superfluid-Mott Insulator Transition Research Articles

Exact Solution of the Bose-Hubbard Model with Unidirectional Hopping.

A one-dimensional Bose-Hubbard model with unidirectional hopping is shown to be exactly solvable. Applying the algebraic Bethe ansatz method, we prove the integrability of the model and derive the Bethe ansatz equations. The exact eigenvalue spectrum can be obtained by solving these equations. The distribution of Bethe roots reveals the presence of a superfluid-Mott insulator transition at the ground state, and the critical point is determined. By adjusting the boundary parameter, we demonstrate the existence of a non-Hermitian skin effect even in the presence of interaction, but it is completely suppressed for the Mott insulator state in the thermodynamical limit. Our result represents a new class of exactly solvable non-Hermitian many-body systems, which has no Hermitian correspondence and can be used as a benchmark for various numerical techniques developed for non-Hermitian many-body systems.

A first order superfluid-Mott insulator transition for a Bose–Hubbard model in an emergent lattice

The combination of strong correlation and emergent lattice can be achieved when quantum gases are confined in a superradiant Fabry–Perot cavity. In addition to the discoveries of exotic phases, such as density wave ordered Mott insulator and superfluid, a surprising kink structure is found in the slope of the cavity strength as a function of the pumping strength. In this article, we show that the appearance of such a kink is a manifestation of a liquid–vapour-like transition between two superfluids with different densities. The slopes in the immediate neighborhood of the kink become divergent at the liquid–vapour critical points and display a critical scaling law with a critical exponent 1 in the quantum critical region.

Orbital order in a bosonic p -band triangular lattice

We present a detailed study of the Bose-Hubbard model in a $p$-band triangular lattice by focusing on the evolution of orbital order across the superfluid-Mott insulator transition. Two distinct phases are found in the superfluid regime. One of these phases adiabatically connects the weak interacting limit. This phase is characterized by the intertwining of axial $p_\pm=p_x \pm ip_y$ and in-plane $p_\theta=\cos\theta p_x+\sin\theta p_y$ orbital orders, which break the time-reversal symmetry and lattice symmetries simultaneously. In addition, the calculated Bogoliubov excitation spectrum gaps the original Dirac points in the single-particle spectrum but exhibits emergent Dirac points. The other superfluid phase in close proximity to the Mott insulator with unit boson filling shows a detwined in-plane ferro-orbital order. Finally, an orbital exchange model is constructed for the Mott insulator phase. Its classical ground state has an emergent SO$(2)$ rotational symmetry in the in-plane orbital space and therefore enjoys an infinite degeneracy, which is ultimately lifted by the orbital fluctuation via the order by disorder mechanism. Our systematic analysis suggests that the in-plane ferro-orbital order in the Mott insulator phase agrees with and likely evolves from the latter superfluid phase.

Structural superfluid–Mott-insulator transition for a Bose gas in multirods

We report on a structural superfluid--Mott-insulator (SF-MI) quantum phase transition for an interacting one-dimensional Bose gas within permeable multirod lattices, where the rod lengths are varied from zero to the lattice period length. We use the ab initio diffusion Monte Carlo method to calculate the static structure factor, the insulation gap, and the Luttinger parameter, which we use to determine if the gas is a superfluid or a Mott insulator. For the Bose gas within a square Kronig-Penney (KP) potential, where barrier and well widths are equal, the SF-MI coexistence curve shows the same qualitative and quantitative behavior as that of a typical optical lattice with equal periodicity but slightly larger height. When we vary the width of the barriers from zero to the length of the potential period, keeping the height of the KP barriers, we observe a way to induce the SF-MI phase transition. Our results are of significant interest, given the recent progress on the realization of optical lattices with a subwavelength structure that would facilitate their experimental observation.

Quantum Monte Carlo study of strongly interacting bosonic one-dimensional systems in periodic potentials

We present diffusion Monte Carlo (DMC) and path-integral Monte Carlo (PIMC) calculations of a one-dimensional Bose system with realistic interparticle interactions in a periodic external potential. Our main aim is to test the predictions of the Luttinger liquid (LL) theory, in particular with respect to the superfluid-Mott insulator transition at both zero and finite temperatures, in the predicted robust and fragile superfluid regimes. For that purpose, we present our results of the superfluid fraction $\rho_s/\rho_0$, the one-body density matrix, the two-body correlation functions, and the static structure factor. The DMC and PIMC results in the limit of very low temperature for $\rho_s/\rho_0$ agree, but the LL model for scaling $\rho_s/\rho_0$ does not fit the data well. The critical depth of the periodic potential is close to the values obtained for ultracold gases with different models of interaction, but with the same value of the bare LL parameter, demonstrating the universality of LL description. Algebraic decay of correlation functions is observed in the superfluid regime and exponential decay in the Mott-insulator one, as well as in all regimes at finite temperature for distances larger than a characteristic length.

Quantum-Granularity Effect in the Formation of Supermixed Solitons in Ring Lattices

We investigate a notable class of states peculiar to a bosonic binary mixture featuring repulsive intraspecies and attractive interspecies couplings. We evidence that, for small values of the hopping amplitudes, one can access particular regimes marked by the fact that the interwell boson transfer occurs in a jerky fashion. This property is shown to be responsible for the emergence of a staircase-like structure in the phase diagram of a mixture confined in a ring trimer and to resemble the mechanism of the superfluid-Mott insulator transition strongly. Under certain conditions, in fact, we show that it is possible to interpret the interspecies attraction as an effective chemical potential and the supermixed soliton as an effective particle reservoir. Our investigation is developed both within a fully quantum approach based on the analysis of several quantum indicators and by means of a simple analytical approximation scheme capable of capturing the essential features of this ultraquantum effect.

Superfluid–Mott-insulator transition of ultracold superradiant bosons in a cavity

We investigate harmonically-trapped, laser-pumped bosons with infinite-range interactions induced by a dissipative high-finesse red-detuned optical cavity with numerical and analytical methods. We obtain multiple cavity and atomic observables as well as the full phase diagram of the system using the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X) approach. Besides the transition from an unorganized normal phase to a superradiant phase where atoms self-organize, we focus on an in-depth investigation of the self-organized superfluid to self-organized Mott insulator phase transition in the superradiant phase as a function of the cavity-atom coupling. The numerical results are substantiated by an analytical study of an effective Bose-Hubbard model. We numerically analyze cavity fluctuations and emergent strong correlations between atoms in the many-body state across the Mott transition via the atomic density distributions and Glauber correlation functions. Unexpectedly, the weak harmonic trap leads to features like a lattice switching between the two symmetry-broken $\mathbb{Z}_2$ configurations of the untrapped system and a reentrance of superfluidity in the Mott insulating phase. Our analytical considerations quantitatively explain the numerically observed correlation features.

Critical points of the three-dimensional Bose-Hubbard model from on-site atom number fluctuations

We discuss how positions of critical points of the three-dimensional Bose-Hubbard model can be accurately obtained from variance of the on-site atom number operator, which can be experimentally measured. The idea that we explore is that the derivative of the variance, with respect to the parameter driving the transition, has a pronounced maximum close to critical points. We show that Quantum Monte Carlo studies of this maximum lead to precise determination of critical points for the superfluid-Mott insulator transition in systems with mean number of atoms per lattice site equal to one, two, and three. We also extract from such data the correlation-length critical exponent through the finite-size scaling analysis and discuss how the derivative of the variance can be reliably computed from numerical data for the variance. The same conclusions apply to the derivative of the nearest-neighbor correlation function, which can be obtained from routinely measured time-of-flight images.

Effective many-body Hamiltonians of qubit-photon bound states

Quantum emitters (QEs) coupled to structured baths can localize multiple photons around them and form qubit-photon bound states. In the Markovian or weak coupling regime, the interaction of QEs through these single-photon bound states is known to lead to effective many-body QE Hamiltonians with tuneable but yet perturbative interactions. In this work we study the emergence of such models in the non-Markovian or strong coupling regime in different excitation subspaces. The effective models for the non-Markovian regime with up to three excitations are characterized using analytical methods, uncovering the existence of doublons or triplon states. Furthermore, we provide numerical results for systems with multiple excitations and demonstrate the emergence of polariton models with optically tuneable interactions, whose many-body ground state exhibits a superfluid-Mott insulator transition.

Quantum critical behavior of a three-dimensional superfluid-Mott glass transition

The superfluid to insulator quantum phase transition of a three-dimensional particle-hole symmetric system of disordered bosons is studied. To this end, a site-diluted quantum rotor Hamiltonian is mapped onto a classical (3+1)-dimensional XY model with columnar disorder and analyzed by means of large-scale Monte Carlo simulations. The superfluid-Mott insulator transition of the clean, undiluted system is in the 4D XY universality class and shows mean-field critical behavior with logarithmic corrections. The clean correlation length exponent $\nu = 1/2$ violates the Harris criterion, indicating that disorder must be a relevant perturbation. For nonzero dilutions below the lattice percolation threshold of $p_c = 0.688392$, our simulations yield conventional power-law critical behavior with dilution-independent critical exponents $z=1.67(6)$, $\nu = 0.90(5)$, $\beta/\nu = 1.09(3)$, and $\gamma/\nu = 2.50(3)$. The critical behavior of the transition across the lattice percolation threshold is controlled by the classical percolation exponents. Our results are discussed in the context of a classification of disordered quantum phase transitions, as well as experiments in superfluids, superconductors and magnetic systems.

Stable-unstable transition for a Bose-Hubbard chain coupled to an environment

Interactions in quantum systems may induce transitions to exotic correlated phases of matter which can be vulnerable to coupling to an environment. Here, we study the stability of a Bose-Hubbard chain coupled to a bosonic bath at zero and non-zero temperature. We show that only above a critical interaction the chain loses bosons and its properties are significantly affected. The transition is of a different nature than the superfluid-Mott insulator transition and occurs at a different critical interaction. We explain such a stable-unstable transition by the opening of a charge gap. The comparison of accurate matrix product state simulations to approximative approaches that miss this transition reveals its many-body origin.

Critical behavior of an impurity at the boson superfluid–Mott-insulator transition

We present a universal theory for the critical behavior of an impurity at the two-dimensional superfluid-Mott insulator transition. Our analysis is motivated by a numerical study of the Bose-Hubbard model with an impurity site by Huang et al. (Phys. Rev. B 94, 220502 (2016)), who found an impurity phase transition as a function of the trapping potential. The bulk theory is described by the $O(2)$ symmetric Wilson-Fisher conformal field theory, and we model the impurity by a localized spin-1/2 degree of freedom. We also consider a generalized model by considering an $O(N)$ symmetric bulk theory coupled to a spin-$S$ degree of freedom. We study this field theory using the $\epsilon = 3 - d$ expansion, where the impurity-bulk interaction flows to an infrared stable fixed point at the critical trapping potential. We determine the scaling dimensions of the impurity degree of freedom and the associated critical exponents near the critical point. We also determine the universal contribution of the impurity to the finite temperature compressibility of the system at criticality. Our results are compared with recent numerical simulations.

Superfluid–Mott-insulator transition in superconducting circuits with weak anharmonicity

We investigate theoretically the ground-state property of a two-dimensional array of superconducting circuits including the on-site superconducting qubits (SQs) with weak anharmonicity. In particular, we analyse the influence of this anharmonicity on the Mott insulator to superfluid quantum phase transition. The complete ground-state phase diagrams are presented under the mean field approximation. Interestingly, the anharmonicity of SQs affects the Mott lobes enormously, and the single excitation Mott lobe disappears when the anharmonicity become zero. Our results can be used to guide the implementations of quantum simulations using the superconducting circuits, which have nice integrating and flexibility.

Locating the quantum critical point of the Bose-Hubbard model through singularities of simple observables.

We show that the critical point of the two-dimensional Bose-Hubbard model can be easily found through studies of either on-site atom number fluctuations or the nearest-neighbor two-point correlation function (the expectation value of the tunnelling operator). Our strategy to locate the critical point is based on the observation that the derivatives of these observables with respect to the parameter that drives the superfluid-Mott insulator transition are singular at the critical point in the thermodynamic limit. Performing the quantum Monte Carlo simulations of the two-dimensional Bose-Hubbard model, we show that this technique leads to the accurate determination of the position of its critical point. Our results can be easily extended to the three-dimensional Bose-Hubbard model and different Hubbard-like models. They provide a simple experimentally-relevant way of locating critical points in various cold atomic lattice systems.

Mott lobes of theS=1Bose-Hubbard model with three-body interactions

Using the density matrix renormalization group method, we studied the ground state of the one-dimensional $S=1$ Bose-Hubbard model with local three-body interactions, which can be a superfluid or a Mott insulator state. We drew the phase diagram of this model for both ferromagnetic and antiferromagnetic interaction. Regardless of the sign of the spin-dependent coupling, we obtained that the Mott lobes area decreases as the spin-dependent strength increases, which means that the even-odd asymmetry of the two-body antiferromagnetic chain is absent for local three-body interactions. For antiferromagnetic coupling, we found that the density drives first-order superfluid-Mott insulator transitions for even and odd lobes. Ferromagnetic Mott insulator and superfluid states were obtained with a ferromagnetic coupling, and a tendency to a "long-range" order was observed.

Ultracold bosons with cavity-mediated long-range interactions: A local mean-field analysis of the phase diagram

Ultracold bosonic atoms in optical lattices self-organize into a variety of structural and quantum phases when placed into a single-mode cavity and pumped by a laser. Cavity optomechanical effects induce an atom density modulation at the cavity-mode wavelength that competes with the optical lattice arrangement. Simultaneously short-range interactions via particle hopping promote superfluid order such that a variety of structural and quantum coherent phases can occur. We analyze the emerging phase diagram in two dimensions by means of an extended Bose-Hubbard model using a local mean-field approach combined with a superfluid cluster analysis. For commensurate ratios of the cavity and external lattice wavelengths, the Mott insulator-superfluid transition is modified by the appearance of charge density wave and supersolid phases, at which the atomic density supports the buildup of a cavity field. For incommensurate ratios, the optomechanical forces induce the formation of Bose-glass and superglass phases, namely, nonsuperfluid and superfluid phases, respectively, displaying quasiperiodic density modulations, which in addition can exhibit structural and superfluid stripe formation. The onset of such structures is constrained by the on-site interaction and is favorable at fractional densities. Experimental observables are identified and discussed.

Multiband effects and the Bose-Hubbard model in one-dimensional lattices

We study phase diagrams of one-dimensional bosons with contact interactions in the presence of a lattice. We use the worm algorithm in continuous space and focus on the incommensurate superfluid Mott-insulator transition. Our results are compared to those from the one-band Bose-Hubbard model. When Wannier states are used to determine the Bose-Hubbard model parameters, the comparison unveils an apparent breakdown of the one-band description for strong interactions, even for the Mott-insulating state with an average of one particle per site ($n=1$) in deep lattices. We introduce an inverse confined scattering analysis to obtain the ratio $U/J$, with which the Bose-Hubbard model provides correct results for strong interactions, deep lattices, and $n=1$.

Quantum coherence in a coupled-cavity array

The dynamical properties of quantum coherence in the system of two-coupled-cavities, each of which resonantly interacts with a two-level atom, is investigated via the relative entropy measure. We focus on the coherences for the atom–atom, atom–cavity and cavity–cavity subsystems and find that the dynamical behaviors of these coherences depend largely on the cavity–cavity coupling, which may indicate the Mott insulator-superfluid transition in the thermodynamic limit. We also study the influences of the initial cavity–cavity correlation on the coherences and show that the initial correlation of the cavity–cavity subsystem can enhance the revival ability for the atom–atom and cavity–cavity coherences while reduce that for the atom–cavity coherence. Besides, we demonstrate the qualitative difference of dynamics between coherence and entanglement. Finally, the influences of dissipations including cavity losses and atomic decays on the coherence are explored.

From quantum to thermal topological-sector fluctuations of strongly interacting Bosons in a ring lattice

Inspired by recent experiments on Bose–Einstein condensates in ring traps, we investigate the topological properties of the phase of a one-dimensional Bose field in the presence of both thermal and quantum fluctuations—the latter ones being tuned by the depth of an optical lattice applied along the ring. In the regime of large filling of the lattice, quantum Monte Carlo simulations give direct access to the full statistics of fluctuations of the Bose-field phase, and of its winding number W along the ring. At zero temperature the winding-number (or topological-sector) fluctuations are driven by quantum phase slips localized around a Josephson link between two lattice wells, and their susceptibility is found to jump at the superfluid-Mott insulator transition. At finite (but low) temperature, on the other hand, the winding number fluctuations are driven by thermal activation of nearly uniform phase twists, whose activation rate is governed by the superfluid fraction. A quantum-to-thermal crossover in winding-number fluctuations is therefore exhibited by the system, and it is characterized by a conformational change in the topologically non-trivial configurations, from localized to uniform phase twists, which can be experimentally observed in ultracold Bose gases via matter–wave interference.

Chemical potential for light by parametric coupling

Usually photons are not conserved in their interaction with matter. Consequently, for the thermodynamics of photons, while we have a concept of temperature for energy conservation, there is no equivalent chemical potential for particle number conservation. However, the notion of a chemical potential is crucial in understanding a wide variety of single- and many-body effects, from transport in conductors and semiconductors to phase transitions in electronic and atomic systems. Here we show how a direct modification of the system-bath coupling via parametric oscillation creates an effective chemical potential for photons even in the thermodynamic limit. In particular, we show that the photonic system equilibrates to the temperature of the bath, with a tunable chemical potential that is set by the frequency of the parametric coupler. Specific implementations, using circuit-QED or optomechanics, are feasible using current technologies, and we show a detailed example demonstrating the emergence of Mott insulator-superfluid transition in a lattice of nonlinear oscillators. Our approach paves the way for quantum simulation, quantum sources, and even electron-like circuits with light.