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Conditional Operator Shift: Generation of states and the Wigner Function Measure

Simone Silva Frutuoso de [UNESP] Souza

Published Mar 24, 2006• 0 citations
OpenAlex

Abstract

We present a feasible proposal for the construction of the conditional displacement operator using a Kerr medium between two beam splitters fed from coherent states highly excited. The device allows the implementation of the generation of a new class of states the quantized electromagnetic field (arbitrary superpositions of states with states moved) and the measurement of the Wigner function for arbitrary states. The application special case of the number of states and study their nonclassical properties were also considered.

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We present a feasible proposal for the construction of the conditional displacement operator using a Kerr medium between two beam splitters fed from coherent states highly excited. The device allows the implementation of the generation of a new class of states the quantized electromagnetic field (arbitrary superpositions of states with states moved) and the measurement of the Wigner function for arbitrary states. The application special case of the number of states and study their nonclassical properties were also considered.
The generation of arbitrary single-mode quantum states from the vacuum by alternate coherent displacement and photon adding as well as the measurement of the overlap of a signal with an arbitrarily chosen quantum state are studied. With regard to implementations, the transformation of the quantum state of a traveling optical field at an array of beam splitters is considered, using conditional measurement. Allowing for arbitrary quantum states of both the input reference modes and the output reference modes on which the measurements are performed, the setup is described within the concept of two-port non-unitary transformation, and the overall non-unitary transformation operator is derived. It is shown to be a product of operators, where each operator is assigned to one of the beam splitters and can be expressed in terms of an s-ordered operator product, with s being determined by the beam splitter transmittance or reflectance. As an example we discuss the generation of and overlap measurement with Schroedinger-cat-like states.
A scheme for generating Schr\"odinger-cat-like states of a single-mode optical field by means of conditional measurement is proposed. Feeding a squeezed vacuum into a beam splitter and counting the photons in one of the output channels, the conditional states in the other output channel exhibit a number of properties that are very similar to those of superpositions of two coherent states with opposite phases. We present analytical and numerical results for the photon-number and quadrature-component distributions of the conditional states and their Wigner and Husimi functions. Further, we discuss the effect of realistic photocounting on the states.
We construct a distinct class of nonlinear displaced Kerr states by application of the displacement operator upon a state which is prepared by sending the well-known photon-added coherent state through a normal Kerr medium. A sketch for the experimental setup for preparing the state is suggested. We evaluate some statistical properties such as the photon number distribution, Mandel’s Q parameter, Husimi-Q and Wigner functions, and quadrature squeezing for the nonlinear displaced Kerr state and then analyze the nonclassicality in terms of these standard parameters. We reduce the infinite-level problem to a truncated discrete two-level system by using a low Kerr parameter approximation and then convert the generated nonclassicality into bipartite entanglement between the two modes of an output state of a linear optical device.