Session Z4: Disorder and Pairing in Ultracold Systems

Many Body Localization in Incommensurate Potentials

A long-standing problem concerns the survival of Anderson localization in a many body system with interparticle interactions. In recent years, this problem has resurfaced due to work by Basko, Aleiner, and Altshuler, who have argued that highly excited states of an interacting, many body system can be localized in Fock space. Consequently, a dynamical quantum phase transition may separate such a many body localized phase from a delocalized, ergodic phase, and there is now numerical evidence for the existence of such a transition in disordered 1D systems. Meanwhile, 1D lattice models that lack genuine disorder, but which instead contain a periodic potential that is incommensurate with the lattice spacing, are known to have a localization transition even in the absence of interactions. Here, we numerically investigate whether this transition survives the introduction of interactions and, if so, how it is modified. These questions are increasingly experimentally relevant, because ultracold atom experiments sometimes use incommensurate potentials in place of true disorder to probe localization physics.   

Mobile impurities in one-dimensional cold gases: subdiffusive, diffusive and ballistic regimes

Advances in cold gases physics are beginning to enable experiments involving the direct manipulation and observation of single- or few-atom mobile impurities [1] within a many-body quantum system, a topic of longstanding interest for condensed matter theory, where it is related to studies of e.g. conductivity and the X-ray edge problem. Further progress in this direction is expected from the latest generation of experiments offering single-site addressability in optical lattices [2,3]. In light of these developments we study the dynamics of mobile impurities in 1D quantum liquids using a DMRG technique. We address the recently proposed subdiffusive regime of impurity motion [4], a class of excitations beyond those described by the standard Tomonaga-Luttinger theory. We study the conditions for observing this regime and its' crossover to the ballistic regime. We furthermore examine the possibilities to observe the intermediate diffusive motion of impurities in these systems. \\[4pt] [1] J. Catani, G. Lamporesi, D. Naik et. al., arXiv:1106.0828\\[0pt] [2] W. S. Bakr, J. I. Gillen, A. Peng et. al., Nature 462, 74 (2009)\\[0pt] [3] J. F. Sherson, C. Weitenberg, M. Endres et. al., Nature, 467, 7311 (2010)\\[0pt] [4] M. B. Zvonarev, V. V. Cheianov, T. Giamarchi, PRL 99, 240404 (2007); PRL 103, 110401 (2009)   

Collective mode of an impurity and a Tonks-Girardeau gas

We investigate the quantum dynamics of an impurity immersed in a one-dimensional gas of strongly repulsive bosons, or equivalently fully-polarized fermions, interacting via a contact interaction. Using Bethe Ansatz we obtain essentially exact results at all timescales and for all couplings to the impurity. We find at strong coupling that if the impurity starts off with a momentum of the order of the Fermi momentum or higher a new type of collective mode is excited, corresponding to long lived oscillations of the impurity with respect to the background gas. We characterize this mode and discuss how it can be observed experimentally.   

Dynamics of mobile impurities in one-dimensional quantum liquids

We consider the dynamics of mobile impurities immersed in one-dimensional (1d) quantum liquids. Such systems have been realized experimentally in the context of ultracold atomic gases in optical lattices. We show that, on very general grounds, the dispersion relation of the impurity dressed by the liquid is a periodic function of momentum with period $2\pi \hbar n$, $n$ being the 1d density. An impurity subject to a small external force thus exhibits the phenomenon of Bloch oscillations about a fixed point in real space, in the absence of a periodic potential. To compare with experiments,we set out to address the consequences of both finite temperature and finite force on the Bloch oscillation sequence. Our main results are as follows: (i) There exists a finite window of parameters where Bloch oscillations exist $F_{\textrm{min}}(T) [Preview Abstract]

Gapless superfluid phase with spin-dependent disorder

Motivated by the recent experimental development on spin-dependent optical lattices and disordered lattices, we show that the presence of a spin-dependent random potential on a superconductor or a superfluid atomic gas leads to distinct transitions at which the energy gap and average order parameter vanish, generating an intermediate gapless superfluid phase. This behavior is in marked contrast to the case of spin-symmetric randomness. The calculations are performed for a two dimensional attractive Hubbard model within Bogoliubov-de Gennes mean field theory. We characterize the different phases by correlating the local order parameter and the density of states.   

Superdiffusive nonequilibirum transport of an impurity in a Fermi sea

We discuss a nonequilibrium transport of a single impurity atom immersed in a low-temperature Fermi sea with a short range interaction. We find that the impurity does a superdiffusive geometric random walk in which the characteristic momentum decay rate shows a quartic decrease in its momentum in three dimension. Then, we construct a master equation and its scaled form that governs the time evolution of the impurity. Next, we discuss two dimensional case in which the momentum decay rate decreases with the third power of its momentum.   

Repulsive polarons in two-dimensional Fermi gases

We consider a single spin-down impurity atom interacting via an attractive, short-range potential with a spin-up Fermi sea in two dimensions (2D). Similarly to 3D, we show that the impurity can form a metastable state (the ``repulsive polaron'') with energy greater than that of the non-interacting impurity. Moreover, we find that the repulsive polaron can acquire a finite momentum for sufficiently weak attractive interactions. Even though the energy of the repulsive polaron can become sizeable, we argue that saturated ferromagnetism is unfavorable in 2D because of the polaron's finite lifetime and small quasiparticle weight.   

Universal bound states of two atoms near a Feshbach resonance

The Efimov effect was traditionally thought to exist for three or more particles only. It will be shown how to make universal shallow bound states of TWO atoms only, which will exhibit a universal energy spectrum reminiscent of the Efimov effect, by using potentials to constrain the spatial motion of atoms. Several related types of such two-body states will be described. These diatomic ``artificial molecules", if isolated from each other, will be free from three-body recombination, and can have long lifetimes in principle.   

Feshbach Correlations and Closed Channel Amplitudes

The magnetically controlled Feshbach resonance is a prominent member of the cold atom toolkit. The ability to tune binary particle interactions in a quantum many body system has given access to collapsing BEC-physics in bosenovas, to BEC-BCS crossover physics, to the unitarity regime, and to quantum phase transitions. The resonance is accessed by tuning the energy of a quasi-bound spin-rearranged molecular state near the vaccuum of the interacting particles. Does the amplitude of the spin-rearranged or ``closed channel'' state play a significant role in the many body physics? We present a microscopic derivation of the Feshbach resonance interactions and obtain the parameters of the two-channel model in a optical lattice. We study two atoms interacting in a harmonic oscillator potential near a Feshbach resonance to derive the closed channel probabibilty and to uncover the validity-range of the two channel lattice model.   

Superfluid pairing in a mixture of a spin-polarized Fermi gas and a dipolar condensate

We consider a mixture of a spin-polarized Fermi gas and a dipolar Bose-Einstein condensate in which s-wave scattering between fermions and the quasiparticles of the dipolar condensate can result in an effective attractive Fermi-Fermi interaction anisotropic in nature and tunable by the dipolar interaction. We show that such an interaction can significantly increase the prospect of realizing a superfluid with a gap parameter characterized with a coherent superposition of all odd partial waves. We formulate, in the spirit of the Hartree-Fock-Bogoliubov mean-field approach, a theory which allows us to estimate the critical temperature when the anisotropic Fock potential is taken into consideration and study how to prepare the mixture in order to optimize the critical temperature at which such a superfluid emerges before the system starts to phase separate.   

Superfluid transition temperature and its zero density limit extrapolation in a unitary atomic Fermi gas on a lattice

The superfluid transition temperature $T_c$ of a unitary Fermi gas has been of great interest. One way to study $T_c$ in a 3D continuum is to study fermions on a lattice at finite densities and then extrapolate to the zero density limit, as has been done in quantum Monte Carlo (QMC) simulation studies. For this extrapolation to work, it is essential to probe the densities in the asympotic regime. In this talk, we study fermions on a three-dimensional isotropic lattice with an attractive on-site interaction as a function of density $n$, from half filling down to $5.0\times 10^{-7}$ per unit cell, using a pairing fluctuation theory. As $n$ decreases towards $n=0$, $T_c/E_F$ increases to the leading order linearly in $n^{1/3}$, and reaches the zero density limit $T_c/E_F = 0.256$, consistent with that calculated directly in the continuum for a contact potential. Inclusion of the particle-hole channel reduces $T_c/E_F$ to 0.217, in agreement with experiment. However, except for very low $n$, $T_c/E_F$ exhibits significant higher order nonlinear dependence on $n^{1/3}$. The densities accessed by QMC studies are still not low enough to be in the asymptotic regime. References: Q.J. Chen, arXiv:1109.5327; arXiv:1109.2307; Q.J. Chen et al, PRL 81, 4708(1998); PRB 59, 7083(1999).   

Pair Condensation in a Finite Trapped Fermi Gas

Cold atomic fermi gases are widely studied examples of strongly interacting quantum systems. Examples include $^{40}{\rm K}$, $^6{\rm Li}$ and neutron matter. In the unitary regime, where the scattering length is very large compared to the mean inter-particle distance, they are nonperturbative and exhibit universal behavior. Moreover, they can be created in the lab, providing an excellent testing ground for theory. In this talk I will describe quantum Monte Carlo calculations we have been performing to study the signatures of pairing and the superfluid phase transtion in finite-size systems. Using the Auxillary Field Monte Carlo (AFMC) method, we study the pairing gap, condensate fraction, pair wavefunction and density profile as a function of temperature. Defining the onset of condensation $T_{\rm cond}$ as the temperature when the condensate fraction crosses its (finite) noninteracting limit, we consider the question of whether pairing occurs prior to condensation in the unitary regime.   

Cooling across the superfluid-normal interface of a unitary Fermi gas - an analogue of a dilution fridge?

Phase separation between paired superfluid and partially polarized normal phases has been observed by various experimental groups around the world using resonantly-interacting spin-imbalanced, hyperfine states of fermionic atoms. In this work we phenomenologically study the effect of the evaporation of atoms and explore the possibility of realizing a non-equilibrium steady state with chemical potential and temperature gradients in some of these experiments.   

Upper Branch Bosons at High Temperatures

We use a generalized Nozieres-Schmitt-Rink (NSR) approach, which excludes the molecule poles in the T-matrix, to study the ``upper branch'' Bose gases at high temperatures. We show that when we tune the scattering length from positive side across the resonance, the Bose system can remain stable even with attractive interactions at relatively high temperatures. The energy of this upper branch Bose gas has a maximum at negative scattering length, which indicates pair formations are enhanced by Bose statistics in a many body system, in contrast to the Fermionic case where the maximum occurs at positive scattering length.\footnote{V.B.Shenoy and Tin-Lun Ho, arXiv:1106.0960, to appear in PRL.}