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Markovian dynamics of the two-mode bose-einstein condensate

Kalai Kumar Rajagopal, Bakhram Umarov, Sithi Vinayakam Muniandy

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

The Mean-field dynamics of atomic condensate loaded in two symmetric traps coupled to a reservoir is studied. In this work we discuss the effect of damping on the boson Josephson junction (BJJ) and the macroscopic quantum self-trapping (MQST) states which are peculiar to the dynamics of the two-mode BEC. We found that damping causes the destruction of quantum self-trapping state and could set in chaos.

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arXiv:cond-mat/0309009•Sep 1, 2003•0 citations
The Mean-field dynamics of atomic condensate loaded in two symmetric traps coupled to a
reservoir is studied. In this work we discuss the effect of damping on the boson Josephson
junction (BJJ) and the macroscopic quantum self-trapping (MQST) states which are peculiar
to the dynamics of the two-mode BEC. We found that damping causes the destruction of
quantum self-trapping state and could set in chaos.
We present particular examples of tunneling and transport dynamics of Bose–Einstein condensate (BEC) in a two-well trap: Josephson oscillations (JO), macroscopic quantum self-trapping (MQST) and complete adiabatic transport. Being quite general, these dynamical regimes have close analogies with Josephson junctions in superconductors and transport problems in nanosystems. The calculations are performed within the time-dependent mean-field prescription within (transport) and beyond (JO and MQST) two-mode approximation. For the transport a universal adiabatic population transfer scheme is proposed, allowing a robust and complete transport even under strong nonlinear effects.
In this paper, tunnelling dynamics of squeezed Bose–Einstein condensates (BEC's) in the presence of the nonlinear self-interaction of each species, the interspecies nonlinear interaction, and the Josephson-like tunnelling interaction is investigated by using the second quantization approach. The influence of BEC squeezing on macroscopic quantum self-trapping (MQST) and quantum coherent atomic tunnelling is analyzed in detail. It is shown that the MQST and coherent atomic tunnelling between two squeezed BEC's can be manipulated through changing squeezing amplitude and squeezing phase of BEC squeezed states.
Abstract: In this work, we study the dissipative dynamics of a double-well Bose-Einstein condensate (BEC) out-coupled to reservoir at each side of its trap. The sub-system comprises of a simple Bose-Hubbard model, where the interplay of atom-tunneling current and inter-particle interaction are the main quantum features. The contact with two separate heat baths causes dissipation and drives the system into a non-equilibrium state. The system is well described by the Generalized Quantum Heisenberg-Langevin equation. We considered two Markovian dissipative BEC systems based on (i) the mean-field model (MF), where the internal noise has been averaged out and (ii) the noise-correlated model (FDT). Physical quantities, such as population imbalance, coherence and entanglement of the system, are computed for the models. The two-mode BEC phases, such as the quantum tunneling state and the macroscopic quantum-trapping state, evolved into complicated dynamics by controlling the non-linear interaction and dissipation strengths. We found that many important quantum features produced by the noise-correlated FDT model are not captured by the mean-field model. Keywords: Double-well BEC, Dissipation, Noise, Markovian, Non-Markovian, Fixed points. PACS: 03.75 Lm, 03.65 Yz, 03.75 Gg, 05.
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.
We discuss the coherent atomic oscillations between two weakly coupled Bose-Einstein condensates. The weak link is provided by a laser barrier in a (possibly asymmetric) double-well trap or by Raman coupling between two condensates in different hyperfine levels. The boson Josephson junction (BJJ) dynamics is described by the two-mode nonlinear Gross-Pitaevskii equation that is solved analytically in terms of elliptic functions. The BJJ, being a neutral, isolated system, allows the investigations of dynamical regimes for the phase difference across the junction and for the population imbalance that are not accessible with superconductor Josephson junctions (SJJ's). These include oscillations with either or both of the following properties: (i) the time-averaged value of the phase is equal to $\ensuremath{\pi} (\ensuremath{\pi}$-phase oscillations); (ii) the average population imbalance is nonzero, in states with macroscopic quantum self-trapping. The (nonsinusoidal) generalization of the SJJ ac and plasma oscillations and the Shapiro resonance can also be observed. We predict the collapse of experimental data (corresponding to different trap geometries and the total number of condensate atoms) onto a single universal curve for the inverse period of oscillations. Analogies with Josephson oscillations between two weakly coupled reservoirs of ${}^{3}\mathrm{He}\ensuremath{-}B$ and the internal Josephson effect in ${}^{3}\mathrm{He}\ensuremath{-}A$ are also discussed.
The tunnelling quantum dynamics of bimodal BJJ system is modified through introducing an equilibrium condition, which is based on the assumption that the BJJ is tend to keep on its ground state (with a lowest energy) during the oscillation. The tunnelling dynamics of BJJ with symmetric and asymmetric traps is discussed through numerically solving the modified equations. Stationary states are found to exist in the both BJJs. Compared to previous works, the macroscopic quantum self trapping (MQST) is auto-avoided. Meanwhile, it is revealed that the BJJ oscillates with its inherent frequency which is only related to the Josephson energy, which has been testified experimentally in other contexts.