Occupation Statistics of a BEC for a Driven Landau-Zener Crossing

Abstract

We consider an atomic Bose-Einstein condensate (BEC) loaded in a biased double-well trap with tunneling rate $K$ and inter-atomic interaction $U$. The BEC is prepared such that all $N$ atoms are in the left well. We drive the system by sweeping the potential difference $\epsilon$ between the two wells. Depending on the interaction $u=NU/K$, and the sweep rate $\dot{\epsilon }$, we distinguish three dynamical regimes: adiabatic, diabatic, and sudden, and consider the occupation statistics of the final state. The analysis goes beyond mean-field theory and is complemented by a semiclassical picture.

arXiv comment4 pages, 5 figures

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• Macroscopic Superposition of Ultracold Atoms with Orbital Degrees of Freedom
• Optimal time-dependent lattice models for nonequilibrium dynamics
• Adiabatic passage through chaos
• Variational ansatz for the nonlinear Landau-Zener problem for cold atom association
• Finite-rate quenches of site bias in the Bose-Hubbard dimer
• Interaction induced Landau-Zener transitions
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• Generalized formula for the Landau-Zener transition in interacting Bose-Einstein condensates
• Many-body adiabatic passage: Quantum detours around chaos
• Photon-induced sideband transitions in a many-body Landau-Zener process
• Interaction-induced dynamical phase locking of Bose-Einstein condensates
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• Quasistatic transfer protocols for atomtronic superfluid circuits
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• Quantum irreversibility of quasistatic protocols for finite-size quantized systems
• Multiple-time-scale Landau-Zener transitions in many-body systems
• Electric circuit analog of Landau-Zener tunneling using time-varying elements
• Robust states of ultra-cold bosons in tilted optical lattices
• Theory of anomalous Landau-Zener tunneling induced by nonlinear coupling