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Physical Review A

Effect of dissipation on interference in phase space

Gerard J Milburn, Daniel F. Walls

Published Jul 1, 1988• 66 citations
Publisher

Abstract

We will determine the effect of dissipation and nonunit quantum efficiency on the oscillations in the photon-number distribution for squeezed states. These oscillations are evidence of interference in phase space and thus our results show the effect of dissipation on such interference effects. Our method, based on the Q function, enables a direct comparison of the quantum and classical phase-space descriptions.

DOI
10.1103/physreva.38.1087

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We will determine the effect of dissipation and nonunit quantum efficiency on the oscillations in the photon-number distribution for squeezed states. These oscillations are evidence of interference in phase space and thus our results show the effect of dissipation on such interference effects. Our method, based on the Q function, enables a direct comparison of the quantum and classical phase-space descriptions.
In this paper we discuss the nonclassical properties of quantum superpositions of coherent states of light. Using general expressions for the Wigner functions of superposition states we analyze the consequences of quantum interference between coherent states. We describe in detail nonclassical properties of a superposition of two coherent states. In particular, we study the oscillatory behavior of the photon number distribution of the even and odd coherent states. We show under which conditions a superposition of two coherent states can exhibit second- and fourth-order squeezing or sub-Poissonian photon statistics. We examine the sensitivity of nonclassical effects such as oscillations in the photon number distribution or second-order squeezing to dissipation. We demonstrate that quantities such as the photon number distribution and interferences in phase space are highly sensitive to even a quite small dissipative coupling, because they depend on all moments of the field observables, and higher moments decay more rapidly than lower moments. Quantities such as quadrature squeezing, on the other hand, are more robust against dissipation because they involve only lower moments. Finally, we find a remarkable effect whereby fourth-order squeezing is generated by damping.
We discuss a phase-space description of the photon number distribution of non-classical states which is based on Husimi's Q (α) function and does not rely on the WKB approximation. We illustrate this approach using the examples of displaced number states and two photon coherent states and show it to provide an efficient method for computing and interpreting the photon number distribution. This result is interesting in particular for the two photon coherent states which, for high squeezing, have the probabilities of even and odd photon numbers oscillating independently.
We derive the joint photon-number distribution for two-mode squeezed states with coherent amplitudes. For certain ranges of the parameters, the joint distribution exhibits nonclassical oscillations, which are the two-mode analog of the oscillations found in the single-mode case. These nonclassical oscillations are absent from the marginal distributions for each mode. The nonclassical features of the joint distribution may be explained using the interference--in--phase-space concept in four-dimensional phase space.
Photon distinguishability is a fundamental property manifested in multiphoton interference and one of the main sources of noise in any photonic quantum information processing. In this work, rather than relying on first-quantization methods, we build on a generating-function framework based on the phase-space formalism to characterize the effects of partial distinguishability on the interference of single-mode squeezed states. Our approach goes beyond commonly used models that represent distinguishability via additional noninterfering modes and captures genuine multiphoton interference effects induced by the overlap of the internal state of the photons. This description provides a clear physical account of how distinguishability gives rise to effective noise in Gaussian boson sampling protocols while enabling a systematic investigation of phase effects arising from the overlap of the internal states.
In experiments, pulses of two-mode squeezed light were generated by an optical parametric amplifier. For certain ranges of parameters the joint photon number distribution of two-mode squeezed coherent states exhibits nonclassical oscillations. The nonclassical features were explained using the interference-in-phase-space concept in four-dimensional phase space. We investigate joint phase distribution of two- mode squeezed coherent states for presence of peaks and attempt to relate the peaks to the manifest oscillations in the joint photon number distribution.