Quantum glass phases in the disordered Bose-Hubbard model

The phase diagram of the Bose-Hubbard model in the presence of off-diagonal disorder is determined using quantum Monte Carlo simulations. A sequence of quantum glass phases intervene at the interface between the Mott insulating and the superfluid phases of the clean system. In addition to the standard Bose glass phase, the coexistence of gapless and gapped regions close to the Mott insulating phase leads to a novel Mott glass regime which is incompressible yet gapless. Numerical evidence for the properties of these phases is given in terms of global (compressibility, superfluid stiffness) and local (compressibility, momentum distribution) observables.     

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.     

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.     

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.     

Purely electronic transport and localization in the Bose glass

We discuss transport and localization properties on the insulating side of the disorder dominated superconductor‐insulator transition, described in terms of the dirty boson model. Analyzing the spectral properties of the interacting bosons in the absence of phonons, we argue that the Bose glass phase admits three distinct regimes. For strongest disorder the boson system is a fully localized, perfect insulator at any temperature. At smaller disorder, only the low temperature phase exhibits perfect insulation while delocalization takes place above a finite temperature. We argue that a third phase must intervene between these perfect insulators and the superconductor. This conducting Bose glass phase is characterized by a mobility edge in the many body spectrum, located at finite energy above the ground state. In this insulating regime purely electronically activated transport occurs, with a conductivity following an Arrhenius law at asymptotically low temperatures, while a tendency to superactivation is predicted at higher T. These predictions are in good agreement with recent transport experiments in highly disordered films of superconducting materials.     

Zero field Wigner crystal

A candidate for the insulating phase of the 2D electron gas, seen in high mobility 2D MOSFETS and heterojunctions, is a Wigner crystal pinned by the incipient disorder. With this in view, we study the effect of collective pinning on the physical properties of the crystal formed in zero external magnetic field. We use an elastic theory to describe to long wavelength modes of the crystal. The disorder is treated using the standard Gaussian variational method. We calculate various physical properties of the system with particular emphasis on their density dependence. We revisit the problem of compressibility in this system and present results for the compressibility obtained via effective capacitance measurements in experiments using bilayers. We present results for the dynamical conductivity, surface acoustic wave anomalies and the power radiated by the crystal through phonon emission at finite temperatures.     

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.     

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.     

有限温度下一维Hubbard模型的化学势泛函理论研究

通过数值方法求解了有限温度下一维均匀Hubbard模型的热力学Bethe-ansatz方程组,得到了在给定温度和相互作用强度情况下,比热c、磁化率χ和压缩比κ随化学势μ的变化图像.基于有限温度下一维均匀Hubbard模型的精确解,利用化学势(μ)-泛函理论研究了一维谐振势下的非均匀Hubbard模型,给出了金属态和Mott绝缘态下不同温度情况时局域粒子密度n_i和局域压缩比_κi随格点的变化情况.     

Orbital glass and spin glass states of <Superscript>3</Superscript>He-A in aerogel

Glass states of superfluid A-like phase of ³He in aerogel induced by random orientations of aerogel strands are investigated theoretically and experimentally. In anisotropic aerogel with stretching deformation two glass phases are observed. Both phases represent the anisotropic glass of the orbital ferromagnetic vector Ηthe orbital glass (OG). The phases differ by the spin structure: the spin nematic vector \(\hat d\) can be either in the ordered spin nematic (SN) state or in the disordered spin-glass (SG) state. The first phase (OG-SN) is formed under conventional cooling from normal ³He. The second phase (OG-SG) is metastable, being obtained by cooling through the superfluid transition temperature, when large enough resonant continuous radio-frequency excitation is applied. NMR signature of different phases allows us to measure the parameter of the global anisotropy of the orbital glass induced by deformation.     

Critical properties of a three-dimensional p-spin model

In this paper we study the critical properties of a finite dimensional generalization of the p-spin model. We find evidence that in dimension three, contrary to its mean field limit, the glass transition is associated to a diverging susceptibility (and correlation length). Received 13 May 1998     

One-dimensional Bose-Hubbard model with pure three-body interactions

The extended Bose-Hubbard model with pure three-body local interactions is studied using the Density Matrix Renormalization Group approach. The shapes of the first two insulating lobes are discussed, and the values of the critical tunneling for which the system undergoes the quantum phase transition from insulating to superfluid phase are predicted. It is shown that stability of insulating phases, in contrast to the standard Bose-Hubbard model, is enhanced for larger fillings. It is also shown that, on the tip of the boundary of the insulating phase, the model under consideration belongs to the Berenzinskii-Kosterlitz-Thouless universality class.     

Dipolar excitons, spontaneous phase coherence, and superfluid-insulator transition in bilayer quantum Hall systems at nu = 1

The spontaneous interlayer phase coherent (111) state of a bilayer quantum Hall system at filling factor nu = 1 may be viewed as a condensate of interlayer particle-hole pairs or excitons. We show that when the layers are biased in such a way that these excitons are very dilute, they may be viewed as pointlike bosons. We calculate the exciton dispersion relation and show that the exciton-exciton interaction is dominated by the dipole moment they carry. In addition to the phase coherent state, we also find a Wigner crystal/glass phase in the presence/absence of disorder which is an insulating state for the excitons. The position of the phase boundary is estimated and the transition between these two phases is discussed.     

Random on-site interactions versus random potential in ultra cold atoms in optical lattices

We consider the physics of lattice bosons in the presence of either disordered on-site chemical potential or disordered on-site interparticle interactions. By means of analytical results using strong-coupling expansion, and numerical results based on quantum Monte Carlo calculations, we show that important qualitative changes in the zero temperature phase diagram are observed when comparing both cases. Although for both types of disorder superfluid, Mott-insulator and Bose-glass phases may be found, we show that in the case of random interactions the Mott-insulating regions shrink and eventually vanish for any finite disorder strength beyond a sufficiently large filling factor. Furthermore, at low values of the chemical potential both the superfluid and Mott insulator are stable towards the formation of a Bose-glass, leading to a possibly non-trivial tricritical point. We discuss possible experimental realizations of both types of disorder in the context of ultra cold atomic gases in optical lattices. PACS 03.75.Lm; 03.75.Ss; 05.30.Jp; 32.80.Pj     

Transition from a two-dimensional superfluid to a one-dimensional Mott insulator

A two-dimensional system of atoms in an anisotropic optical lattice is studied theoretically. If the system is finite in one direction, it is shown to exhibit a transition between a two-dimensional superfluid and a one-dimensional Mott insulating chain of superfluid tubes. Monte Carlo simulations are consistent with the expectation that the phase transition is of Kosterlitz-Thouless type. The effect of the transition on experimental time-of-flight images is discussed.     

Superfluid and insulating phases of fermion mixtures in optical lattices

The ground state phase diagram of fermion mixtures in optical lattices is analyzed as a function of interaction strength, fermion filling factor, and tunneling parameters. In addition to standard superfluid, phase-separated or coexisting superfluid -- excess-fermion phases found in homogeneous or harmonically trapped systems, fermions in optical lattices have several insulating phases, including a molecular Bose-Mott insulator (BMI), a Fermi-Pauli (band) insulator (FPI), a phase-separated BMI-FPI mixture or a Bose-Fermi checkerboard (BFC). The molecular BMI phase is the fermion mixture counterpart of the atomic BMI found in atomic Bose systems, the BFC or BMI-FPI phases exist in Bose-Fermi mixtures, and lastly the FPI phase is particular to the Fermi nature of the constituent atoms of the mixture.     

Optical Bragg,atomic Bragg and cavity QED detections of quantum phases and excitation spectra of ultracold atoms in bipartite and frustrated optical lattices

Ultracold atoms loaded on optical lattices can provide unprecedented experimental systems for the quantum simulations and manipulations of many quantum phases and quantum phase transitions between these phases. However, so far, how to detect these quantum phases and phase transitions effectively remains an outstanding challenge. In this paper, we will develop a systematic and unified theory of using the optical Bragg scattering, atomic Bragg scattering or cavity QED to detect the ground state and the excitation spectrum of many quantum phases of interacting bosons loaded in bipartite and frustrated optical lattices. The physically measurable quantities of the three experiments are the light scattering cross sections, the atom scattered clouds and the cavity leaking photons respectively. We show that the two photon Raman transition processes in the three detection methods not only couple to the density order parameter, but also the valence bond order parameter due to the hopping of the bosons on the lattice. This valence bond order coupling is very sensitive to any superfluid order or any valence bond (VB) order in the quantum phases to be probed. These quantum phases include not only the well-known superfluid and Mott insulating phases, but also other important phases such as various kinds of charge density waves (CDW), valence bond solids (VBS), and CDW-VBS phases with both CDW and VBS orders unique to frustrated lattices, and also various kinds of supersolids. We analyze respectively the experimental conditions of the three detection methods to probe these various quantum phases and their corresponding excitation spectra. We also address the effects of a finite temperature and a harmonic trap. We contrast the three scattering methods with recent in situ measurements inside a harmonic trap and argue that the two kinds of measurements are complementary to each other. The combination of both kinds of detection methods could be used to match the combination of Scanning tunneling microscopy (STM), the Angle Resolved Photo Emission spectroscopy (ARPES) and neutron scattering in condensed matter systems, therefore achieve the putative goals of quantum simulations     

Energy Spectrum of Two-Component Bose-Einstein Condensates in Optical Lattices

With the method of Green's function, we investigate the energy spectra of two-component ultracold bosonic atoms in optical lattices. We find that there are two energy bands for each component. The critical condition of the superfluid-Mott insulator phase transition is determined by the energy band structure. We also find that the nearest neighboring and on-site interactions fail to change the structure of energy bands, but shift the energy bands only. According to the conditions of the phase transitions, three stable superfluid and Mott insulating phases can be found by adjusting the experiment parameters. We also discuss the possibility of observing these new phases and their transitions in further experiments.     

Quantum emulsion: a glassy phase of bosonic mixtures in optical lattices

We numerically investigate mixtures of two interacting bosonic species with unequal parameters in one-dimensional optical lattices. In large parameter regions full phase segregation is seen to minimize the energy of the system, but the true ground state is masked by an exponentially large number of metastable states characterized by microscopic phase separation. The ensemble of these quantum emulsion states, reminiscent of emulsions of immiscible fluids, has macroscopic properties analogous to those of a Bose glass, namely, a finite compressibility in absence of superfluidity. Their metastability is probed by extensive quantum Monte Carlo simulations generating rich correlated stochastic dynamics. The tuning of the repulsion of one of the two species via a Feshbach resonance drives the system through a quantum phase transition to the superfluid state.