Extended Bose Hubbard Model Research Articles

Revealing discontinuous and continuous quantum phase transitions in shaken optical lattices

We perform the cluster mean-field with density matrix renormalization (CMFT+DMRG) calculation on the two-band extended Bose–Hubbard model to uncover the physics behind the discontinuous transitions observed in the one-dimensional shaken optical lattice with hybridized two lowest Bloch bands. We determine the superfluid, Mott insulator, and staggered superfluid phases associated with this model using the appropriate order parameters. We obtained the phase diagrams for two values of shaking amplitudes and illustrated the phases and nature of phase transitions. The transition from Mott insulator and superfluid to staggered superfluid is discontinuous for small shaking amplitudes. We analyse how the shaking frequency controls the effective chemical potential in the model and, consequently, the ground state energy that drives the discontinuous transition. Finally, we compare our results with those of earlier works.

Bond-order density wave phases in dimerized extended Bose-Hubbard models

Bond-order density wave phases in dimerized extended Bose-Hubbard models

Frustrated Extended Bose-Hubbard Model and Deconfined Quantum Critical Points with Optical Lattices at the Antimagic Wavelength.

The study of geometrically frustrated many-body quantum systems is of central importance to uncover novel quantum mechanical effects. We design a scheme where ultracold bosons trapped in a one-dimensional state-dependent optical lattice are modeled by a frustrated Bose-Hubbard Hamiltonian. A derivation of the Hamiltonian parameters based on Cesium atoms, further show large tunability of contact and nearest-neighbor interactions. For pure contact repulsion, we discover the presence of two phases peculiar to frustrated quantum magnets: the bond-order-wave insulator with broken inversion symmetry and a chiral superfluid. When the nearest-neighbor repulsion becomes sizable, a further density-wave insulator with broken translational symmetry can appear. We show that the phase transition between the two spontaneously symmetry-broken phases is continuous, thus representing a one-dimensional deconfined quantum critical point not captured by the Landau-Ginzburg-Wilson symmetry-breaking paradigm. Our results provide a solid ground to unveil the novel quantum physics induced by the interplay of nonlocal interactions, geometrical frustration, and quantum fluctuations.

Magnetic supersolid phases of two-dimensional extended Bose–Hubbard model with spin–orbit coupling

We investigate the quantum phases and phase transitions for spin–orbit coupled two-species bosons with nearest-neighbor (NN) interaction in a two-dimensional square lattice using inhomogeneous dynamical Guztwiller mean-field method. Under the effect of spin–orbit coupling and NN interaction, we uncover a rich variety of different magnetic supersolid (SS) phases. In the presence of intraspecies NN interaction, the phase diagram exhibits the phase-twisted double-checkerboard SS (PT-DCSS) and phase-striped double-checkerboard SS (PS-DCSS) phases. For both intra- and interspecies NN interactions, apart from the phase-twisted lattice SS (PT-LSS) and phase-striped lattice SS (PS-LSS) phases, some nontrivial SS phases with interesting properties occur. More importantly, we find that the emergences of these nontrivial SS phases are dependent of the interspecies on-site interaction. To further characterize the SS phases, we also discuss the spin-dependent momentum distributions and magnetic textures. The magnetic textures, such as antiferromagnetic, spiral and stripe orders are shown. Finally, we give the fully analytical insights into the numerical results.

NOON state measurement probabilities and outcome fidelities: a Bethe ansatz approach

A recently proposed extended Bose–Hubbard model, one that is a quantum integrable model, provides a framework for a NOON state generation protocol. Here we derive a Bethe ansatz solution for the model. The form of the solution provides the means to obtain exact asymptotic expressions for the energies and eigenstates. These results are used to derive formulae for measurement probabilities and outcome fidelities. We benchmark these results against numerical calculations.

Pairing Superfluid–Insulator Transition Induced by Atom–Molecule Conversion in Bosonic Mixtures in Optical Lattice

Motivated by the recent experiment on bosonic mixtures of atoms and molecules, we investigate pairing superfluid–insulator (SI) transition for bosonic mixtures of atoms and molecules in a one-dimensional optical lattice, which is described by an extended Bose–Hubbard model with atom–molecule conservation (AMC). It is found that AMC can induce an extra pair–superfluid phase though the system does not demonstrate pair-hopping. In particular, the system may undergo several pairing SI or insulator–superfluid transitions as the detuning from the Feshbach resonance is varied from negative to positive, and the larger positive detuning can bifurcate the pair–superfluid phases into mixed superfluid phases consisting of single-atomic and pair-atomic superfluid. The calculation of the second-order Rényi entropy reveals that the discontinuity in its first-order derivative corresponds to the phase boundary of the pairing SI transition. This means that the residual entanglement in our mean-field treatment can be used to efficiently capture the signature of the pairing SI transition induced by AMC.

Realization of a supersolid phase in a two-channel model

We construct a two-channel model based on the one-dimensional extended Bose–Hubbard model, by including a second channel of free bosons. We use the mean-field theory to map the system to a reduced single-channel one and solve this system by means of the density matrix renormalization group method. We find the region where the superfluid and density-wave orders coexist which signals a supersolid state. Our theory can be realized experimentally with state-dependent optical lattices.

Phase diagram detection via Gaussian fitting of number probability distribution

We investigate the number probability density function that characterizes sub-portions of a quantum many-body system with globally conserved number of particles. We put forward a linear fitting protocol capable of mapping out the ground-state phase diagram of the rich one-dimensional extended Bose-Hubbard model: The results are quantitatively comparable with more sophisticated traditional and machine learning techniques. We argue that the studied quantity should be considered among the most informative bipartite properties, being moreover readily accessible in atomic gases experiments.

Mixtures of ultracold atomic gases in optical lattices with nonzero pair or counterflow hopping

We study the critical behavior of a mixture of two species of lattice bosons described by the extended Bose–Hubbard model. Our goal is to analyze in which conditions exotic orderings like pair superfluid or counterflow superfluid could be detected. We use a numerical method based on mean field approximation to calculate the phase diagram of the system, along with particle density, and order parameter profiles in selected multicritical points. We observe that the phase diagram becomes significantly renormalized in the presence of pair flow or counterflow. Furthermore, a critical particle density emerges, which isolates a new region of the phase diagram, in which the exotic order parameter exists for any value of single-particle hopping.

Dimensional cross-over in self-organised super-radiant phases of ultra-cold atoms inside a cavity

We consider a condensate of ultra-cold bosonic atoms in a linear optical cavity illuminated by a two-pump configuration where each pump makes different angles with the direction of the cavity axis. We show that such a configuration allows a smooth transition from a one-dimensional quantum optical lattice configuration to a two-dimensional quantum optical lattice configuration induced by the cavity–atom interaction. Using a Holstein–Primakoff transformation, we find the atomic density profile of such a self-organised ground state in the super-radiant phase as a function of the angular orientations of the pumps in such a dynamical quantum optical lattice, and also provide an analysis of their structures in coordinate and momentum space. In the later part of the paper, we show how the corresponding results can also be qualitatively understood in terms of an extended Bose–Hubbard model in such a quantum optical lattice potential.

Extended Bose-Hubbard model with dipolar excitons.

The Hubbard model constitutes one of the most celebrated theoretical frameworks of condensed-matter physics. It describes strongly correlated phases of interacting quantum particles confined in lattice potentials1,2. For bosons, the Hubbard Hamiltonian has been deeply scrutinized for short-range on-site interactions3-6. However, accessing longer-range couplings has remained elusive experimentally7. This marks the frontier towards the extended Bose-Hubbard Hamiltonian, which enables insulating ordered phases at fractional lattice fillings8-12. Here we implement this Hamiltonian by confining semiconductor dipolar excitons in an artificial two-dimensional square lattice. Strong dipolar repulsions between nearest-neighbour lattice sites then stabilize an insulating state at half filling. This characteristic feature of the extended Bose-Hubbard model exhibits the signatures theoretically expected for a chequerboard spatial order. Our work thus highlights that dipolar excitons enable controlled implementations of boson-like arrays with strong off-site interactions, in lattices with programmable geometries and more than 100 sites.

Entanglement and thermalization in the extended Bose–Hubbard model after a quantum quench: A correlation analysis

Exploring the role of entanglement in quantum nonequilibrium dynamics is important to understand the mechanism of thermalization in an isolated system. We study the relaxation dynamics in a one-dimensional extended Bose–Hubbard model after a global interaction quench by considering several observables: the local Boson numbers, the nonlocal entanglement entropy, and the momentum distribution functions. We calculate the thermalization fidelity for different quench parameters and different sizes of subsystems, and the results show that the degree of thermalization is affected by the distance from the integrable point and the size of the subsystem. We employ the Pearson coefficient as the measurement of the correlation between the entanglement entropy and thermalization fidelity, and a strong correlation is demonstrated for the quenched system.

The quantum vortex states in extended Bose–Hubbard model: effects of lattice geometries, inter-particle interactions and spatial inhomogeneity

We study quantum vortex states of strongly interacting bosons in a two-dimensional rotating optical lattice. The system is modeled by Bose-Hubbard Hamiltonian with rotation. We consider lattices of different geometries, such as square, rectangular and triangular. Using numerical exact diagonalization method we show how the rotation introduces vortex states of different ground-state symmetries and the transition between these states at discrete rotation frequencies. We show how the geometry of the lattice plays crucial role in determining the maximum number of vortex states as well as the general characteristics of these states such as, the average angular momentum $<L_z>$, the current at the perimeter of the lattice, phase winding, the relation between the maximum phase difference, the maximum current and also the saturation of the current between the two neighboring lattice points. The effect of the two- and three-body interactions between the particles, both attractive and repulsive, also depends on the geometry of the lattice as the current flow or the lattice current depends on the interactions. We also consider the effect of the spatial inhomogeneity introduced by the presence of an additional confining harmonic trap potential. It is shown that the curvature of the trap potential and the position of the minimum of the trap potential with respect to the axis of rotation or the center of the lattice have a significant effect on the general characteristics these vortex states.

Topological pump and bulk-edge-correspondence in an extended Bose-Hubbard model

An extended Bose-Hubbard model (EBHM) with three- and four-body constraints can be feasible in cold atoms in an optical lattice. A rich phase structure including various symmetry-protected topological (SPT) phases is obtained numerically with suitable parameter settings and particle filling. The SPT phase is characterized by the Berry phase as a local topological order parameter and the structure of the entanglement spectrum (ES). Based on the presence of various topological phases, separated by gapless phase boundaries, the EBHM exhibits various bosonic topological pumps, which are constructed by connecting the different SPT phases without gap closing. The bulk topological pumps exhibit the plateau transitions characterized by many-body Chern numbers. For the system with boundary, the center of mass (CoM) under grand canonical ensemble elucidates the contributions of multiple edge states and reveals the topology of the system. We demonstrate that the interacting bosonic pumps obey the bulk-edge-correspondence.

Entropy of pair condensed bosons at finite temperatures in optical lattices with bond-charge interaction

This work contains a quantum rotor analysis of the bond-charge interaction extended Bose–Hubbard model. Adding extended interactions to bosonic optical lattice models reveals new phases of matter to observe and study. Many-body correlations further widen the scope of possible discoveries. The U(1) quantum rotor method used in this work preserves three-body correlations, uncovering the presence of pair condensation in this model. Phase transitions between the normal state and both single and pair bosonic condensation are examined through the lens of the thermal behavior of the two superfluid order parameters and entropy, as well as the impact of bond-charge interaction on the properties of Bose–Einstein condensation in the presence of many-body correlations. At low temperatures and high densities, bond-charge interaction reinforces coherence, improving the critical temperature of Bose–Einstein condensation. It also exhibits a temperature-independent dissipative influence on the system.

Quantum phase transitions of interacting bosons on hyperbolic lattices

The effect of many-body interaction in curved space is studied based on the extended Bose–Hubbard model on hyperbolic lattices. Using the mean-field approximation and quantum Monte Carlo simulation, the phase diagram is explicitly mapped out, which contains the superfluid, supersolid and insulator phases at various fillings. Particularly, it is revealed that the sizes of the Mott lobes shrink and the supersolid is stabilized at smaller nearest-neighbor interaction as q in the Schläfli symbol increases. The underlying physical mechanism is attributed to the increase of the coordination number, and hence the kinetic energy and the nearest-neighbor interaction. The results suggest that the hyperbolic lattices may be a unique platform to study the effect of the coordination number on quantum phase transitions, which may be relevant to the experiments of ultracold atoms in optical lattices.

Frustration-induced supersolid phases of extended Bose–Hubbard model in the hard-core limit

We investigate exotic supersolid phases in the extended Bose–Hubbard model with infinite projected entangled-pair state, numerical exact diagonalization, and mean-field theory. We demonstrate that many different supersolid phases can be generated by changing signs of hopping terms, and the interactions along with the frustration of hopping terms are important to stabilize those supersolid states. We argue the effect of frustration introduced by the competition of hopping terms in the supersolid phases from the mean-field point of view. This helps to give a clearer picture of the background mechanism for underlying superfluid/supersolid states to be formed. With this knowledge, we predict and realize the d-wave superfluid, which shares the same pairing symmetry with high-Tc materials, and its extended phases. We believe that our results contribute to preliminary understanding for desired target phases in the real-world experimental systems.

Superconducting quantum many-body circuits for quantum simulation and computing

Quantum simulators are attractive as a means to study many-body quantum systems that are not amenable to classical numerical treatment. A versatile framework for quantum simulation is offered by superconducting circuits. In this perspective, we discuss how superconducting circuits allow the engineering of a wide variety of interactions, which, in turn, allows the simulation of a wide variety of model Hamiltonians. In particular, we focus on strong photon–photon interactions mediated by nonlinear elements. This includes on-site, nearest-neighbor, and four-body interactions in lattice models, allowing the implementation of extended Bose–Hubbard models and the toric code. We discuss not only the present state in analog quantum simulation but also future perspectives of superconducting quantum simulation, which open up when concatenating quantum gates in emerging quantum computing platforms.

Atom-pair tunneling and quantum phase transition in asymmetry double-well trap in strong-interaction regime**Project supported by the National Natural Science Foundation of China (Grant No. 11075099).

The quantum effect of nonlinear co-tunnelling process, which is dependent on atom-pair tunneling and asymmetry of an double-well trap, is studied by using an asymmetrical extended Bose–Hubbard model. Due to the existence of atom-pair tunneling that describes quantum phenomena of ultracold atom-gas clouds in an asymmetrical double-well trap, the asymmetrical extended Bose–Hubbard model is better than the previous Bose–Hubbard model model by comparing with the experimental data cited from the literature. The dependence of dynamics and quantum phase transition on atom-pair tunneling and asymmetry are investigated. Importantly, it shows that the asymmetry of the extended Bose–Hubbard model, corresponding to the bias between double wells, leads to a number of resonance tunneling processes, which tunneling is renamed conditional resonance tunneling, and corrects the atom-number parity effect by controlling the bias between double wells.

Glassy dynamics from quark confinement: Atomic quantum simulation of the gauge-Higgs model on a lattice

In the previous works, we proposed atomic quantum simulations of the U(1) gauge-Higgs model by ultra-cold Bose gases. By studying extended Bose-Hubbard models (EBHMs) including long-range repulsions, we clarified the locations of the confinement, Coulomb and Higgs phases. In this paper, we study the EBHM with nearest-neighbor repulsions in one and two dimensions at large fillings by the Gutzwiller variational method. We obtain phase diagrams and investigate dynamical behavior of electric flux from the gauge-theoretical point of view. We also study if the system exhibits glassy quantum dynamics in the absence and presence of quenched disorder. We explain that the obtained results have a natural interpretation in the gauge theory framework. Our results suggest important perspective on many-body localization in strongly-correlated systems. They are also closely related to anomalously slow dynamics observed by recent experiments performed on Rydberg atom chain, and our study indicates existence of similar phenomenon in two-dimensional space.