Theory of superfluidity and drag force in the one-dimensional Bose gas

  title={Theory of superfluidity and drag force in the one-dimensional Bose gas},
  author={Alexander Yu. Cherny and Jean-S{\'e}bastien Caux and Joachim Brand},
  journal={Frontiers of Physics},
The one-dimensional Bose gas is an unusual superfluid. In contrast to higher spatial dimensions, the existence of non-classical rotational inertia is not directly linked to the dissipationless motion of infinitesimal impurities. Recently, experimental tests with ultracold atoms have begun and quantitative predictions for the drag force experienced by moving obstacles have become available. This topical review discusses the drag force obtained from linear response theory in relation to Landau’s… 

Beyond superfluidity in non-equilibrium Bose–Einstein condensates

The phenomenon of superfluidity in open Bose–Einstein condensates (BEC) is analysed numerically and analytically. It is found that a superfluid phase is feasible above the speed of sound, when forces

Critical velocity for superfluidity in the one-dimensional mean-field regime: From matter to light quantum fluids

We determine in a nonperturbative way the critical velocity for superfluidity of a generic quantum fluid flowing past a localized obstacle in the one-dimensional mean-field regime. We get exact

Influence of quantum fluctuations on the superfluid critical velocity of a one-dimensional Bose gas

Abstract The mean-field Gross-Pitaevskii equation with repulsive interactions exhibits frictionless flow when stirred by an obstacle below a critical velocity. Here we go beyond the mean-field

Critical velocity for superfluidity in one dimension: From matter to light quantum fluids

A one-dimensional quantum fluid flows past an obstacle. Below a certain speed, its motion becomes superfluid, unbraked by the obstacle. How does this critical velocity for superfluidity depend on the

Bogoliubov Theory for a Superfluid Bose Gas Flowing in a Random Potential: Stability and Critical Velocity

We investigate the stability and critical velocity of a weakly interacting Bose gas flowing in a random potential. By applying the Bogoliubov theory to a disordered Bose system with a steady flow,

Landau instability and mobility edges of the interacting one-dimensional Bose gas in weak random potentials

We study the frictional force exerted on the trapped, interacting 1D Bose gas under the influence of a moving random potential. Specifically we consider weak potentials generated by optical speckle

Superfluidity and Chaos in low dimensional circuits

It is shown that the standard Landau and Bogoliubov superfluidity criteria fail in low-dimensional circuits, and novel types of superfluidity are found, associated with irregular or chaotic or breathing vortex states.

Dynamical Structure Factor of the Lieb–Liniger Model and Drag Force Due to a Potential Barrier

In this chapter, whose original results are mostly based on Refs. [1, 2], I take the next step towards the full characterization of a 1D Bose gas through its correlation functions. Going beyond

Superfluidity in Bose-Hubbard circuits

A semiclassical theory is provided for the metastability regime-diagram of atomtronic superfluid circuits. Such circuits typically exhibit high-dimensional chaos; and non-linear resonances that



Drag force on an impurity below the superfluid critical velocity in a quasi-one-dimensional Bose-Einstein condensate.

The next order correction due to quantum and thermal fluctuations is calculated and a nonzero force is found acting on a delta-function impurity moving through a quasi-one-dimensional Bose-Einstein condensate at all subcritical velocities and at all temperatures.

Decay of superfluid currents in the interacting one-dimensional Bose gas

We examine the superfluid properties of a one-dimensional (1D) Bose gas in a ring trap based on the model of Lieb and Liniger. While the 1D Bose gas has nonclassical rotational inertia and exhibits

Heavily damped motion of one-dimensional Bose gases in an optical lattice.

The damping of the dipole oscillations is significant even for shallow lattices, and the motion becomes overdamped with increasing lattice depth as observed, and it is shown that the transition to overdamping is attributed to the decay of superfluid flow accelerated by quantum fluctuations.

Superfluidity versus Anderson localization in a dilute Bose gas.

This work considers the motion of a quasi-one-dimensional beam of Bose-Einstein condensed particles in a disordered region of finite extent and compute analytically the interaction-dependent localization length, explaining the disappearance of the supersonic stationary flow for large disordered samples.

Superfluidity versus Bloch oscillations in confined atomic gases.

This work finds the nucleation rate for phase slips using instanton techniques and finds Bloch oscillations in the chemical potential that describe the individual tunneling of atoms through the defect and thus are a consequence of particle quantization.

Quantum stirring as a probe of superfluidlike behavior in interacting one-dimensional Bose gases

We propose quantum stirring with a laser beam as a probe of superfluidlike behavior for a strongly interacting one-dimensional Bose gas confined to a ring. Within the Luttinger liquid theory

Dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit

While the one-dimensional (1D) Bose gas appears to exhibit superfluid response under certain conditions, it fails the Landau criterion according to the elementary excitation spectrum calculated by

Dynamic polarizability of a one-dimensional harmonically confined strongly interacting Bose gas

We calculate the dynamic polarizability of a one-dimensional Bose gas confined into a parabolic trap near the Tonks–Girardeau limit. We use the duality between the one-dimensional Bose gas with

Phase diagram for a Bose-Einstein condensate moving in an optical lattice.

The phase diagram for the disappearance of superfluidity as a function of momentum and lattice depth between these two limits is studied and the phase boundary extrapolates to the critical lattice Depth for the superfluid-to-MI transition with 2% precision.

Weakly interacting Bose gas in a random environment

The localization-disorder paradigm is analyzed for a specific system of weakly repulsive Bose gas at zero temperature placed into a quenched random potential. We show that at low average density or