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Bulletin of the American Physical Society

Landau-Zener transitions in a two-level system that is coupled to a finite-temperature harmonic oscillator

Sahel Ashhab

Published Mar 5, 2015• 0 citations
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We consider the Landau-Zener problem for a two-level system (or qubit) when this system interacts with one harmonic oscillator mode that is initially set to a finite-temperature thermal equilibrium state. The oscillator could represent an external mode that is strongly coupled to the qubit, e.g., an ionic oscillation mode in a molecule, or it could represent a prototypical uncontrolled environment. We analyze the qubit's occupation probabilities at the final time in a number of regimes, varying the qubit and oscillator frequencies, their coupling strength, and the temperature. In particular, we find a surprising nonmonotonic dependence on the coupling strength and temperature.
Two-level system strongly coupled to a single resonator mode (harmonic oscillator) is a paradigmatic model in many subfields of physics. We study theoretically the Landau-Zener transition in this model. Analytical solution for the transition probability is possible when the oscillator is highly excited, i.e., at high temperatures. Then the relative change of the excitation level of the oscillator in the course of the transition is small. The physical picture of the transition in the presence of coupling to the oscillator becomes transparent in the limiting cases of slow and fast oscillator. A slow oscillator effectively renormalizes the drive velocity. As a result, the transition probability either increases or decreases depending on the oscillator phase. The net effect is, however, the suppression of the transition probability. On the contrary, a fast oscillator renormalizes the matrix element of the transition rather than the drive velocity. This renormalization makes the transition probability a nonmonotonic function of the coupling amplitude.