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arXiv:1608.01020 · Journal of Physics B Atomic Molecular and Optical Physics

Collective modes of trapped spinor Bose–Einstein condensates

C Trallero-Giner, Darío G. Santiago-Pérez, Vı́ctor Romero-Rochı́n, G E Marques

Published Oct 23, 2017• 0 citations
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Abstract

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.

DOI
10.1088/1361-6455/aa8b3f

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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.
We study the damping of the collective excitations of Bose-Einstein condensates in a harmonic trap potential loaded in an optical lattice. In the presence of a confining potential the system is inhomogeneous and the collective excitations are characterized by a set of discrete confined phononlike excitations. We derive a general convenient analytical description for the damping rate, which takes into account the trapping potential and the optical lattice for the Landau and Beliaev processes at any temperature TTT. At high temperature or weak spatial confinement, we show that both mechanisms display a linear dependence on TTT. In the quantum limit, we find that the Landau damping is exponentially suppressed at low temperatures and the total damping is independent of TTT. Our theoretical predictions for the damping rate under the thermal regime is in complete correspondence with the experimental values reported for the one-dimensional (1D) condensate of sodium atoms. We show that the laser intensity can tune the collision process, allowing a resonant effect for the condensate lifetime. Also, we study the influence of the attractive or repulsive nonlinear terms on the decay rate of the collective excitations. A general expression for the renormalized Goldstone frequency is obtained as a function of the 1D nonlinear self-interaction parameter, laser intensity, and temperature.
The dynamics of a Bose-Einstein condensate in a harmonic trap with a nonadiabatically loaded optical lattice is studied analytically. As the global effect of the optical potential can be described in terms of a renormalized interaction coupling constant and of an effective mass in the laser direction, a fast loading can be understood as a sudden change of those characteristic parameters. In this approach, a standard scaling transformation is applied to study the resulting dynamics, in particular, the generation of collective modes. The relevance of the excited modes to the interference patterns obtained after free expansion is analyzed. The applicability of trap-frequency adjustments as a strategy for suppressing the loading induced excitations is discussed.
We investigate the collective excitations of a Raman-induced spin-orbit coupled Bose-Einstein condensate confined in a quasi-one-dimensional harmonic trap using the Bogoliubov method. By tuning the Raman coupling strength, three phases of the system can be identified. By calculating the transition strength, we are able to classify various excitation modes that are experimentally relevant. We show that the three quantum phases possess distinct features in their collective excitation properties. In particular, the spin dipole and the spin breathing modes can be used to clearly map out the phase boundaries. We confirm these predictions by direct numerical simulations of the quench dynamics that excites the relevant collective modes.
We study low-lying collective modes of an elongated 87Rb condensate produced in a 3D magnetic harmonic trap with the addition of a 1D periodic potential which is provided by a laser standing wave along the axial direction. While the transverse breathing mode remains unperturbed, quadrupole and dipole oscillations along the optical lattice are strongly modified. Precise measurements of the collective mode frequencies at different heights of the optical barriers provide a stringent test of the theoretical model recently introduced [M. Krämer, Phys. Rev. Lett. 88, 180404 (2002)]].
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.