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Physics Letters A

Lie algebras for some specific dissipative Landau–Zener problems

M. B. Kenmoe, S. E. Mkam Tchouobiap, J. E. Danga, C. Kenfack-Sadem, Lukong Cornelius Fai

Published Dec 23, 2014• 6 citations
Publisher
DOI
10.1016/j.physleta.2014.12.032

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A qubit may undergo Landau‐Zener transitions due to its coupling to one or several quantum harmonic oscillators. First we show that for a qubit coupled to one oscillator, Landau‐Zener transitions can be used for single‐photon generation and for the controllable creation of qubit‐oscillator entanglement, with state‐of‐the‐art circuit QED as a promising realization. Second, for a qubit coupled to two cavities, we show that Landau‐Zener sweeps of the qubit are well suited for the robust creation of entangled cavity states, in particular symmetric Bell states, with the qubit acting as the entanglement mediator. Finally, for a qubit coupled to an environment or bath we propose to employ dissipative Landau‐Zener sweeps of the qubit for the detection of bath properties. At the heart of our proposals lies the calculation of the exact Landau‐Zener transition probability for the qubit, by summing all orders of the corresponding series in time‐dependent perturbation theory.
We investigate the dissipative influence of environmental fluctuations on the dynamics of driven quantum systems at an avoided crossing. We derive two simple approximative equations valid for weak system-bath coupling and compare results for the dissipative Landau-Zener problem with numerically exact results. Very good agreement is found for slow, i.e., adiabatic, driving. Specifically, the minimum in the Landau-Zener probability resulting from the competition of driving and dissipation is well described. For system-bath couplings and temperatures, where this minimum is observed in the adiabatic driving regime, good agreement is also observed for fast driving when the dynamics tends toward nonadiabatic behavior. Otherwise, however, for large temperatures and fast driving our approximation fails even for weak system-bath couplings, for which an undriven system is still accurately described by weak-coupling approximations.