Abstract :

Nonclassical light beams generated by degenerate and non-degenerate optical parametric oscillators (OPO) have played an important role in studies of nonclassical properties of light such as those reflected in squeezing, quantum entanglement, and other nonclassical features of photon statistics.  Fluctuation properties of these nonclassical light beams have been studied by using several different coherent state representations of the field density matrix. This talk will discuss the use of positive-P representation of the density matrix to map nonlinear quantum dynamics of an OPO onto c-number stochastic equations. By using the insights gained from these equations, exact analytical expressions for the positive-P functions both for the degenerate and nondegenerate OPOs can be obtained. From these functions simple expressions for various experimentally measurable quantities such as the mean and variance of the light intensity, quadrature squeezing, and photon number distributions can be derived. These expressions are valid below, near and above threshold of oscillation. How these properties are transformed as the oscillator makes a transition from below to above threshold will be discussed and the results for the OPOs will be compared and contrasted with those for the single-mode and two-mode lasers.

This will be followed by a discussion of how the quantities we have calculated are related to what is measure in the lab. A photoelectric detector exposed to the light emitted by the parametric oscillator transforms the incident photon sequences into a photoelectric pulse sequence.  By relating the photoelectron statistics to the photon statistics, we construct a physical picture of photoemissions from an optical parametric oscillator. The photoemission sequence and its time dependence then provide us the information on quantum dynamics of the system. Explicit examples of photoelectron statistics for the light from the parametric oscillators will be presented. 

 The third part will deal with quantum dynamics as reflected in the photoemission sequence and what we can learn from fluctuations and correlation of photoemission using conditional measurements.  Emission of a photon by a source signals a quantum fluctuation in progress. A measurement that is conditioned upon a photodetection allows us to follow the time evolution of the fluctuation. The measurement of the second order intensity correlation function is, in fact, a measurement of the fluctuations of light intensity following a conditioning photo-detection. The language of conditional measurements thus provides powerful conceptual tools for unraveling and understanding nonclassical features of quantum dynamics.  We will illustrate this by considering conditional measurements of intensity and field quadrature fluctuations on light generated by optical parametric oscillators.