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arXiv · 1310.0281

Breathing mode in the Bose-Hubbard chain with a harmonic trapping potential

Wladimir Tschischik·Roderich Moessner·Masudul Haque
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Abstract

We investigate the breathing mode of harmonically trapped bosons in an optical lattice at small site occupancies. The Bose-Hubbard model with a trapping potential is used to describe the breathing-mode dynamics initiated through weak quenches of the trap strength. We connect to results for continuum bosons (Lieb-Liniger and Gross-Pitaevskii results) and also present deviations from continuum physics. We take a spectral perspective, identifying the breathing mode frequency with a particular energy gap in the spectrum of the trapped Bose-Hubbard Hamiltonian. We present the low energy eigenspectrum of the trapped many-boson system, and study overlaps of the initial state with eigenstates of the quenched Hamiltonian. There is an intermediate interaction regime, between a "free-boson" limit and a "free-fermion" limit, in which the Bose-Hubbard breathing mode frequency approaches the Gross-Pitaevskii prediction. In addition, we present a striking failure of the time-dependent Gutzwiller approximation for describing breathing modes.

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Wladimir Tschischik, Roderich Moessner, Masudul Haque. 2013-10-01. Breathing mode in the Bose-Hubbard chain with a harmonic trapping potential. https://doi.org/10.1103/physreva.88.063636

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