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arXiv:1610.08982 · Physical Review A

Thermally activated phase slips of one-dimensional Bose gases in shallow optical lattices

Masaya Kunimi, Ippei Danshita

Published Mar 31, 2017• 9 citations
arXivHTMLPDF

Abstract

We study the decay of superflow via thermally activated phase slips in one-dimensional Bose gases in a shallow optical lattice. By using the Kramers formula, we numerically calculate the nucleation rate of a thermally activated phase slip for various values of the filling factor and flow velocity in the absence of a harmonic trapping potential. Within the local density approximation, we derive a formula connecting the phase-slip nucleation rate with the damping rate of a dipole oscillation of the Bose gas in the presence of a harmonic trap. We use the derived formula to directly compare our theory with the recent experiment done by the LENS group [L. Tanzi et al., Sci. Rep. 6, 25965 (2016)]. From the comparison, the observed damping of dipole oscillations in a weakly correlated and small velocity regime is attributed dominantly to thermally activated phase slips rather than quantum phase slips.

DOI
10.1103/physreva.95.033637

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We study the decay of superflow via thermally activated phase slips in one-dimensional Bose gases in a shallow optical lattice. By using the Kramers formula, we numerically calculate the nucleation rate of a thermally activated phase slip for various values of the filling factor and flow velocity in the absence of a harmonic trapping potential. Within the local density approximation, we derive a formula connecting the phase-slip nucleation rate with the damping rate of a dipole oscillation of the Bose gas in the presence of a harmonic trap. We use the derived formula to directly compare our theory with the recent experiment done by the LENS group [L. Tanzi et al., Sci. Rep. 6, 25965 (2016)]. From the comparison, the observed damping of dipole oscillations in a weakly correlated and small velocity regime is attributed dominantly to thermally activated phase slips rather than quantum phase slips.
We study superflow decay via quantum phase slips in trapped one-dimensional (1D) quantum gases through dipole oscillations induced by sudden displacement of the trapping potential. We find the relation between the damping rate of the dipole oscillation G and the phase-slip nucleation rate Γ as G∝Γ/v, where v is the flow velocity. This relation allows us to show that damping of 1D Bose gases in optical lattices, which has been extensively studied in experiment, is due to quantum phase slips. It is also found that the damping rate versus the flow velocity obeys the scaling formula for an impurity potential even in the absence of an explicit impurity. We suggest that the damping rate at a finite temperature exhibits a universal crossover behavior upon changing the flow velocity.
We study the decay of superflow of a one-dimensional (1D) superfluid in the presence of a periodic potential. In 1D, superflow at zero temperature can decay via quantum nucleation of phase slips even when the flow velocity is much smaller than the critical velocity predicted by mean-field theories. Applying the instanton method to the O(2) quantum rotor model, we calculate the nucleation rate of quantum phase slips $\ensuremath{\Gamma}$. When the flow momentum ppp is small, we find that the nucleation rate per unit length increases algebraically with ppp as $\ensuremath{\Gamma}/L\ensuremath{\propto}{p}^{2K\ensuremath{-}2}$, where LLL is the system size and KKK is the Tomonaga-Luttinger parameter. Based on the relation between the nucleation rate and the quantum superfluid-insulator transition, we present a unified explanation on the scaling formulas of the nucleation rate for periodic, disorder, and single-barrier potentials. Using the time-evolving block decimation method, we compute the exact quantum dynamics of the superflow decay in the 1D Bose-Hubbard model at unit filling. From the numerical analyses, we show that the scaling formula is valid for the case of the Bose-Hubbard model, which can quantitatively describe Bose gases in optical lattices.
Quantum phase slips are the primary excitations in one-dimensional superfluids and superconductors at low temperatures but their existence in ultracold quantum gases has not been demonstrated yet. We now study experimentally the nucleation rate of phase slips in one-dimensional superfluids realized with ultracold quantum gases, flowing along a periodic potential. We observe a crossover between a regime of temperature-dependent dissipation at small velocity and interaction and a second regime of velocity-dependent dissipation at larger velocity and interaction. This behavior is consistent with the predicted crossover from thermally-assisted quantum phase slips to purely quantum phase slips.
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 present an analytical derivation for the quantum decay rate of the superflow through a weak link in a one-dimensional Bose-Einstein-condensate. The effective action for the phase difference across the link reduces to that of a massive particle with damping subject to a periodic potential. We find an algebraic flow-pressure relation, characteristic for quantum nucleation of phase slips in the link and show how short-wave length fluctuations renormalizing the interaction between the Bosons remove the quantum phase transition expected in this class of systems.
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.