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Chinese Journal of Physics

Analytical Evolution of Displaced Thermal States for Amplitude Damping

Weifeng Wu

Published Aug 1, 2015• 1 citation
Publisher

Abstract

A displaced thermal state (DTS) is first introduced by Jeong et al. [Phys. Rev. Lett. 97, 100401 (2006)] and its superpositions can be used in transfer of nonclassicality. In this paper, the analytical evolution law of the DTS exposed to dissipative environments is obtained according to the Kraus operator for amplitude damping. The results manifestly show that, after undergoing the amplitude damping, the initial DTSs still keep mixed and thermal with the exponential decay due to amplitude damping. An appealing feature is that the entropy evolution in this process completely depends on the mixedness.

DOI
10.6122/cjp.20150522b

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A displaced thermal state (DTS) is first introduced by Jeong et al. [Phys. Rev. Lett. 97, 100401 (2006)] and its superpositions can be used in transfer of nonclassicality. In this paper, the analytical evolution law of the DTS exposed to dissipative environments is obtained according to the Kraus operator for amplitude damping. The results manifestly show that, after undergoing the amplitude damping, the initial DTSs still keep mixed and thermal with the exponential decay due to amplitude damping. An appealing feature is that the entropy evolution in this process completely depends on the mixedness.
We investigate how displaced thermal states (DTSs) evolve in a laser channel. Remarkably, the initial DTS, an example of a mixed state, still remains mixed and thermal. At long times, they finally decay to a highly classical thermal field only related to the laser parameters κ and g . The normal ordering product of density operator of the DTS in the laser channel leads to obtaining the analytical time-evolution expressions of the photon number, Wigner function, and von Neumann entropy. Also, some interesting results are presented via numerically investigating these explicit time-dependent expressions.
Using the correspondence of the operators between the real and fictitious modes, we find the Kraus operator-sum form of the analytical solution of the diffusion equation and obtain the evolution of a displaced thermal state in the diffusion channel. Also, we investigate the quantum statistical properties of the initial displaced thermal state and its von Neumann entropy evolution in the diffusion channel, especially find that the entropy evolution is affected by diffusion and mixedness, but without the displacement. These results provide theoretical basis for quantifying the evolved entropy in quantum information.
In this paper, the decoherence features of the photon-added displaced thermal state (PADTS) in the amplitude decay channel were studied by analytically and numerically investigating the time evolution of the Wigner function. The normal product representation of density for the PADTS is presented. The results indicate that the nonclassicality of PADTS can revive after disappearing with time. This kind of revival can maintain for a period of time and inevitably disappear eventually. However, we find that the operation of adding photons has the effect of reducing the decoherence rate of PADTS in the amplitude decay channel, although it also can decrease the PADTS’s nonclassicality markedly.
We investigate how the squeezed thermal state (STS) and squeezed number state (SNS) evolve undergoing decoherence in the laser process. Remarkably, the initial SNS, an example of a pure state, evolves into a mixed state, which turns out to be a Laguerre polynomial of combination of creation and annihilation operators within normal ordering; however, the STS, a mixed state, still keeps squeezed and thermal. At long times, these fields lose their nonclassical nature and decay to a highly classical thermal field. The normally ordered density operators of such states in the laser channel lead to deriving the analytical time-evolution expressions of the Wigner functions (WFs). Their nonclassicality is investigated in reference to the time-evolution WFs, which indicates that both of the WFs decay to the same thermal WF as a result of decoherence when the decay time t or the cavity loss κ of the laser is large enough.
We set up the fermionic thermal entangled state approach to address Fermi operator master equations for the amplitude- and phase-decay processes and find the explicit Kraus operator-sum representations (KOSR) describing time-evolution of Fermi systems. As an application of KOSR, the evolution law of the two-level atomic system interacting with a photon field in these two decay processes is analytically derived, which shows that the interaction system has a quantum jump as a result of dissipation, but it always remains unchanged in the phase-decay process.
Squeezing of a thermal bath introduces features absent in an open quantum system interacting with an uncorrelated (zero squeezing) thermal bath. The resulting dynamics, governed by a Lindblad-type evolution, extends the concept of a generalized amplitude damping channel, which corresponds to a dissipative interaction with a purely thermal bath. Here we present the Kraus representation of this map, which we call the squeezed generalized amplitude damping channel. As an application of this channel to quantum information, we study the classical capacity of this channel.