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Soviet Journal of Low Temperature Physics

Quasi-one-dimensional superfluidity in Bose systems

S. I. Shevchenko

Published Oct 1, 1988• 30 citations
Publisher

Abstract

The theory of superfluidity of bosons in narrow channels forming a network in space is constructed. It is shown that the temperature Tc of superfluidity transition, below which the system has a long-range order, is equal to h2n/Ml in order of magnitude (here, n is the one-dimensional density of bosons of mass M and l the characteristic length of a link in the network). A generalization of the Ginzburg–Gross–Pitaevskii (GGP) equation permitting an analysis of the decay of current state is proposed. The relaxation time τ for the current state at T > Tc is estimated. It is shown that for a flow velocity υ→0, the relaxation time τ ∝ exp (ħnc/T), where c is the velocity of sound. For ħnc ≫ T ≫ Tc, the supercurrent decay time is astronomically large and quasisuperfluidity cannot be distinguished from true superfluidity in spite of the absence of a long-range order.

DOI
10.1063/10.0032031

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The theory of superfluidity of bosons in narrow channels forming a network in space is constructed. It is shown that the temperature Tc of superfluidity transition, below which the system has a long-range order, is equal to h2n/Ml in order of magnitude (here, n is the one-dimensional density of bosons of mass M and l the characteristic length of a link in the network). A generalization of the Ginzburg–Gross–Pitaevskii (GGP) equation permitting an analysis of the decay of current state is proposed. The relaxation time τ for the current state at T > Tc is estimated. It is shown that for a flow velocity υ→0, the relaxation time τ ∝ exp (ħnc/T), where c is the velocity of sound. For ħnc ≫ T ≫ Tc, the supercurrent decay time is astronomically large and quasisuperfluidity cannot be distinguished from true superfluidity in spite of the absence of a long-range order.
The possibility of delocalization of particles in a quantum crystal at the nucleus of a dislocation and the transition of delocalized particles into a superfluid state are predicted. A theory is constructed for the one-dimensional superfluidity of a slightly nonideal Bose gas. The effect of impurities on the superfluid density is studied and it is shown that impurities do not destroy the superfluidity, but rather make an additional contribution to the normal component, different from zero even at T = 0. The flow of the superfluid current through a weak link is studied. It is established that in spite of the fact that there is no long-range order in the one-dimensional case, a superfluid current will flow through a weak link without dissipation. Some experimental manifestations of dislocation superfluidity are discussed.
We investigate the zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with power-law hopping decaying with distance as 1/r^{α} using exact large scale quantum Monte Carlo simulations. For all 1<α≤3 the quantum phase transition from a superfluid and a Mott insulator at unit filling is found to be continuous and scale invariant, in marked contrast with the Berezinskii-Kosterlitz-Thouless (BKT) scenario that is recovered only for α>3. By performing finite-size scaling collapses of the superfluid stiffness and extracting dynamical and correlation-length exponents from the low-energy spectrum, we establish that these transitions define a distinct universality class throughout the long-range regime 1<α≤3. Analysis of the single-particle correlation functions and grand canonical phase diagram further reveals a sequence of ordering regimes within the superfluid phase: true long-range order for α≤2, anomalous quasi-long-range order for 2<α≤3, and conventional algebraic decay for α>3. Our exact numerical results provide a benchmark to compare theories of long-range quantum models and are relevant for experiments with cold neutral atom, molecules and ion chains.
This paper develops and implements the stochastic projected Gross-Pitaevskii equation for spin-1 Bose gases, addressing key considerations for numerical simulations. As an application of the theory we explore equilibrium phases in a two-dimensional spin-1 gas, where quasi-long-range order emerges via a Berezinskii-Kosterlitz-Thouless transition. Our analysis includes the definition of superfluid densities for both mass and spin degrees of freedom in a manner suitable for implementation within a stochastic projected Gross-Pitaevskii equation simulation. We present a finite-temperature phase diagram for the ferromagnetic spin-1 Bose gas and identify three distinct superfluid phases: two exhibiting conventional Berezinskii-Kosterlitz-Thouless-like behavior and an additional phase that simultaneously supports independent mass and spin superflows. As temperature increases, the stability region of this additional phase shrinks. We provide a characterization of the phase transitions through consideration of the spin-component densities and the unbinding of multiple types of vortices. This work provides a foundation for further studies of nonequilibrium and finite-temperature phenomena in spinor Bose gases.
Spinor Bose gases may exhibit both phase and ferromagnetic order. Consequently, they may support superflow of both mass and spin currents. In this thesis we utilize a stochastic Gross-Pitaevskii model to investigate the superfluid properties of a two-dimensional spin-1 Bose gas with ferromagnetic interactions. Owing to the low dimensionality, the superfluidity of this system can not be attributed to the presence of a Bose-Einstein condensate, with thermal fluctuations precluding long-range order. Rather, mass and spin superfluidity emerge via respective Berezinskii-Kosterlitz-Thouless (BKT) transitions. Such transitions are characterized by the emergence of quasi-long-range order, driven by the binding of topological defect pairs. First, we consider an easy-plane ferromagnetic gas. We find the system superfluidity may be understood by direct application of existing BKT theory. In particular, mass and spin superfluidity are respectively associated with quasi-long-range order in the global phase and local magnetization. The former arises from the binding of mass vortex pairs, while the latter arises from the binding of polar-core spin vortex pairs. Following this, we introduce axial magnetization, and consider a gas in the broken-axisymmetric phase. We find axial magnetization acts to couple mass and spin superflows via a mechanism analogous to the superfluid drag exhibited by two-component superfluids. This coupling renders invalid the direct applicability of existing BKT theory: here mass and spin superfluidity may each be associated with both phase and magnetic order. We remedy this with a generalization making concrete the relation between superfluidity and quasi-long-range order in this system. In addition, through variations of the quadratic Zeeman energy and axial magnetization we identify three distinct superfluid phases, which serve as finite-temperature generalizations of the polar, broken-axisymmetric, and easy-axis ferromagnetic ground states.
Superfluid density in quasi-one-dimensional boson systems with two different transverse density profiles is calculated: In one case, bosons fill a tube almost uniformly, and in the other case, bosons are restricted on the internal surface of a tube and form a film. In both cases, the superfluid density approaches the prediction by the Tomonaga-Luttinger liquid theory as the system length becomes long, and no evidence for the scaling behavior characteristic to the Berezinskii-Kosterlitz-Thouless transition is found in the case of a film. A dimensionless quantity characterizing the one-dimensionality is introduced in each case (a filled tube and a film).