Classical Chaos with Bose-Einstein Condensates in Tilted Optical Lattices

Thommen, Quentin; Garreau, Jean Claude; Zehnlé, Véronique

doi:10.1103/physrevlett.91.210405

Cited by 82 publications

(80 citation statements)

References 24 publications

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“…For three and more modes, the classical dynamics is chaotic (see, e.g., the studies of the three-mode system [4,31] or tilted optical lattices [32]). Chaoticity also appears in periodically driven two-mode systems [20,33] or the related kicked tops [24].…”

Section: Discussionmentioning

confidence: 99%

Semiclassical quantization of anN-particle Bose-Hubbard model

Graefe

Korsch

2007

Phys. Rev. A

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A semiclassical Bohr-Sommerfeld approximation is derived for an N -particle, two-mode BoseHubbard system modeling a Bose-Einstein condensate in a double-well potential. This semiclassical description is based on the 'classical' dynamics of the mean-field Gross-Pitaevskii equation and is expected to be valid for large N . We demonstrate the possibility to reconstruct quantum properties of the N -particle system from the mean-field dynamics. The resulting semiclassical eigenvalues and eigenstates are found to be in very good agreement with the exact ones, even for small values of N , both for subcritical and supercritical particle interaction strength where tunneling has to be taken into account.

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Section: Discussionmentioning

confidence: 99%

Semiclassical quantization of anN-particle Bose-Hubbard model

Graefe

Korsch

2007

Phys. Rev. A

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“…The triple-well system is not integrable anymore leading to an even richer dynamical behaviour than the double-well setup [45][46][47]. Despite the simplicity of the system, the resulting dynamics is affected by an inner instability accompanied by chaotic behaviour [45,48,49], originating from the nonlinear dynamics in a four dimensional phase space leading to non-integrability. Depending on the system parameters there are different regimes: Integrable subsystems lead to regular dynamics and self-trapping, while there occurs chaotic dynamics out of the regular islands.…”

Section: The Triple-well Systemmentioning

confidence: 99%

“…Depending on the system parameters there are different regimes: Integrable subsystems lead to regular dynamics and self-trapping, while there occurs chaotic dynamics out of the regular islands. The system has been investigated comprehensively by several groups [45][46][47][48][49]. Roughly speaking again, the dynamics in the triple-well system depends sensitively on the parameter Λ and the initial imbalance between the wells.…”

Section: The Triple-well Systemmentioning

confidence: 99%

Time-dependent semiclassics for ultracold bosons

Simon

Strunz

2014

Phys. Rev. A

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We study the out-of-equilibrium dynamics of ultracold bosons in a double-and triple-well potential within the Bose-Hubbard model by means of the semiclassical Herman-Kluk propagator and compare the results to the frequently applied "classical dynamics" calculation in terms of the truncated Wigner approximation (TWA). For the double-well system we find the semiclassical results in excellent agreement with the numerically exact ones, while the TWA is not able to reproduce any revivals of the wave function. The triple-well system turns out to be more difficult to handle due to the irregularity of the corresponding classical phase space. Here, deviations of the TWA from the exact dynamics appear even for short times, while better agreement is obtained using the semiclassical approach presented in this article.

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“…In the present model, the presence of chaos (which was studied in BECs in, e.g., Refs. [12,14,62,16]) would reflect an irregular spatial profile R(x) (where |R(x)| = |ψ(x, t)| is the amplitude of the BEC wave function), whereas invariant tori correspond to regular (i.e., quasiperiodic) spatial profiles.…”

Section: Physical Backgroundmentioning

confidence: 99%

Quasiperiodic Dynamics in Bose-Einstein Condensates in Periodic Lattices and Superlattices

Noort

Porter

et al. 2006

J Nonlinear Sci

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Authors' note: We rephrased the abstract. We employ KAM theory to rigorously investigate quasiperiodic dynamics in cigar-shaped Bose-Einstein condensates (BEC) in periodic lattices and superlattices. Toward this end, we apply a coherent structure ansatz to the GrossPitaevskii equation to obtain a parametrically forced Duffing equation describing the spatial dynamics of the condensate. For shallow-well, intermediatewell, and deep-well potentials, we find KAM tori and Aubry-Mather sets to prove that one obtains mostly quasiperiodic dynamics for condensate wave functions of sufficiently large amplitude, where the minimal amplitude depends on the experimentally adjustable BEC parameters. We show that this threshold scales with the square root of the inverse of the two-body scattering length, whereas the rotation number of tori above this threshold is proportional to the amplitude. As a consequence, one obtains the same dynamical picture for lattices of all depths, as an increase in depth essentially only affects scaling in phase space. Our approach is applicable to periodic superlattices with an arbitrary number of rationally dependent wave numbers.MSC: 37J40, 70H99, 37N20

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Classical Chaos with Bose-Einstein Condensates in Tilted Optical Lattices

Cited by 82 publications

References 24 publications

Semiclassical quantization of anN-particle Bose-Hubbard model

Semiclassical quantization of anN-particle Bose-Hubbard model

Time-dependent semiclassics for ultracold bosons

Quasiperiodic Dynamics in Bose-Einstein Condensates in Periodic Lattices and Superlattices

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