Two-stage continuation algorithms for Bloch waves of Bose–Einstein condensates in optical lattices

Chien, C.-S.; Chang, S.-L.; Wu, Biao

doi:10.1016/j.cpc.2010.06.030

Cited by 10 publications

(4 citation statements)

References 20 publications

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“…The most prominent feature is the emergence of a looped band structure when a lattice staggering V 1 = 0 is introduced. Similar phenomena were also discovered in interacting BECs on regular 1D [19-21, 37, 38] and 2D [39,40] lattices. However, a substantial looped band on a regular (unstaggered) lattice requires the interaction energy to be much larger than the lattice depth, which is experimentally a stringent condition.…”

Section: Mean-field Analysis Of the Interacting Band Structuresupporting

confidence: 72%

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: Mean-field Analysis Of the Interacting Band Structuresupporting

confidence: 72%

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

Hui¹,

Barnett²,

Porto³

et al. 2012

Phys. Rev. A

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“…Continuation methods are reliable and powerful tools for computing multiform solutions of a system of nonlinear equations involving one or more parameters. Various algorithms based on the continuation method have been successful in solving some challenging problems [31,34,14,35,27]. Recently, some numerical methods based on the gradient flow with discrete normalization (GFDN) have been proposed for computing ground states of spin-1 BEC systems [26,28,36].…”

Section: Pseudo-arclength Continuation Methods (Pacm)mentioning

confidence: 99%

A Complete Study of the Ground State Phase Diagrams of Spin-1 Bose–Einstein Condensates in a Magnetic Field Via Continuation Methods

2014

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We present a complete investigation of the ground state patterns and phase diagrams of the spin-1 Bose-Einstein condensates (BEC) confined in a harmonic or box potential under the influence of a homogeneous magnetic field. A pseudoarclength continuation method with parameter switching technique is developed to study the BEC systems numerically. The continuation process is performed on the parameter space consisting of the spin-independent interaction, spinexchange interaction and the quadratic Zeeman (QZ) energy parameters. In the first stage of the parameter switching process, we fix the QZ energy term to be zero and vary the interaction parameters from zero to the desired physical values. Next, we fix the interaction parameters and vary the QZ energy parameter in both positive and negative regions. Two types of phase transitions are found, as we vary the QZ parameter. The first type is a transition from a two-component (2C) state to a three-component (3C) state. The second type is a symmetry breaking in the 3C state. Then, a phase separation of the spin components follows. In the semi-classical regime, we find that these two phase transition curves are gradually merged.

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“…We emphasize that the appearance of the tubed structure in the BEC Bloch bands for arbitrary small c is a unique feature for a honeycomb lattice: In one dimensional lattice [16][17][18][19][20][21][22] and two dimensional square lattice [23,24], the looped or tubed nonlinear structure in the Bloch bands appears only when c is bigger than a threshhold value. This unique feature has a profound implication when the tight-binding limit is considered.…”

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confidence: 99%

Bose-Einstein Condensate in a Honeycomb Optical Lattice: Fingerprint of Superfluidity at the Dirac Point

Chen

2011

Phys. Rev. Lett.

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Mean-field Bloch bands of a Bose-Einstein condensate in a honeycomb optical lattice are computed. We find that the topological structure of the Bloch bands at the Dirac point is changed completely by atomic interaction of arbitrary small strength: the Dirac point is extended into a closed curve and an intersecting tube structure arises around the original Dirac point. These tubed Bloch bands are caused by the superfluidity of the system. Furthermore, they imply the inadequacy of the tight-binding model to describe an interacting Boson system around the Dirac point and the breakdown of adiabaticity by interaction of arbitrary small strength.

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Two-stage continuation algorithms for Bloch waves of Bose–Einstein condensates in optical lattices

Cited by 10 publications

References 20 publications

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

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

A Complete Study of the Ground State Phase Diagrams of Spin-1 Bose–Einstein Condensates in a Magnetic Field Via Continuation Methods

Bose-Einstein Condensate in a Honeycomb Optical Lattice: Fingerprint of Superfluidity at the Dirac Point

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