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Chinese Physics B

Decoherence and evolution of a general quadratic state for amplitude decay

Zhi-Long Wan, Hong-Chun Yuan, Xiangyu Yin, Chang-Ying Wang

Published Jul 3, 2025• 0 citations
Publisher

Abstract

Abstract Making full use of the operator ordering method and the integration within ordered products, we obtain the analytical evolution law of a general quadratic state in the amplitude decay channel, and find that it is determined not only by the decay rate of the amplitude decay channel but also by the coefficients of the initial quadratic state. Further, the quantum statistical properties of the initial quadratic state for amplitude decay are investigated via its average photon number and photon-counting distribution, and its Wigner distribution function evolution is discussed in detail.

DOI
10.1088/1674-1056/adeb5f

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Abstract We theoretically investigate the nonclassicality of the squeezed Hermite polynomial state (SHPS) by examining the squeezing feature, the oscillation of photon-number distribution (PND) and the negativity of the Wigner function (WF). Our results indicate that the squeezing operation leads to a large squeezing degree and negative volume of the WF, but the Hermite polynomial creation operation has less impact on them, and the two operations have opposite modulations of the PND. In addition, we study the evolution law of the SHPS in the amplitude decay channel (ADC). It is found that the density-operator evolution is related to two conjugated operator Hermite polynomials within normal ordering, which brings about a new two-variable special function and its generating function. We also find that the analytical WF evolution is represented as the compact form of this new special function, and that the large squeezing is more robust against the decoherence of the SHPS in the ADC.
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