Majorana Corner Modes with Solitons in an Attractive Hubbard-Hofstadter Model of Cold Atom Optical Lattices.

Higher-order topological superconductors hosting Majorana-Kramers pairs (MKPs) as corner modes have recently been proposed in a two-dimensional quantum spin Hall insulator proximity-coupled to unconventional cuprate or iron-based superconductors. Here, we show that such MKPs can be realized using a conventional s-wave superfluid with a soliton in cold atom systems governed by the Hubbard-Hofstadter model. The MKPs emerge in the presence of interaction at the "corners" defined by the intersections of line solitons and the one-dimensional edges of the system. Our scheme is based on the recently realized cold atom Hubbard-Hofstadter lattice and will pave the way for observing possible higher-order topological superfluidity with conventional s-wave superfluids or superconductors.

Publisher Correction: Disordered Supersolids in the Extended Bose-Hubbard Model.

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Disordered Supersolids in the Extended Bose-Hubbard Model.

The extended Bose-Hubbard model captures the essential properties of a wide variety of physical systems including ultracold atoms and molecules in optical lattices, Josephson junction arrays, and certain narrow band superconductors. It exhibits a rich phase diagram including a supersolid phase where a lattice solid coexists with a superfluid. We use quantum Monte Carlo to study the supersolid part of the phase diagram of the extended Bose-Hubbard model on the simple cubic lattice. We add disorder to the extended Bose-Hubbard model and find that the maximum critical temperature for the supersolid phase tends to be suppressed by disorder. But we also find a narrow parameter window in which the supersolid critical temperature is enhanced by disorder. Our results show that supersolids survive a moderate amount of spatial disorder and thermal fluctuations in the simple cubic lattice.

Equilibration Dynamics of Strongly Interacting Bosons in 2D Lattices with Disorder.

Motivated by recent optical lattice experiments [J.-y. Choi et al., Science 352, 1547 (2016)SCIEAS0036-807510.1126/science.aaf8834], we study the dynamics of strongly interacting bosons in the presence of disorder in two dimensions. We show that Gutzwiller mean-field theory (GMFT) captures the main experimental observations, which are a result of the competition between disorder and interactions. Our findings highlight the difficulty in distinguishing glassy dynamics, which can be captured by GMFT, and many-body localization, which cannot be captured by GMFT, and indicate the need for further experimental studies of this system.

Thermometry for Laughlin States of Ultracold Atoms.

Cooling atomic gases into strongly correlated quantum phases requires estimates of the entropy to perform thermometry and establish viability. We construct an ansatz partition function for models of Laughlin states of atomic gases by combining high temperature series expansions with exact diagonalization. Using the ansatz we find that entropies required to observe Laughlin correlations with bosonic gases are within reach of current cooling capabilities.

Dzyaloshinskii-Moriya Interaction and Spiral Order in Spin-orbit Coupled Optical Lattices.

We show that the recent experimental realization of spin-orbit coupling in ultracold atomic gases can be used to study different types of spin spiral order and resulting multiferroic effects. Spin-orbit coupling in optical lattices can give rise to the Dzyaloshinskii-Moriya (DM) spin interaction which is essential for spin spiral order. By taking into account spin-orbit coupling and an external Zeeman field, we derive an effective spin model in the Mott insulator regime at half filling and demonstrate that the DM interaction in optical lattices can be made extremely strong with realistic experimental parameters. The rich finite temperature phase diagrams of the effective spin models for fermions and bosons are obtained via classical Monte Carlo simulations.

Emergent kinetics and fractionalized charge in 1D spin-orbit coupled flatband optical lattices.

Recent ultracold atomic gas experiments implementing synthetic spin-orbit coupling allow access to flatbands that emphasize interactions. We model spin-orbit coupled fermions in a one-dimensional flatband optical lattice. We introduce an effective Luttinger-liquid theory to show that interactions generate collective excitations with emergent kinetics and fractionalized charge, analogous to properties found in the two-dimensional fractional quantum Hall regime. Observation of these excitations would provide an important platform for exploring exotic quantum states derived solely from interactions.

Enhancing the thermal stability of Majorana fermions with redundancy using dipoles in optical lattices.

Pairing between spinless fermions can generate Majorana fermion excitations that exhibit intriguing properties arising from nonlocal correlations. But, simple models indicate that nonlocal correlation between Majorana fermions becomes unstable at nonzero temperatures. We address this issue by showing that anisotropic interactions between dipolar fermions in optical lattices can be used to significantly enhance thermal stability. We construct a model of oriented dipolar fermions in a square optical lattice. We find that domains established by strong interactions exhibit enhanced correlation between Majorana fermions over large distances and long times even at finite temperatures, suitable for stable redundancy encoding of quantum information. Our approach can be generalized to a variety of configurations and other systems, such as quantum wire arrays.

Stroboscopic generation of topological protection.

Trapped neutral atoms offer a powerful route to robust simulation of complex quantum systems. We present here a stroboscopic scheme for realization of a Hamiltonian with n-body interactions on a set of neutral atoms trapped in an addressable optical lattice, using only 1- and 2-body physical operations together with a dissipative mechanism that allows thermalization to finite temperature or cooling to the ground state. We demonstrate this scheme with application to the toric code Hamiltonian, ground states of which can be used to robustly store quantum information when coupled to a low temperature reservoir.

Robustness of topologically protected surface states in layering of Bi2Te3 thin films.

Bulk Bi2Te3 is known to be a topological insulator. We investigate surface states of Bi2Te3(111) thin films of one to six quintuple layers using density-functional theory including spin-orbit coupling. We construct a method to identify topologically protected surface states of thin film topological insulators. Applying this method to Bi2Te3 thin films, we find that the topological nature of the surface states remains robust with the film thickness and that the films of three or more quintuple layers have topologically nontrivial surface states, which agrees with experiments.

Discerning incompressible and compressible phases of cold atoms in optical lattices.

Experiments with cold atoms trapped in optical lattices offer the potential to realize a variety of novel phases but suffer from severe spatial inhomogeneity that can obscure signatures of new phases of matter and phase boundaries. We use a high temperature series expansion to show that compressibility in the core of a trapped Fermi-Hubbard system is related to measurements of changes in double occupancy. This core compressibility filters out edge effects, offering a direct probe of compressibility independent of inhomogeneity. A comparison with experiments is made.

Anyonic braiding in optical lattices.

Topological quantum states of matter, both Abelian and non-Abelian, are characterized by excitations whose wavefunctions undergo nontrivial statistical transformations as one excitation is moved (braided) around another. Topological quantum computation proposes to use the topological protection and the braiding statistics of a non-Abelian topological state to perform quantum computation. The enormous technological prospect of topological quantum computation provides new motivation for experimentally observing a topological state. Here, we explicitly work out a realistic experimental scheme to create and braid the Abelian topological excitations in the Kitaev model built on a tunable robust system, a cold atom optical lattice. We also demonstrate how to detect the key feature of these excitations: their braiding statistics. Observation of this statistics would directly establish the existence of anyons, quantum particles that are neither fermions nor bosons. In addition to establishing topological matter, the experimental scheme we develop here can also be adapted to a non-Abelian topological state, supported by the same Kitaev model but in a different parameter regime, to eventually build topologically protected quantum gates.

Edge transport in 2D cold atom optical lattices.

We theoretically study the observable response of edge currents in two-dimensional cold atom optical lattices. As an example, we use Gutzwiller mean-field theory to relate persistent edge currents surrounding a Mott insulator in a slowly rotating trapped Bose-Hubbard system to time of flight measurements. We briefly discuss an application, the detection of the Chern number using edge currents of a topologically ordered optical lattice insulator.

Emergence of artificial photons in an optical lattice.

We establish the theoretical feasibility of direct analog simulation of the compact U(1) lattice gauge theories in optical lattices with dipolar bosons. We discuss the realizability of the topological Coulomb phase in extended Bose-Hubbard models in several optical lattice geometries. We predict the testable signatures of this emergent phase in noise correlation measurements, thus suggesting the possible emergence of artificial light in optical lattices.

Quantum phases of the extended Bose-Hubbard hamiltonian: possibility of a supersolid state of cold atoms in optical lattices.

Cold atom optical lattices typically simulate zero-range Hubbard models. We discuss the theoretical possibility of using excited states of optical lattices to generate extended range Hubbard models. We find that bosons confined to higher bands of optical lattices allow for a rich phase diagram, including the supersolid phase. Using Gutzwiller, mean-field theory we establish the parameter regime necessary to maintain metastable states generated by an extended Bose-Hubbard model.

Chirality in quantum computation with spin cluster qubits.

We study corrections to the Heisenberg interaction between several lateral, single-electron quantum dots. We show, using exact diagonalization, that three-body chiral terms couple triangular configurations to external sources of flux rather strongly. The chiral corrections impact single-qubit encodings utilizing loops of three or more Heisenberg coupled quantum dots.

Pseudospin quantum computation in semiconductor nanostructures.

We theoretically show that spontaneously interlayer-coherent bilayer quantum Hall droplets should allow robust and fault-tolerant pseudospin quantum computation in semiconductor nanostructures with voltage-tuned external gates providing qubit control and a quantum Ising Hamiltonian providing qubit entanglement. Using a spin-boson model, we estimate decoherence to be small (approximately 10(-5)).

Even-odd effect in spontaneously coherent bilayer quantum Hall droplets.

Using exact diagonalization in the disk geometry we predict a novel even-odd effect in the Coulomb-blockade spectra of vertically coupled double quantum dots under an external magnetic field. The even-odd effect in the tunneling conductance is a direct manifestation of spontaneous interlayer phase coherence, and is similar to the even-odd resonance in the Cooper pair box problem in mesoscopic superconducting grains. Coherent fluctuations in the number of Cooper pairs in superconductors are analogous to the fluctuations in the relative number difference between the two layers in quantum Hall droplets.

Possible pairing-induced even-denominator fractional quantum Hall effect in the lowest Landau level.

We report on our theoretical investigations that point to the possibility of a fractional quantum Hall effect with partial spin polarization at nu = 3/8. The physics of the incompressible state proposed here involves p-wave pairing of composite fermions in the spin reversed sector. The temperature and magnetic field regimes for the realization of this state are estimated.

Stripe formation in the fractional quantum Hall regime.

An understanding of the physics of the half-filled lowest Landau level has been achieved in terms of a Fermi sea of composite fermions, but the nature of the state at other even-denominator fractions has remained unclear. We investigate theoretically Landau level fillings of the form nu = (2n + 1)/(4n + 4), which correspond to composite-fermion fillings nu* = n + 1/2. By considering various plausible candidate states with complete spin polarization, we rule out the composite-fermion Fermi sea and paired composite-fermion state at these filling factors, and predict that the system phase separates into stripes of n and n + 1 filled Landau levels of composite fermions.