Kinetic Thomas–Fermi solutions of the Gross–Pitaevskii equation

Ölschläger, Matthias; Wirth, Georg; Smith, C. Morais; Hemmerich, Andreas

doi:10.1016/j.optcom.2008.12.054

Cited by 2 publications

(2 citation statements)

References 34 publications

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“…[25]. Reference [36] found an analytical solution at the band edge for a specific interaction energy by employing the Thomas-Fermi approximation. However, the computation of the Bogoliubov spectrum, and hence the stability, around the states of a two-dimensional (2D) loop structure is lacking in the literature.…”

Section: Introductionmentioning

confidence: 99%

Loop-structure stability of a double-well-lattice Bose-Einstein condensate

Hui¹,

Barnett²,

Porto³

et al. 2012

Phys. Rev. A

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In this work, we consider excited many-body mean-field states of bosons in a double-well optical lattice by investigating stationary Bloch solutions to the nonlinear equations of motion. We show that, for any positive interaction strength, a loop structure emerges at the edge of the band structure whose existence is entirely due to interactions. This can be contrasted to the case of a conventional optical (Bravais) lattice where a loop appears only above a critical repulsive interaction strength. Motivated by the possibility of realizing such nonlinear Bloch states experimentally, we analyze the collective excitations about these nonlinear stationary states and thereby establish conditions for the system's energetic and dynamical stability. We find that there are regimes that are dynamically stable and thus apt to be realized experimentally.

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Section: Introductionmentioning

confidence: 99%

Loop-structure stability of a double-well-lattice Bose-Einstein condensate

Hui¹,

Barnett²,

Porto³

et al. 2012

Phys. Rev. A

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show abstract

“…It has been shown in Refs. [24,25] that this can be experimentally realized in a bichromatic optical lattice, produced in an optical set-up comprising two nested Michelson interferometers. This yields an optical potential V (x, y, t) = V L (x, y)+V R (x, y, t) consisting of the stationary square lattice V L (x, y) = −V 0 sin 2 (kx) + sin 2 (ky) of Eq.…”

Section: D Optical Lattice With Staggered Rotationmentioning

confidence: 99%

Effective time-independent description of optical lattices with periodic driving

Hemmerich

2010

Phys. Rev. A

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For a periodically driven quantum system an effective time-independent Hamiltonian is derived with an eigen-energy spectrum, which in the regime of large driving frequencies approximates the quasi-energies of the corresponding Floquet Hamiltonian. The effective Hamiltonian is evaluated for the case of optical lattice models in the tight-binding regime subjected to strong periodic driving. Three scenarios are considered: a periodically shifted one-dimensional (1D) lattice, a twodimensional (2D) square lattice with inversely phased temporal modulation of the well depths of adjacent lattice sites, and a 2D lattice subjected to an array of microscopic rotors commensurate with its plaquette structure. In case of the 1D scenario the rescaling of the tunneling energy, previously considered by Eckardt et al. in Phys. Rev. Lett. 95, 260404 (2005), is reproduced. The 2D lattice with well depth modulation turns out as a generalization of the 1D case. In the 2D case with staggered rotation, the expression previously found in the case of weak driving by Lim et al. in Phys. Rev. Lett. 100, 130402 (2008) is generalized, such that its interpretation in terms of an artificial staggered magnetic field can be extended into the regime of strong driving.

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Kinetic Thomas–Fermi solutions of the Gross–Pitaevskii equation

Cited by 2 publications

References 34 publications

Loop-structure stability of a double-well-lattice Bose-Einstein condensate

Loop-structure stability of a double-well-lattice Bose-Einstein condensate

Effective time-independent description of optical lattices with periodic driving

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