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arXiv:cond-mat/0507050 · AIP conference proceedings

Localization of Bose-Einstein Condensate and Disappearance of Superfluidity of Strongly Correlated Bose Fluid in a Confined Potential

Michikazu Kobayashi, Makoto Tsubota

Published Jan 1, 2006• 2 citations
arXivHTMLPDF

Abstract

We develop a model for a Bose fluid in a confined potential to study a new quantum phase caused by the localization of the Bose‐Einstein condensate and the disappearance of superfluidity which was recently observed in liquid 4He in porous glass at high pressures. The critical pressure for the transition to this phase can be defined by our new analytical criterion, which assumes that the size of the localized Bose‐Einstein condensate is comparable to the scale of confinement. The critical pressure is quantitatively consistent with observations without free parameters.

DOI
10.1063/1.2354704

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Physics and Chemistry of Liquids•Aug 1, 2003•3 citations
We develop a model for a Bose fluid in a confined potential to study a new quantum phase caused by the localization of the Bose‐Einstein condensate and the disappearance of superfluidity which was recently observed in liquid 4He in porous glass at high pressures. The critical pressure for the transition to this phase can be defined by our new analytical criterion, which assumes that the size of the localized Bose‐Einstein condensate is comparable to the scale of confinement. The critical pressure is quantitatively consistent with observations without free parameters.
There is a growing interest in the relation between Bose-Einstein condensation (BEC) and the superfluidity. A Bose system confined in random media such as porous glass is suitable for studying this relation because BEC and superfluidity can be suppressed and controlled in such a disordered environment. However, it is not clear how this relation is affected by disorder and there are few theoretical studies that can be quantitatively tested by experiment. In this work we develop a dilute Bose gas model with a random potential that takes into account the pore-size dependence of porous glass. Then we compare our model with the measured low-temperature specific heat, condensate density, and superfluid density of 4He{}^{4}\mathrm{He}4He in Vycor glass. This comparison uses no free parameters. We predict phenomena at low temperatures: First, the random potential causes a T-linear specific heat instead of the T3{T}^{3}T3 dependence that is usually caused by phonons. Second, the BEC can remain even when the superfluidity disappears at low densities. Third, the system makes a reentrant transition at low densities; that is, the superfluid phase changes to the normal phase again as the temperature is reduced. This reentrant transition is more likely to be observed when the strength of the random potential is increased.
4 He confined in nanoporous media is an excellent model boson system in a confinement potential. We have studied the superfluid and thermodynamic properties of 4 He confined in a porous glass that has nanopores of 2.5 nm diameter. It is shown that the confinement of 4 He in nanopores produces a new quantum state, the localized Bose–Einstein condensation (LBEC) state, and markedly alters the pressure–temperature ( P – T ) phase diagram. In the LBEC state the global phase coherence is destroyed by strong atomic correlation or by the random potential of a substrate. The formation of LBEC leads to an anomalous reduction of the superfluid transition temperature T c , determined by the torsional oscillator technique, and the behavior of a quantum phase transition near 0 K. The contributions of roton and phonon excitations to the heat capacity provide definitive evidence of the LBEC state.
It is shown that the assumption that the many particle wave functions describing superfluid 4He have some phase coherence properties of correlated basis functions provides a new explanation of the link between Bose-Einstein condensation and two fluid behavior. This assumption also implies that the condensate fraction is proportional to the superfluid fraction, in agreement with experiment, and provides a simple quantitative explanation of the anomalous reduction in spatial order and liquid density, observed as the temperature is lowered in superfluid 4He.
We evaluate the Bose-Einstein condensate density and the superfluid fraction of bosons in a periodic external potential using path-integral Monte Carlo methods. The periodic lattice consists of a cubic cell containing a potential well that is replicated along one dimension using periodic boundary conditions. The aim is to describe bosons in a one-dimensional optical lattice or helium confined in a periodic porous medium. The one-body density matrix is evaluated and diagonalized numerically to obtain the single boson natural orbitals and the occupation of these orbitals. The condensate fraction is obtained as the fraction of bosons in the orbital that has the highest occupation. The superfluid density is obtained from the winding number. From the condensate orbital and superfluid fraction, we investigate (1) the impact of the periodic external potential on the spatial distribution of the condensate, and (2) the correlation of localizing the condensate into separated parts and the loss of superflow along the lattice. For high-density systems, as the well depth increases, the condensate becomes depleted in the wells and confined to the plateaus between successive wells, as in pores between necks in a porous medium. For low-density systems, as the well depth increases the BEC is localized at the center of the wells (tight binding) and depleted between the wells. In both cases, the localization of the condensate suppresses superflow leading to a superfluid-insulator crossover. The impact of the external potential on the temperature dependence of the superfluidity is also investigated. The external potential suppresses the superfluid fraction at all temperatures, with a superfluid fraction significantly less than one at low temperature. The addition of an external potential does not, however, significantly reduce the transition temperature.
Abstract The critical properties of the phase transition from a normal gas to a Bose–Einstein condensate (superfluid) of a harmonically confined Bose gas are addressed with the knowledge of an equation of state of the underlying homogeneous Bose fluid. It is shown that while the presence of the confinement trap arrests the usual divergences of the isothermal compressibility and heat capacities, the critical behavior manifests itself now in the divergence of derivatives of the mentioned susceptibilities. This result is illustrated with a mean-field like model of an equation of state for the homogeneous particle density as a function of the chemical potential and temperature of the gas. The model assumes the form of an ideal Bose gas in the normal fluid while in the superfluid state a function is proposed such that, both, asymptotically reaches the Thomas–Fermi solution of a weakly interacting Bose gas at large densities and low temperatures and, at the transition, matches the critical properties of the ideal Bose gas. With this model we obtain the global thermodynamics of the harmonically confined gas, from which we analyze its critical properties. We discuss how these properties can be experimentally tested.
Motivated by recent experiments on alkali gases in atom traps, a largely pedagogical account is given of the implications of the existence of a single-particle Bose-Einstein condensate for the phenomenon of superfluidity. The first conclusion is that, for alkalis in traps at the lowest temperatures, Bose-Einstein condensation coexists with superfluidity. Both experimental evidence and basic microscopic theory are reviewed in this context, with superfluidity in finite systems, quantized vortices and the threshold for breakdown of superfluidity all being referred to. The contrast between liquid 4He below the λ point and the alkali atom gases is then emphasized. Both exhibit superfluidity, but the manifestations of a Bose-Einstein condensate are quite different. For the atomic vapours, near to 100% of the atoms are condensed at the lowest temperatures, whereas from (i) neutron scattering and (ii) computer simulations in liquid 4He present evidence is that 7% is the condensate fraction. This leads finally into a brief discussion of superfluidity without a condensate, with specific reference to the two-dimensional Bose Coulomb gas. The main conclusion is that Bose-Einstein condensation and superfluidity are distinct consequences of deeper topological properties of the many-body wavefunction.