Non-Markovian qubit dynamics in a thermal field bath: Relaxation, decoherence, and entanglement

Abstract

We study the non-Markovian dynamics of a qubit made up of a two-level atom interacting with an electromagnetic field (EMF) initially at finite temperature. Unlike most earlier studies where the bath is assumed to be fixed, we study the coherent evolution of the combined qubit-EMF system, thus allowing for the back-action from the bath on the qubit and the qubit on the bath in a self-consistent manner. In this way we can see the development of quantum correlations and entanglement between the system and its environment, and how that affects the decoherence and relaxation of the system. We find non-exponential decay for both the diagonal and non-diagonal matrix elements of the qubit's reduced density matrix in the pointer basis. From the diagonal elements we see the qubit relaxes to thermal equilibrium with the bath. From the non-diagonal elements, we see the decoherence rate beginning at the usually predicted thermal rate, but changing to the zero temperature decoherence rate as the qubit and bath become entangled. These two rates are comparable, as was shown before in the zero temperature case [C. Anastopoulos and B. L. Hu, Phys. Rev. A 62 (2000) 033821]. On the entanglement of a qubit with the EMF under this type of resonant coupling we calculated, for the qubit reduced density matrix, the fidelity and the von Neumann entropy, which is a measure of the purity of the density matrix. The present more accurate non-Markovian calculations predict lower loss of fidelity and purity as compared with the Markovian results. Generally speaking, with the inclusion of quantum correlations between the qubit and its environment, the non-Markovian processes tend to slow down the drive of the system to equilibrium, prolonging the decoherence and better preserving the fidelity and purity of the system.

Exact non-Markovian master equation for a driven damped two-level system

“…[64], we introduce a couple of conjugate Grassmann variables ζ andζ imposing standard anticorrelation with the annihilation and creation operators of the system. Therefore, coherent states are defined as a tensor product of states generated by exponentiated operation of a creation operator and a suitable label on a chosen fiducial state [29,33,[65][66][67] …”

Bath dynamics in an exactly solvable qubit model with initial qubit-environment correlations

“…Its importance is dictated by the prospects of applications in quantum optics, quantum computing, quantum measurements and control [1,2], as well as by the necessity of a deeper understanding of the theory itself [3][4][5][6][7][8]. The dynamics of open quantum systems was studied in several aspects: (i) the effect of initial correlations between an open system and its environment has been investigated in [9,10]; (ii) a new viewpoint concerning the nature and the measure of non-Markovianity has been presented in [11,12]; (iii) the effect of non-equilibrium environment on quantum coherence and the level populations has been considered in [13,14].…”

“…Usually, when constructing a master equation for the reduced density matrix of an open system, one considers the bath to be at thermal equilibrium [1], even though there is a build-up of dynamical correlations [4,9] caused by the entanglement of quantum states. Moreover, even if the effect of non-equilibrium environment on the system behavior is not neglected [13], the intrinsic bath dynamics is beyond consideration, since the corresponding bath variables are always integrated out from the equations of motion. Although this approach seems to be quite natural as long as one studies solely the open system dynamics, the investigation of the bath evolution itself can undoubtedly be an interesting problem, yielding some useful hints about how to deal with more realistic systems, especially with those which possess slow relaxation to equilibrium and do not admit exact solutions.…”

Relaxation and decoherence in a resonantly driven qubit

“…For this reason, environment-induced decoherence has been and is still a main obstacle to the practical application of superconducting qubits in quantum computation. [2,13,14,15,16] The environment-induced decoherence of superconducting qubits has been extensively studied both theoretically [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33] and experimentally [2,8,13,21,25,34,35,36,37,38,39,40] in the absence of ac driving fields (free decay). Quite a few proposals, such as dynamical decoupling, [41,42,43,44,45,46,47,48] decoherence free subspaces, [49,50,51,52] spin echoes, …”