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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 a trapped system 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).
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