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arXiv:0712.1257 · Physical Review A

Quasienergies and Floquet states of two weakly coupled Bose-Einstein condensates under periodic driving

Xiaobing Luo, Qiongtao Xie, Biao Wu

Published May 6, 2008• 47 citations
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Abstract

We investigate the quasienergies and Floquet states of two weakly coupled Bose-Einstein condensates driven by a periodic force. The quasienergies and Floquet states of this system are computed within two different theoretical frameworks: the mean-field model and the second-quantized model. The mean-field approach reveals a triangular structure in the quasienergy band. Our analysis of the corresponding Floquet states shows that this triangle signals the onset of a localization phenomenon, which can be regarded as a generalization of the well-known phenomenon called coherent destruction of tunneling. With the second-quantized model, we find also a triangular structure in the quantum quasienergy band, which is enveloped by the mean-field triangle. The close relation between these two sets of quasienergies is further explored by a semiclassical method. With a Sommerfeld rule generalized to time-dependent systems, the quantum quasienergies are computed by quantizing semiclassically the mean-field model and they are found to agree very well with the results obtained directly with the second-quantized model.

DOI
10.1103/physreva.77.053601

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We investigate nonlinear Floquet states and quasienergies of a Bose-Einstein condensate in a double-well potential subject to a high-frequency driving field. A multiple time scale method is used to obtain the nonlinear Floquet states and quasienergies in both weak and strong nonlinearity regimes. It is shown that there are more nonlinear Floquet states without linear counterparts in the strong nonlinearity regime than in the weak nonlinearity regime, and they are phase-locked to an integer multiple of the external driving frequency. The validity of the effective description in the two different regimes is discussed. The stability criterion for these nonlinear Floquet states is found analytically and confirmed numerically.
We study the tunneling dynamics and energy bands of three Bose-Einstein condensates which are coupled weakly with each other. The study is carried out with both the mean-filed model and the second-quantized model. The results from these two models are compared and found to agree with each other when the particle number is large. Without interaction, this system possesses a Dirac point in its energy band. This Dirac point is immediately destroyed and develops into a loop structure with arbitrary small interaction. This loop structure has a strong effect on the tunneling dynamics. We find that the tunneling dynamics in this system is very sensitive to the system parameter, e.g., the interaction strength. This sensitivity is found to be caused by the chaos in the mean-field model and the avoided energy crossings with tiny gaps in the second-quantized model. This result gives a certain indication on how the classical dynamics and quantum dynamics are connected in the semi-classical limit. Our mean-field results are also valid for three mutually coupled optical nonlinear waveguides.
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We consider a two-component Bose-Einstein condensate in two spatially localized modes of a double-well potential, with periodic modulation of the tunnel coupling between the two modes. We treat the driven quantum field using a two-mode expansion and define the quantum dynamics in terms of the Floquet Operator for the time periodic Hamiltonian of the system. It has been shown that the corresponding semiclassical mean-field dynamics can exhibit regions of regular and chaotic motion. We show here that the quantum dynamics can exhibit dynamical tunneling between regions of regular motion, centered on fixed points (resonances) of the semiclassical dynamics.
We study a system of three coherently coupled states, where one state is shifted periodically against the other two. We discover that this system possesses a dark Floquet state that has zero quasi-energy and negligible population at the intermediate state. This dark Floquet state manifests itself dynamically in terms of the suppression of inter-state tunneling, a phenomenon known as coherent destruction of tunneling (CDT). Owing to its different origin from the CDT found in a two-state-driven system, we call it dark CDT. At a high-frequency limit for the periodic driving, this Floquet state reduces to the well-known dark state. Our results can be generalized to systems with more states and be verified with easily implemented experiments within the current technologies.