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 focusing 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 and thus fundamentally alters the dynamics. It is shown that essentially all the 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 of exploiting Landau–Zener sweeps to generate squeezed states for spectroscopic tasks is analyzed 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 the noise has significant effect on the transition rate for slow parameter variations.
Highlights
We present a detailed analysis of the Landau–Zener problem for an interacting Bose–Einstein condensate in a time-varying double-well trap, especially focusing on the relation between the full many-particle problem and the mean-field approximation
We show that many features of the many-particle dynamics can be captured to astonishing accuracy within the phase-space description, including the depletion of the condensate mode as well as number squeezing of the final state
We have presented an analysis of nonlinear Landau–Zener tunneling between two modes in quantum phase space
Summary
Describes the dynamics of ultracold bosonic atoms in a double-well potential or the dynamics of a system of two-level atoms [29]–[32]. A convenient representation of the Bloch vector is given by the polar decomposition s sin θ cos φ sin θ sin φ In this setting, the Landau–Zener tunneling probability in the level j = 1, 2 is defined as PLmZf. Again we assume that all particles are initially localized in one of the modes, i.e. ψ j (t → −∞) = 1. While the common mean-field approach allows only statements about expectation values, the phase-space description takes the higher moments and their time evolution approximately into account. The truncated phase-space evolution defined above clearly goes beyond the common mean-field dynamics as it enables us to approximate the dynamics of the higher moments of the quantum state. As we show in the following, this approach resolves the non-commutability of the adiabatic and the semiclassical limit, which must be considered as an artifact of the single-trajectory description
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