Effect of environmental spins on Landau-Zener transitions

Abstract

Landau-Zener (LZ) transitions of a two-level system (e. g., electronic spin in molecular magnets) coupled to one or many environmental spins (e. g., nuclear spins) are studied. For rather general interactions the LZ problem is reduced to that of a Landau-Zener grid. It is shown analytically that environmental spins initially in their ground state do not influence the staying probability P. This changes if they are prepared in a statistical ensemble. For a more specific model with environmental spins in a transverse field, LZ transitions are studied in the case of well-separated resonances in the LZ grid. The full evolution of the system is described as a succession of elemenary transitions at avoided crossings and free evolution between them. If the environmental spins are strongly coupled to the central spin, their effect on P is weak. In other cases LZ transitions are strongly suppressed and P is decreasing very slowly with the sweep-rate parameter epsilon ~ 1/v, v being the energy sweep rate.

arXiv comment12 PR pages, 8 figures, submitted to PRB

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• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Competition between relaxation and external driving in the dissipative Landau-Zener problem
• Landau-Zener transitions mediated by an environment: population transfer and energy dissipation
• Landau-Zener transition in a two-level system coupled to a single highly-excited oscillator
• Nonadiabatic transitions in Landau-Zener grids: integrability and semiclassical theory
• Landau-Majorana-Stuckelberg-Zener dynamics driven by coupling for two interacting qutrit systems
• Generalized Adiabatic Impulse Approximation
• Partial Landau-Zener transitions and applications to qubit shuttling
• Dipolar-controlled spin tunneling and relaxation in molecular magnets