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arXiv:0710.3158 · Semiconductors

Superfluid-insulator transition in “Dirty” ultracold Fermi gas

Boris I. Shklovskii

Published Aug 1, 2008• 18 citations
arXivHTMLPDF

Abstract

Superfluid-insulator transition in an ultracold Fermi gas in the external disorder potential of the amplitude V 0 is studied as a function of its concentration n and the magnetic field B in the presence of the Feshbach resonance. We find the zero temperature phase diagrams in the plane (B, n) at a given V 0 and in the plane (V 0, n) at a given B. We study the transition between cases of classical and quantum random potentials which can be implemented by tuning intensity of speckles. Our results for the Bose-Einstein condensation side of the diagram are also valid for a Bose gas.

DOI
10.1134/s1063782608080058

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Superfluid-insulator transition in an ultracold Fermi gas in the external disorder potential of the amplitude V 0 is studied as a function of its concentration n and the magnetic field B in the presence of the Feshbach resonance. We find the zero temperature phase diagrams in the plane (B, n) at a given V 0 and in the plane (V 0, n) at a given B. We study the transition between cases of classical and quantum random potentials which can be implemented by tuning intensity of speckles. Our results for the Bose-Einstein condensation side of the diagram are also valid for a Bose gas.
We study the phase diagram of ultracold bosons in an optical lattice near a Feshbach resonance. Depending on the boson density, the strength of the optical-lattice potential and the detuning from resonance, the ground state can be a Mott insulator, a superfluid phase with both an atomic and a molecular condensate, or a superfluid phase with only a molecular condensate. Mott insulator to superfluid transitions can be induced either by decreasing the strength of the optical-lattice potential or by varying the detuning from the Feshbach resonance. Quite generally, we find that for a commensurate density the ground state may undergo several insulator-superfluid or superfluid-insulator transitions as the magnetic field is varied through the resonance.
Trapped ultracold Fermi gases provide a system that can be tuned between the BCS and Bose-Einstein condensation regimes by means of a magnetic-field Feshbach resonance. Condensation of fermionic atom pairs in a 40K^{40}\mathrm{K}40K gas was demonstrated experimentally by a sweep technique that pairwise projects fermionic atoms onto molecules. In this paper, we examine previous data obtained with this technique that probed the phase boundary in the temperature-magnetic field plane. Comparison of the 40K^{40}\mathrm{K}40K data to a theoretically computed phase diagram demonstrates good agreement between the two.
Ultracold bose gase systems can perform quantum simulations of high temperature superconductors in certain parameter regimes. Specifically, 2D bose gases at low temperatures exhibit a superfluid to thermal gas phase transition analogous to the superconductor to insulator transition in certain superconductors. The unbinding of thermally activated vortex pairs drives this phase transition, and disorder is expected to affect vortex motion in this system. In addition, disorder itself can drive phase transitions in superconductors. We have designed and built a system which produces two 2D ultracold Bose gas systems separated by a few microns. In addition, we have also produced a disordered speckled laser intensity pattern with a grain size of ~1 μm, small enough to provide a disordered potential for the two systems. We have observed the superfluid phase transition with and without the presence of disorder. The coherence of the system, which is related to superfluidity, is strongly reduced by the presence of disorder, even at small disorder strength, but the effect of the disorder on observed vortices in the system is less clear.
The phase diagrams and phase transitions of bosons with short-ranged repulsive interactions moving in periodic and/or random external potentials at zero temperature are investigated with emphasis on the superfluid-insulator transition induced by varying a parameter such as the density. Bosons in periodic potentials (e.g., on a lattice) at T=0 exhibit two types of phases: a superfluid phase and Mott insulating phases characterized by integer (or commensurate) boson densities, by the existence of a gap for particle-hole excitations, and by zero compressibility. Generically, the superfluid onset transition in d dimensions from a Mott insulator to superfluidity is ``ideal,'' or mean field in character, but at special multicritical points with particle-hole symmetry it is in the universality class of the (d+1)-dimensional XY model. In the presence of disorder, a third, ``Bose glass'' phase exists. This phase is insulating because of the localization effects of the randomness and analogous to the Fermi glass phase of interacting fermions in a strongly disordered potential.The Bose glass phase is characterized by a finite compressibility, no gap, but an infinite superfluid susceptibility. In the presence of disorder the transition to superfluidity is argued to occur only from the Bose glass phase, and never directly from the Mott insulator. This zero-temperature superfluid-insulator transition is studied via generalizations of the Josephson scaling relation for the superfluid density at the ordinary \ensuremath{\lambda} transition, highlighting the crucial role of quantum fluctuations. The transition is found to have a dynamic critical exponent z exactly equal to d and correlation length and order-parameter correlation exponents \ensuremath{\nu} and \ensuremath{\eta} which satisfy the bounds \ensuremath{\nu}\ensuremath{\ge}2/d and \ensuremath{\eta}\ensuremath{\le}2-d, respectively. It is argued that the superfluid-insulator transition in the presence of disorder may have an upper critical dimension dc{d}_{c}dc​ which is infinite, but a perturbative renormalization-group calculation wherein the critical exponents have mean-field values for weak disorder above d=4 is also discussed. Many of these conclusions are verified by explicit calculations on a model of one-dimensional bosons in the presence of both random and periodic potentials. The general results are applied to experiments on 4He^{4}\mathrm{He}4He absorbed in porous media such as Vycor. Some measurable properties of the superfluid onset are predicted exactly [e.g., the exponent x relating the \ensuremath{\lambda} transition temperature to the zero-temperature superfluid density is found to be d/2(d-1)], while stringent bounds are placed on others. Analysis of preliminary data is consistent with these predictions.
We consider a weakly interacting two-component Fermi gas of dipolar particles (magnetic atoms or polar molecules) in two-dimensional geometry. The dipole-dipole interaction (together with the short-range interaction at Feshbach resonances) for dipoles perpendicular to the plane of translational motion may provide a superfluid transition. The dipole-dipole scattering amplitude is momentum dependent, which violates the Anderson theorem that claims the independence of the transition temperature on the presence of weak disorder. We have shown that the disorder can strongly increase the critical temperature (up to 10nK10\phantom{\rule{0.16em}{0ex}}\mathrm{nK}10nK at realistic densities). This opens wide possibilities for the studies of the superfluid regime in weakly interacting Fermi gases, which has not been observed so far.
We present a description of the behavior of a superfluid gas of fermions in the presence of a Feshbach resonance over the complete range of magnetic field detunings. Starting from a resonance Hamiltonian, we exploit a functional method to describe the continuous behavior from Bardeen-Cooper-Schrieffer to Bose-Einstein condensation type superfluidity. Our results show an ability for a resonance system to exhibit a high critical temperature comparable to the Fermi temperature. The results are derived in a manner that is shown to be consistent with the underlying microscopic scattering physics.