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arXiv:1109.0655 · Physical Review A

Decoherence-free evolution of time-dependent superposition states of two-level systems and thermal effects

F. O. Prado, N. G. de Almeida, Eduardo I. Duzzioni, M. H. Y. Moussa, Celso J. Villas-Bôas

Published Jul 21, 2011• 5 citations
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Abstract

In this paper we detail some results advanced in a recent letter [Prado et al., Phys. Rev. Lett. 102, 073008 (2009).] showing how to engineer reservoirs for two-level systems at absolute zero by means of a time-dependent master equation leading to a nonstationary superposition equilibrium state. We also present a general recipe showing how to build nonadiabatic coherent evolutions of a fermionic system interacting with a bosonic mode and investigate the influence of thermal reservoirs at finite temperature on the fidelity of the protected superposition state. Our analytical results are supported by numerical analysis of the full Hamiltonian model.

DOI
10.1103/physreva.84.012112

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In this paper we detail some results advanced in a recent letter [Prado et al., Phys. Rev. Lett. 102, 073008 (2009).] showing how to engineer reservoirs for two-level systems at absolute zero by means of a time-dependent master equation leading to a nonstationary superposition equilibrium state. We also present a general recipe showing how to build nonadiabatic coherent evolutions of a fermionic system interacting with a bosonic mode and investigate the influence of thermal reservoirs at finite temperature on the fidelity of the protected superposition state. Our analytical results are supported by numerical analysis of the full Hamiltonian model.
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We study the quantum dynamics of an open network of two-level systems which is coupled to a correlated common environment represented by a bosonic field in a thermal equilibrium state. Extensive numerical simulations of the full second-order time-convolutionless quantum master equation for the density matrix of various types of networks are performed, in order to investigate dissipation and decoherence processes and, in particular, their dependence on the spatial separation of the network sites and on the speed of the bosonic field modes. In the limit of an infinite speed the influence of the environment disappears due to the emergence of a decoherence-free subspace, while the limit of zero speed corresponds to the case in which the network sites are coupled to independent reservoirs, a case which is much easier to treat numerically. The main result of the paper is a general intuitive criterion which states that the simpler model of independent reservoirs can be used as long as the network relaxation time is smaller than the time it takes for the modes to travel the minimal distance between the network sites.
We developed this work at the moment with the objective to resolver the master equation for both thermal reservoir: bosonic and fermionic, as well as the master equation in reservoirs of vacuum and of Fock compressed . the bosonic thermal reservoir is modeled by a collection of coupled harmonic oscillators and the fermionic reservoir by a collection of two-level atoms. We made use of the Jaynes-Cummings model and the Bohr, Bohr-Markov and Markov approaches. In the end we discussed the application to the master equation for two distinct phenomena, Cooling by Heating (CBH) analyzing average energy graphs to the atomic system versus number of photons, and the average energy of the bosonic system as a function of the mean number of phonons, we observed the negative temperature in the absolute scale due to the inversion of population of states in function of cooperativity, we also analyzed a signature of negative response in a three level system interacting in a optical cavity, that comes as a result of decrease in the output field intensity when the input field intensity is increased.
We propose experimental methods to engineer reservoirs at arbitrary temperature which are feasible with current technology. Our results generalize to mixed states the possibility of quantum state engineering through controlled decoherence. Finite-temperature engineered reservoirs can lead to the experimental observation of thermal entanglement---the appearance and increase of entanglement with temperature---to the study of the dependence of finite-time disentanglement and revival with temperature, quantum thermodynamical effects, and others, enlarging the comprehension of temperature-dependent entanglement properties. Our proposal is discussed in detail in two model systems, consisting of different modes of a single photon and a trapped-ion system.
We present a formalism to study many-particle quantum transport across a lattice locally connected to two finite, nonstationary (bosonic or fermionic) reservoirs, both of which are in a thermal state. We show that, for conserved total particle number, a system of nonlinear quantum-classical master equations describes the concurrent many-particle time evolution on the lattice and in the reservoirs. The finiteness of the reservoirs makes a macroscopic current emerge, which decreases exponentially in time and asymptotically drives the many-particle configuration into an equilibrium state where the particle flow ceases. We analytically derive the timescale of this equilibration process, and, furthermore, investigate the imprint of many-particle interferences on the transport process.
Time-evolution of the dispersive Jaynes–Cummings model interacting with a bosonic reservoir is considered in the presence of an initial correlation between the cavity field and reservoir. When there is at most one excitation in the whole system, the exact time-evolution can be obtained. The effects of the initial correlation on the decoherence of the two-level system and cavity field are investigated. Furthermore, the validity of the time-convolutionless quantum master equation in the second-order approximation with respect to the system-reservoir interaction is examined by means of the exact solution.