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Soviet Journal of Low Temperature Physics

One-dimensional superfluidity in Bose crystals

S. I. Shevchenko

Published Feb 1, 1987• 33 citations
Publisher

Abstract

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.

DOI
10.1063/10.0031643

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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.
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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.
A well-known paradox in the theory of superfluidity is studied: superfluidity is linked to Bose condensation, but the superfluid density is always greater than the density of the Bose condensate. Based on the model of a weakly nonideal Bose gas, it is demonstrated that supercondensate particles, forming pairs which are correlated in momentum space—the two-particle condensate—make the missing contribution to the superfluid density. It is shown that in the case of slow spatial variations of superfluid flows it is possible to introduce a macroscopic wave function describing the entire superfluid component and not only the single-particle condensate. The characteristic features of weak superfluidity in Bose systems are studied and it is shown that the tunneling effect is a sensitive tool for studying the structure of the superfluid component. It is hypothesized that the superfluid component of real He II consists of the sum of one-, two-, three-, and many-particle condensates.
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 criterion of superfluidity. Based upon improved analytical and numerical understanding of the dynamical structure factor, results for different obstacle potentials are obtained, including single impurities, optical lattices and random potentials generated from speckle patterns. The dynamical breakdown of superfluidity in random potentials is discussed in relation to Anderson localization and the predicted superfluid-insulator transition in these systems.
This thesis is devoted to the study of the effect of disorder on low-dimensional weakly interacting Bose gases. In particular, the disorder triggers a quantum phase transition in one dimension at zero temperature that is investigated here through the study of the long-range behaviour of the one-body density matrix. An algebraic spatial decay of the coherence marks the quasicondensate, whereas, in the case of strong disorder, an exponential decay is recovered and it characterizes the insulating Bose-glass phase. This analysis is performed using an extended Bogoliubov theory to treat low dimensional Bose gases within a density-phase approach. A systematic numerical study allowed to draw the phase diagram of 1D weakly interacting bosons. The phase boundary obeys two different power laws between interaction and disorder strength depending on the regime of the gas where the transition occurs. These relations can be explained by means of scaling arguments valid in the white noise limit and in the Thomas-Fermi regime of the Bose gas. The phase transition to a quasicondensed phase comes along with the onset of superfluidity: the inspection of the superfluid fraction of the gas is consistent with these predictions for the boundary. The finite temperature case and the scenario in two dimensions are briefly discussed. The quantum phase transition is caused by low-energy phase fluctuations that destroy the quasi-long-range order characterizing the uniform system. Within the approach presented here, the phase fluctuations are identified as the low-lying Bogoliubov modes. Their properties have been investigated in detail to understand which changes trigger the phase transition and we found that the transition to the insulating phase is accompanied by a diverging density of states and a localization length, measured through the inverse participation ratio, that diverges as a power-law with power – 1 for vanishing energy. The fragmentation of the gas is also studied: this notion is very often associated with the onset of the insulating phase. The characterization of the density fragmentation is performed by analyzing the probability distribution of the density. A density profile is defined as fragmented when the probability distribution at vanishing density is finite or divergent and this happens for a gas in the Bose-glass phase. On the contrary, the superfluid phase is characterized by a zero limiting probability of having vanishing densities. This definition is derived analytically, and confirmed by a numerical study. This fragmentation criterion is particularly suited for detecting the phase transition in experiments: when a harmonic trap is included, the transition to the insulating phase can be extracted from the statistics of the local density distribution.
We study the quantum phase transition of the 1D weakly interacting Bose gas in the presence of disorder. We characterize the phase transition as a function of disorder and interaction strengths, by inspecting the long-range behavior of the one-body density matrix as well as the drop in the superfluid fraction. We focus on the properties of the low-energy Bogoliubov excitations that drive the phase transition and find that the transition to the insulator state is marked by a diverging density of states and a localization length that diverges as a power-law with power 111. We draw the phase diagram and we observe that the boundary between the superfluid and the insulator phase is characterized by two different algebraic relations. These can be explained analytically by considering the limiting cases of zero and infinite disorder correlation length.