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

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

doi:10.1103/physreva.88.013636

Cited by 13 publications

(45 citation statements)

References 33 publications

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“…From the symmetry of the lattice, the jump in the phase is ∆β k = ∆β = Θ. If the velocity field in the localized WL function w k is homogeneous, and hence V k (r) = Ω × r k cm , one can use (25) to calculate the circulation from r k,k−1 to r k,k+1 as their phase difference, yielding…”

Section: Relation Between θ and The Velocity Field Circulationmentioning

confidence: 99%

Bose–Einstein condensates in rotating ring-shaped lattices: a multimode model

Nigro¹,

Capuzzi²,

Jezek³

2019

J. Phys. B: At. Mol. Opt. Phys.

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We develop a multimode model that describes the dynamics on a rotating Bose-Einstein condensate confined by a ring-shaped optical lattice with large filling numbers. The parameters of the model are obtained as a function of the rotation frequency using full 3D Gross-Pitaevskii simulations. From such numerical calculations, we extract the velocity field induced at each site and analyze the relation and the differences between the phase of the hopping parameter of our model and the Peierls phase. To this end, a detailed discussion of such phases is presented in geometrical terms which takes into account the position of the junctions for different configurations. For circularly symmetric onsite densities a simple analytical relation between the hopping phase and the angular momentum is found for arbitrary number of sites. Finally, we confront the results of the rotating multimode model dynamics with Gross-Pitaevskii simulations finding a perfect agreement.

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Section: Relation Between θ and The Velocity Field Circulationmentioning

confidence: 99%

Bose–Einstein condensates in rotating ring-shaped lattices: a multimode model

Nigro¹,

Capuzzi²,

Jezek³

2019

J. Phys. B: At. Mol. Opt. Phys.

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“…Moreover, one can infer the change of sign of ∂ρ M (r, t)/∂t at the junctions by analyzing Eq. (20). One can thus conclude that particles oscillate across both junctions of a given site without changing its net population.…”

Section: Underlying Dynamicsmentioning

confidence: 91%

“…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%

“…As shown in Refs. [18,20], the introduction of f 3D is crucial for obtaining an accurate dynamics. From this system of equations only 2N c −2 are independent since the variables must fulfill k n k = 1 and k ϕ k = 0.…”

Section: A Multimode Model Equations Of Motion Including Interactionmentioning

confidence: 99%

“…In previous works, we have described in detail the method for obtaining the localized states in terms of GP stationary states [18,20,25]. Summarizing, first the stationary states ψ n (r, θ, z) are obtained as the numerical solutions of the three-dimensional GP equation [26] with different winding numbers n, with n restricted to the values − [27] for large barrier heights [25].…”

Section: B Localized Statesmentioning

confidence: 99%

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Blocked populations in ring-shaped optical lattices

2018

Self Cite

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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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Parity‐Induced Localization in Periodically Driven Ring Lattices

Wang

et al. 2021

Annalen der Physik

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Tunneling dynamics are investigated theoretically in ring shaped lattice with a site shifted periodically with respect to the others. A surprising finding on parity‐induced localization suggests that localization in the driven ring lattice can be generally divided into two types: odd‐parity‐induced localization and even‐parity‐induced localization, depending on the parity of number of quasi‐energy levels. Moreover, odd‐parity‐induced localization is proved to have its own distinct feature and it is not the crucial requirement to be an exact zero quasi‐energy state of classic dark state form for broad suppression of tunneling. These results deepen one's understanding about localization in a driven system and have great potential in the manipulation of quantum control.

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

Cited by 13 publications

References 33 publications

Bose–Einstein condensates in rotating ring-shaped lattices: a multimode model

Bose–Einstein condensates in rotating ring-shaped lattices: a multimode model

Blocked populations in ring-shaped optical lattices

Parity‐Induced Localization in Periodically Driven Ring Lattices

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