Session T31: Quantum Phase Transitions in Atomic and Molecular Systems

Mott Insulators of Ultracold Alkaline Earth Fermions

A crucial basic property of antiferromagnetic insulators with SU(2) spins is that adjacent spins can (and tend to) combine to form singlets, or valence bonds. The classical analog of this fact is that adjacent spins prefer to be antiparallel. These two facts underly much of our thinking about ground states of quantum antiferromagnets. Ultracold alkaline earth atoms can be used to realize magnetic insulators where a minimum of N spins is required to form a singlet, where N can be as large as 10. These systems belong to a virtually unexplored class of quantum magnets. I will show that even the simplest such models on the square lattice hold remarkable surprises.   

Finite Momentum Pairing Instability of Band-Insulators With Multiple Bands

We show, based on microscopic models, that fermionic band insulators with multiple bands and strong interband attraction are generically unstable towards nonzero momentum Cooper pairing leading to a pair density wave (PDW) superfluid state. Our first model considers a band insulating state of fermionic atoms in a three-dimensional cubic optical lattice. We show that this insulator is unstable towards an incommensurate PDW in the vicinity of a Feshbach resonance. Our second model is a two-band tight binding model relevant to electrons in solids; we show that the insulating state of this model has a PDW instability analogous to the Halperin-Rice exciton condensation instability in indirect bandgap semiconductors. We discuss relevant experimental signatures of the PDW state.   

Probing Topological Order in the Hard-Core Bose-Haldane Model

Recent years have seen the observation of topological phases of matter characterized by robust conducting edge states with the bulk of the material remaining an insulator. To investigate the physical mechanism inherent in these topological insulators beyond the more commonly studied noninteracting fermionic case, here we consider the Haldane model with interacting hard-core bosons. We probe the existance of topological order in this model using exact diagonalization, Gutzwiller mean field, and quantum Monte Carlo. As topological insulators are not described by a local order parameter, we contrast the conducting properties of the bulk of the system and its edge and investigate new possible signatures of topological order.   

Topological Phase Transition with Cold Atoms Trapped in an Optical Lattice

Recently, great attention has been attracted by the study of topological phase transition between usual insulating phase and topological insulating phase, which has not only the potential applications but also fundamental importance from a basic physics point of view. In this work we propose the realization of topological insulators in an optical lattice which can be generated from available experimental set-ups with minor modifications. In the time-reversal symmetry breaking and time-reversal symmetric case, we show the topological phase transition from usual insulating phase to the quantum anomalous Hall phase and quantum spin Hall phase, respectively. The experimental detection of the topological states is also studied in detail.   

Phase diagram of the hardcore Bose-Hubbard model with a superlattice

The quantum phase transition from a Bose-Einstein condensate to a state composed of localized atoms is usually described by the Bose-Hubbard model, where the transition is thought to be from a superfluid phase to a Mott-insulating one. It has recently been argued that this transition can also be examined by considering a simpler variant of the model, namely the limit of hardcore bosons in the presence of a period-two superlattice. In this talk, I will present the results of a new study that explores the phase diagram of this model. While the boundary of the Mott phase is obtained by quantum Monte Carlo techniques, the boundaries between the empty and completely filled lattices and the superfluid phase have simple analytical expressions. The study also examines the extent to which approximation schemes, such as mean-field theory (with and without spin-wave corrections) and fourth-order strong-coupling expansion, give an accurate description of the phase diagram. I will show that the phase diagram produced by the strong-coupling expansion is the most accurate.   

Even-odd correlations in optical lattices

We study how different many body states appear in a quantum gas microscope, such as the one developed at Harvard. We focus on the spatial correlations of the microscope images, which are related to the correlations of the parity of the number of atoms at each site. We consider a number of well-known models: free or weakly interacting bosons, the large U Bose-Hubbard model, and noninteracting fermions.   

Quantum phase diagram of fermion mixtures with population imbalance in one-dimensional optical lattices

With a recently developed time evolving block decimation (TEBD) algorithm, we numerically study the ground state quantum phase diagram of fermi mixtures with attractive inter-species interactions loaded in one-dimensional optical lattices. For our study, we adopt a general asymmetric Hubbard model (AHM) with species-dependent tunneling rates to incorporate the possibility of mass imbalance in the mixtures. We find clear signatures for the existence of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in this model in the presence of population imbalance. Our simulation also reveals that in the presence of mass imbalance, the parameter space for FFLO states shrinks or even completely vanishes depending on the strength of the attractive interaction and the degree of mass imbalance.   

Polarons, molecules and trimers in spin-polarized fermi gases

We consider the problem of a single spin-down impurity atom interacting with a spin-polarized atomic Fermi gas. By constructing variational wavefunctions for polarons, molecules and trimers, we perform a detailed study of the various quantum phase transitions as a function of mass imbalance and interaction strength. Furthermore, we obtain an accurate characterization of the Fulde-Ferrell superfluid region in this limit by allowing the center-of-mass momentum of the molecule to be non-zero. We detail what our results imply for the phase diagram for general mass imbalance, and make experimental predictions on how to see the physics we are describing.   

Excitation spectra of the Bose-Hubbard model studied with QMC

Ultracold atoms are nearly ideal experimental realizations of strongly correlated models. With the invention of new experimental techniques it is crucial to understand dynamical processes in such systems. We present QMC results of the dynamical structure factor and the one particle spectral function in one and two dimensions. We study the spectral signatures of the superfluid to normal fluid phase transition in 2D as well as the superfluid to Mott insulating transition in one and two dimensions. In addition, we present excitation spectra of trapped Bose-Einstein condensates.   

Approaching the two-dimensional dirty boson problem with n-leg ladders

We provide insight on the two-dimensional dirty boson problem by studying the disordered Bose Hubbard Model on n-leg ladders. We use Green's Function Monte Carlo and Variational Monte Carlo to establish the nature of the superfluid-insulator transition when the number of bosons equals the number of sites. Our numerical data is consistent with an intervening Bose Glass phase between the superfluid and Mott insulator phases, as recently suggested by Pollet and coworkers. Our data are useful to understand the difficulties observed in direct numerical and experimental determinations of the phase diagram of such systems.   

Frustrated Cooper pairing and the f-wave supersolidity

Geometric frustration in quantum magnetism refers to that magnetic interactions on different bonds cannot be simultaneously minimized. The usual Cooper pairing systems favor the uniform distribution of the pairing phase among lattice sites without frustration. In contrast, we propose ``frustrated Cooper pairing'' in non-bipartite lattices which leads to frustrated supersolid states with non-uniform distributions of the Cooper pair phase and density. This exotic pairing state naturally occurs in the p-orbital band in optical lattices with ultra-cold spinless fermions. In the triangular lattice, it exhibits an unconventional supersolid state with the f-wave symmetry.   

Magnetism and pairing of two-dimensional trapped fermions

We present results obtained using exact quantum Monte Carlo simulations for two dimensional trapped fermions and address the effect that temperature, interaction strength, and inhomogeneity play in quantum gases when they are cooled towards the magnetic scale. We show how antiferromagnetism emerges in the Mott insulating domains, around which d-wave pairing is significantly enhanced.   

Center-of-mass p-wave fermionic superfluidity

We propose a new kind of pairing between two fermion species where the pairs condense at a finite momentum equal to the sum of two Fermi momenta and exhibit a $p$-wave center-of-mass wavefunction in a quasi-one dimensional system. This pairing phase is therefore related to but is fundamentally different from both the modulated superfluidity of Fulde-Ferrell-Larkin-Ovchinnikov, where the ordering wavevector is given by the Fermi mometum difference, and the usual $p$-wave superfluid such as $^3$He, where the orbital symmetry refers to the relative motion within each pair. Our numerical simulation and mean field calculation confirm that this occurs for spin imbalanced Fermi gases under a new experimental condition-- -the spin up and down Fermi levels lie within the $p_x$ and $s$ orbital bands of optical lattices, respectively.   

Berry phase mediated chiral p-wave superfluids of fermionic cold atoms

Two-dimensional px+ipy superfluids or superconductors offer a playground for studying intriguing physics such as quantum teleportation, non-Abelian statistics, and topological quantum computation. Creating such a superfluid in cold fermionic atom optical traps using p-wave Feshbach resonance is turning out to be challenging. Here we propose a method to create a px+ipy superfluid directly from an s-wave interaction making use of a topological Berry phase. Methods to generate the required topological Berry phase in cold atomic systems will be discussed.   

Smearing of the superfluid-normal phase transition in layered systems by c-axis disorder

We study the effect of disorder on a system composed of a stack of Josephson coupled 2D superfluid layers. In the absence of disorder, this system has 3D XY type superfluid-normal transition as a function of temperature. We introduce c-axis disorder in the form of random superfluid stiffnesses and vortex fugacities in the various layers as well as random inter-layer couplings. As the lower-critical dimension of the transition matches the effective dimensionality of the c-axis disorder, the disorder is expected to have a strong effect on the properties of the phase transition. Indeed, using a functional renormalization group that we construct, we show that disorder smears the phase transition via the formation of a Griffith phase that smoothly fits in-between the usual superfluid and normal phases. Remarkably, in the Griffith phase, due to the power law distribution of the inter-layer couplings, the system becomes essentially two dimensional. This is reflected in the very strong anisotropy of experimental observables like the superfluid response.