Nonlinear Landau-Zener tunneling in quantum phase space

TL;DR

This paper analyzes nonlinear Landau-Zener tunneling in a Bose-Einstein condensate within a double-well trap, revealing how nonlinear interactions cause dynamical instabilities and affect adiabaticity, with implications for quantum state manipulation and decoherence probing.

Contribution

It demonstrates that the complex many-particle dynamics can be understood via a semiclassical phase space approach, clarifying the limits of adiabatic and semiclassical approximations.

Findings

Nonlinear interactions induce dynamical instability and breakdown of adiabaticity.

Semiclassical phase space effectively explains Landau-Zener features.

Landau-Zener sweeps can generate squeezed states and probe decoherence.

Abstract

We present a detailed analysis of the Landau-Zener problem for an interacting Bose-Einstein condensate in a time-varying double-well trap, especially focussing on the relation between the full many-particle problem and the mean-field approximation. Due to the nonlinear self-interaction a dynamical instability occurs, which leads to a breakdown of adiabaticity condition and thus fundamentally alters the dynamics. It is shown that essentially all features of the Landau-Zener problem including the depletion of the condensate mode can be already understood within a semiclassical phase space picture. In particular, this treatment resolves the formerly imputed incommutability of the adiabatic and semiclassical limits. The possibility to exploit Landau-Zener sweeps to generate squeezed states for spectroscopic tasks is analysed in detail. Moreover, we study the influence of phase noise and propose a Landau-Zener sweep as a sensitive, yet readily implementable probe for decoherence, since this has a significant effect on the transition rate for slow parameter variations.