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arXiv:0906.2314 · Physical Review A

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

Alexander Yu. Cherny, Jean-Sébastien Caux, Joachim Brand

Published Oct 9, 2009• 19 citations
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Abstract

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 quantization of velocities, the metastability of currents depends sensitively on the strength of interactions in the gas: the stronger the interactions, the faster the current decays. It is shown that the Landau critical velocity is zero in the thermodynamic limit due to the first supercurrent state, which has zero energy and finite probability of excitation. We calculate the energy dissipation rate of ring currents in the presence of weak defects, which should be observable on experimental time scales.

DOI
10.1103/physreva.80.043604

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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 quantization of velocities, the metastability of currents depends sensitively on the strength of interactions in the gas: the stronger the interactions, the faster the current decays. It is shown that the Landau critical velocity is zero in the thermodynamic limit due to the first supercurrent state, which has zero energy and finite probability of excitation. We calculate the energy dissipation rate of ring currents in the presence of weak defects, which should be observable on experimental time scales.
Different aspects of superfluidity in one dimension (1D) are discussed in this paper. It is shown that the Hess-Fairbank effect takes place in 1D at zero temperature. In particular, the rotational inertia of an interacting 1D Bose gas in a finite ring is zero. Nevertheless, our results indicate that the frictionless motion of impurities depends sensitively on the strength of interactions in the gas. In general, this is possible only in a limit of weak interactions. We obtain the phase diagram of frictionless motion for the gas immersed into a moving shallow optical lattice. In this case the drag force, a quantitative measure of superfluidity, can be zero at specific values of lattice velocity and the gas density even for strong
This is a chapter for a book. The first paragraph of this chapter is as follows: "Ultracold quantum gases offer a wonderful playground for quantum many body physics, as experimental systems are widely controllable, both statically and dynamically. One such system is the one-dimensional (1D) Bose gas on a ring. In this system binary contact interactions between the constituent bosonic atoms, usually alkali metals, can be controlled in both sign and magnitude; a recent experiment has tuned interactions over seven orders of magnitude, using an atom-molecule resonance called a Feshbach resonance. Thus one can directly realize the Lieb-Liniger Hamiltonian, from the weakly- to the strongly-interacting regime. At the same time there are a number of experiments utilizing ring traps. The ring geometry affords us the opportunity to study topological properties of this system as well; one of the main properties of a superfluid is the quantized circulation in which the average angular momentum per particle, L/N, is quantized under rotation. Thus we focus on a tunable 1D Bose system for which the main control parameters are interaction and rotation. We will show that there is a critical boundary in the interaction-rotation control-parameter plane over which the topological properties of the system change. This is the basis of our concept of \textit{metastable quantum phase transitions} (QPTs). Moreover, we will show that the finite domain of the ring is necessary for the QPT to occur at all because the zero-point kinetic pressure can induce QPTs, i.e., the system must be finite; we thus seek to generalize the concept of QPTs to inherently finite, mesoscopic or nanoscopic systems."
We propose quantum stirring with a laser beam as a probe of superfluidity in a strongly interacting one-dimensional Bose gas confined to a ring. Within the Luttinger liquid theory framework, we calculate the fraction of stirred particles per period as a function of the stirring velocity, the interaction strength and the coupling between the stirring beam and the bosons. The fraction of stirred particles crosses over at a critical velocity from a constant at low velocities to a characteristic power law at high velocities. The critical velocity depends on the size of the ring and vanishes in the thermodynamic limit. Details of this cross-over depend on the interaction strength and on the coupling between the stirring beam and the bosons. Our results are relevant for ongoing experiments on ring-trapped Bose-Einstein condensates.
We propose quantum stirring with a laser beam as a probe of superfluid behavior for a strongly interacting one-dimensional Bose gas confined to a ring. Within the Luttinger liquid theory framework, we calculate the fraction of stirred particles per period as a function of the stirring velocity, the interaction strength and the coupling between the stirring beam and the bosons. The fraction of stirred particles allows to probe superfluidity of the system. We find that it crosses over at a critical velocity, lower than the sound one, from a characteristic power law at high velocities to a constant at low velocities. Some experimental issues on quantum stirring in ring-trapped condensates are discussed.
We have investigated the superfluid properties of a ring of weakly interacting and degenerate 1D Bose gas at thermal equilibrium with a rotating vessel. The conventional definition of superfluidity predicts that the gas has a significant superfluid fraction only in the Bose condensed regime. In the opposite regime, it is found that a superfluid behaviour can still be identified when the probability distribution of the total momentum of the gas has a multi-peaked structure, revealing unambiguously the existence of ‘superfluid’ supercurrent states that did not show up in the conventional definition of superfluidity.