Decoherence of adiabatically steered quantum systems

Abstract

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.

Measurement scheme for the Lamb shift in a superconducting circuit with broadband environment

“…By adiabatically tuning the control fields of the sluice (left and right effective Josephson couplings and gate voltage of the island) along a closed path in the parameter space, the accumulated Berry phase [13] has been studied experimentally by observing the transferred Cooper pair current as a function of the total phase across the sluice [14]. Furthermore, the impact of the environmental degrees of freedom have been investigated in a setup where an additional resistor is coupled capacitively to the sluice island [15][16][17][18]. The peculiarity of this architecture is that the temperature of the system is determined by that of the resistor.…”

Decoherence of a solid-state qubit by different noise correlation spectra

“…When we departure from pure dephasing, i.e., when the noise-system interaction is not longitudinal, no exact analytic solution for the system time evolution is available even for the spinfluctuator model. In [11], authors resorted to a master equation approach to study the influence of an environment on a two-level system with an adiabatically changing external field where they have also considered temperature effects. However, authors resorted to a secular approximation for the ground state only, assuming that the excitation rates are exponentially small with respect to the relaxation ones in the quasi-stationary regime.…”

Environment-Governed Dynamics in Driven Quantum Systems

“…The main source of decoherence in the sluice is charge noise, due to fluctuations in the gate voltage [7,14]. We describe it by putting A ¼ z , ¼ 1 and g ¼ C g =C AE , where C g and C AE are the gate-to-island capacitance and total island capacitance, respectively.…”

“…While this approach has successfully described a variety of quantum systems, it only offers a limited insight into the dynamics of decoherence. A promising line of work developed in the last decade exploits the possibility of coupling the system to an engineered reservoir [4][5][6][7][8][9][10][11][12].As new and more accurate ways are found of harnessing the dynamic evolution of quantum systems, it becomes increasingly important to understand how the interaction with the environment is affected by a time-dependent modulation of the system parameters. Indeed, the study of dissipation in driven quantum systems is a longestablished topic [13] that keeps finding new applications to quantum pumping [14][15][16], quantum computation [17,18], and possibly even biological systems [19,20].…”

“…While this approach has successfully described a variety of quantum systems, it only offers a limited insight into the dynamics of decoherence. A promising line of work developed in the last decade exploits the possibility of coupling the system to an engineered reservoir [4][5][6][7][8][9][10][11][12].…”