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Physica B Condensed Matter

Dynamics of a Landau–Zener non-dissipative system with fluctuating energy levels

Lukong Cornelius Fai, J.T. Diffo, Mathurin Esouague Ateuafack, Martin Tchoffo, Georges Collince Fouokeng

Published Aug 7, 2014• 7 citations
Publisher
DOI
10.1016/j.physb.2014.07.081

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The Landau-Zener transition in a two level system can be suppressed or enhanced by coupling to an environment, depending on the temperature and the environment spectral function. We consider the marginal spectral function, when the dissipation effects are important for arbitrarily slow motion. Landau-Zener transition rate demonstrates a non-trivial dependence of the on the ``bias'', i. e. on the rate of the two energy levels relative motion. The Landau-Zener transition is fully suppressed for the values of the bias below a threshold bias set by the coupling strength. Above the threshold, the transition rate for zero temperature is found using the instanton method. At finite temperature, the Landau-Zener transition rate has a non-monotonic dependence on the coupling strength, being suppressed at the strong coupling.
The Landau-Zener formula provides an analytical expression for the final excitation of a quantum system after passage of an avoided crossing of two energy levels. If the two levels correspond to a ground state and to an excited state which is subject to radiative decay, the probability of exciting the system by adiabatic passage of the level crossing is reduced. In this article we use a stochastic master equation to study the level crossing dynamics when the system is subject to continuous probing of the emitted radiation. The measurement back action on the system associated with the fluctuating homodyne detection record alters the level crossing dynamics, leading to significant excitation in spite of decay and imperfect transfer.
We establish a stochastic thermodynamics for a Fermionic level driven by a time-dependent force and interacting with initially thermalized levels playing the role of a reservoir. The driving induces consecutive avoided crossings between system and reservoir levels described within Landau-Zener theory. We derive the resulting system dynamics and thermodynamics and identify energy, work, heat, entropy, and dissipation. Our theory perfectly reproduces the numerically exact quantum work statistics obtained using a two point measurements approach of the total energy and provides an explicit expression for the dissipation in terms of diabatic transitions.