Bose-Hubbard model in a ring-shaped optical lattice with high filling factors

Cataldo, H. M.; Jezek, D. M.

doi:10.1103/physreva.84.013602

Cited by 25 publications

(37 citation statements)

References 35 publications

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“…As a tractable quantum many-body generalization of this effectively one-dimensional system, we use a periodic Bose-Hubbard model with fixed particle number. Here the model can be regarded as a discretization of the ring geometry or a ring lattice formed by a toroidal trap in superposition with radial barriers [31]. Given in hopping units, where the time scale becomes the hopping time /J and energies are scaled by J, we havê…”

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confidence: 99%

Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet

et al. 2018

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We uncover signatures of quantum chaos in the many-body dynamics of a Bose-Einstein condensate-based quantum ratchet in a toroidal trap. We propose measures including entanglement, condensate depletion, and spreading over a fixed basis in many-body Hilbert space, which quantitatively identify the region in which quantum chaotic many-body dynamics occurs, where random matrix theory is limited or inaccessible. With these tools, we show that many-body quantum chaos is neither highly entangled nor delocalized in the Hilbert space, contrary to conventionally expected signatures of quantum chaos.

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confidence: 99%

Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet

et al. 2018

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“…It is interesting to recall that J may be negative, as occurs in the present calculations, while J eff remains always positive [14]. The TM equations (18) and (19) can also be derived from the "classical" Hamiltonian…”

Section: B Dynamical Equations In Terms Of the Particle Imbalance Anmentioning

confidence: 51%

“…This can be easily verified by noting that the stationary state with 013636-2 winding number n = 1 has uniform phases at the right and left wells with values φ = 0 and φ = π , respectively [20]. Here we may recall that this only occurs in the regime of large barriers [14], where ψ 1 (r) = ψ −1 (r) may be taken as a real function that does not carry any angular momentum and hence does not correspond to a "vortex" state [20].…”

Section: A Dynamical Equations In Terms Of the Coefficients Of Well-mentioning

confidence: 74%

“…Here it is important to recall that the main difference between our WL function and a "true" Wannier function results from the fact that only the former depends on the filling factor, i.e., the number of particles at each site, as seen in Ref. [14]. One may also write the above stationary states in terms of these localized functions,…”

Section: A Localized Wl Statesmentioning

confidence: 96%

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Multimode model for an atomic Bose-Einstein condensate in a ring-shaped optical lattice

Jezek

Cataldo

2013

Phys. Rev. A

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We study the population dynamics of a ring-shaped optical lattice with a high number of particles per site and a low (less than ten) number of wells. Using a localized on-site basis defined in terms of stationary states, we were able to construct a multiple-mode model depending on relevant hopping and on-site energy parameters. We show that in the case of two wells, our model corresponds exactly to a recent improvement of the two-mode model. We derive a formula for the self-trapping period, which turns out to be chiefly ruled by the on-site interaction energy parameter. By comparing to time-dependent Gross-Pitaevskii simulations, we show that the multimode model results can be enhanced in a remarkable way over all the regimes by only renormalizing such a parameter. Finally, using a different approach which involves only the ground-state density, we derive an effective interaction energy parameter that turns out to be in accordance with the renormalized one.

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“…The equations of motion of the multimode model has been previously studied both for multiple-well systems in general [20,25] and also in the case of a four-well system [16,18]. Here, we only review its main ingredients, focusing in the definition of their localized states extracted from the stationary solutions of the GP equations.…”

Section: Multimode Modelmentioning

confidence: 99%

Blocked populations in ring-shaped optical lattices

2018

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We study a special dynamical regime of a Bose-Einstein condensate in a ring-shaped lattice where the populations in each site remain constant during the time evolution. The states in this regime are characterized by equal occupation numbers in alternate wells and non-trivial phases, while the phase differences between neighboring sites evolve in time yielding persistent currents that oscillate around the lattice. We show that the velocity circulation around the ring lattice alternates between two values determined by the number of wells and with a specific time period that is only driven by the onsite interaction energy parameter. In contrast to the self-trapping regime present in optical lattices, the occupation number at each site does not show any oscillation and the particle imbalance does not possess a lower bound for the phenomenon to occur. These findings are predicted with a multimode model and confirmed by full three-dimensional Gross-Pitaevskii simulations using an effective onsite interaction energy parameter.

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Bose-Hubbard model in a ring-shaped optical lattice with high filling factors

Cited by 25 publications

References 35 publications

Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet

Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet

Multimode model for an atomic Bose-Einstein condensate in a ring-shaped optical lattice

Blocked populations in ring-shaped optical lattices

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