We study the effect of Markovian environmental noise on the dynamics of a two-level quantum system which is steered adiabatically by an external driving field. We express the master equation taking consistently into account all the contributions to the lowest nonvanishing order in the coupling to the Markovian environment. We study the master equation numerically and analytically and we find that, in the adiabatic limit, a zero-temperature environment does not affect the ground-state evolution. As a physical application, we discuss extensively how the environment affects Cooper-pair pumping. The adiabatic ground-state pumping appears to be robust against environmental noise. In fact, the relaxation due to the environment is required to avoid the accumulation of small errors from each pumping cycle. We show that neglecting the nonsecular terms in the master equation leads to unphysical results, such as charge nonconservation. We discuss also a possible way to control the environmental noise in a realistic physical setup and its influence on the pumping process.
This paper presents the results of a functional-integral approach to the dynamics of a two-state system coupled to a dissipative environment. It is primarily an extended account of results obtained over the last four years by the authors; while they try to provide some background for orientation, it is emphatically not intended as a comprehensive review of the literature on the subject. Its contents include (1) an exact and general prescription for the reduction, under appropriate circumstances, of the problem of a system tunneling between two wells in the presence of a dissipative environment to the "spin-boson" problem; (2) the derivation of an exact formula for the dynamics of the latter problem; (3) the demonstration that there exists a simple approximation to this exact formula which is controlled, in the sense that we can put explicit bounds on the errors incurred in it, and that for almost all regions of the parameter space these errors are either very small in the limit of interest to us (the "slow-tunneling" limit) or can themselves be evaluated with satisfactory accuracy; (4) use of these results to obtain quantitative expressions for the dynamics of the system as a function of the spectral density $J(\ensuremath{\omega})$ of its coupling to the environment. If $J(\ensuremath{\omega})$ behaves as ${\ensuremath{\omega}}^{s}$ for frequencies of the order of the tunneling frequency or smaller, the authors find for the "unbiased" case the following results: For
s<1 the system is localized at zero temperature, and at finite
T relaxes incoherently at a rate proportional to $\mathrm{exp}\ensuremath{-}{(\frac{{T}_{0}}{T})}^{1\ensuremath{-}s}$. For
s>2 it undergoes underdamped coherent oscillations for all relevant temperatures, while for
1<s<2 there is a crossover from coherent oscillation to overdamped relaxation as
T increases. Exact expressions for the oscillation and/or relaxation rates are presented in all these cases. For the "ohmic" case,
s=1, the qualitative nature of the behavior depends critically on the dimensionless coupling strength $\ensuremath{\alpha}$ as well as the temperature
T: over most of the ($\ensuremath{\alpha}$,
T) plane (including the whole region $\ensuremath{\alpha}>1$) the behavior is an incoherent relaxation at a rate proportional to ${T}^{2\ensuremath{\alpha}\ensuremath{-}1}$, but for low
T and $0<\ensuremath{\alpha}<\frac{1}{2}$ the authors predict a combination of damped coherent oscillation and incoherent background which appears to disagree with the results of all previous approximations. The case of finite bias is also discussed.
A phase relaxation process of interacting two qubits is studied by means of the quantum master equation, where each qubit is influenced by an independent thermal reservoir. The damping operator of the quantum master equation consists of two parts; one includes the effects of the interaction between the qubits and the other does not. It is shown that the interaction significantly affects the phase relaxation process. The decoherence of entanglement is investigated for the two qubits initially prepared in the
X state.
In this paper, the problem of the decoherence of two\|state quantum systems interacting with a bath through an external controllable driving field is discussed. The time evolution of the off-diagonal elements of the density operator in two\|state quantum systems is obtained. The relation between the decoherence and the external controllable driving field is also obtained. Thus we establish the restriction equation that must be satisfied by the external controllable driving field when the decoherence is to vanish.
A general theory is presented for the treatment of decoherence of a multilevel quantum system (with many degrees of freedom) interacting with multi-bath reservoir and driven by ac fields. In this approach, the system is described by a reduced density operator and the multi-bath reservoir is characterized by a number of spectral densities. The reduced density operator is governed by the master equation in which the effect of ac driving fields and the leakage to non-computational states are included. The theory is applied to the study of decoherence of a two-dimensional (2D) SQUID flux qubit coupled to control and readout circuits. The predicted results are in very good agreement with available experimental results in the absence of driving fields and with the analytic results of a dissipative two-level system in the presence of weak driving fields. The relaxation and decoherence times versus the parameters and temperature of the control and readout circuits are also explored in details to facilitate the optimization of the 2D SQUID qubit.