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arXiv:cond-mat/0410491 · Physical Review Letters

Strongly Inhibited Transport of a Degenerate 1D Bose Gas in a Lattice

Chad Fertig, K. O’Hara, J. H. Huckans, S. L. Rolston, William D. Phillips, J. V. Porto

Published Apr 1, 2005• 214 citations
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Abstract

We report the observation of strongly damped dipole oscillations of a quantum degenerate 1D atomic Bose gas in a combined harmonic and optical lattice potential. Damping is significant for very shallow axial lattices (0.25 photon recoil energies), and increases dramatically with increasing lattice depth, such that the gas becomes nearly immobile for times an order of magnitude longer than the single-particle tunneling time. Surprisingly, we see no broadening of the atomic quasimomentum distribution after damped motion. Recent theoretical work suggests that quantum fluctuations can strongly damp dipole oscillations of a 1D atomic Bose gas, providing a possible explanation for our observations.

DOI
10.1103/physrevlett.94.120403

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We report the observation of strongly damped dipole oscillations of a quantum degenerate 1D atomic Bose gas in a combined harmonic and optical lattice potential. Damping is significant for very shallow axial lattices (0.25 photon recoil energies), and increases dramatically with increasing lattice depth, such that the gas becomes nearly immobile for times an order of magnitude longer than the single-particle tunneling time. Surprisingly, we see no broadening of the atomic quasimomentum distribution after damped motion. Recent theoretical work suggests that quantum fluctuations can strongly damp dipole oscillations of a 1D atomic Bose gas, providing a possible explanation for our observations.
We study the dynamics of strongly correlated one-dimensional Bose gases in a combined harmonic and optical lattice potential subjected to sudden displacement of the confining potential. Using the time-evolving block decimation method, we perform a first-principles quantum many-body simulation of the experiment of Fertig et al. [Phys. Rev. Lett. 94, 120403 (2005)] across different values of the lattice depth ranging from the superfluid to the Mott insulator regimes. We find good quantitative agreement with this experiment: the damping of the dipole oscillations is significant even for shallow lattices, and the motion becomes overdamped with increasing lattice depth as observed. We show that the transition to overdamping is attributed to the decay of superfluid flow accelerated by quantum fluctuations, which occurs well before the emergence of Mott insulator domains.
We study damping of the dipole oscillation in a Bose-condensed gas in a combined cigar-shaped harmonic trap and one-dimensional (1D) optical lattice potential at finite temperatures. In order to include the effect of thermal excitations in the radial direction, we derive a quasi-1D model of the Gross-Pitaevskii equation and the Bogoliubov equations. We use the Popov approximation to calculate the temperature dependence of the condensate fraction with varying lattice depth. We then calculate the Landau damping rate of the dipole oscillation as a function of the lattice depth and temperature. The damping rate increases with increasing lattice depth, which is consistent with experimental observations. The magnitude of the damping rate is in reasonable agreement with experimental data. We also find that the damping rate has a strong temperature dependence, showing a sharp increase with increasing temperature. Finally, we emphasize the importance of the radial thermal excitations in both equilibrium properties and the Landau damping.
We present a theoretical treatment of the surprisingly large damping observed recently in one-dimensional Bose-Einstein atomic condensates in optical lattices. We show that time-dependent Hartree-Fock-Bogoliubov (HFB) calculations can describe qualitatively the main features of the damping observed over a range of lattice depths. We also derive a formula of the fluctuation-dissipation type for the damping, based on a picture in which the coherent motion of the condensate atoms is disrupted as they try to flow through the random local potential created by the irregular motion of noncondensate atoms. When parameters for the characteristic strength and correlation times of the fluctuations, obtained from the HFB calculations, are substituted in the damping formula, we find very good agreement with the experimentally observed damping, as long as the lattice is shallow enough for the fraction of atoms in the Mott insulator phase to be negligible. We also include, for completeness, the results of other calculations based on the Gutzwiller ansatz, which appear to work better for the deeper lattices.
We present a theoretical treatment of the surprisingly large damping observed recently in one-dimensional Bose-Einstein atomic condensates in optical lattices. We show that time-dependent Hartree-Fock-Bogoliubov (HFB) calculations can describe qualitatively the main features of the damping observed over a range of lattice depths. We also derive a formula of the fluctuation-dissipation type for the damping, based on a picture in which the coherent motion of the condensate atoms is disrupted as they try to flow through the random local potential created by the irregular motion of noncondensate atoms. We expect this irregular motion to result from the well-known dynamical instability exhibited by the mean-field theory for these systems. When parameters for the characteristic strength and correlation times of the fluctuations, obtained from the HFB calculations, are substituted in the damping formula, we find very good agreement with the experimentally-observed damping, as long as the lattice is shallow enough for the fraction of atoms in the Mott insulator phase to be negligible. We also include, for completeness, the results of other calculations based on the Gutzwiller ansatz, which appear to work better for the deeper lattices.
We theoretically study the dipolar motion of bosonic atoms in a very shallow, strongly confined 1D optical lattice using the parameters of the recent experiment [C. D. Fertig, Phys. Rev. Lett. 94, 120403 (2005)]. We find that, due to momentum uncertainty, a small, but non-negligible, atom population occupies the unstable velocity region of the corresponding classical dynamics, resulting in the observed dissipative atom transport. This population is generated even in a static vapor, due to quantum fluctuations which are enhanced by the lattice and the confinement, and is not notably affected by the motion of atoms or finite temperature.
We study the dynamics of Bose–Einstein condensed atoms in a one-dimensional (1D) optical lattice potential in a regime where the collective (Josephson) tunnelling energy is comparable with the on-site interaction energy, and the number of particles per lattice site is mesoscopically large. By directly imaging the motion of atoms in the lattice, we observe an abrupt suppression of atom transport through the array for a critical ratio of these energies, consistent with quantum fluctuation induced localization. Directly below the onset of localization, the frequency of the observed superfluid transport can be explained by a phonon excitation but deviates substantially from that predicted by the hydrodynamic/Gross–Pitaevskii equations.