In this paper, we study the dynamics of the Bose-Hubbard model with the nearest-neighbor repulsion by using time-dependent Gutzwiller methods. Near the unit filling, the phase diagram of the model contains density wave (DW), supersolid (SS) and superfluid (SF). The three phases are separated by two second-order phase transitions. We study "slow-quench" dynamics by varying the hopping parameter in the Hamiltonian as a function of time. In the phase transitions from the DW to SS and from the DW to SF, we focus on how the SF order forms and study scaling laws of the SF correlation length, vortex density, etc. The results are compared with the Kibble-Zurek scaling. On the other hand from the SF to DW, we study how the DW order evolves with generation of the domain walls and vortices. Measurement of first-order SF coherence reveals interesting behavior in the DW regime.
In the present paper, we study finite-temperature phase structure of two-component hard-core bosons in a cubic optical lattice. The system that we study in the present paper is an effective model for the Bose-Hubbard model with strong on-site repulsions and is called bosonic t-J model. This model is a bosonic counterpart of the t-J model for the strongly-correlated electron systems like the high-temperature superconducting materials. We study the model by means of path-integral methods and Monte-Carlo simulations. We found that this system has a very rich phase structure including checkerboard…
Experiments on dipolar Bose-Einstein condensates have recently reported the observation of supersolidity. Although quantized vortices constitute a key probe of superfluidity, their observability in dipolar supersolids is largely prevented by the strong density depletion caused by the formation of droplets. We present a novel approach to the nucleation of vortices and their observation, based on the quenching of the s-wave scattering length across the superfluid-supersolid transition. Starting from a slowly rotating, vortex-free, configuration in the superfluid phase, we predict vortex nucleati…
Sub-unity superfluid fraction of a supersolid from self-induced Josephson effect
Università degli studi di Firenze（佛罗伦萨大学）；CNR-INO（意大利国家研究委员会光学研究所）；European Laboratory for Nonlinear Spectroscopy（欧洲非线性光谱学实验室）；QSTAR（量子与统计热力学研究前沿中心）；Università degli studi di Napoli “Federico II”（那不勒斯费德里科二世大学）
We study the effect of an artificial gauge field on the zero temperature phase diagram of extended Bose Hubbard model, that describes ultra cold atoms in optical lattices with long range interaction using strong coupling perturbation theory . We determine analytically the effect of the artificial gauge field on the density wave - supersolid (DW-SS) and the the Mott insulator-superfluid (MI -SF) transition boundary . The momentum distribution at these two transition boundaries is also calculated in this approach. It is shown that such momentum distribution which can be observed in time of fligh…
Recent studies have suggested a new phase in the extended Bose-Hubbard model in one dimension at integer filling [1,2]. In this work, we show that this new phase is phase-separated into a supersolid and superfluid part, generated by mechanical instability. Numerical simulations are performed by means of the density matrix renormalization group algorithm in terms of matrix product states. In the phase-separated phase and the adjacent homogeneous superfluid and supersolid phases, we find peculiar spatial patterns in the entanglement spectrum and string-order correlation functions and show that t…
Recent breakthrough experiments on dipolar condensates have reported the creation of supersolids, including two-dimensional arrays of quantum droplets. Droplet arrays are, however, not the only possible non-trivial density arrangement resulting from the interplay of mean-field instability and quantum stabilization. Several other possible density patterns may occur in trapped condensates at higher densities, including the so-called honeycomb supersolid, a phase that exists, as it is also the case of a triangular droplet supersolid, in the thermodynamic limit. We show that compared to droplet su…
A key manifestation of superfluidity in liquids and gases is a reduction of the moment of inertia under slow rotations. Non-classical rotational effects have been searched for a long time also for the elusive supersolid phase of matter, in which superfluidity coexists with a lattice structure. Here we show that the recently discovered supersolid phase in dipolar quantum gases features a reduced moment of inertia. We study a peculiar rotational oscillation mode in a harmonic potential, the scissors mode, already employed for superfluids. From the measured moment of inertia, we infer a superflui…
We investigate the zero-temperature excitation spectrum of two-dimensional soft-core bosons for a wide range parameters and across the phase transition from a superfluid to a supersolid state. Based on mean field calculations and recent Quantum Monte Carlo results, we demonstrate the applicability of the Bogoliubov-de Gennes equations, even at high interaction strengths where the system forms an insulating cluster crystal. Interestingly, our study reveals that the maximum energy of the longitudinal phonon band in the supersolid phase connects to the maxon energy of the superfluid at the phase …
We investigate quantum turbulence in a two-dimensional trapped supersolid and demonstrate that both the wave and vortex turbulence involve triple rather than dual cascades, as in a superfluid. Because of the presence of a second gapless mode associated with translation symmetry breaking, a new $k^{-13/3}$ scaling law is predicted to occur in the wave turbulence. Simultaneous fast vortex-antivortex creation and annihilation in the interior of the oscillating supersolid results in a $k^{-1}$ scaling law in the vortex turbulence. Numerical simulations based on the Gross-Pitaevskii equation confir…
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. 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.
We study ground-state properties in a hard-core Bose-Hubbard model on a layered triangular lattice. Combining cluster mean-field theory with the density matrix renormalization group method, we discuss the effect of the interlayer coupling on the supersolid states realized in a single layered model. By examining the distributions for the particle density and superfluid order parameter, the rich phase diagram of the system is obtained. We find that the supersolid states are widely stabilized at a commensurate filling, in contrast to the case of the single layered model. The nature of the superso…
High-energy scattering spectroscopy is a widely-established technique for probing the characteristic properties of complex physical systems. Motivated by the recent observation of long-sought supersolid states in dipolar quantum Bose gases, I investigate the general relationships existing between the density contrast, the superfluid fraction, and the response to a high-energy scattering probe of density-modulated states within a classical-field approach. I focus on the two extreme regimes of "shallow" and "deep" supersolids, which are of particular interest in describing the phase transitions …
The effect of the next-nearest-neighbor (nnn) tunneling on the hard-core extended Bose-Hubbard model on square lattices is investigated. By means of the cluster mean-field theory, the ground-state phase diagrams are determined. When a modest nnn tunneling is introduced, depending on its sign, two distinct supersolid states with checkerboard crystal structures are found away from half-filing. The characters of various phase transitions out of these two supersolid states are discussed. In particular, for the case with kinetic frustration, the existence of a half supersolid phase possessing both …
The Bose-Hubbard model is well-defined description of a Bose solid which may be realistic for cold atoms in a periodic optical lattice. We show that contrary to accepted theories it can never have as a ground state a perfect Mott insulator solid and that it has a low-energy spectrum of vortex-like phase fluctuations. Whether the ground state is necessarily commensurate remains an open question.
We study the behavior of the excitation spectrum across the quantum phase transition from a superfluid to a supersolid phase of a dipolar Bose gas confined to a one-dimensional geometry. Including the leading beyond-mean-field effects within an effective Hamiltonian, the analysis is based on Bogoliubov theory with several order parameters accounting for the superfluid as well as solid structure. We find fast convergence of the ground-state energy in the supersolid with the number of order parameters and demonstrate a stable excitation spectrum with two Goldstone modes and an amplitude mode in …
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 supersol…
Supersolids are characterized by the counter-intuitive coexistence of superfluid and crystalline order. Here we study a supersolid phase emerging in the steady state of a driven-dissipative system. We consider a transversely pumped Bose-Einstein condensate trapped along the axis of a ring cavity and coherently coupled to a pair of degenerate counter-propagating cavity modes. Above a threshold pump strength the interference of photons scattered into the two cavity modes results in an emergent superradiant lattice, which spontaneously breaks the continuous translational symmetry towards a period…
A novel supersolid phase is predicted for an ensemble of Rydberg atoms in the dipole-blockade regime, interacting via a repulsive dipolar potential "softened" at short distances. Using exact numerical techniques, we study the low temperature phase diagram of this system, and observe an intriguing phase consisting of a crystal of mesoscopic superfluid droplets. At low temperature, phase coherence throughout the whole system, and the ensuing bulk superfluidity, are established through tunnelling of identical particles between neighbouring droplets.
We examine the zero and finite temperature phase diagrams of soft-core bosons of the extended Bose-Hubbard model on a square optical lattice. To study various quantum phases and their transitions we employ single-site and cluster Gutzwiller mean-field theory. We have observed that the Mott insulator phase vanishes above a critical value of nearest-neighbour interaction and the supersolid phase occupies a larger region in the phase diagram. We show that the presence of artificial gauge field enlarges the domain of supersolid phase. The finite temperature destroys the crystalline structure of th…
We investigate topological supersolidity of dipolar Fermi gases in a spin-dependent 2D optical lattice. Numerical results show that the topological supersolid states can be synthesized via the combination of topological superfluid states with the stripe order, where the topological superfluid states generated with dipolar interaction possess the $Δ_{x}+iΔ_{y}$ order, and it is of D class topological classification. By adjusting the ratio between hopping amplitude $t_{x}/t_{y}$ and interaction strength $U$ with dipole orientation $ϕ\approx \fracπ{4}$, the system will undergo phase transitions a…
We use microscopic Bogoliubov-de Gennes formalism to explore the ground-state phase diagram of the single-band attractive Hofstadter-Hubbard model on a square lattice. We show that the interplay between the Hofstadter butterfly and superfluidity breaks spatial symmetry, and gives rise to stripe-ordered superfluid and supersolid phases in large parameter spaces. We also discuss the effects of a trapping potential and comment on the viability of observing stripe-ordered phases with cold Fermi gases.
Dislocation model of the supersolid state of $^4$He was proposed in 1987 by one of the authors of the review. The model obtained strong support by numerous experimental and theoretical investigations from 2007 to date. In these investigations the validity of the idea put forward in 1987 was confirmed, and new conceptions of superclimb of dislocations and of the giant isochoric compressibility or the syringe effect were proposed. In this paper we review main achievements of theoretical and experimental studies of dislocation-induced supersolid and present current understanding of this phenomeno…
We investigate two-species bosons in a two-dimensional square lattice by quantum Monte Carlo method. We show that the inter-species attraction and nearest-neighbor intra-species repulsion results in the pair-supersolid phase, where a diagonal solid order coexists with an off-diagonal pair-superfluid order. The quantum and thermal transitions out of the pair-supersolid phase are characterized. It is found that there is a direct first order transition from the pair-supersolid phase to the double-superfluid phase without an intermediate region. Furthermore, the melting of the pair-supersolid occu…
We demonstrate that low-lying triplon excitations in a bilayer Heisenberg antiferromagnet provide a promising avenue to realize magnetic analogs of twisted superfluid and supersolid phases that were recently reported for two-component ultracold atomic condensate in an optical lattice. Using a cluster Gutzwiller mean-field theory, we establish that Dzyaloshinskii-Moriya interactions (DMI), that are common in many quantum magnets, stabilize these phases in a magnetic system, in contrast to the pair hopping process that is necessary for ultracold atoms. The critical value of DMI for transition to…
We revisited the phase diagram of the second layer of 4He on top of graphite using quantum Monte Carlo methods. Our aim was to explore the existence of the novel phases suggested recently in experimental works, and determine their properties and stability limits. We found evidence of a superfluid quantum phase with hexatic correlations, induced by the corrugation of the first Helium layer, and a quasi-two-dimensional supersolid corresponding to a 7/12 registered phase. The 4/7 commensurate solid was found to be unstable, while the triangular incommensurate crystals, stable at large densities, …
We study superfluidity of supersolid phases of dipolar Bose gases in two-dimensional optical lattices. We perform linear stability analyses for the corresponding dipolar Bose-Hubbard model in the hardcore boson limit to show that a supersolid can have stable superflow until the flow velocity reaches a certain critical value. The critical velocity for the supersolid is found to be significantly smaller than that for a conventional superfluid phase. We propose that the critical velocity can be used as a signature to identify the superfluidity of the supersolid phase in experiment.
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 mec…
Phase transitions share the universal feature of enhanced fluctuations near the transition point. Here we show that density fluctuations reveal how a Bose-Einstein condensate of dipolar atoms spontaneously breaks its translation symmetry and enters the supersolid state of matter -- a phase that combines superfluidity with crystalline order. We report on the first direct in situ measurement of density fluctuations across the superfluid-supersolid phase transition. This allows us to introduce a general and straightforward way to extract the static structure factor, estimate the spectrum of eleme…
The Haldane Insulator is a gapped phase characterized by an exotic non-local order parameter. The parameter regimes at which it might exist, and how it competes with alternate types of order, such as supersolid order, are still incompletely understood. Using the Stochastic Green Function (SGF) quantum Monte Carlo (QMC) and the Density Matrix Renormalization Group (DMRG), we study numerically the ground state phase diagram of the one-dimensional bosonic Hubbard model (BHM) with contact and near neighbor repulsive interactions. We show that, depending on the ratio of the near neighbor to contact…
By the photoassociation method, the trimer superfluid phase disappears in the one dimensional state-dependent optical lattice if the ratio of the three-body interaction $W$ to the trimer tunneling $J$is kept at $W/J=12$ [Phys Rev A. {\bf 90}, 033622(2014)]. To search for a trimer superfluid and trimer supersolid, we load the cold atom into two-dimensional lattices, whose coordinate number $z$ and kinetic energy $-zJ$ are respectively larger and lower than those of a one dimensional lattice. Herein, we study the Bose-Hubbard model, which has an additional trimer tunneling term, a three-body int…
We study the phase diagram of a dipolar fermi gas at half-filling in a cubic optical lattice with dipole moments aligned along the z-axis. The anisotropic dipole-dipole interaction leads to the competition between pz-wave superfluid and nematic charge-density-wave (CDW) orders at low temperatures. We find that the superfluid phase survives with weak interactions and the CDW phase dominates with strong interactions. In between, the supersolid phase appears as a balance between superfluid and CDW orders. The superfluid density is anisotropic in the supersolid and superfluid phases. In the CDW ph…
We study the extended Jaynes-Cummings-Hubbard model on triangular cavity lattices and zigzag ladders. By using density-matrix renormalization group methods, we observe various types of solids with different density patterns and find evidence for light supersolids, which exist in extended regions of the phase diagram of the zigzag ladder. Furthermore, we observe strong pair correlations in the supersolid phase due to the interplay between the atoms in the cavities and atom-photon interaction. By means of cluster mean-field simulations and a scaling of the cluster size extending our analysis to …
We report our findings on quantum phase transitions in cold bosonic atoms in a one dimensional optical lattice using the finite size density matrix renormalization group method in the framework of the extended Bose-Hubbard model. We consider wide ranges of values for the filling factors and the nearest neighbor interactions. At commensurate fillings, we obtain two different types of charge density wave phases and a Mott insulator phase. However, departure from commensurate fillings yield the exotic supersolid phase where both the crystalline and the superfluid orders coexist. In addition, we o…
Supersolid phases as a result of a coexistence of superfluid and density ordered checkerboard phases are predicted to appear in ultracold Fermi molecules confined in a bilayer array of two-dimensional square optical lattices. We demonstrate the existence of these phases within the inhomogeneous mean-field approach. In particular, we show that tuning the interlayer separation distance at a fixed value of the chemical potential produces different fractions of superfluid, density ordered, and supersolid phases.
We explore spatial symmetry breaking of a dipolar Bose Einstein condensate in the thermodynamic limit and reveal a critical point in the phase diagram at which crystallization occurs via a second order phase transition. This behavior is traced back to the significant effects of quantum fluctuations in dipolar condensates, which moreover stabilize a new supersolid phase, namely a regular honeycomb pattern with maximal modulational contrast and near-perfect superfluidity.
We discuss a model of dipolar bosons trapped in a weakly coupled planar array of one-dimensional tubes. We consider the situation where the dipolar moments are aligned by an external field, and find a rich phase diagram as a function of the angle of this field exhibiting quantum phase transitions between solid, superfluid and supersolid phases. In the low energy limit, the model turns out to be identical to one describing quasi-one-dimensional superconductivity in condensed matter systems. This opens the possibility of using bosons as a quantum analogue simulator of electronic systems, a scena…
Distintictive features of supersolids show up in their rotational properties. We calculate the moment of inertia of a harmonically trapped dipolar Bose-Einstein condensed gas as a function of the tunable scattering length parameter, providing the transition from the (fully) superfluid to the supersolid phase and eventually to an incoherent crystal of self-bound droplets. The transition from the superfluid to the supersolid phase is characterized by a jump in the moment on inertia, revealing its first order nature. In the case of elongated trapping in the plane of rotation we show that the the …
