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Journal of the Physical Society of Japan

Tunneling Between Floquet States using a Bose–Einstein Condensate

Robert Luter, L. E. Reichl

Published Jan 1, 2003• 1 citation
Publisher

Abstract

Dynamical tunneling was observed in atom optics experiments at NIST using a Bose–Einstein condensate. The oscillations observed in these experiments result from the interference of a few Floquet states that were excited by the initial conditions in the experiment. In this paper we discuss properties of the dominant Floquet states for an extended range of experimental parameters.

DOI
10.1143/jpsjs.72sc.134

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Dynamical tunneling was observed in atom optics experiments at NIST using a Bose–Einstein condensate. The oscillations observed in these experiments result from the interference of a few Floquet states that were excited by the initial conditions in the experiment. In this paper we discuss properties of the dominant Floquet states for an extended range of experimental parameters.
Dynamical tunneling has been observed in atom optics experiments by two groups, one in Texas using Cesium atoms and the other at NIST using a Bose–Einstein condensate. This tunneling is classically forbidden due to the isolation of the atoms in momentum space. The experimental results are extremely well described by time-periodic Hamiltonians with momentum quantized in units of the atomic recoil. The oscillations observed in these experiments are due to a few Floquet states that were excited by the initial conditions in the experiment. The observed tunneling has a well defined period when only two Floquet states dominate the dynamics. Beat frequencies are observed when three Floquet states dominate. Frequencies which are calculted theoretically match those observed by both experiments. The dynamical origin of the dominant Floquet states is identified as resulting from states which are excited by the initial conditions of the experiment.
Dynamical tunneling has been observed in atom-optics experiments by two groups. We show that the experimental results are extremely well described by time-periodic Hamiltonians with momentum quantized in units of the atomic recoil. The observed tunneling has a well-defined period when only two Floquet states dominate the dynamics. Beat frequencies are observed when three Floquet states dominate. We find frequencies that match those observed in both experiments. The dynamical origin of the dominant Floquet states is identified.
A Bose-Einstein condensate in a modulated, one-dimensional, anharmonic potential can exhibit dynamical tunneling between islands of regular motion in phase space. With increasingly repulsive atomic interactions, dynamical tunneling is predicted to cease due to self-trapping [S. Wüster ]. This suppression of tunneling oscillations is related to the same phenomenon that occurs in the two-mode dynamics of a repulsively interacting Bose-Einstein condensate in a double-well potential. Here we present a two-mode model for dynamical tunneling based on nonlinear Floquet states and examine the range of validity of the approximation. We characterize nonlinear dynamical tunneling for different trap strengths, modulation amplitudes, and effective Planck constants. Using the linear Floquet states we derive an expression for the critical nonlinearity beyond which tunneling ceases. Finally we demonstrate the dynamical instability of selected nonlinear Floquet states and show how to initialize some Floquet states in experiments. Our detailed survey will enable experiments to target accessible parameter regimes for the study of nonlinear dynamical tunneling.
Dynamical tunneling is a quantum phenomenon where a classically forbidden process occurs that is prohibited not by energy but by another constant of motion. The phenomenon of dynamical tunneling has been recently observed in a sodium Bose-Einstein condensate. We present a detailed analysis of these experiments using numerical solutions of the three-dimensional Gross-Pitaevskii equation and the corresponding Floquet theory. We explore the parameter dependency of the tunneling oscillations and we move the quantum system towards the classical limit in the experimentally accessible regime.
Dynamical tunneling is a quantum phenomenon where a classically forbidden process occurs that is prohibited not by energy but by another constant of motion. The phenomenon of dynamical tunneling has been recently observed in a sodium Bose-Einstein condensate. We present a detailed analysis of these experiments using numerical solutions of the three-dimensional Gross-Pitaevskii equation and the corresponding Floquet theory. We explore the parameter dependency of the tunneling oscillations and we move the quantum system towards the classical limit in the experimentally accessible regime