Spatial period-doubling in Bose-Einstein condensates in an optical lattice

Abstract

We demonstrate that there exist stationary states of Bose-Einstein condensates in an optical lattice that do not satisfy the usual Bloch periodicity condition. Using the discrete model appropriate to the tight-binding limit we determine energy bands for period-doubled states in a one-dimensional lattice. In a complementary approach we calculate the band structure from the Gross-Pitaevskii equation, considering both states of the usual Bloch form and states which have the Bloch form for a period equal to twice that of the optical lattice. We show that the onset of dynamical instability of states of the usual Bloch form coincides with the occurrence of period-doubled states with the same energy. The period-doubled states are shown to be related to periodic trains of solitons.

4 pages, 3 figures, change of content

References in corpus (11)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Josephson Junction Arrays with Bose-Einstein Condensates
• Landau and Dynamical Instabilities of the Superflow of Bose-Einstein Condensates in Optical Lattices
• Superfluid and Dissipative Dynamics of a Bose-Einstein Condensate in a Periodic Optical Potential
• Bose-Einstein condensates in standing waves: The cubic nonlinear Schroedinger equation with a periodic potential
• Dynamical Superfluid-Insulator Transition in a Chain of Weakly Coupled Bose-Einstein Condensates
• Band structure, elementary excitations, and stability of a Bose-Einstein condensate in a periodic potential
• Superfluid current disruption in a chain of weakly coupled Bose-Einstein Condensates
• Expansion of a coherent array of Bose-Einstein condensates
• Loop structure of the lowest Bloch band for a Bose-Einstein condensate
• Bose-Einstein condensates in 1D optical lattices: compressibility, Bloch bands and elementary excitations

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