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arXiv:1503.04919 · Journal of the Optical Society of America B

Generating Hermite polynomial excited squeezed states by means of conditional measurements on a beam splitter

Xue-xiang Xu, Hong‐Chun Yuan, Hong-Yi Fan

Published May 15, 2015• 19 citations
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Abstract

A scheme for conditional generating Hermite polynomial excited squeezed vacuum states (HPESVS) is proposed. Injecting a two-mode squeezed vacuum state (TMSVS) into a beam splitter (BS) and counting the photons in one of the output channels, the conditional state in the other output channel is just a HPESVS. To exhibit a number of nonclassical effects and non-Gaussianity, we mainly investigate the photon number distribution, sub-Poissonian distribution, quadrature component distribution, and Wigner function of the conditional HPESVS. We find that its nonclassicality closely relates to the control parameter of the BS, the squeezed parameter of TMSVS, and the photon number of conditional measurement. These further demonstrate that performing the conditional measurement on a BS is an effective approach to generate non-Gaussian state.

DOI
10.1364/josab.32.001146

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A scheme for conditional generating Hermite polynomial excited squeezed vacuum states (HPESVS) is proposed. Injecting a two-mode squeezed vacuum state (TMSVS) into a beam splitter (BS) and counting the photons in one of the output channels, the conditional state in the other output channel is just a HPESVS. To exhibit a number of nonclassical effects and non-Gaussianity, we mainly investigate the photon number distribution, sub-Poissonian distribution, quadrature component distribution, and Wigner function of the conditional HPESVS. We find that its nonclassicality closely relates to the control parameter of the BS, the squeezed parameter of TMSVS, and the photon number of conditional measurement. These further demonstrate that performing the conditional measurement on a BS is an effective approach to generate non-Gaussian state.
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In this work, the basic idea of the quantum scissors (QS) device is slightly modified to generate finite-dimensional quantum states by means of conditional measurements on beam splitters (BSs). It turns out that a QS device with two single-photon inputs and two single-photon detections is just a projection operator composed of the vacuum state, one-photon state, and two-photon state, depending upon the transmission coefficients of BSs. As the most general example, we consider the squeezed coherent state as the input state and derive the analytical expression of the output state. Its nonclassical characteristics are analyzed in detail by means of the average photon number, intensity gain, and Wigner function. In addition, we extend this technique to the two-mode squeezed vacuum state (TMSVS). The resulting state is just the generalized Bell state, containing only the twin vacuum, twin one-photon, and twin two-photon components, whose entanglement properties are quantified by the von Neumann entropy and Einstein–Podolsky–Rosen correlation. The results show that the entanglement of the truncated TMSVS is stronger than that of TMSVS within a certain range of squeezing parameter and transmissivity.
Abstract We use the quadrature measurement to generate the novel nonclassical states via the beam splitter with two input states, i.e., a Fock state and a vacuum state. It is interesting to find that the desired target states are the Hermite polynomial excited vacuum states. Our results have shown that the zero-position detection for the position detector, the little photon number in the input state, and the high transmittance of the beam splitter (BS) are beneficial to improve the detection efficiency of finding the output states. The proposed states quantum statistical properties and squeezing effects are also studied in detail via different criteria. Our numerical analysis demonstrates that the output quantum states are new nonclassical states. Compared with the method of photon catalysis, position detection is easier to realize in experiments. Therefore, the results in this paper shall provide theoretical support for the experimental generation of several new nonclassical states.
Abstract In this work, we theoretically construct an orthogonal state of a coherent state where the orthogonalizer is based on the Hermite polynomial excited operation with H m ( x ) being a Hermite polynomial of order m and creation operator , called the Hermite-excite-orthogonalized coherent state (HEOCS). Then, in comparison with the Hermite polynomial excited coherent state (HPECS), we numerically investigate their different nonclassical properties by examining several measurable features, such as photon number distribution, sub-Poisson statistics, the antibunching effect, the quadrature squeezing effect, and the negative Wigner function. The results demonstrate that both HEOCS and HPECS are non-Gaussian quantum states with highly nonclassical characteristics by improving and modulating the order of the Hermite polynomial and coherent amplitude, which indicates that performing the Hermite-excited operation on given Gaussian states is an effective approach to generating non-Gaussian states.
Abstract We propose a theoretical protocol to generate a kind of non-Gaussian state—a Laguerre polynomial excited coherent state (LPECS) by exploiting a two-mode squeezing transformation and a conditional measurement with a coherent state input. Then we investigate the nonclassical features of the LPECS according to the Glauber–Sudarshan P ( α ) function, photon number distribution, Mandel’s Q parameter, second-order correlation function, and squeezing properties as well as negative Wigner distribution. Our results show that the generated output state presents obvious nonclassical properties which can be modulated by a coherent amplitude, a squeezing parameter and a conditional measurement. In particular, the squeezing and negative Wigner function are clear.