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انجمن اپتیک و فوتونیک ایران

A Non-classicality indicator for the properties of Squeezed photonic states in the Wigner representation

Farzaneh Rasti, Siamak Khademi, Parvin Sadeghi

Published Feb 15, 2014• 0 citations
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Abstract

Non-classicality indicators are widely applied to describe the physical properties of quantum states. One category of these indicators is defined in terms of negativities portion of Wigner distribution function. These indicators are not indicating to some quantum properties, e.g.: squeezing. Because the squeezing operations don’t effect on, the amount of negativities of Wigner distribution functions. Therefore the non-classicality indicators, e.g.: Kenfak or Benedict, which are working based on the negativities of distribution functions, cannot recognize the squeezing properties. In this paper a non-classicality indicator is introduced, in terms of the radial and angular distribution of absolute value of Wigner distribution function, which can recognize the squeezing properties, e.g.: squeezing parameter and squeezing angle. This non-classicality indicator is applied for the squeezed photonic states. We show that this indicator can evaluate the number of photons as well as the squeezing parameter and squeezing angle.

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Non-classicality indicators are widely applied to describe the physical properties of quantum states. One category of these indicators is defined in terms of negativities portion of Wigner distribution function. These indicators are not indicating to some quantum properties, e.g.: squeezing. Because the squeezing operations don’t effect on, the amount of negativities of Wigner distribution functions. Therefore the non-classicality indicators, e.g.: Kenfak or Benedict, which are working based on the negativities of distribution functions, cannot recognize the squeezing properties. In this paper a non-classicality indicator is introduced, in terms of the radial and angular distribution of absolute value of Wigner distribution function, which can recognize the squeezing properties, e.g.: squeezing parameter and squeezing angle. This non-classicality indicator is applied for the squeezed photonic states. We show that this indicator can evaluate the number of photons as well as the squeezing parameter and squeezing angle.
Many non-classicality indicators are used to measure quantum effects of different systems. Kenfack's and Sadeghi's non-classicality indicators are introduced in terms of the amount of Wigner function's negativities and interferences in phase space quantum mechanics, respectively. They are, effectively, applied for some real distribution functions. In this paper, we compared these non-classicality indicators for the entangled state of photonic number states in the Wigner, Husimi and Rivier representations. It is shown that for a two-level entangled state, Sadeghi's indicator has more benefits with respect to the Kenfack's indicator. For the two-level entangled state, we show a correspondence between the Sadeghi's non-classicality indicator and the Von Neumann entropy. It is also shown that for the superposition of squeezed number state the Sadeghi's (and no Kenfack's) non-classicality indicators is sensible with respect to the squeezing parameter for a superposition of squeezed number states.
Benedict et al. and Kenfack et al. advocated nonclassicality indicators based on the measurement of negativity of the Wigner distribution functions. These indicators have some applications in quantum mechanics and quantum optics. In this paper we define a nonclassicality indicator in terms of the interference in phase space, which is applicable to some real distribution functions including those of Wigner. As a special case one may reproduce the previous results using our indicator for the Wigner distribution functions. This indicator is examined for cases of the Schr\"odinger cat state and the thermal states and the results are compared with those obtained by previous methods. It seems that the physical behavior of nonclassicality indicators originates in the uncertainty principle. This is shown by an onto correspondence between these indicators and the uncertainty principle.
Based on the expressions of Wigner functions in Fock-spaces,we reconstruct the Wigner functions of photon-added and-subtracted states of squeezed vacuum states.Negativities of these Wigner functions numerically indicate that these states are really non-classical quantum states.We also discuss how these negativities depend on the photon number k added to and subtraced from the squeezed vacuum states.The negativities are greater when k is odd numbers than those when k is even numbers.The result provides a theoretical foundation for measuring these states.
In this paper, a quantitative investigation of the non-classical and quantum non-Gaussian characters of the photon-subtracted displaced Fock state [Formula: see text], where k is the number of photons subtracted and n is Fock parameter, is performed by using a collection of measures like Wigner logarithmic negativity, linear entropy potential, skew information-based measure, and relative entropy of quantum non-Gaussianity. It is noticed that the number of photons subtracted ( k) changes the nonclassicality and quantum non-Gaussianity in a significant amount in the regime of small values of the displacement parameter, whereas the Fock parameter ( n) presents a notable change in the large regime of the displacement parameter. In this respect, the role of the Fock parameter is found to be stronger as compared to the photon subtraction number. Finally, the Wigner function dynamics considering the effects of photon loss channel is used to show that the Wigner negativity can only be detected by highly efficient detectors.