Session Q4: Focus Session: Many-body Quantum Phases in Cold Atom Systems

Orbital ice: an exact Coulomb phase on the diamond optical lattice

The rapid advances in loading and controlling alkali atoms on the excited bands of optical lattices have made it possible to investigate orbital-related many-body physics in new settings. Here we demonstrate the existence of orbital Coulomb phase as the exact ground state of $p$-orbital exchange Hamiltonian on the diamond lattice. The Coulomb phase is an emergent state characterized by algebraic dipolar correlations and a gauge structure resulting from local constraints (ice~rules) of the underlying lattice models. For most ice models on the pyrochlore lattice, these local constraints are a direct consequence of minimizing the energy of each individual tetrahedron. On the contrary, the orbital ice rules are emergent phenomena resulting from the quantum orbital dynamics. We show that the orbital ice model exhibits an emergent geometrical frustration by mapping the degenerate quantum orbital ground states to the spin-ice states obeying the 2-in-2-out constraints on the pyrochlore lattice. We also discuss possible realization of the orbital ice model in optical lattices with $p$-band fermionic cold atoms. [1] Gia-Wei~Chern and Congjun Wu, arXiv:1104.1614 (2011).   

Time reversal symmetry breaking of $p$-orbital bosons in a one-dimensional optical lattice

We study bosons loaded in a one-dimensional optical lattice of two-fold $p$-orbital degeneracy at each site. Our numerical simulations find an anti-ferro-orbital p$_x$+ip$_y$, a homogeneous p$_x$ Mott insulator phase and two kinds of superfluid phases distinguished by the orbital order (anti-ferro-orbital and para-orbital). The anti-ferro-orbital order breaks time reversal symmetry. Experimentally observable evidence is predicted for the phase transition between the two different superfluid phases. We also discover that the quantum noise measurement is able to provide a concrete evidence of time reversal symmetry breaking in the first Mott phase.   

Correlated phases of bosons in tilted, frustrated lattices

We study the ``tilting'' of Mott insulators of bosons into metastable states. These are described by Hamiltonians acting on resonant subspaces, and have rich possibilities for correlated phases with non-trivial entanglement of pseudospin degrees of freedom measuring the boson density. We extend a previous study (Phys. Rev. B {\bf 66}, 075128 (2002)) of cubic lattices to a variety of lattices and tilt directions in 2 dimensions: square, triangular, decorated square, and kagome, while noting the significance of three-body interactions. We find quantum phases with Ising density wave order, with superfluidity transverse to the tilt direction, a sliding Luttinger liquid phase, and quantum liquid states with no broken symmetry. Some cases map onto effective quantum dimer models.   

Quantum simulations with ultracold atoms

Precise understanding of strongly interacting systems, from electrons in materials and frustrated magnets to nuclear matter, is a major challenge for modern physics. Often, theoretical description of key models is severely plagued by the intricate quantum mechanics at play. This prompted a challenging effort of using ultra-cold atoms to realize Feynman's emulators of fundamental microscopic models. I will discuss some of the current efforts in realizing quantum simulators for cold bosonic and fermionic systems and how the theory tries to caught up with the experiment in making reliable predictions for strongly interacting quantum matter.   

A Mott Glass to Superfluid Transition for Random Bosons in Two Dimensions

We study the zero temperature superfluid-insulator transition for a two-dimensional model of interacting, lattice bosons in the presence of quenched disorder and particle-hole symmetry. We follow the approach of a recent series of papers by Altman, Kafri, Polkovnikov, and Refael, in which the strong disorder renormalization group is used to study disordered bosons in one dimension. Adapting this method to two dimensions, we study several different species of disorder and uncover universal features of the superfluid-insulator transition. In particular, we locate an unstable finite disorder fixed point that governs the transition between the superfluid and a gapless, glassy insulator. We present numerical evidence that this glassy phase is the incompressible Mott glass and that the transition from this phase to the superfluid is driven by percolation-type process. Finally, we provide estimates of the critical exponents governing this transition.   

Disordered Supersolids in the Extended Bose-Hubbard Model

Studies of the extended Bose-Hubbard model seek to capture the essential properties of a wide variety of physical systems including helium, Josephson junction arrays, certain narrow-band superconductors, and bosons in optical lattices. We theoretically study the stability of lattice supersolid states in the extended Bose-Hubbard model with bounded spatial disorder. We construct a disorder mean field theory and compare with quantum Monte Carlo calculations. We find that the supersolid survives weak disorder on the simple cubic lattice. We also find that increasing disorder strength can transform a lattice solid into a supersolid as it tends to percolate through the disorder landscape.   

Density instabilities in a two-dimensional dipolar Fermi gas

We investigate the inhomogeneous phases of fermionic polar molecules confined in a single two-dimensional (2D) layer, where the molecule dipole moments are all aligned by an external electric field. We show that the Random Phase Approximation (RPA) for the density-density response function is never accurate for the 2D dipolar Fermi gas. To incorporate correlations beyond RPA, we use an improved version of the Singwi-Tosi-Land-Sjolander scheme, which has been successful for electron systems. In addition to density-wave instabilities, our formalism captures the collapse instability that is expected from Hartree-Fock calculations but is absent from RPA. Crucially, we find that when the dipoles are oriented perpendicular to the layer, the system spontaneously breaks rotational symmetry and forms a stripe phase, in defiance of conventional wisdom.   

Scaling of noise correlations of hard-core bosons in incommensurate lattices

We study the scaling of the momentum distribution function and the noise correlations in the Mott insulator, Bose glass, and superfluid quantum phases of hard-core bosons subjected to quasi-periodic disorder. The exponents of the correlation functions at the superfluid to Bose-glass transition are found to be approximately one half of the ones that characterize the superfluid phase. We also find a divergence in the derivative of the noise correlation peaks with respect to the strength of disorder at the superfluid to Bose-glass critical point. This behavior is found not to occur in the corresponding free fermion system, where an Anderson-like transition takes place at the same critical point.   

Quantum Orders and Space-Time Vortices for Spin 2 Atomic Chains

Laser cooled atoms with spin can become magnetically ordered, like electrons in solids, but a greater variety of orders is possible in this setting. Spin one atoms can form nematic states with the symmetry of an undirected line segment while spin two atoms can form states with the symmetry of a tetrahedron. Such atoms could be confined to a one-dimensional optical lattice. In one dimension, quantum fluctuations become much more significant, and lead to a few interesting phases. In particular, the nematic state spontaneously breaks translational symmetry. If a state has a Berry's phase of a certain order under rotations, the fluctuations will often be modulated with a period of the same order. I will argue that this connection can be broken for a non-abelian symmetry group--both uniform and periodic phases can be stabilized. As an example, computer calculations (with DMRG) on a tetrahedral state find both a uniform and a period 3 phase.   

Thermal versus quantum fluctuations of optical lattice fermions

We show that, for fermionic atoms in a one-dimensional optical lattice, the fraction of atoms in doubly occupied sites is a highly non-monotonic function of temperature. We demonstrate that this property persists even in the presence of realistic harmonic confinement, and that it leads to a suppression of entropy at intermediate temperatures that offers a clear route to adiabatic cooling. Our interpretation of the suppression is that such intermediate temperatures are simultaneously too high for quantum coherence and too low for significant thermal excitation of double occupancy thus offering a clear indicator of the onset of quantum fluctuations.   

Tunable quantum glasses and phase transitions of atoms and photons: firstpredictions for glassy physics with many-body cavity QED

Recent studies of strongly interacting atoms and photons in opticalhave rekindled interest in the Dicke model of atomic qubitsto discrete photon cavity modes. In this talk, we argue thatof the Dicke model with variable atom-photon couplings canrise to a ground state phase diagram exhibiting quantum phasebetween paramagnetic, ferromagnetic, and a spin glass phase. These quantum optics realizations of quantum glasses are distinctive to condensed matter systems and provide new opportunities for glassy physics with many-bodyQED. The photon-mediated random couplings between the atomic qubitsIsing spins) are truly long-ranged and the theory for these systemsanalytically tractable. We compute atomic and photon spectralfunctions across this phase diagram, and outline how ourcan be observed in experiments.   

The boson-Hubbard model on a kagome lattice with a sextic ring-exchange term

We present exact quantum Monte Carlo simulations of hard-core bosons in a two-dimensional Kagome lattice with a sextic ring-exchange term. We study how the superfluid density evolves as the ring-exchange interactions are increased. We show that the system becomes unstable in the limit of large interactions at all fillings and undergoes a phase separation, except at $\frac13$ and $\frac23$ fillings for which the superfluid density vanishes and a solid state forms.