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Journal of the Optical Society of America B

Statistical properties of the squeezing-enhanced thermal state

Shuai Wang, Hong-Yi Fan

Published Dec 9, 2011• 12 citations
Publisher

Abstract

We introduce a new (to our best knowledge) type of squeezing-enhanced thermal states (SETS) that is generated by operating a new two-parameter generalized squeezing operator on a thermal (chaotic) field. By using the operator’s Weyl-ordering invariance under the similarity transformation and the Weyl correspondence scheme, we derive the normally ordered form of the density operator of SETS. Based on it, we study the resulting squeezing effects of the SETS and investigate its statistical properties by the second-order correlation function, photon-number distribution, and the Wigner function. Compared with the usual squeezed thermal state, SETS exhibits stronger squeezing and some new statistical properties. We find that the effect of the new type of squeezing operator is rotated squeezing.

DOI
10.1364/josab.29.000015

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We introduce a new (to our best knowledge) type of squeezing-enhanced thermal states (SETS) that is generated by operating a new two-parameter generalized squeezing operator on a thermal (chaotic) field. By using the operator’s Weyl-ordering invariance under the similarity transformation and the Weyl correspondence scheme, we derive the normally ordered form of the density operator of SETS. Based on it, we study the resulting squeezing effects of the SETS and investigate its statistical properties by the second-order correlation function, photon-number distribution, and the Wigner function. Compared with the usual squeezed thermal state, SETS exhibits stronger squeezing and some new statistical properties. We find that the effect of the new type of squeezing operator is rotated squeezing.
We put forward the photon-added squeezing-enhanced thermal states (PASETS) theoretically by adding photon to the squeezed enhancing thermal states (SETS) repeatedly. Based on the normally ordered density operator of PASETS, we investigate the nonclassical behavior of the PASETS by evaluating, both analytically and numerically, Mandel's Q-parameter, photon-number distribution (PND), and Wigner function (WF). It is found that smaller squeezing parameter r and thermal photon number nc can lead to more chance of the appearance of sub-Poissonian statistics. And it is shown that the PND of PASETS exhibit more remarkable oscillations than that of SETS in stronger squeezing case. The WF exhibit partial negativity in phase space and the squeezing parameter r can result in both squeezing and rotating effect. By investigating the fidelity between PASETS and SETS shows that the fidelity tender to steady values in the high value of squeezing parameter or thermal photon number. In addition, the decoherence effect on the PASETS is examined by the time-evolution of the analytical WF in thermal channel. The results show that the PASETS shall lose nonclassicality and non-Gaussianity and reduce to classical states with Gaussian distribution after sufficient time interaction with the thermal noise. And larger photon-added number or thermal photon number shall render shorter decoherence time.
Much attention has been given in the past to two classes of squeezed states: the squeezed vacuum and coherent states. Here we study the effects of squeezing on number states and on thermal field states. The statistical properties of these various squeezed states are discussed using the second-order correlation functions. The quasiprobabilities of the Wigner, Q, and positive P representations are calculated and compared for the squeezed states. The Glauber P representation for the squeezed thermal state explicitly shows the limit of its applicability. The photon number distributions of the squeezed number and squeezed thermal states are extensively discussed and new interference effects in phase space are shown to lead to highly structured number distributions.
One- and two-mode successively squeezed state, obtained through re-squeezing two single mode squeezed states by the two-mode squeezing operator, is studied in terms of the technique of integration within an ordered product (IWOP) of operators. We first derive the normally ordered form of this one- and two-mode successively squeezing operator, and then investigate the quantum statistical properties of the corresponding squeezed state. Particularly, we use the Weyl ordering invariance under a similar transformation to derive the analytical expression of its Wigner function, which seems very easy and concise. Finally, the experimental generation of one- and two-mode successively squeezed state is also proposed simply.
We investigate nonclassicality and decoherence of field states generated with the non-Gaussian operation of photon addition to a two-mode squeezed thermal state (TSTS) using the normally ordered density operator of the photon-added TSTS (PTSTS). The normalization factor of the PTSTS is just a Jacobi polynomial of the squeezing parameter γ and the average photon number n¯ of the thermal field. We show that the fields in such states exhibit remarkable quantum features, such as sub-Poissonian photon statistics, the anti-bunching effect, and photon-number distribution. The nonclassicality is discussed in phase space based on the partial negativity of the Wigner function (WF) with two-variable Hermite polynomials. The results show that the non-Gaussian WF always exhibits the quantum interference structure caused by the two-mode squeezing operation and has some negative regions for any value of n¯, γ, and the photon-addition numbers m, n. In addition, the effect of decoherence on the PTSTS in the thermal channel is studied by analytically deriving the time-evolution WF. We find that the WF becomes Gaussian (corresponding to a classical thermal state) at long times, losing its nonclassicality as a result of decoherence, and a larger m (or n) leads to a longer decoherence time κt.