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arXiv:cond-mat/0506407 · International Journal of Modern Physics B

JOSEPHSON DYNAMICS OF A BOSE–EINSTEIN CONDENSATE IN AN ACCELERATED DOUBLE-WELL POTENTIAL

Aranya B. Bhattacherjee

Published Mar 20, 2007• 0 citations
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Abstract

Motivated by a recent experiment on Bloch oscillation of Bose–Einstein condensates (BEC) in accelerated optical lattices, we consider the Josephson dynamics of a BEC in an accelerated double-well potential. We show that acceleration suppresses coherent population / phase oscillation between the two wells. Accelerating the double-well renders the Josephson coupling energy EJ time-dependent and this emerges as a source of dissipation. This dissipative mechanism helps to stabilize the system. The results are used to interpret a recent experimental result (M. Jona-Lasinio, O. Morsh, M. Cristiani E. Arimonod and C. Menotti, cond-mat / 0501572).

DOI
10.1142/s0217979207036874

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Motivated by a recent experiment on Bloch oscillation of Bose–Einstein condensates (BEC) in accelerated optical lattices, we consider the Josephson dynamics of a BEC in an accelerated double-well potential. We show that acceleration suppresses coherent population / phase oscillation between the two wells. Accelerating the double-well renders the Josephson coupling energy EJ time-dependent and this emerges as a source of dissipation. This dissipative mechanism helps to stabilize the system. The results are used to interpret a recent experimental result (M. Jona-Lasinio, O. Morsh, M. Cristiani E. Arimonod and C. Menotti, cond-mat / 0501572).
Abstract The Josephson oscillation of a Bose-Einstein condensate (BEC) in a double-well potential is typically characterized by the population imbalance between the two wells. Within the two-mode approximation, the dynamics of the center of mass of the condensate is predicted to coincide with that of the population imbalance. However, numerical simulations reveal a discrepancy between the dynamics of the center of mass and that of the population imbalance, indicating that the two-mode model fails to fully capture the dynamics of BEC Josephson oscillations. To address this limitation, a four-mode approximation is employed to describe the dynamics of the system. The four-mode model not only describes the dynamics of the population imbalance but also accounts for the oscillation of the center of mass, thereby explaining the origin of the discrepancy between the two-mode model and the simulation results. Moreover, we find that although higher-order excitation modes are always present in Josephson oscillations, the two-mode model can still describe the dynamics of the population imbalance. This phenomenon is explained by the interference of population oscillations between local states. PACS: 03.75.Lm, 03.75.Kk, 67.85.De
Dynamics of the repulsive Bose–Einstein condensate (BEC) in a double-well trap is explored within the 3D time-dependent Gross–Pitaevskii equation. The model avoids numerous common approximations (two-mode treatment, time-space factorization, fixed values of the chemical potential and barrier penetrability, etc) and thus may provide a realistic description of BEC dynamics, including both weak-coupling (sub-barrier) and strong-coupling (above-barrier) regimes and their crossover. The strong coupling regime is achieved by increasing the number N of BEC atoms and thus the chemical potential. The evolution with N of Josephson oscillations (JO) and macroscopic quantum self-trapping (MQST) is examined and the crucial impact of the BEC interaction is demonstrated. At weak coupling, the calculations well reproduce the JO/MQST experimental data. At strong coupling with a significant overlap of the left and right BECs, we observe a remarkable persistence of the Josephson-like dynamics: the JO and MQST converge to a high-frequency JO-like mode where both population imbalance and phase difference oscillate around the zero averages.
Experiments on the nonequilibrium dynamics of an isolated Bose-Einstein condensate (BEC) in a magnetic double-well trap exhibit a puzzling divergence: While some show dissipation-free Josephson oscillations, others find strong damping. Such damping in isolated BECs cannot be understood on the level of the coherent Gross-Pitaevskii dynamics. Using the Keldysh functional-integral formalism, we describe the time-dependent system dynamics by means of a multimode BEC coupled to fluctuations (single-particle excitations) beyond the Gross-Pitaevskii saddle point. We find that the Josephson oscillations excite an excess of fluctuations when the effective Josephson frequency ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}_{J}$ is in resonance with the effective fluctuation energy ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\varepsilon}}}_{m}$, where both ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}_{J}$ and ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\varepsilon}}}_{m}$ are strongly renormalized with respect to their noninteracting values. By evaluating and using the model parameters for the respective experiments, we describe quantitatively the presence or absence of damping.
Bose Einstein condensates (BECs) in double well potentials have drawn a lot of attention for the possibilities they offer to study fundamental quantum mechanical effects at the macroscopic level as well as for potential applications like interferometry, high precision measurements or thermometry. In contrast to Josephson junctions realized in superconductors and superfluids, in BEC the interatomic interactions play a crucial role leading to anharmonic Josephson oscillations, if the initial population imbalance of the two wells is below a critical value, and to macroscopic quantum self-trapping i.e, inhibition of large amplitude Josephson oscillations above the threshold for the population imbalance. In this paper, a novel technique to adiabatically control of BEC in a double-well potential is proposed. The adiabatic dynamics of a BEC in a double well potential can be described in terms of a dark variable resulting from a combination of the population imbalance and the spatial atomic coherence.
We study dynamical behaviors of the weakly interacting Bose-Einstein condensate in the one-dimensional optical lattice with an overall double-well potential by solving the time-dependent Gross-Pitaevskii equation. It is observed that the double-well potential dominates the dynamics of such a system even if the lattice depth is several times larger than the height of the double-well potential. This result suggests that the condensate flows without resistance in the periodic lattice just like the case of a single particle moving in periodic potentials. Nevertheless, the effective mass of atoms is increased, which can be experimentally verified since it is connected to the Josephson oscillation frequency. Moreover, the periodic lattice enhances the nonlinearity of the double-well condensate, making the condensate more “self-trapped” in the π -mode self-trapping regime.
The dynamics of the Bose–Einstein condensate (BEC) in a double-well potential is often investigated under the mean-field theory (MFT). This works successfully for large particle numbers with dynamical stability. But for dynamical instabilities, quantum corrections to the MFT becomes important [J. R. Anglin and A. Vardi, Phys. Rev. A64, 013605 (2001)]. Recently the adiabatic dynamics of the double-well BEC is investigated under the MFT in terms of a dark variable [C. Ottaviani et al., Phys. Rev. A81, 043621 (2010)], which generalizes the adiabatic passage techniques in quantum optics to the nonlinear matter-wave case. We give a fully quantized version of it using second-quantization and introduce new correction terms from higher order interactions beyond the on-site interaction, which are interactions between the tunneling particle and the particle in the well and interactions between the tunneling particles. If only the on-site interaction is considered, this reduces to the usual two-mode BEC.