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Journal of Jiangxi Normal University

Entanglement and Statistical Properties of Squeezed Vacuum State after an Beam Splitter

Hu Pen

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

Based on phase space method,we study entanglement and statistical properties of squeezed vacuum state after an beam splitter.We adopt the criterion of logarithmic negativity to study the entanglement properties of the output light field.The results show that the maximum entanglement is found for the symmetrical beam splitter and the amount of entanglement increases with the squeezing parameter.In addition,we also use the Wigner-Weyl rules to study the statistical properties of light field in one of the output ports.It is found that the nonclassicality of the output field will change by adjusting the relative parameter of the input light field and the beam splitter.

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Based on phase space method,we study entanglement and statistical properties of squeezed vacuum state after an beam splitter.We adopt the criterion of logarithmic negativity to study the entanglement properties of the output light field.The results show that the maximum entanglement is found for the symmetrical beam splitter and the amount of entanglement increases with the squeezing parameter.In addition,we also use the Wigner-Weyl rules to study the statistical properties of light field in one of the output ports.It is found that the nonclassicality of the output field will change by adjusting the relative parameter of the input light field and the beam splitter.
Properties of the entanglement at the outputs of a cascade beam-splitter are investigated for two single-mode squeezed vacuum state inputs. It is shown that the entanglement depends on the squeezing amplitudes of the input states and the reflection coefficients of the cascade beam-splitter and the composite phase shift Δ between the cascade beam-splitter and the input fields has a great effect on the entanglement. In particular, the properties of the entanglement of a cascade beam-splitter differ from those of only one beam-splitter. A further method for manipulating entanglement by adjusting the parameters of the cascade beam-splitter and the input fields is proposed.
Abstract A theoretical scheme of generating a new kind of two-mode non-Gaussian entangled state is presented by means of beam splitters (BSs) and conditional measurement. Here, after detecting photon numbers at the output port of each BS with two kinds of two-mode squeezed vacuum-state inputs, the output state is proved to be two-variable Hermite polynomial excited squeezed vacuum states. Its success probability of detection, namely, normalization factor, is derived in compact expression related to the Jacobi polynomials. Based on the general expression of expectation value, the statistical properties are discussed by exploring the cross-correlation function and anti-bunching effect. The entanglement properties are also investigated by using the Shchukin–Vogel criteria and Einstein–Podolsky–Rosen correlation. The results show that the entanglement of the output state can be enhanced with the increasing photon detection number under the condition of simultaneously detecting the same photon number at the two output ports, which may have good potential for applications in the field of quantum information processing.
We investigate the coupling of the fully degenerate triple-photon state generated by three-mode spontaneous parametric down-conversion with the vacuum at a beam splitter via numerical modeling. By using fully degenerate triple-photon states with distinct pump phases as input states, four different squeezed states are extracted at the output, which can be referred to as zero-phase, $\ensuremath{\pi}/2$-phase, $\ensuremath{\pi}$-phase, and $3\ensuremath{\pi}/2$-phase positive Wigner squeezed states. The non-Gaussianity evolution during the coupling process is quantitatively analyzed via quantum relative entropy, and the entanglement between the two output modes is confirmed from an entropic perspective. Furthermore, the entanglement properties of the zero-phase and $\ensuremath{\pi}$-phase positive Wigner squeezed states at the third- and sixth-order moments are revealed by applying the partial transpose positive criterion based on the higher-order covariance matrix. In particular, it is found that the steerability of the two output modes at the third- and sixth-order moments can be dynamically controlled by adjusting the intensity of the input light and the transmission of the beam splitter. These results enrich the repertoire of squeezed states in quantum optics and offer a feasible approach for the deterministic preparation of non-Gaussian entanglement via coupling fully degenerate triple-photon states with vacuum.
Abstract In this work, we present a theoretical scheme for generating a new kind of tunable non-Gaussian entangled state, by means of beam splitters and multi-photon conditional measurement with two-mode squeezed vacuum state (TMSVS) inputs. The output state is proven to be two-variable Hermite polynomial excited squeezed vacuum states, whose success probability of detection relates to the Jacobi polynomials. We then mainly study the entanglement properties of the output state for the symmetric case quantified by the von Neumann entropy and Einstein–Podolsky–Rosen correlation. It is shown that the entropy of entanglement is valid for verifying the improvement of entanglement within a certain range of squeezing parameter and transmissivity, and the resulting state case may possess a stronger correlation than the initial TMSVS by increasing the transmissivity or photon number of detection. In addition, the violation of the Clauser–Horne–Shimony–Holt (CHSH) inequality for the output state is also evaluated in terms of Wigner representation in phase space. It is found that the negative region of Wigner function distribution becomes more visible with the increase of the photon number of detection, and the degree of the violation of the CHSH inequality significantly increases as the photon number of detection for the symmetrical case increases. The resulting state with highly nonclassical characteristics will provide a useful application in the fields of quantum information processing.
Any number state is truncated from the beam splitters' input coherent state by the conditional measurement if the coherent state and single-number state are the beam splitters' input states .The various properties of this kind of the truncated optical field state are studied, the results show that the output states truncated with vacuum state and the single-number state have nonclassical properties of squeeze and sub-Poissonian distribution. The output state has quantum entangle property if the input state of the beam splitter are the former truncated state and vacuum state, so we generate quantum entangle states and verify the nonclassical properties of the truncated state at the same time.