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Acta Optica Sinica

Generation and detection of macroscopically istinguishable quantum states

Zhu B, Z Wang

Published Jan 1, 1990• 0 citations
OpenAlex

Abstract

An exact solution for the nonlinear birefringent medium model is obtained by using SO(3) rotation group property. It is proved that coherent light entering the medium will evolve into a superposition of maorosoopioally distinguishable quantum states. In order to detect their interference fringes, holodyne detection scheme is used and the probability distribution for the output of homodyne detector is calculated when the intial states being linear and circular polarization coherent light.

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An exact solution for the nonlinear birefringent medium model is obtained by using SO(3) rotation group property. It is proved that coherent light entering the medium will evolve into a superposition of maorosoopioally distinguishable quantum states. In order to detect their interference fringes, holodyne detection scheme is used and the probability distribution for the output of homodyne detector is calculated when the intial states being linear and circular polarization coherent light.
Here it is shown that, for a wide class of nonlinear Hamiltonians, an essentially classical initial state will evolve into the coherent superposition of distinguishable quantum states. The detection of the interference fringes can be performed by beating the light leaving the nonlinear optical medium with light from a local oscillator. A model for the loss in the detection apparatus is introduced. The squeezed-vacuum technique is introduced finally as a means of enhancing the interference fringes displaying the distinguishable quantum state.
It is pointed out here that a coherent state propagating through an amplitude dispersive medium will, under suitable conditions, evolve into a quantum superposition of two coherent states 180\ifmmode^\circ\else\textdegree\fi{} out of phase with each other. The response of a homodyne detector to this superposition of macroscopically distinguishable states is calculated. Signatures which an experimentalist might look for in the homodyne detector's output in order to verify the generation of such states are described.
A four-wave mixer model is presented for which exact analytic results can be obtained in a regime where the usual perturbation procedures no longer apply. It is shown that under suitable conditions the output of such a four-wave mixer consists of a superposition of macroscopically distinguishable states. Such states can be identified with a homodyne detector which is able to observe the interference between the macroscopically distinguishable components. Further, it is shown that the device can act as an even-odd filter which will switch incoming pump light between two output ports depending on whether there is an even or odd number of pump photons.
We show that optical homodyne measurements of coherent states, and of superpositions of coherent states, can be described using the joint photon-number distribution for entangled coherent states. The quadrature-phase distribution interference fringes for superpositions of macroscopically distinct coherent states (the so-called ``Schr\"odinger cat states'') are shown to arise from interference in the photon-number distribution for entangled coherent states. The entangled squeezed states are introduced here as squeezed superposition states which are optically mixed with an antisqueezed coherent local oscillator field (squeezing in the other quadrature) at a beam splitter, and we discuss the connection between entangled squeezed states and squeezed-state homodyne detection of squeezed light. Finally the relationship between interference in phase space and fringes in the joint photon-number distribution for the entangled squeezed state is explored.