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arXiv:cond-mat/0512716 · Physical Review A

Oscillations of Bose-Einstein condensates in a one-dimensional optical superlattice

Chou-Chun Huang, W. C. Wu

Published Dec 5, 2005• 11 citations
arXivHTMLPDF

Abstract

Oscillations of atomic Bose-Einstein condensates in a 1D optical lattice with a two-point basis is investigated. In the low-frequency regime, four branches of modes are resolved, that correspond to the transverse in-phase and out-of-phase breathing modes, and the longitudinal acoustic and optical phonon modes of the condensates. Dispersions of these modes depend intimately on the values of two intersite Josephson tunneling strengths, ${J}_{1}$ and ${J}_{2}$, and the on-site repulsion $U$ between the atoms. Observation of these mode dispersions is thus a direct way to access them.

DOI
10.1103/physreva.72.065601

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Oscillations of atomic Bose-Einstein condensates in a 1D optical lattice with a two-point basis is investigated. In the low-frequency regime, four branches of modes are resolved, that correspond to the transverse in-phase and out-of-phase breathing modes, and the longitudinal acoustic and optical phonon modes of the condensates. Dispersions of these modes depend intimately on the values of two intersite Josephson tunneling strengths, J1{J}_{1}J1​ and J2{J}_{2}J2​, and the on-site repulsion UUU between the atoms. Observation of these mode dispersions is thus a direct way to access them.
We derive and study the Bloch and Bogoliubov spectrum of a Bose–Einstein condensate (BEC) confined in a one-dimensional optical superlattice (created by interference between a primary optical lattice and a secondary optical lattice of small strength), using the Bogoliubov approximation and the hydrodynamic theory with mode coupling. We show that a BEC in an optical superlattice experiences two different tunnelling parameters and hence behaves like a diatomic chain. We derive expressions for the tunnelling parameters as a function of the strength of the primary and secondary lattice. This gives rise to a gapped branch in addition to the gapless acoustical branch in the Bogoliubov spectrum. The spectrum strongly depends on the strength of the secondary lattice, the interaction parameter and the number density of atoms. The effective mass is found to increase as the depth of the secondary optical lattice increases, a property that was utilized in Paraedes et al (2004 Nature 429 277) to achieve the Tonks–Girardeau regime. The coupling between the inhomogeneous density in the radial plane and the density modulation along the optical lattice gives rise to a multibranch Bogoliubov spectrum.
We investigate the low-lying excitations of a stack of weakly coupled two-dimensional Bose-Einstein condensates, which is formed by a one-dimensional optical lattice. In particular, we calculate the dispersion relations of the monopole and quadrupole modes, both for the ground state as well as for the case in which the system contains a vortex along the direction of the lasers creating the optical lattice. Our variational approach enables us to determine analytically the dispersion relations for an arbitrary number of atoms in every two-dimensional condensate and for an arbitrary momentum. We also discuss the feasibility of observing our results experimentally.
We explore the dynamics of a Bose–Einstein condensate created in the combined potential of a far-detuned laser standing wave superimposed to a 3D harmonic magnetic potential. We report the investigation of low-lying collective modes showing that the macroscopic dynamics along the optical lattice is strongly modified, resulting in a shift of the dipole and quadrupole mode frequencies depending on the height of the optical lattice, whereas the transverse breathing mode, occurring perpendicularly to the lattice axis, is not perturbed. The experimental findings are compared with the theoretical treatment that generalizes the hydrodynamic equation of superfluids for a weakly interacting Bose gas to include the effects of the periodic potential. We show that the array of condensates trapped in the optical wells and driven by the harmonic magnetic potential is equivalent to an array of Josephson junctions. In the regime of ‘small’ amplitude dipole oscillation the system performs a collective motion and we investigate the current–phase dynamics measuring the critical Josephson current. Increasing the amplitude of the dipole oscillation, we observe a transition from the coherent oscillation (superfluid regime) to a localization of the condensates in the harmonic trap (‘insulator’ regime). The onset of the coherent regime breakdown is interpreted as the result of a discrete modulational instability occurring when the velocity of the centre of mass of the system is larger than a critical velocity proportional to the tunnelling rate between adjacent wells.
We have loaded Bose-Einstein condensates into one-dimensional, off-resonant optical lattices and accelerated them by chirping the frequency difference between the two lattice beams. For small values of the lattice well depth, Bloch oscillations were observed. Reducing the potential depth further, Landau-Zener tunneling out of the lowest lattice band, leading to a breakdown of the oscillations, was also studied and used as a probe for the effective potential resulting from mean-field interactions as predicted by Choi and Niu [Phys. Rev. Lett. 82, 2022 (1999)]. The effective potential was measured for various condensate densities and trap geometries, yielding good qualitative agreement with theoretical calculations.
Abstract We study the structure of quasi-one-dimensional Bogoliubov–de Genes collective excitations of inhomogeneous F = 1 spinor Bose–Einstein condensates confined by a harmonic trap potential and loaded into an optical lattice. Employing a perturbative method, we report general analytical expressions for the polar and ferromagnetic confined collective oscillations. In both cases, the excited eigenfrequencies are given as functions of the effective 1D coupling constants, the trap frequency and the optical lattice parameters. While the presence of the trap yields quantized longitudinal collective modes, whose spectra depends on the collision scattering lengths, the optical lattice shifts their frequencies and, more importantly, yields tunable oscillations of the spin populations, for the even modes, as experimentally observed.