Insulating phases and superfluid-insulator transition of disordered boson chains

Using a strong disorder real-space renormalization group, we study the phase diagram of a fully disordered chain of interacting bosons. Since this approach does not suffer from runaway flows, it allows a direct study of the insulating phases, not accessible in a weak disorder perturbative treatment. We find that the universal properties of the insulating phase are determined by the details and symmetries of the on-site chemical-potential disorder. Three insulating phases are possible: (i) an incompressible Mott glass with a finite superfluid susceptibility, (ii) a random-singlet glass with diverging compressibility and superfluid susceptibility, (iii) a Bose glass with a finite compressibility but diverging superfluid susceptibility. In addition to characterizing the insulating phases, we show that the superfluid-insulator transition is always described by Kosterlitz-Thouless-like flows.     

Superfluid-Mott-Insulator Phase Transition Phases of Bosons in an and Collective Fluctuations in both Optical Lattice

The Bose Hubbard model describing interacting bosons in an optical lattice is reduced to a simple spin-1 XY model with single-ion anisotropy in the vicinity of the Mott phase. In the strong coupling Mott insulating regime, we propose a mean t~eld theory based on a constraint SU（3） pseudo-boson representation on the effective model and discuss the excitation spectra and the phase transition to the superfluid state. Further to the superfluid phase, we use the coherent-state approach to derive the collective excitation modes. It is found that the Mort phase has two degenerate gapped quadratic excitation spectra which graduate into two degenerate gapless linear ones at the transition point, and one gapless linear mode with one gapped quadratic mode in the superfluid phase.     

Noise correlations of fermions and hard core bosons in a quasi-periodic potential

We use Hanbury-Brown-Twiss interferometry (HBTI) to study various quantum phases of hard core bosons (HCBs) and ideal fermions confined in a one-dimensional quasi-periodic (QP) potential. For HCBs, the QP potential induces a cascade of Mott-like band-insulator phases in the extended regime, in addition to the Mott insulator, Bose glass, and superfluid phases. At critical filling factors, the appearance of these insulating phases is heralded by a peak to dip transition in the interferogram, which reflects the fermionic aspect of HCBs. On the other hand, ideal fermions in the extended phase display various complexities of incommensurate structures such as devil’s staircases and Arnold tongues. In the localized phase, the HCB and the fermion correlations are identical except for the sign of the peaks. Finally, we demonstrate that HBTI provides an effective method to distinguish Mott and glassy phases.     

Quantum magnetism with multicomponent dipolar molecules in an optical lattice

We consider bosonic dipolar molecules in an optical lattice prepared in a mixture of different rotational states. The 1/R(3) interaction between molecules for this system is produced by exchanging a quantum of angular momentum between two molecules. We show that the Mott states of such systems have a large variety of quantum phases characterized by dipolar orderings including a state with an ordering wave vector that can be changed by tilting the lattice. As the Mott insulating phase is melted, we also describe several exotic superfluid phases that will occur.     

A review of Monte Carlo simulations for the Bose–Hubbard model with diagonal disorder

We review the physics of the Bose–Hubbard model with disorder in the chemical potential focusing on recently published analytical arguments in combination with quantum Monte Carlo simulations. Apart from the superfluid and Mott insulator phases that can occur in this system without disorder, disorder allows for an additional phase, called the Bose glass phase. The topology of the phase diagram is subject to strong theorems proving that the Bose Glass phase must intervene between the superfluid and the Mott insulator and implying a Griffiths transition between the Mott insulator and the Bose glass. The full phase diagrams in 3d and 2d are discussed, and we zoom in on the insensitivity of the transition line between the superfluid and the Bose glass in the close vicinity of the tip of the Mott insulator lobe. We briefly comment on the established and remaining questions in the 1d case, and give a short overview of numerical work on related models.     

Quantum field theoretical study of an effective spin model in coupled optical cavity arrays

Atoms trapped in micro-cavities and interacting through the exchange of virtual photons can be modeled as an anisotropic Heisenberg spin-1/2 lattice. We do the quantum field theoretical study of such a system using the Abelian bosonization method followed by the renormalization group analysis. An infinite order Berezinskii-Kosterliz-Thouless transition is replaced by second order XY transition even when an infinitesimal anisotropy in exchange coupling is introduced. We predict a quantum phase transition between the photonic Coulomb blocked induce Mott insulating and photonic superfluid phases due to detuning between the cavity and laser frequency. A large detuning favors the photonic superfluid phase. We also perform the analysis of Jaynes and Cumming Hamiltonian to support the results of quantum field theoretical study.     

Mott domains of bosons confined on optical lattices

In the absence of a confining potential, the boson-Hubbard model exhibits a superfluid to Mott insulator quantum phase transition at commensurate fillings and strong coupling. We use quantum Monte Carlo simulations to study the ground state of the one-dimensional bosonic Hubbard model in a trap. Some, but not all, aspects of the Mott insulating phase persist. Mott behavior occurs for a continuous range of incommensurate fillings, very different from the unconfined case, and the establishment of the Mott phase does not proceed via a traditional quantum phase transition. These results have important implications for interpreting experiments on ultracold atoms on optical lattices.     

Phase glass is a Bose metal: a new conducting state in two dimensions

In the quantum rotor model with random exchange interactions having a nonzero mean, three phases, a (i) phase (Bose) glass, (ii) superfluid, and (iii) Mott insulator, meet at a bicritical point. We demonstrate that proximity to the bicritical point and the coupling between the energy landscape and the dissipative degrees of freedom of the phase glass lead to a metallic state at T = 0. Consequently, the phase glass is unique in that it represents a concrete example of a metallic state that is mediated by disorder, even in 2D. We propose that the experimentally observed metallic phase which intervenes between the insulator and the superconductor in a wide range of thin films is in actuality a phase glass.     

Staggered-vortex superfluid of ultracold bosons in an optical lattice

We show that the dynamics of cold bosonic atoms in a two-dimensional square optical lattice produced by a bichromatic light-shift potential is described by a Bose-Hubbard model with an additional effective staggered magnetic field. In addition to the known uniform superfluid and Mott insulating phases, the zero-temperature phase diagram exhibits a novel kind of finite-momentum superfluid phase, characterized by a quantized staggered rotational flux. An extension for fermionic atoms leads to an anisotropic Dirac spectrum, which is relevant to graphene and high-T(c) superconductors.     

Topological Mott insulators

We consider extended Hubbard models with repulsive interactions on a honeycomb lattice, and the transitions from the semimetal to Mott insulating phases at half-filling. Because of the frustrated nature of the second-neighbor interactions, topological Mott phases displaying the quantum Hall and the quantum spin Hall effects are found for spinless and spin fermion models, respectively. The mean-field phase diagram is presented and the fluctuations are treated within the random phase approximation. Renormalization group analysis shows that these states can be favored over the topologically trivial Mott insulating states.     

Mean-field phase diagram for Bose-Hubbard Hamiltonians with random hopping

The zero temperature phase diagram for ultracold bosons in a random 1D potential is obtained through a site decoupling mean-field scheme performed over a Bose-Hubbard (BH) Hamiltonian, whose hopping term is considered as a random variable. As for the model with random on-site potential, the presence of disorder leads to the appearance of a Bose glass phase. The different phases—i.e., Mott insulator, superfluid, and Bose glass—are characterized in terms of condensate fraction and superfluid fraction. Furthermore, the boundary of the Mott lobes is related to an off-diagonal Anderson model featuring the same disorder distribution as the original BH Hamiltonian.     

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 twofold 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 paraorbital). 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.     

Quantum simulation of zero-temperature quantum phases and incompressible states of light via non-Markovian reservoir engineering techniques

We review recent theoretical developments on the stabilization of strongly correlated quantum fluids of light in driven-dissipative photonic devices through novel non-Markovian reservoir engineering techniques. This approach allows one to compensate losses and refill selectively the photonic population so as to sustain a desired steady state. It relies in particular on the use of a frequency-dependent incoherent pump, which can be implemented, e.g., via embedded two-level systems maintained at a strong inversion of population. As specific applications of these methods, we discuss the generation of Mott Insulator (MI) and Fractional Quantum Hall (FQH) states of light. As a first step, we present the case of a narrowband emission spectrum and show how this allows for the stabilization of MI and FQH states under the condition that the photonic states are relatively flat in energy. As soon as the photonic bandbwidth becomes comparable to the emission linewidth, important non-equilibrium signatures and entropy generation appear, and a novel dissipative phase transition from a Mott Insulating state toward a superfluid (SF) phase is unveiled. As a second step, we review a more advanced configuration based on reservoirs with a broadband frequency distribution, and we highlight the potential of this configuration for the quantum simulation of equilibrium quantum phases at zero temperature with tunable chemical potential. As a proof of principle, we establish the applicability of our scheme to the Bose–Hubbard model by confirming the presence of a perfect agreement with the ground-state predictions both in the Mott insulating and superfluid regions, and more generally in all parts of the parameter space. Future prospects towards the quantum simulation of more complex configurations are finally outlined, along with a discussion of our scheme as a concrete realization of quantum annealing.     

Nodal Topological Phases in s-wave Superfluid of Ultracold Fermionic Gases

The gapless Weyl superfluid has been widely studied in the three-dimensional ultracold fermionic superfluid.In contrast to Weyl superfluid, there exists another kind of gapless superfluid with topologically protected nodal lines,which can be regarded as the superfluid counterpart of nodal line semimetal in the condensed matter physics, just as Weyl superfluid with Weyl semimetal. In this paper we study the ground states of the cold fermionic gases in cubic optical lattices with one-dimensional spin-orbit coupling and transverse Zeeman field and map out the topological phase diagram of the system. We demonstrate that in addition to a fully gapped topologically trivial phase, some different nodal line superfluid phases appear when the Zeeman field is adjusted. The presence of topologically stable nodal lines implies the dispersionless zero-energy flat band in a finite region of the surface Brillouin zone. Experimentally these nodal line superfluid states can be detected via the momentum-resolved radio-frequency spectroscopy. The nodal line topological superfluid provide fertile grounds for exploring exotic quantum matters in the context of ultracold atoms.     

Oscillating superfluidity of bosons in optical lattices

Following a suggestion by Orzel et al. [Science 291, 2386 (2001)]], we analyze bosons in an optical lattice undergoing a sudden parameter change from the Mott to superfluid phase. We introduce a modified coherent states path integral to describe both phases. The saddle point theory yields collective oscillations of the uniform superfluid order parameter. We calculate its damping rate by phason pair emission. In two dimensions the overdamped region largely overlaps with the quantum critical region. Measurements of critical dynamics on the Mott side are proposed.     

Quantum criticality between topological and band insulators in 3+1 dimensions

Four-component massive and massless Dirac fermions in the presence of long range Coulomb interaction and chemical potential disorder exhibit striking fermionic quantum criticality. For an odd number of flavors of Dirac fermions, the sign of the Dirac mass distinguishes the topological and the trivial band insulator phases, and the gapless semimetallic phase corresponds to the quantum critical point that separates the two. Up to a critical strength of disorder, the semimetallic phase remains stable, and the universality class of the direct phase transition between two insulating phases is unchanged. Beyond the critical strength of disorder the semimetallic phase undergoes a phase transition into a disorder controlled diffusive metallic phase, and there is no longer a direct phase transition between the two types of insulating phases.     

One-dimensional phase transitions in a two-dimensional optical lattice

A phase transition for bosonic atoms in a two-dimensional anisotropic optical lattice is considered. If the tunnelling rates in two directions are different, the system can undergo a transition between a two-dimensional superfluid and a one-dimensional Mott insulating array of strongly coupled tubes. The connection to other lattice models is exploited in order to better understand the phase transition. Critical properties are obtained using quantum Monte Carlo calculations. These critical properties are related to correlation properties of the bosons and a criterion for commensurate filling is established.     

Benchmark study of the SF-MI phase transition of the Bose–Hubbard model with density-induced tunneling

The Bose–Hubbard model (BHM) is a standard model which describes the quantum behavior of ultracold bosons in optical lattice. When tuning the model parameters, a quantum phase transition from superfluid (SF) phase to Mott insulating (MI) phase emerges. However, an extra tunneling process – the density-induced tunneling – is usually ignored in the standard BHM. Using process-chain method, we give a thorough study of the phase diagram of the BHM with density-induced tunneling in different particle density regions and spatial dimensions. We find the density-induced tunneling process can affect the SF-MI phase boundary dramatically, by suppressing the MI region and tune the tip of the phase boundary to lower chemical potential. Our unbiased numerical study gives benchmark results of the phase diagram of the BHM with density-induced tunneling.     

Interplay of the Staggered and Three-Body Interaction Potentials on the Quantum Phases of a Spin-1 Ultracold Atom in an Optical Lattice

The interplay of the staggered and the three-body interaction potentials on the quantum phases of a spin-1 Bose Hubbard model using a mean field approximation (MFA) is studied. In the antiferromagnetic (AF) case, a smaller value of the staggered potential (SP) results in the charge and the spin density wave ordering along with the Mott insulator (MI) and the staggered superfluid (SSF) phases. While the competition between two types of the potential leads to the stabilization of the higher order MI and charge density wave (CDW) phases with increasing three-body interaction strength. Further, the spin eigenvalue and nematic order parameters are calculated to scrutinize the spin singlet-nematic formation in the MI and the CDW phases and spin population fractions to analyze the nature of the SSF phase. A signature of the spin density wave (SDW) pattern is also observed in the gapped phase lobes. In case of a purely three-body interaction, the third and higher order insulating lobes become dominant with increasing staggered potential strength. Subsequently, all MFA phase diagrams are then nicely corroborated with the analytical results obtained using a perturbative expansion corresponding to the AF and ferromagnetic cases.