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Chinese Physics Letters

Tunnelling Dynamics of Bose—Einstein Condensates in a Five-Well Trap

Ai‐Xia Zhang, Tian Shi-Ling, Rong-An Tang, Xue Ju-Kui

Published Oct 1, 2008• 0 citations
Publisher

Abstract

We develop a five-well model for describing the tunnelling dynamics of Bose-Einstein condensates (BECs) trapped in 2D optical lattices. The tunnelling dynamics of BECs in this five-well model are investigated both analytically and numerically. We focus on the self-trapped states and the difference of the tunnelling dynamics among two-well, three-well and five-well systems. The criterions for the self-trapped states and the phase diagrams of the five trapped BECs in zero-phase mode and π-phase mode are obtained. We find that the criterions and the phase diagrams are largely modified by the dimension of the system and the phase difference between wells. The five-well model is a good model and can give us an insight into the tunnelling dynamics of BECs trapped in 2D optical lattices.

DOI
10.1088/0256-307x/25/10/013

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We develop a five-well model for describing the tunnelling dynamics of Bose-Einstein condensates (BECs) trapped in 2D optical lattices. The tunnelling dynamics of BECs in this five-well model are investigated both analytically and numerically. We focus on the self-trapped states and the difference of the tunnelling dynamics among two-well, three-well and five-well systems. The criterions for the self-trapped states and the phase diagrams of the five trapped BECs in zero-phase mode and π-phase mode are obtained. We find that the criterions and the phase diagrams are largely modified by the dimension of the system and the phase difference between wells. The five-well model is a good model and can give us an insight into the tunnelling dynamics of BECs trapped in 2D optical lattices.
In the present paper, we analytically and numerically investigate the dynamics of Bose-Einstein condensates (BECs) loaded into deep optical lattices of one dimension (1D), 2D, and 3D. We focus on the self-trapped state and the effect of the lattice dimension. Under the tight-binding approximation, we obtain an analytical criterion for the self-trapped state of BEC using the time-dependent variational method. The phase diagram for self-trapping, soliton, breather, or diffusion of a BEC cloud is obtained accordingly and verified by directly solving a discrete Gross-Pitaevskii equation numerically. In particular, we find that the criterion and the phase diagrams are modified dramatically by the dimension of the optical lattices.
In this paper, we consider the macroscopic quantum tunnelling and self-trapping phenomena of Bose–Einstein condensates (BECs) with three-body recombination losses and atoms feeding from thermal cloud in triple-well potential. Using the three-mode approximation, three coupled Gross–Pitaevskii equations (GPEs), which describe the dynamics of the system, are obtained. The corresponding numerical results reveal some interesting characteristics of BECs for different scattering lengths. The self-trapping and quantum tunnelling both are found in zero-phase and π-phase modes. Furthermore, we observe the quantum beating phenomenon and the resonance character during the self-trapping and quantum tunnelling. It is also shown that the initial phase has a significant effect on the dynamics of the system.
We study the dynamics of self-trapping in Bose-Einstein condensates (BECs) loaded in deep optical lattices with Gaussian initial conditions, when the dynamics is well described by the discrete nonlinear Schrödinger equation (DNLSE). In the literature an approximate dynamical phase diagram based on a variational approach was introduced to distinguish different dynamical regimes: diffusion, self-trapping, and moving breathers. However, we find that the actual DNLSE dynamics shows a completely different diagram than the variational prediction. We calculate numerically a detailed dynamical phase diagram accurately describing the different dynamical regimes. It exhibits a complex structure that can readily be tested in current experiments in BECs in optical lattices and in optical waveguide arrays. Moreover, we derive an explicit theoretical estimate for the transition to self-trapping in excellent agreement with our numerical findings, which may be a valuable guide as well for future studies on a quantum dynamical phase diagram based on the Bose-Hubbard Hamiltonian.
The self-trapping phenomenon of Bose-Einstein condensates (BECs) in optical lattices is studied by numerically solving the Gross-Pitaevskii equation. Our numerical results reproduce the self-trapping that was observed in a recent experiment [Anker et al., Phys. Rev. Lett. 94, 020403 (2005)]. However, we do not find that the appearance of the steep edges on the boundaries of the wave packet is the critical signal of the self-trapping. More importantly, we discover that the self-trapping breaks down at long evolution times; that is, the self-trapping in optical lattices is only temporary and has a lifetime. This temporariness is caused by the tunneling of atoms at the edge of the BEC wave packet towards outside wells. Our analysis shows that the phenomena observed numerically can all be understood by regarding the optical lattice as a train of double-well potentials.
We study inter-well coherent quantum tunneling of Bose-Einstein condensates (BEC's) in optical lattices. Irrespective of whether the BEC is a superfluid in the whole lattice, it may or may not be a superfluid within each well of the lattice depending on whether the ratio of the well kinetic energy to the interaction energy is small or large. When the bosons in each well are superfluid, we have Josephson tunneling among the wells driven by the phase difference between the superfluids in the different wells. For typical lattice parameters the Josephson tunneling rate will be somewhat enhanced from the naive estimate of (tunneling energy scale)/ℏ/\hbar/ℏ. Whether it is enhanced or not will depend on lattice parameters, but it can never be zero. When the bosons in each well are not superfluid, there is coherent quantum tunneling of essentially free bosons between the wells. This tunneling is proportional to the boson number difference between the wells.
The impurity-induced self-trapping and stable moving soliton and breather of two-component Bose-Einstein condensates (BEC's) in deep DDD-dimensional optical lattices are discussed both analytically and numerically. Under the tight-binding approximation and within a time-dependent variational approach, analytical criteria for occurrences of a self-trapping, moving soliton and breather in the system are obtained. The analytical results are confirmed by direct numerical simulation. It is shown that the dynamics of the condensates can be modified significantly by a minor admixture of an impurity (the second component). The diffusion state of the single-component BEC will transit to the self-trapped state due to the minor admixture of an impurity, even if the two condensates are only with marginal spatial overlap. Furthermore, we find that, in certain conditions, a stable moving soliton can exist in high-dimensional lattices for the two-component BEC's, which is very different from the single-component BEC (where a moving soliton cannot be stabilized in high-dimensional lattices). On the other hand, the impurity can play a crucial role in causing important coherence-decoherence and localization-delocalization phase transitions.