Thermalized displaced squeezed thermal states

Abstract

In the coordinate representation of thermofield dynamics, we investigate the thermalized displaced squeezed thermal state which involves two temperatures successively. We give the wavefunction and the matrix element of the density operator at any time, and accordingly calculate some quantities related to the position, momentum and particle number operator, special cases of which are consistent with the results in the literature. The two temperatures have different correlations with the squeeze and coherence components. Moreover, different from the properties of the position and momentum, the average value and variance of the particle number operator as well as the second-order correlation function are time-independent.Introducing finite temperature effects into squeezed states is important, because a squeezed state can possesses minimum uncertainty and squeezability and accordingly technological applicability [1] and, on the other hand, a finite-temperature influence on it is inevitable. This problem has received extensive investigations [2][3][4][5][6][7][8][9][10][11]. Analyzing these investigations, Ref. [2,3] divided the squeezed states with finite temperature effects into the thermalized squeezed states [4][5][6] and the squeezed thermal states [7][8][9][10][11]. The thermalized squeezed states and the squeezed thermal states are physically distinct states, albeit they are turned into each other by some parameter transformation [3]. Each of these two states has its several possible representations, and Ref.[2] gave a detailed discussion about them and elucidated their physical interpretations. From Ref.[2], it is not difficult to understand that the squeezed thermal states correspond to the output from a squeezed device whose input is a thermal chaotic state with Bose-Einstein distribution, while the thermalized squeezed states are prepared by thermalizing a squeezed state provided the thermalizing source is such a device that it can bring a vacuum state into a thermal chaotic state. Both the thermalized squeezed state and the squeezed thermal state are involved in one thermal source only. In this paper, we intend to consider yet another different state which we call the thermalized displaced squeezed thermal state (TDSTS). This state can be prepared by thermalizing a displaced squeezed thermal state, and obviously contains the thermalized displaced squeezed state (TDSS) and the displaced squeezed thermal state (DSTS) as its special cases. The TDSTS is involved in two thermal sources successively and perhaps is more practical than the TDSS and the DSTS, because, in general, there exist thermal noises for the input and output of a displacement-squeeze device which generates a displaced squeezed state, and furthermore the thermal noises have perhaps different temperatures for the input and output, respectively.In this paper, within the framework of thermofield dynamics [12,13], we shall first give the definition of the thermalized displaced squeezed state, then give the time-dependent wavefunction and calcula...

Quasi-Bell entangled coherent states and its quantum discrimination problem in the presence of thermal noise

“…where mode 3 is the fictitious mode for calculating the effect of thermal noise that affects only on mode 2, so that we have setT 23…”

“…, 0 (iv) thermal squeezed state -thermalizing a squeezed state -, [17][18][19][20][21] (v) squeezed thermal state -squeezing a thermal state -, 17,21 and so on. 22,23 Thus the thermalizing operator provides a useful tool in the analysis of optical quantum states in a thermal environment.…”