Session C41: Quantum Simulation with Cold Atoms and Molecules

Towards Strongly Interacting Quantum Mixtures of Light Fermions and Heavy Bosons

Cold atomic gases have attracted interest as many body quantum simulators due to the tunable nature of the basic parameters, such as lattice depth, particle density, and interaction. However, for single species alkali atoms, simulations are limited by the nature of the interactions between atoms, which is necessarily short-range. Heteronuclear mixtures offer the potential for more exotic interactions, either by formation of cold molecules with a permanent electric dipole moment, or by allowing one species to mediate interactions between the other. With the addition of an optical lattice, an analog of electron-phonon interactions should be possible, with heavy bosons playing the role of material ions. In all of these scenarios, $^{6}\rm{Li}$ and $^{133}\rm{Cs}$ are a compelling choice, as they maximize the mass ratio within the stable alkali family. Furthermore, either species by itself offers significant tunability. Recently, we have discovered a family of interspecies Feshbach resonances between 800 and 900 G in the $^{6}\rm{Li}$-$^{133}\rm{Cs}$ system. These resonances are in a favorable position for the production of dual degenerate quantum gases. The implications for universal few-body states and strategies for sympathetic evaporation to dual degeneracy will be discussed.   

Making Dipolar Chain Liquid and Crystal

Recent experimental progress on ultra-cold polar molecules opens new realms to explore intriguing quantum phase with dipolar interaction. One of possible phenomena is self assembled chain liquid in a stack of strongly confined pancake traps. It is, however, not easy for polar molecules to form a spontaneous chain liquid due to lack of binding mechanism. Here, we propose an adiabatic process and calculate the entropy and resulting temperature for the formation of dipolar chain liquis after adiabatically switching on the electric field and then followed by reducing the optical lattice field. We further investigate the elementary excitations of the dipolar chain crystal and derived the finite temperature KTNHY transition as well as compressibility of such many-body system. We also discuss how such interesting large-composite object can be experimentally measured even above the quantum degenerate temperature.   

Pomeranchuk Cooling in Frustrated Magnets -- a Route to Spin Liquids in Cold Atoms

Fermions hopping on a two-dimensional triangular lattice at half filling with moderate repulsive interactions are expected to form an exotic Mott insulating state. This Mott insulator, also known as a quantum spin liquid (QSL), does not order magnetically, nor break any other symmetry. It hosts many gapless excitations which give rise to a parametrically larger low-temperature entropy than in magnetically ordered states. We show that adiabatically tuning the strength of the interaction from the metallic into the QSL state leads to a significant reduction in temperature. This makes such a system a good candidate for accessing novel quantum phases in cold atom experiments.   

Symmetry-protected topological phases of alkaline-earth cold fermionic atoms in one dimension

We investigate the existence of symmetry-protected topological phases in one-dimensional alkaline-earth cold fermionic atoms with general half-integer nuclear spin I at half filling. Using complementary techniques, we show that SU(2) topological phases are stabilized where the SU(2) symmetry stems from the existence of a metastable excited state in alkaline-earth atoms. On top of these phases, we find the emergence of topological phases with enlarged SU(2I+1) symmetry which depend only on the nuclear spins degrees of freedom. The main physical properties of the latter phases are further studied using a matrix-product state approach. We find that these phases are symmetry-protected topological phases, with respect to inversion symmetry, when I=1/2,5/2,9/2..., which is directly relevant to ytterbium and strontium cold fermions.   

Quantum Monte Carlo simulation of the power-law correlated SU(6) quantum magnets with $^{132}$Yb fermions

We systematically investigate the half-filled SU(2N) Hubbard model on the two dimensional square lattice, using the projector quantum Monte-Carlo method which is free of sign problem. We find that the ground state changes from the long-range Neel order in the SU(2) case to a paramagnetic state in the large N limit, in which no long-range order was observed. Employing Maximum entropy method to analytically continue imaginary-time data, we obtain both one-particle and two-particle spectral functions in the whole Brillouin zone. As N increases, the charge gap is quickly suppressed and the spin-wave feature with linear dispersion around ($\pi$,$\pi$) is finally destroyed. The related physics is discussed as well as some applications to the experiments.   

Thermodynamics for reaching SU(N) quantum magnetism in ultracold alkaline earth atoms

Motivated by the prediction that SU($N$) Hubbard models in a large-$N$ limit possess a chiral spin liquid ground state, we investigate how to exploit the large number of degrees of freedom to cool alkaline earth atoms in optical lattices, which are described by the SU($N$) Hubbard model with $N$ as large as 10. Combining analytic high temperature expansions and sophisticated quantum Monte Carlo calculations, we show that the entropy increases with $N$ for $T> t^2/U$ independent of dimension and lattice geometry, and down to temperatures $T=0.1 t^2/U$ in one dimensional chains. As a consequence, when one loads these atoms into optical lattices, the final temperatures can be orders of magnitude colder for $N=10$ than for the usual $N=2$ case. The use of alkaline earths with large $N$ is thus particularly exciting for cold atoms experiments, where achieving low entropy states displaying quantum magnetism remains an outstanding challenge. This finding explains the dramatic cooling seen in recent Yb ($N=6$) experiments [ Y. Tanaka et al., Nature Physics 8, 800 (2012) ].   

Superfluid state of repulsively interacting three-component fermionic atoms in optical lattices

We investigate the superfluid state of repulsively interacting three-component (color) fermionic atoms in optical lattices using Feynman diagrammatic approaches and the dynamical mean field theory [1]. When the anisotropy of the three repulsive interactions is strong, atoms of two of the three colors form Cooper pairs and atoms of the third color remain a Fermi liquid. This superfluid emerges close to half filling at which the Mott insulating state characteristic of the three-component repulsive fermions appears [2]. An effective attractive interaction is induced by density fluctuations of the third-color atoms. The superfluid state is stable against the phase separation that occurs in the strongly repulsive region. We determine the phase diagrams in terms of temperature, filling, and the anisotropy of the repulsive interactions.\\[4pt] [1] K. Inaba and S. Suga, \textit{Phys. Rev. Lett.} \textbf{108}, 255301 (2012)\\[0pt] [2] K. Inaba, S. Miyatake, and S. Suga, \textit{Phys. Rev.} A \textbf{82}, 051602(R) (2009).   

Short-Range Correlations and Cooling of Ultracold Fermions in the Honeycomb Lattice

We study experimentally relevant thermodynamic properties and spin correlations of the Hubbard model in the honeycomb lattice by using determinantal quantum Monte Carlo simulations and numerical linked-cluster expansions. We find that the honeycomb lattice exhibits a more pronounced anomalous region in the double occupancy that leads to stronger adiabatic cooling than in the square lattice. We also find that, at half filling and finite temperature, nearest-neighbor spin correlations can be stronger in the honeycomb lattice than in the square lattice, even in regimes where the ground state in the former is a semimetal or a spin liquid while it is an antriferromagnetic Mott insulator in the latter. The implications of these findings for optical experiments are also discussed.   

From Topological Insulator to Topological Superfluid

Majorana zero bound state exists in the vortex core of a chiral p$+$ip superconductor (SC), which can be driven from an s-wave SC by spin-orbit (SO) coupling. In cold atoms, an s-wave superfluid (SF) can be obtained by Feshbach resonance. Together with the Rashba SO interaction and Zeeman field, the s-wave SF gives rise to a chiral topological SF. However, a Rashba-type SO interaction is not experimentally realistic for cold atom gas. We propose here a novel scheme to study exotic topological phases in an optical lattice, where we can observe both the topological insulating phase and chiral topological SF under different parameter regimes. We examine in detail our prediction with realistic experimental platforms, and show its great feasibility in the experimental realization.   

Direct Measurement of the Zak phase in Topological Bloch Bands

Geometric phases that characterize the topological properties of Bloch bands play a fundamental role in the modern band theory of solids. Here we report on the direct measurement of the geometric phase acquired by cold atoms moving in one-dimensional optical lattices. Using a combination of Bloch oscillations and Ramsey interferometry, we extract the Zak phase -- the Berry phase acquired during an adiabatic motion of a particle across the Brillouin zone -- which can be viewed as an invariant characterizing the topological properties of the band. For a dimerized optical lattice, which models polyacetylene, we measure a difference of the Zak phase equal to $\pi$ for the two possible polyacetylene phases with different dimerization. This indicates that the two dimerized phases belong to different topological classes, such that for a filled band, domain walls have fractional quantum numbers. Our work establishes a new general approach for probing the topological structure of Bloch bands in optical lattices.   

Ground-state properties of spin-imbalanced fermions on square lattices

Atoms in optical lattices offer the opportunity to probe exotic pairing states experimentally. We consider spin-imbalanced fermions on a square lattice. Using Bogoliubov-de Gennes theory and fully self-consistent numerical calculations reaching the thermodynamic limit, we make several predictions of the physics of the ground state and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) order. We show, in particular, that the experimentally accessible momentum distribution can be used to identify the hidden Fermi surface of the condensate and the presence of Fermi arcs. There exists a regime of density (away from half-filling) and interactions where the system can support a supersolid order. Finally, we address the crystallography of the inhomogeneous state by determining the leading wave vector as a function of U, density and polarization.   

Enhancing the thermal stability of entanglement between Majorana fermions with dipoles in optical lattices

Pairing between spinless fermions can generate Majorana fermion excitations. Such excitations may exhibit intriguing properties arising from non-local entanglement, including anyonic braid statistics and enough stability to encode quantum information. But simple models indicate that non-local entanglement between Majorana fermions becomes unstable at non-zero temperatures. We discuss this issue and show that anisotropic interactions between dipolar fermions in optical lattices can be used to form domains that significantly enhance thermal stability. We construct a model of oriented dipolar fermions in a square optical lattice. We explicitly compute the correlation functions defining entanglement. We find that domains established by strong interactions exhibit enhanced entanglement between Majorana fermions over large distances and long times even at finite temperatures.   

Structures forming out of quantum seeds in Bose condensates with time-dependent tunnel coupling

Quantum fluctuations can be amplified into macroscopic structures in the course of time. This can happen in quench scenarious, where some parameter is time-dependent, and it has wide-ranging implications, from condensed matter physics to cosmology. Here, we investigate the behaviour of a model system of two 1D clouds of bosonic atoms. Specifically, we track the time-evolution of the quantum field that describes the relative phase between the quasi-condensates as a function of position. When suddenly switching on the tunnel-coupling, the subsequent dynamics is first governed by parametric amplification of the initial quantum fluctuations. At a later stage, nonlinear dynamics takes over, and localized phase structures form. These structures, which we term 'quasi-breathers', then stochastically form and decay, and we characterize their features using numerical simulations of the underlying sine-Gordon equation based on the truncated Wigner approximation. We then turn to a scenario where the tunnel coupling is changed smoothly over time. It turns out this can be mapped to the evolution of the quantum sine-Gordon field in an expanding 1+1 dimensional toy universe, giving insight into nonlinear structure formation in cosmology.