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Annual Meeting Optical Society of America

Homodyne and heterodyne statistics of squeezed light from parametric oscillators

Reeta Vyas

Published Jan 1, 1991• 0 citations
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Abstract

We discuss homodyne and heterodyne statistics when squeezed light from a parametric oscillator is mixed with coherent light from a local oscillator. We also consider the case where the fields or the intensities of the two nondegenerate beams from a parametric oscillator are combined. By using a dynamic model of these beams we discuss photon sequences underlying these beams in terms of photoelectric pulse sequences recorded by a detector. Analytic expressions for quantities directly measurable in photon counting experiments are derived, using the method developed in our earlier investigations.1

DOI
10.1364/oam.1991.wl15

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We discuss homodyne and heterodyne statistics when squeezed light from a parametric oscillator is mixed with coherent light from a local oscillator. We also consider the case where the fields or the intensities of the two nondegenerate beams from a parametric oscillator are combined. By using a dynamic model of these beams we discuss photon sequences underlying these beams in terms of photoelectric pulse sequences recorded by a detector. Analytic expressions for quantities directly measurable in photon counting experiments are derived, using the method developed in our earlier investigations.1
Homodyne statistics when the light from a degenerate parametric oscillator (DPO) is mixed with coherent light from a local oscillator are discussed. By using dynamical models of these beams we discuss the photon sequences underlying the superposed beam in terms of photoelectric pulse sequences recorded by a detector. The field produced by the parametric oscillator is expressed in terms of two independent real Gaussian random variables. Using this property of the field variables, we derive the generating function for the photoelectron statistics analytically. From this generating function, expressions for the photoelectron-counting distribution, factorial moments, and the waiting-time distribution are derived. These quantities are directly measurable in photon-counting experiments. The results reported here are applicable to arbitrary strengths of the signal and the local-oscillator fields. We also show that, depending on the relative strength and relative phase between coherent light from the local oscillator and squeezed light from the DPO, the superposed light beam may exhibit many interesting nonclassical features. These and other effects are described and curves are presented to illustrate the behavior.
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.
We discuss two- and three-fold photon statistics for the squeezed light generated by subthreshold degenerate (DPO) and nondegenerate (NDPO) parametric oscillators. In higher-order statistics details of coherence properties are more strongly reflected than in the single-fold statistics. Many experiments use two-fold statistics to extract spectral information about the incident beam. We use phase-space representation to express the operator field variables in terms of independent Gaussian random processes.1 Using the Gaussian property of these field variables and making a Karhunen-Loeve expansion in terms of orthogonal functions, analytical expressions for the two- and three-fold generating functions for the DPO and the NDPO are obtained. From this generating function various statistical quantities such as factorial moments and joint photon counting probability distributions are calculated.
The theory of balanced homodyne and heterodyne detection is developed for inputs in which the signal field is in an arbitrary quantum state and the local-oscillator field is in a highly excited coherent state. Exact expressions are derived for the photocount moment-generating functions in the special case of a coherent signal. For more general signals, the first two moments of the photocount probability distribution are determined. The moments are evaluated for the examples of a coherent signal with a chaotic noise component, and for squeezed light derived from a degenerate and from a non-degenerate parametric amplifier. The corresponding moments for direct detection are obtained so that comparisons can be made. The Kelley-Kleiner photocount distribution formula is adapted to balanced detection schemes. Light beams are characterized throughout by their energy fluxes, and the theory accordingly describes steady-state experiments.