We study the quantum phase diagram of a Bose-Hubbard chain whose dynamics conserves both boson number and boson dipole moment, a situation which can arise in strongly tilted optical lattices. The conservation of dipole moment has a dramatic effect on the phase diagram, which we analyze by combining a field theory analysis with DMRG simulations. Unlike the conventional Bose-Hubbard model, the phase diagram contains no compressible phases, and is instead dominated by various types of exotic dipolar condensates. We suggest ways by which these condensates can be identified in near-term cold atom experiments.
We study the Mott phase of the Bose-Hubbard model on a tilted lattice. On the (Gutzwiller) mean-field level, the tilt has no effect -- but quantum fluctuations entail particle-hole pair creation via tunneling. For small potential gradients (long-wavelength limit), we derive a quantitative analogy to the Sauter-Schwinger effect, i.e., electron-positron pair creation out of the vacuum by an electric field. For large tilts, we obtain resonant tunneling related to Bloch oscillations.
Motivated by recent observations of ergodicity breaking due to Hilbert space fragmentation in 1D Fermi-Hubbard chains with a tilted potential [Scherg et al., arXiv:2010.12965], we show that the same system also hosts quantum many-body scars in a regime $U\approx Δ\gg J$ at electronic filling factor $ν=1$. We numerically demonstrate that the scarring phenomenology in this model is similar to other known realisations such as Rydberg atom chains, including persistent dynamical revivals and ergodicity-breaking many-body eigenstates. At the same time, we show that the mechanism of scarring in the F…
Quantum many-body systems may defy thermalization even without disorder. Intriguingly, non-ergodicity may be caused by a fragmentation of the many-body Hilbert-space into dynamically disconnected subspaces. The tilted one-dimensional Fermi-Hubbard model was proposed as a platform to realize fragmented models perturbatively in the limit of large tilt. Here, we demonstrate the validity of this effective description for the transient dynamics using ultracold fermions. The effective analytic model allows for a detailed understanding of the emergent microscopic processes, which in our case exhibit …
We numerically examine slow and hierarchical relaxation dynamics of interacting bosons described by a tilted two-band Bose-Hubbard model. The system is found to exhibit signatures of quantum chaos within the spectrum and the validity of the eigenstate thermalization hypothesis for relevant physical observables is demonstrated for certain parameter regimes. Using the truncated Wigner representation in the semiclassical limit of the system, dynamics of relevant observables reveal hierarchical relaxation and the appearance of prethermalized states is studied from the perspective of statistics of …
We study the tunneling decay of a Bose-Einstein condensate out of tilted optical lattices within the mean-field approximation. We introduce a novel method to calculate also excited resonance eigenstates of the Gross-Pitaevskii equation, based on a grid relaxation procedure with complex absorbing potentials. This algorithm works efficiently in a wide range of parameters where established methods fail. It allows us to study the effects of the nonlinearity in detail in the regime of resonant tunneling, where the decay rate is enhanced by resonant coupling to excited unstable states.
Bloch oscillations appear for a particle in a weakly tilted periodic potential. The intrinsic spin Hall effect is an outcome of a spin-orbit coupling. We demonstrate that both these phenomena can be realized simultaneously in a gas of weakly interacting ultracold atoms exposed to a tilted optical lattice and to a set of spatially dependent light fields inducing an effective spin-orbit coupling. It is found that both the spin Hall as well as the Bloch oscillation effects may coexist, showing, however, a strong correlation between the two. These correlations are manifested as a transverse spin c…
The thermalization of isolated quantum many-body systems is deeply related to fundamental questions of quantum information theory. While integrable or many-body localized systems display non-ergodic behavior due to extensively many conserved quantities, recent theoretical studies have identified a rich variety of more exotic phenomena in between these two extreme limits. The tilted one-dimensional Fermi-Hubbard model, which is readily accessible in experiments with ultracold atoms, emerged as an intriguing playground to study non-ergodic behavior in a clean disorder-free system. While non-ergo…
The dynamics of a (quasi)one-dimensional interacting atomic Bose-Einstein condensate in a tilted optical lattice is studied in a discrete mean-field approximation, i.e., in terms of the discrete nonlinear Schrödinger equation. If the static field is varied the system shows a plethora of dynamical phenomena. In the strong field limit we demonstrate the existence of (almost) non-spreading states which remain localized on the lattice region populated initially and show coherent Bloch oscillations with fractional revivals in the momentum space (so called quantum carpets). With decreasing field, th…
This paper investigates the synchronization of chaotic behavior in a model of Bose-Einstein condensate (BEC) held in a 1D tilted bichromatical optical lattice potential by using the active control technique. The synchronization is presented in the master-slave configuration which implies that the master system evolves freely and drives the dynamics of the slave system. Also the numerical simulations are given to indicate the practicability and the effectiveness of the used controllers.
Bloch oscillations of Bose-Einstein condensates realize sensitive matter-wave interferometers. We investigate the dynamics and stability of bright-soliton wave packets in one-dimensional tilted optical lattices with a modulated mean-field interaction $g(t)$. By means of a time-reversal argument, we prove the stability of Bloch oscillations of breathing solitons that would be quasistatically unstable. Floquet theory shows that these breathing solitons can be more stable against certain experimental perturbations than rigid solitons or even non-interacting wave packets.
We study the effects of an artificial gauge field on the ground-state phases of the Bose-Hubbard model on a checkerboard superlattice in two dimensions, including the superfluid phase and the Mott and alternating Mott insulators. First, we discuss the single-particle Hofstadter problem, and show that the presence of a checkerboard superlattice gives rise to a magnetic flux-independent energy gap in the excitation spectrum. Then, we consider the many-particle problem, and derive an analytical mean-field expression for the superfluid-Mott and superfluid--alternating-Mott insulator phase transiti…
We study the dynamics of Bose-Einstein condensates in tilted and driven optical superlattices. For a bichromatic lattice, each Bloch band split up into two minibands such that the dynamics is governed by the interplay of Bloch oscillations and transitions between the bands. Thus, bichromatic potentials provide an excellent model system for the study of nonlinear Landau-Zener tunneling and allow for a variety of applications in matter wave interferometry and quantum metrology. In the present paper we investigate the coherent dynamics of an interacting Bose-Einstein condensate as well as its sta…
We compute ground state fidelity of the one-dimensional Bose-Hubbard model at unit filling factor. To this aim, we apply the DMRG algorithm to systems with open and periodic boundary conditions. We find that fidelity differs significantly in the two cases and study its scaling properties in the quantum critical regime.
Ultracold atoms in optical lattices provide a unique opportunity to study Bose- Hubbard physics. In this work we show that by considering a spatially varying onsite interaction it is possible to manipulate the motion of excitations above the Mott phase in a Bose-Hubbard system. Specifically, we show that it is possible to "engineer" regimes where excitations will negatively refract, facilitating the construction of a flat lens.
For strongly interacting bosons in optical lattices the standard description using Bose-Hubbard model becomes questionable. The role of excited bands becomes important. In such a situation we compare results of simulations using multiband Bose-Hubbard model with a recent proposition based on a time dependent variational approach. It is shown that the latter, in its original formulation, uses too small variational space leading often to spurious effects. Possible expansion of variational approach is discussed.
We study theoretically the dynamics of two weakly-coupled Bose-Josephson junctions, prepared with the same particle number $N$ and Josephson excitation number $ν$ but with different reduced one-particle purity $γ$. A novel entropy oscillation mode is predicted, in which one-particle coherence is transferred between the Bose-Hubbard dimers with no particle or energy transfer. We explain this purity oscillation using a semiclassical picture.
We consider a $^{168}$Er-$^{164}$Dy dipolar mixture, trapped by a cigar shaped harmonic potential. We derive the quasi-1D inter-species effective potential exhibiting the tilting angles and show that it is a quite natural generalization of the situation of a single dipolar gas. By solving the coupled Gross-Pitaevskii equations, we observe a transition from miscible to immiscible mixture as the orientations of the magnetic moments are varied. The atom numbers are also shown to lead to noticeable effects on the mixture.
We develop a novel approach to understand the phases of one-dimensional Bose-Hubbard models. We integrate the simplicity of the mean-field theory and the numerical power of the density matrix renormalization group method to build an effective numerical technique with moderate computational resources to determine superfluid order parameters and correlation functions of large one-dimensional systems. We demonstrate the applicability of this method to directly identify superfluid, Mott insulator, and density wave phases in Bose-Hubbard models.
We discuss applications of the theory of Quantum Chaos to one of the paradigm models of many-body quantum physics -- the Bose-Hubbard model, which describes, in particular, interacting ultracold Bose atoms in an optical lattice. After preliminary, pure quantum analysis of the system we introduce the classical counterpart of the Bose-Hubbard model and the governing semiclassical equations of motion. We analyze these equations for the problem of Bloch oscillations of cold atoms where a number of experimental results are available. The review is written for non-experts and can be viewed as an int…
We analyze the momentum distribution function and its artificial-gauge-field dependence for the Mott insulator phases of the Hofstadter-Bose-Hubbard model. By benchmarking the results of the random-phase approximation (RPA) approach against those of the strong-coupling expansion (SCE) for the Landau and symmetric gauges, we find pronounced corrections to the former results in two dimensions.
We study the attractive Bose-Hubbard model with a tunable, on-site three-body constraint. It is shown that the critical behavior of the system undergoing a phase transition from pair-superfluid to superfluid at unit filling depends on the value of the three-body repulsion. In particular, we calculate critical exponents and the central charge governing the quantum phase transition.
We predict the effect of the roton instability for a two-dimensional weakly interacting gas of tilted dipoles in a single homogeneous quantum layer. Being typical for strongly correlated systems, the roton phenomena appear to occur in a weakly interacting gas. It is important that in contrast to a system of normal to wide layer dipoles, breaking of the rotational symmetry for a system of tilted dipoles leads to the convergence of the condensate depletion even up to the threshold of the roton instability, with mean-field approach being valid. Predicted effects can be observed in a wide class of…
We theoretically investigate a Bose-Einstein condensate confined by a rotating harmonic trap whose rotation axis is not aligned with any of its principal axes. The principal axes of the Thomas-Fermi density profiles of the resulting stationary solutions are found to be tilted with respect to those of the rotating trap, representing an extra degree of freedom that is associated with the existence of additional branches of stationary solutions for any given rotation axis alignment. By linearizing the time-dependent theory about the stationary states, we obtain a semi-analytical prediction of the…
We propose a scheme for the detection of quantum phase transitions in the 1D Bose-Hubbard (BH) and 1D Extended Bose-Hubbard (EBH) models, using the non-demolition measurement technique of quantum polarization spectroscopy. We use collective measurements of the effective total angular momentum of a particular spatial mode to characterise the Mott insulator to superfluid phase transition in the BH model, and the transition to a density wave state in the EBH model. We extend the application of collective measurements to the ground states at various deformations of a super-lattice potential.
We show that a two-atoms Bose-Hubbard model exhibits three different phases in the behavior of thermal entanglement in its parameter space. These phases are demonstrated to be traceable back to the existence of quantum phase transitions in the same system. Significant similarities between the behaviors of thermal entanglement and heat capacity in the parameter space are brought to light thus allowing to interpret the occurrence and the meaning of all these three phases.
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 th…
We study the dynamics of strongly repulsive Bose gas in tilted or driven bichromatic optical lattices. Using the Bose-Fermi mapping and exact numerical method, we calculate the reduced single-particle density matrices, and study the dynamics of density profile, momentum distribution and condensate fraction. We show the oscillating and breathing mode of dynamics, and depletion of condensate for short time dynamics. For long time dynamics, we clearly show the reconstruction of system at integer multiples of Bloch-Zener time. We also show how to achieve clear Bloch oscillation and Landau-Zener tu…
I present a currents algebra for the two-sites Bose-Hubbard model, generalize the Heisenberg equation of motion to write the second time derivative of the currents operators and use it to get the quantum dynamics of the currents. For different choices of the Hamiltonian parameters I get different currents dynamics and determine the period of the oscillations in function of the parameters.
A PT-symmetric Bose-Einstein condensate can theoretically be described using a complex optical potential, however, the experimental realization of such an optical potential describing the coherent in- and outcoupling of particles is a nontrivial task. We propose an experiment for a quantum mechanical realization of a PT-symmetric system, where the PT-symmetric currents are implemented by an accelerating Bose-Einstein condensate in a titled optical lattice. A defect consisting of two wells at the same energy level then acts as a PT-symmetric double-well if the tilt in the energy offsets of all …
In this paper, we analyze the quantum phases of multiple component Bose-Hubbard model in optical superlattices, using a mean-field method, the decoupling approximation. We find that the phase diagrams exhibit complected patterns and regions with various Charge Density Wave (CDW) for both one- and two- component cases. We also analyze the effective spin dynamics for the two-component case in strong-coupling region at unit filling, and show the possible existence of a Spin Density Wave (SDW) order.
In this paper, we studied a generalized Bose-Hubbard model on a checkerboard lattice with topologically nontrivial flat-band. We used mean-field method to decouple the model Hamiltonian and obtained phase diagram by Landau theory of second-order phase transition. We further calculate the energy gap and the dispersion of quasi-particle or quasi-hole in Mott insulator state and found that in strong interaction limit the quasi-particles or the quasi-holes also have flat bands.
We study the quench from the Mott to the superfluid phase in the Bose-Hubbard model and investigate the spatial-temporal growth of phase coherence, i.e., phase locking between initially uncorrelated sites. To this end, we establish a hierarchy of correlations via a controlled expansion into inverse powers of the coordination number $1/Z$. It turns out that the off-diagonal long-range order spreads with a constant propagation speed, forming local condensate patches, whereas the phase correlator follows a diffusion-like growth rate.
We study the off-equilibrium dynamics of the infinite dimensional Bose Hubbard Model after a quantum quench. The dynamics can be analyzed exactly by mapping it to an effective Newtonian evolution. For integer filling, we find a dynamical transition separating regimes of small and large quantum quenches starting from the superfluid state. This transition is very similar to the one found for the fermionic Hubbard model by mean field approximations.
We investigate the Bose-Hubbard chain in the presence of nearest-neighbor pairing. The pairing term gives rise to an unusual gapped $\mathbb{Z}_2$ Ising phase that has number fluctuation but no off-diagonal long range order. This phase has a strongly correlated many-body doubly degenerate ground state which is effectively a gap-protected macroscopic qubit. In the strongly interacting limit, the system can be mapped onto an anisotropic transverse spin chain, which in turn can be mapped to the better-known fermionic sister of the paired Bose-Hubbard chain: the Kitaev chain which hosts zero-energ…
Phase transitions in systems described by Bose-Fermi-Hubbard model on a lattice with two nonequivalent sublattices are investigated in this work. The case of hard-core bosons is considered and pseudospin formalism is used. Phase diagrams are built in the plain of chemical potential of the bosons-bosonic hopping parameter. It is shown that in the case of anisotropic hopping, the region of the supersolid phase existence is possible for a smaller parameter space.
Bose-Hubbard models are simple paradigmatic lattice models used to study dynamics and phases of quantum bosonic matter. We combine the extended Bose-Hubbard model in the hard-core regime with ring-exchange hoppings. By investigating the symmetries and low-energy properties of the Hamiltonian we argue that the model hosts fractonic defect excitations. We back up our claims with exact numerical simulations of defect dynamics exhibiting mobility constraints. Moreover, we confirm the robustness of our results against fracton symmetry breaking perturbations. Finally we argue that this model can be …
The hallmark of superfluidity is the appearance of metastable flow-states that carry a persistent circulating current. Considering Bose-Hubbard superfluid rings, we clarify the role of "quantum chaos" in this context. We show that the standard Landau and Bogoliubov superfluidity criteria fail for such low-dimensional circuits. We also discuss the feasibility for a coherent operation of a SQUID-like setup. Finally, we address the manifestation of the strong many-body dynamical localization effect.
We investigate the open dynamics of an atomic impurity embedded in a one-dimensional Bose-Hubbard lattice. We derive the reduced evolution equation for the impurity and show that the Bose-Hubbard lattice behaves as a tunable engineered environment allowing to simulate both Markovian and non-Markovian dynamics in a controlled and experimentally realisable way. We demonstrate that the presence or absence of memory effects is a signature of the nature of the excitations induced by the impurity, being delocalized or localized in the two limiting cases of superfluid and Mott insulator, respectively…
We address the effects of quenched disorder averaging in the time-evolution of systems of ultracold atoms in optical lattices in the presence of noise, imposed by of an environment. For bosonic systems governed by the Bose-Hubbard Hamiltonian, we quantify the response of disorder in Hamiltonian parameters in terms of physical observables, including bipartite entanglement in the ground state and report the existence of disorder-induced enhancement in weakly interacting cases. For systems of two-species fermions described by the Fermi-Hubbard Hamiltonian, we find similar results. In both cases, …
Dynamical Signatures and Kibble-Zurek Scaling of Localization in Tilted Bose-Einstein Condensates
Harish-Chandra Research Institute（哈里希-钱德拉研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Faculty of Physics, Adam Mickiewicz University（亚当·密茨凯维奇大学物理学院）；Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所）
In their preprint Anders et al. [arXiv:1004.0510] propose a crucial modification of the Bosonic Dynamical Mean-Field Theory (B-DMFT) derived by us [Phys. Rev. B 77, 235106 (2008)]. Here we show that the modification consists of two steps which, in fact, cancel each other. Consequently their self-consistency equations are identical to ours.
We present the effective action and self-consistency equations for the bosonic dynamical mean field (B-DMFT) approximation to the bosonic Hubbard model and show that it provides remarkably accurate phase diagrams and correlation functions. To solve the bosonic dynamical mean field equations we use a continuous-time Monte Carlo method for bosonic impurity models based on a diagrammatic expansion in the hybridization and condensate coupling. This method is readily generalized to bosonic mixtures, spinful bosons, and Bose-Fermi mixtures.
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 potentials. For bosons, the Hubbard Hamiltonian has been deeply scrutinised for short-range on-site interactions. However, accessing longer-range couplings has remained elusive experimentally. This marks the frontier towards the extended Bose-Hubbard Hamiltonian that allows insulating ordered phases at fractional lattice fillings. Here we implement this Hamiltonian by confining semiconductor dip…
We explore the dynamical properties of a one-dimensional Bose-Hubbard model, where two bosonic species interact via Feshbach resonance. We focus on the region in the phase diagram which is described by an effective, low-energy ferromagnetic Ising model in both transverse and longitudinal fields. In this regime, we numerically calculate the dynamical structure factor of the Bose-Hubbard model using the time-evolving block decimation method. In the ferromagnetic phase, we observe both the continuum of excitations and the bound states in the presence of a longitudinal field. Near the Ising critic…
Lieb-Robinson and related bounds set an upper limit on the rate of spreading of information in non-relativistic quantum systems. Experimentally, they have been observed in the spreading of correlations in the Bose-Hubbard model after a quantum quench. Using a recently developed two particle irreducible (2PI) strong coupling approach to out-of-equilibrium dynamics in the Bose-Hubbard model we calculate both the group and phase velocities for the spreading of single-particle correlations in one, two and three dimensions as a function of interaction strength. Our results are in quantitative agree…
Krylov complexity of a tilted extended Bose-Hubbard chain with Rydberg-dressed interactions
School of Physics and Astronomy, University of Nottingham（诺丁汉大学物理与天文学学院）；Taishan College, Shandong University（山东大学泰山学堂）；Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham（诺丁汉大学量子非平衡系统数学与理论物理中心）；School of Physics, Henan Normal University（河南师范大学物理学院）
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…
The effect of dipolar orientation with respect to the soliton plane on the physics of two-dimensional bright solitons in dipolar Bose-Einstein condensates is discussed. Previous studies on such a soliton involved dipoles either perpendicular or parallel to the condensate-plane. The tilting angle constitutes an additional tuning parameter, which help us to control the in-plane anisotropy of the soliton as well as provides access to previously disregarded regimes of interaction parameters for soliton stability. In addition, it can be used to drive the condensate into phonon instability without c…
I introduce a new parametrization of a bosonic Lax operator for the algebraic Bethe ansatz method with the $gl(2)$-invariant $R$-matrix and use it to present the exact solution of a generalized two-sites Bose-Hubbard model with asymmetric tunnelling. In the no interaction limit I show that the Bethe ansatz equations can be written as a $S^{N-1}$ sphere, where $N$ is the total number of atoms in the condensate.
We present calculations of the ground state and excitations of an anisotropic dipolar Bose gas in two dimensions, realized by a non-perpendicular polarization with respect to the system plane. For sufficiently high density an increase of the polarization angle leads to a density instability of the gas phase in the direction where the anisotropic interaction is strongest. Using a dynamic many-body theory, we calculate the dynamic structure function in the gas phase which shows the anisotropic dispersion of the excitations. We find that the energy of roton excitations in the strongly interacting…
We study the zero temperature phase diagram of the disordered spin-1 Bose-Hubbard model in a 2-dimensional square lattice. To this aim, we use a mean field Gutzwiller ansatz and a probabilistic mean field perturbation theory. The spin interaction induces two different regimes corresponding to a ferromagnetic and antiferromagnetic order. In the ferromagnetic case, the introduction of disorder reproduces analogous features of the disordered scalar Bose-Hubbard model, consisting in the formation of a Bose glass phase between Mott insulator lobes. In the antiferromagnetic regime the phase diagram …
We study the dynamical stability of Bose-Einstein condensates in an optical lattice with a time-periodic modulation potential and a constant acceleration force simultaneously. We derive the explicit expressions of quasienergies and obtain the stability diagrams in the parameter space of the interaction strength and the modulation amplitude. The ratio of the acceleration force to the modulation frequency characterizes two cases: integer and non-integer resonances. For integer resonances, the critical interaction strength $g_{\mathrm{c}}$ shows an alternate behavior where the completely unstable…
