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In recent years, experiments with ultracold atoms [1,2,3,4] have investigated transport properties of one-dimensional (1D) Bose gases in optical lattices and shown that the transport in 1D is drastically suppressed even in the superfluid state compared to that in higher dimensions. Motivated by the experiments, we study superfluid transport of 1D Bose gases. 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. Using instanton techniques, we calculate the nucleation rate \Gamma_{prd} of a quantum phase slip for a 1D superfluid in a periodic potential and show that it increases in a power-law with the flow momentum p, as \Gamma_{prd} ~ p^{2K-2}, when p is much smaller than the critical momentum [5]. Here, L and K denote the system size and the Luttinger parameter. To make a connection with the experiments, we simulate the dipole oscillations of 1D Bose gases in the presence of a trapping potential with use of the quasi-exact numerical method of time-evolving block decimation. From the simulations, we relate the nucleation rate with the damping rate of dipole oscillations, which is a typical experimental observable [1,3], and show that the damping rate indeed obeys the power-law, meaning that the suppression of the transport in 1D is due to quantum phase slips. We also suggest a way to identify the superfluid-insulator transition point from the dipole oscillations.
References:
[1] C. D. Fertig et al., Phys. Rev. Lett. 94, 120403 (2005).
[2] J. Mun et al., Phys. Rev. Lett. 99, 150604 (2007).
[3] E. Haller et al., Nature 466, 597 (2010).
[4] B. Gadway et al., Phys. Rev. Lett. 107, 145306 (2011).
[5] I. Danshita and A. Polkovnikov, Phys. Rev. A 85, 023638 (2012).
