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arXiv:quant-ph/0610166 · Europhysics Letters (EPL)

Dynamical realization of macroscopic superposition states of cold bosons in a tilted double well

Lincoln D. Carr, Dimitri R. Dounas-Frazer, Miguel Ángel García-March

Published Apr 1, 2010• 58 citations
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Abstract

We present exact expressions for the quantum sloshing of Bose-Einstein condensates in a tilted two-well potential. Tunneling is suppressed by a small potential difference between wells, or tilt. However, tunneling resonances occur for critical values of the tilt when the barrier is high. At resonance, tunneling times on the order of 10–100 ms are possible. Furthermore, such tilted resonances lead to a dynamical scheme for creating few-body NOON-like macroscopic superposition states which are protected by the many-body wave function against potential fluctuations.

DOI
10.1209/0295-5075/90/10005

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We present exact expressions for the quantum sloshing of Bose-Einstein condensates in a tilted two-well potential. Tunneling is suppressed by a small potential difference between wells, or tilt. However, tunneling resonances occur for critical values of the tilt when the barrier is high. At resonance, tunneling times on the order of 10–100 ms are possible. Furthermore, such tilted resonances lead to a dynamical scheme for creating few-body NOON-like macroscopic superposition states which are protected by the many-body wave function against potential fluctuations.
We present a thorough description of the physical regimes for ultracold bosons in double wells, with special attention paid to macroscopic superpositions (MSs). We use a generalization of the Lipkin-Meshkov-Glick Hamiltonian of up to eight single particle modes to study these MSs, solving the Hamiltonian with a combination of numerical exact diagonalization and high-order perturbation theory. The MS is between left and right potential wells; the extreme case with all atoms simultaneously located in both wells and in only two modes is the famous NOON state, but our approach encompasses much more general MSs. Use of more single particle modes brings dimensionality into the problem, allows us to set hard limits on the use of the original two-mode LMG model commonly treated in the literature, and also introduces a mixed Josephson-Fock regime. Higher modes introduce angular degrees of freedom and MS states with different angular properties.
Abstract Bose-Einstein Condensate (BEC) is a paradigmatic representative of macroscopic quantum states. 39 K atoms serve as an ideal system for realizing a nearly ideal BEC owing to their ultra-small background scattering length. This study further investigates the nonlinear dynamics of 39 K BEC confined in a double-well potential under attractive interactions. In this work, a Gaussian barrier is integrated with a double-well potential, and we innovatively adopt a transient dynamics approach to construct a highly non-equilibrium initial state where all atoms are confined to the left well. We track the full evolutionary process of the system from non-equilibrium excitation to stable self-trapping, elucidating wave function contraction and energy conversion. Under high barrier height conditions, tunneling is substantially suppressed: atoms localize in a single well, the longitudinal position expectation value remains constant, and the phase difference is locked, leading to the formation of a macroscopic quantum self-trapping state. Radial oscillations exhibit reduced amplitude and a slower evolution rate owing to density homogenization. A smooth, fluctuation-free momentum density profile corresponds to the static localized regime of self-trapping. Coherence transitions from dynamic oscillation to static locking, and weak attractive interactions in 39 K atoms further prolong the coherence time. This study elucidates key microscopic mechanisms, including the nonlinear coupling mechanism of attractive interactions, the dynamic-static transition rules of coherence, and momentum density acting as a microscopic probe for tunneling and soliton dynamics, thereby providing a quantitative basis for the preparation of tunable quantum states.
We analyze the periodic tunneling of a Bose-Einstein condensate in a double-well potential which has an oscillating energy barrier. We show that the dynamics of the Bose condensate critically depends on the frequency ωωω of the oscillating energy barrier. In the regime of periodic macroscopic quantum tunneling (PMQT) with frequency ωJω_JωJ​, the population imbalance of the condensate in the two wells can be enhanced under the condition of parametric resonance ω=2ωJω= 2 ω_Jω=2ωJ​. Instead, in the regime of macroscopic quantum self-trapping (MQST), we find that MQST can be reduced or suppressed under the condition of parametric resonance between the frequency ωωω of the energy barrier and the frequency ωSTω_{ST}ωST​ of oscillation through the barrier of the very small fraction of particles which remain untrapped during MQST.
We predict wideband suppression of tunneling of spin-orbit-coupled atoms (or noninteracting Bose-Einstein condensate) in a double-well potential with periodically varying depths of the potential wells. The suppression of tunneling is possible for a single state and for superposition of two states, i.e., for a qubit. By varying spin-orbit coupling one can drastically increase the range of modulation frequencies in which an atom remains localized in one of the potential wells, the effect connected with crossing of energy levels. This range of frequencies is limited because temporal modulation may also excite resonant transitions between lower and upper states in different wells. The resonant transitions enhance tunneling and are accompanied by pseudospin switching. Since the frequencies of the resonant transitions are independent of the potential modulation depth, in contrast to frequencies at which suppression of tunneling occurs, by varying this depth one can dynamically control both the spatial localization and pseudospin of the final state.
It is well known that increasing the nonlinearity due to repulsive atomic interactions in a double-well Bose-Einstein condensate suppresses quantum tunneling between the two sites. Here we find analogous behavior in the dynamical tunneling of a Bose-Einstein condensate between period-one resonances in a single driven potential well. For small nonlinearities we find unhindered tunneling between the resonances, but with an increasing period as compared to the noninteracting system. For nonlinearities above a critical value we generally observe that the tunneling shuts down. However, for certain regimes of modulation parameters we find that dynamical tunneling reemerges for large enough nonlinearities, an effect not present in spatial double-well tunneling. We develop a two-mode model in good agreement with full numerical simulations over a wide range of parameters, which allows the suppression of tunneling to be attributed to macroscopic quantum self-trapping.