the output of the DOPO, but usually involves interferometric investigations, as in the spectrum of squeezing, or a Mandel–Hong–Ou interferometer. We discuss a conditioned measurement of the second-order intensity correlation function g(2)(τ) that yields antibunching. By only measuring the second-order intensity correlation function g(2)(τ) after a photon has been detected, large bunching is turned into almost perfect antibunching.

DOI
10.1088/1464-4266/6/8/013

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The output of a degenerate optical parametric oscillator (DOPO), for weak driving fields, is highly bunched. The photons tend to come out in pairs. Nonclassical behaviour is evident in the output of the DOPO, but usually involves interferometric investigations, as in the spectrum of squeezing, or a Mandel–Hong–Ou interferometer. We discuss a conditioned measurement of the second-order intensity correlation function g(2)(τ) that yields antibunching. By only measuring the second-order intensity correlation function g(2)(τ) after a photon has been detected, large bunching is turned into almost perfect antibunching.
We consider two systems in the weak driving field limit. The first is an optical parametric oscillator, the transmitted field of which is highly bunched. We discuss a conditioned measurement of the second order intensity correlation function that yields antibunching. The second system we consider is a single two level atom inside a weakly driven cavity. Here we consider cross correlations between the transmitted and fluorescent fields. A strong asymmetry in delay time has been noted by Denisov et. al., here we find strong violations of a classical inequality for the cross correlation.
We consider intensity-field correlation functions for a two-level atom in a degenerate optical parametric oscillator (OPO), which would result from a conditioned homodyne measurement. Analytic results are obtained in the limit of weak driving fields using quantum trajectory methods for both the transmitted and fluorescent fields. This system is unique in that after detection of a photon, it is known that one excitation is in the system, in either the atom or cavity mode. We find large violations of inequalities satisfied by classical fields, for both transmitted and fluorescent fields. This is in contrast to the usual cavity QED system of an atom in a driven cavity where we do not find nonclassical behavior in the intensity-field correlation function in fluorescence. This is understood in terms of a relationship between the intensity-field correlation function and the second-order intensity correlation function, as well as the different amount of field-atom entanglement in the two systems. We show that for weak-field cavity QED one must have photon bunching to have nonclassical behavior in the intensity-field correlation function. We compare our results to those of an ordinary OPO. Finally, we also consider cross correlations, where we examine the transmitted (fluorescent) field conditioned by detection of a fluorescent (transmitted) photon.
Nonclassical effects exhibited by the homodyned field when light from an optical parametric oscillator (OPO) is mixed with coherent light from a local oscillator are discussed. Calculations are carried out exactly without making the strong local oscillator approximation. It is found that, depending upon the local oscillator phase and the parameters characterizing the light from the OPO, the second order intensity correlation function of the superposed field violates various classical inequalities g(2)(0) ≥ 1, g(2)(0) ≥g(2)(τ), and |g(2)(0) –1| ≥ | g(2)(τ)–1|. Thus we can see sub-Poissonian or super-Poissonian statistics and bunching or antibunching. We express the fields at the beam splitter in terms of independent real Gaussian stochastic processes with coherent component. Using these properties of the dynamical field variables, we derive analytic expressions for quantities directly measurable in photon counting experiments. It is found that the waiting time distribution shows two extrema at nonzero times. The second order intensity correlation function is found to vanish at nonzero time in violation of a classical inequality.
Photon statistics of the weak squeezed vacuum field from an optical parametric oscillatior (OPO) is investigated both in theory and by experiment . The strong photon bunching effect of weak squeezed vacuum field, which can be used as an important source in quantum optics and quantum measurement, was demonstrated. We have experimentally produced the weak squeezed vacuum at the center wavelength of D2 line of the cesium atom by the OPO operating far below the threshold . The second-order correlation function was measured based on the Hanbury-Brown-Twiss scheme, and the result is consistent with theoretical analysis.