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arXiv:0711.4633 · Physical Review A

Dynamics of periodic anticrossings: Decoherence, pointer states, and hysteresis curves

Péter Földi, M. G. Benedict, François Maria Peeters

Published Jan 16, 2008• 11 citations
arXivHTMLPDF

Abstract

We consider a strongly driven two-level (spin) system, with a periodic external field that induces a sequence of avoided level crossings. The spin system interacts with a bosonic reservoir which leads to decoherence. A Markovian dynamical equation is introduced without relying on the rotating wave approximation in the system-external field interaction. We show that the time evolution of the two-level system is directed toward an incoherent sum of periodic Floquet states regardless of the initial state and even the type of the coupling to the environment. Analyzing the time scale of approaching these time-dependent pointer states, information can be deduced concerning the nature and strength of the system-environment coupling. The inversion as a function of the external field is usually multivalued, and the form of these hysteresis curves is qualitatively different for low and high temperatures. For moderate temperatures we found that the series of Landau-Zener-St\"uckelberg-type transitions still can be used for state preparation, regardless of the decoherence rate. Possible applications include quantum information processing and molecular nanomagnets.

DOI
10.1103/physreva.77.013406

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We consider a strongly driven two-level (spin) system, with a periodic external field that induces a sequence of avoided level crossings. The spin system interacts with a bosonic reservoir which leads to decoherence. A Markovian dynamical equation is introduced without relying on the rotating wave approximation in the system-external field interaction. We show that the time evolution of the two-level system is directed toward an incoherent sum of periodic Floquet states regardless of the initial state and even the type of the coupling to the environment. Analyzing the time scale of approaching these time-dependent pointer states, information can be deduced concerning the nature and strength of the system-environment coupling. The inversion as a function of the external field is usually multivalued, and the form of these hysteresis curves is qualitatively different for low and high temperatures. For moderate temperatures we found that the series of Landau-Zener-St"uckelberg-type transitions still can be used for state preparation, regardless of the decoherence rate. Possible applications include quantum information processing and molecular nanomagnets.
We analyze the dynamics of a two-level system subject to driving by large-amplitude external fields, focusing on the resonance properties in the case of driving around the region of avoided level crossing. In particular, we consider three main questions that characterize resonance dynamics: (1) the resonance condition, (2) the frequency of the resulting oscillations on resonance, and (3) the width of the resonance. We identify the regions of validity of different approximations. In a large region of the parameter space, we use a geometric picture in order to obtain both a simple understanding of the dynamics and quantitative results. The geometric approach is obtained by dividing the evolution into discrete time steps, with each time step described by either a phase shift on the basis states or a coherent mixing process corresponding to a Landau-Zener crossing. We compare the results of the geometric picture with those of a rotating wave approximation. We also comment briefly on the prospects of employing strong driving as a useful tool to manipulate two-level systems.
We study the dynamics of open quantum systems driven by an external time-periodic force. Combining Floquet theory and the time-convolutionless projection operator technique we derive a time-local quantum master equation which exactly takes into account the periodic driving, while treating the system-environment interaction within second order in the coupling strength without performing the Markov approximation. The resulting equation of motion for the reduced density matrix is called Floquet time-convolutionless master equation. Employing the example of the driven spin-boson system, we demonstrate that this master equation is capable of describing strong non-Markovian effects, while yielding the Floquet-Lindblad master equation in the Markovian limit. A characteristic feature of memory effects in such driven dissipative systems is the emergence of sharp peaks of the trace-distance based non-Markovianity measure as a function of the driving amplitude, which can be traced back to quasienergy crossings leading to almost decoherence-protected subspaces through a quasienergy-induced dissipative decoupling mechanism.
The time evolution of low energy spin states of a single molecular magnet in a local electric field is investigated. The decoherence of the driven single molecular magnet weakly coupled to a thermal bosonic environment is analyzed by the second-order time-convolutionless non-Markovian master equation. If the characteristic time of the system is much smaller than the correlation time of the environment, the analytical expression of the reduced density matrix of the system is obtained. The non-Markovian dynamics of the spin states at low temperatures is induced by the memory effects in the decay rates. The non-Markovian oscillation of the Bloch vector is presented. The quantum decoherence can be effectively restrained with the help of the reasonable manipulation of the environment spectral density function and local electric field. The influence of the dissipation on the pointer states are investigated by the von Neumann entropy. The pointer states can be selected by the environment.
Stimulated by the experimental realization of spin-dependent tunneling via a gradient magnetic field [C. J. Kennedy et al., Phys. Rev. Lett. 111, 225301 (2013); M. Aidelsburger et al., Phys. Rev. Lett. 111, 185301 (2013)], we investigate the dynamics of Bloch oscillations and Landau-Zener tunneling of single spin-half particles in a periodic potential under the influence of a spin-dependent constant force. In analogy to the Wannier-Stark system, we call our system the Wannier-Zeeman system. If there is no coupling between the two spin states, the system can be described by two crossing Wannier-Stark ladders with opposite tilts. The spatial crossing between two Wannier-Stark ladders becomes a spatial anticrossing if the two spin states are coupled by external fields. For a wave packet away from the spatial anticrossing, due to the spin-dependent constant force, it will undergo spatial Landau-Zener transitions assisted by the intrinsic intraband Bloch oscillations, which we call the Bloch-Landau-Zener dynamics. If the interspin coupling is sufficiently strong, the system undergoes adiabatic Bloch-Landau-Zener dynamics, in which the spin dynamics follows the local dressed states. Otherwise, for nonstrong interspin couplings, the system undergoes nonadiabatic Bloch-Landau-Zener dynamics.
Some aspects of the Landau-Zener-type transition of a periodically driven two-level system with dephasing are clarified. Under the condition that the transition is well localized around the level-crossing region, the transition dynamics for the typical cases is described by simple formulas; namely, by the transfer-matrix method for the long-range coherence, by the application of the incoherent Landau-Zener formula for the short-range coherence, and by the strong-dephasing formula in the limit of complete decoherence.
We investigate Landau-Zener processes modeled by a two-level quantum system, with its finite bias energy varied in time and in the presence of a single broadened cavity mode at zero temperature. By applying the hierarchy equation method to the Landau-Zener problem, we computationally study the survival fidelity of adiabatic states without Born, Markov, rotating-wave, or other perturbative approximations. With this treatment it also becomes possible to investigate cases with very strong system-bath coupling. Different from a previous study of infinite-time Landau-Zener processes, the fidelity of the time-evolving state as compared with instantaneous adiabatic states shows nonmonotonic dependence on the system-bath coupling and on the sweep rate of the bias. We then consider the effect of applying a counterdiabatic driving field, which is found to be useful in improving the fidelity only for sufficiently short Landau-Zener processes. Numerically exact results show that different counterdiabatic driving fields can have very different robustness against environment effects. Lastly, using a case study, we discuss the possibility of introducing a dynamical decoupling field in order to eliminate the decoherence effect of the environment and, at the same time, to retain the positive role of a counterdiabatic field. Our work indicates that finite-time Landau-Zener processes with counterdiabatic driving offer a fruitful testbed to understand controlled adiabatic processes in open systems.