Multitime correlation functions in nonclassical stochastic processes

Abstract

A general method is introduced for verifying multitime quantum correlations through the characteristic function of the time-dependent P functional that generalizes the Glauber-Sudarshan P function. Quantum correlation criteria are derived which identify quantum effects for an arbitrary number of points in time. The Magnus expansion is used to visualize the impact of the required time ordering, which becomes crucial in situations when the interaction problem is explicitly time dependent. We show that the latter affects the multi-time-characteristic function and, therefore, the temporal evolution of the nonclassicality. As an example, we apply our technique to an optical parametric process with a frequency mismatch. The resulting two-time-characteristic function yields full insight into the two-time quantum correlation properties of such a system.

arXiv comment6 pages, 3 figures

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Cited by in corpus (10)

• Quasi-probability distributions for observables in dynamic systems
• Bloch-Messiah decomposition and Magnus expansion for parametric down-conversion with monochromatic pump
• Time-dependent nonlinear Jaynes-Cummings dynamics of a trapped ion
• Relaxation of Multitime Statistics in Quantum Systems
• Quantum correlations in composite systems
• Time-dependent quantum correlations in phase space
• Multi-time correlations in the positive-P, Q, and doubled phase-space representations
• Classical evolution in quantum systems
• Quantum effects of operator time ordering in the nonlinear Jaynes-Cummings model
• Accessing the non-equal-time commutators of a trapped ion