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Physical Review A

Conditional measurements as probes of quantum dynamics

Shabnam Siddiqui, Daniel B. Erenso, Reeta Vyas, Surendra Singh

Published Jun 17, 2003• 8 citations
Publisher

Abstract

We discuss conditional measurements as probes of quantum dynamics and show that they provide different ways to characterize quantum fluctuations. We illustrate this by considering the light from a subthreshold degenerate parametric oscillator. Analytic results and curves are presented to illustrate the behavior.
DOI
10.1103/physreva.67.063808

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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.
Summary form only given. Conditional quantum measurements allow the observation of quantum fluctuations which result from a measurement on a quantum system. These dynamics are characterized with time-ordered correlation functions. Control and observation of these dynamics presents a challenging new direction in cavity QED from both the technological and theoretical point of view. Wiseman has considered quantum limited feedback on a continuously monitored system to reduce the noise in the evolution of the system below the shot noise level. It is assumed that the flux of information out of the system is large. We study the opposite limit, where the amount of information available following the feedback is much less than one quantum.
Statistics of photons emitted by a nondegenerate parametric oscillator (NDPO) operating below threshold are discussed. Analytical expressions for the generating function are obtained when two nondegenerate modes of the NDPO are mixed on a photocathode or when the intensities of the two modes are added. From the generating function, photon-counting distributions and waiting-time distributions as measured by a detector placed outside the cavity are derived. Similarities and differences between the distributions for the NDPO, the degenerate parametric oscillator, degenerate four-wave mixing, nondegenerate four-wave mixing, and thermal light are also discussed.