Spectral excitations of ultracold gases of bosonic atoms trapped in one dimensional optical lattices with disorder are investigated by means of the variational cluster approach applied to the Bose-Hubbard model. In particular, qualitatively different disorder distributions typically employed in experiments are considered. The computed spectra exhibit a strong dependence on both the shape of the disorder distribution and the disorder strength. We compare alternative results for the Mott gap obtained from its formal definition and from the minimum peak distance, which is the quantity available from experiments.
We employ ultracold atoms with controllable disorder and interaction to study the paradigmatic problem of disordered bosons in the full disorder-interaction plane. Combining measurements of coherence, transport and excitation spectra, we get evidence of an insulating regime extending from weak to strong interaction and surrounding a superfluid-like regime, in general agreement with the theory. For strong interaction, we reveal the presence of a strongly-correlated Bose glass coexisting with a Mott insulator.
Disorder is everywhere in nature and it has a fundamental impact on the behavior of many quantum systems. The presence of a small amount of disorder, in fact, can dramatically change the coherence and transport properties of a system. Despite the growing interest in this topic, a complete understanding of the issue is still missing. An open question, for example, is the description of the interplay of disorder and interactions, which has been predicted to give rise to exotic states of matter such as quantum glasses or many-body localization. In this review, we will present an overview of exper…
Clarifying the interplay of interactions and disorder is fundamental to the understanding of many quantum systems, including superfluid helium in porous media, granular and thin-film superconductors, and light propagating in disordered media. One central aspect for bosonic systems is the competition between disorder, which tends to localize particles, and weak repulsive interactions, which instead have a delocalizing effect. Since the required degree of independent control of the disorder and of the interactions is not easily achievable in most available physical systems, a systematic experime…
Using the exact Bose-Fermi mapping, we study universal properties of ground-state density distributions and finite-temperature quantum critical behavior of one-dimensional hard-core bosons in trapped incommensurate optical lattices. Through the analysis of universal scaling relations in the quantum critical regime, we demonstrate that the superfluid to Bose glass transition and the general phase diagram of disordered hard-core bosons can be uniquely determined from finite-temperature density distributions of the trapped disordered system.
We describe repulsively interacting Bose-Einstein condensates in spatially correlated disorder potentials of arbitrary dimension. The first effect of disorder is to deform the mean-field condensate. Secondly, the quantum excitation spectrum and condensate population are affected. By a saddle-point expansion of the many-body Hamiltonian around the deformed mean-field ground state, we derive the fundamental quadratic Hamiltonian of quantum fluctuations. Importantly, a basis is used such that excitations are orthogonal to the deformed condensate. Via Bogoliubov-Nambu perturbation theory, we compu…
We investigate the topological classification of excitations in quadratic bosonic systems with an excitation band gap. Time-reversal, charge-conjugation, and parity symmetries in bosonic systems are introduced to realize a ten-fold symmetry classification. We find a specific decomposition of the quadratic bosonic Hamiltonian and use it to prove that each quadratic bosonic system is homotopic to a direct sum of two single-particle subsystems. The topological classification table is thus derived via inheriting from that of Atland-Zirnbauer classes and unique topological phases of bosons are pred…
Energy-Resolved Quantum Geometry from Středa Response: Driven-Dissipative Bosonic Lattices and Disordered Systems
Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université（卡斯勒-布罗塞尔实验室，法兰西学院，法国国家科学研究中心，巴黎高等师范学院-巴黎文理研究大学，索邦大学）；International Solvay Institutes（国际索尔维研究所）；Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles（非线性现象与复杂系统中心，布鲁塞尔自由大学）
We investigate the role of squeezing interaction in inducing topological Bogoliubov excitations of a bosonic system. We introduce a squeezing transformation which is capable of reducing the corresponding Bogoliubov-de Gennes Hamiltonian to an effective non-interacting one with the spectra and topology unchanged. In the weak interaction limit, we apply the perturbation theory to investigate the squeezing-induced topological gap opening on bosonic Bogoliubov excitations and find that the squeezing interaction plays an equivalent role as a spin-orbit or Zeeman-like coupling in the effective Hamil…
An approach is proposed to analyze an interacting bosonic system using two-time temperature Green's functions on the collective variables. Two systems are studied: liquid helium-4 and the Yukawa Bose-liquid being a model of the nuclear matter. The suggested decoupling in the equations of motion for Green's functions yields a good description of the elementary excitation spectrum in the long-wavelength limit.
We study the effect of disorder on the propagation of collective excitations in a disordered Bose superfluid. We incorporate local density depletion induced by strong disorder at the meanfield level, and formulate the transport of the excitations in terms of a screened scattering problem. We show that the competition of disorder, screening, and density depletion induces a strongly non-monotonic energy dependence of the disorder parameter. In three dimensions, it results in a rich localization diagram with four different classes of mobility spectra, characterized by either no or up to three mob…
We investigate the low-temperature properties of a ultracold gas made of bosonic alkali-metal atoms with finite-range interaction under the effect of a disordered environment. The statistical characterization of the disorder is investigated within an effective-field-theory formalism for a generic spatial dimension $d$. Moving to $d=3$, where all the arising divergences are properly regularized, we focus on the depletion of both the condensate and superfluid densities. At zero temperature we obtain meaningful analytical formulas for the condensate fraction and the superfluid fraction which take…
We investigate the low-energy dynamics of two coupled anisotropic Bose-Einstein condensates forming a long Josephson junction. The theoretical study is performed in the framework of the two-dimensional Gross-Pitaevskii equation and the Bogoliubov-de Gennes formalism. We analyze the excitation spectrum of the coupled Bose condensates and show how low-energy excitations of the condensates lead to multiple-frequency oscillations of the atomic populations in the two wells. This analysis generalizes the standard bosnic Josephson euqation approach. We also develop a one-dimensional hydrodynamic mode…
When a strongly disordered system of interacting quantum dipoles is locally excited, the excitation relaxes on some (potentially very long) timescale. We analyze this relaxation process, both for electron glasses with strong Coulomb interactions - in which particle-hole dipoles are emergent excitations - and for systems (e.g., quantum magnets or ultracold dipolar molecules) made up of microscopic dipoles. We consider both energy relaxation rates ($T_1$ times) and dephasing rates ($T_2$ times), and their dependence on frequency, temperature, and polarization. Systems in both two and three dimen…
The transport of excitations governs fundamental properties of matter. Particularly rich physics emerges in the interplay between disorder and environmental noise, even in small systems such as photosynthetic biomolecules. Counterintuitively, noise can enhance coherent quantum transport, which has been proposed as a mechanism behind the high transport efficiencies observed in photosynthetic complexes. This effect has been called "environmental-assisted quantum transport" (ENAQT). Here, we propose a quantum simulation of the excitation transport in an open quantum network, taking advantage of t…
We investigate the interaction-driven instability of a quadratic band crossing arising for ultracold bosonic atoms loaded into a two-dimensional optical lattice. We consider the case when the degenerate point becomes a local minimum of both crossing energy bands such that it can support a stable Bose-Einstein condensate. Repulsive contact interaction among the condensed bosons induces a spontaneously time-reversal symmetry broken superfluid phase and a topological gap is opened in the excitation spectrum. We propose two concrete realizations of the desired quadratic band crossing in lattices w…
The characterization of excitations in disordered quantum systems is a central issue in connection with glass physics and many-body localization. Here, we show that quench spectroscopy of a disordered model, as realized from its out-of-equilibrium dynamics following a global quench, allows us to fully characterize the spectral properties of the disordered phases. In the Bose-Hubbard model, a clear signature of gapless excitations in momentum-resolved spectroscopy enables us to accurately locate the Mott insulator to Bose glass transition, while the presence or absence of a well-defined soundli…
We study interacting 1D two-component mixtures of cold atoms in a random potential, and extend the results reported earlier [{\it Phys. Rev. Lett.} {\bf 105}, 115301 (2010)]. We construct the phase diagram of a disordered Bose-Fermi mixture as a function of the strength of the Bose-Bose and Bose-Fermi interactions, and the ratio of the bosonic sound velocity and the Fermi velocity. Performing renormalization group and variational calculations, three phases are identified: (i) a fully delocalized two-component Luttinger liquid with superfluid bosons and fermions (ii) a fully localized phase wit…
We study the topological properties of elementary excitations in a staggered $p_x \pm i p_y$ Bose-Einstein condensate realized in recent orbital optical lattice experiments. The condensate wave function may be viewed as a configuration space variant of the famous $p_x+ ip_y$ momentum space order parameter of strontium ruthenate superconductors. We show that its elementary excitation spectrum possesses Dirac bosons with $π$ Berry flux. Remarkably, if we induce a population imbalance between the $p_x+ip_y$ and $p_x-ip_y$ condensate components, a gap opens up in the excitation spectrum resulting …
Motivated by recent advance in orbitally tuned Feshbach resonance experiments, we analyze the ground-state phase diagram and related low-energy excitation spectra of a d-wave interacting Bose gas. A two-channel model with d-wave symmetric interactions and background s-wave interactions is adopted to characterize the gas. The ground state is found to show three interesting phases: atomic, molecular, and atomic-molecular superfluidity. Remarkably differently from what was previously known in the p-wave case, the atomic superfluid is found to be momentum-independent in the present d-wave case. Bo…
We investigate the condensate wave function and elementary excitations of strongly interacting bosonic polar molecules in a harmonic trap, treating the scattering amplitude beyond the standard first Born approximation (FBA). By using an appropriate trial wave function in the variational method, effects of the leading order correction beyond the FBA have been investigated and shown to be significantly enhanced when the system is close to the phase boundary of collapse. How such leading order effect of going beyond the FBA can be observed in a realistic experiment is also discussed.
We show that tunneling and localization properties of interacting ultracold atoms in an optical lattice can be controlled by adiabatically turning on a fast oscillatory force even in the presence of disorder. Our calculations are based on the exact solution of the time-dependent Schroedinger equation, using the Floquet formalism. Implications of our findings for larger systems and the possibility of controlling the phase diagram of disordered-interacting bosonic systems are discussed.
We consider a system of weakly interacting bosons confined on a planar double lattice ring subjected to two artificial gauge fields. This system is known to display three phases, the Meissner phase where the flow of particles is carried at the edges of the system without transverse current, a vortex phase characterized by non-zero transverse current, and a biased-ladder phase, characterized by an imbalance of the population of the two rings. We use the Bogoliubov approximation to determine the excitation spectrum in the three phases, the dynamic structure factor and the quantum fluctuation cor…
We employ the MultiConfiguraional Time-Dependent Hartree for Bosons (MCTDHB) method to study excited states of interacting Bose-Einstein condensates confined by harmonic and double-well trap potentials. Two approaches to access excitations, a static and a dynamic one, have been studied and contrasted. In static simulations the low-lying excitations have been computed by utilizing the LR-MCTDHB method - a linear response theory constructed on-top of a static MCTDHB solution. Complimentary, we propose two dynamic protocols that address excitations by propagating the MCTDHB wave-function. In part…
We study the low-energy excitations of a bosonic lattice gas with cavity-mediated interactions. By performing two successive Hubbard-Stratonovich transformations, we derive an effective field theory to study the strongly-coupling regime. Taking into account the quantum fluctuation, we report the unusual effect of the superradiant cavity light induced density imbalance, which has been shown to have a negligible effect on the single particle excitation in the previous studies. Instead, we show that such negligible fluctuation of density imbalance dramatically changes the behavior of the low-ener…
Motivated by the Penrose-Onsager criterion for Bose-Einstein condensation we propose a functional theory for targeting low-lying excitation energies of bosonic quantum systems through the one-particle picture. For this, we employ an extension of the Rayleigh-Ritz variational principle to ensemble states with spectrum $\boldsymbol{w}$ and prove a corresponding generalization of the Hohenberg-Kohn theorem: The underlying one-particle reduced density matrix determines all properties of systems of $N$ identical particles in their $\boldsymbol{w}$-ensemble states. Then, to circumvent the $v$-repres…
We present a quantum Monte Carlo study of two-dimensional dipolar Bose gases in the limit of zero temperature. The analysis is mainly focused on the anisotropy effects induced in the homogeneous gas when the polarization angle with respect to the plane is changed. We restrict our study to the regime where the dipolar interaction is strictly repulsive, although the strength of the pair repulsion depends on the vector interparticle distance. Our results show that the effect of the anisotropy in the energy per particle scales with the gas parameter at low densities as expected, and that this scal…
We study the process of absorption or emission of a bosonic collective excitation by a fermionic quasiparticle in a superfluid of paired fermions. From the RPA equation of motion of the bosonic excitation annihilation operator, we obtain an expression of the coupling amplitude of this process which is limited neither to resonant processes nor to the long wavelength limit. We confirm our result by independently deriving it in the functional integral approach using the gaussian fluctuation approximation, and by comparing it in the long wavelength limit to the quantum hydrodynamic result. Last, w…
The recent progress in engineering topological band structures in optical-lattice systems makes it promising to study fractional Chern insulator states in these systems. Here we consider a realistic finite system of a few repulsively interacting bosons on a square lattice with magnetic flux and sharp edges, as it can be realized in quantum-gas microscopes. We investigate under which conditions a fractional Chern insulator state corresponding to the Laughlin-like state at filling $ν=1/2$ can be stabilized and its fractional excitations probed. Using numerical simulations, we find an incompressi…
We develop an inhomogeneous quantum mean-field approach to the behavior of collective excitations across the superfluid-Mott glass quantum phase transition in two dimensions, complementing recent quantum Monte Carlo simulations [Phys. Rev. Lett. {\bf 125}, 027002 (2020)]. In quadratic (Gaussian) approximation, the Goldstone (phase) and Higgs (amplitude) modes completely decouple. Each is described by a disordered Bogoliubov Hamiltonian which can be solved by an inhomogeneous multi-mode Bogoliubov transformation. We find that the Higgs mode is spatially localized in both phases. The correspondi…
We consider the dynamics of rotational excitations placed on a single molecule in spatially disordered 1D, 2D and 3D ensembles of ultracold molecules trapped in optical lattices. The disorder arises from incomplete populations of optical lattices with molecules. This leads to a model corresponding to a quantum particle with long-range tunnelling amplitudes moving on a lattice with the same on-site energy but with forbidden access to random sites (vacancies). We examine the time and length scales of Anderson localization for this type of disorder with realistic experimental parameters in the Ha…
A two-component two-dimensional (2D) dipolar bosonic system in the bilayer geometry is considered. By performing quantum Monte Carlo simulations in a wide range of layer spacings we analyze in detail the pair correlation functions, the static response function, the kinetic and interaction energies. By reducing the layer spacing we observe a transition from weakly to strongly bound dimer states. The transition is accompanied by the onset of short-range correlations, suppression of the superfluid response, and rotonization of the excitation spectrum. A dispersion law and a dynamic structure fact…
We present a versatile scheme for creating topological Bogoliubov excitations in weakly interacting bosonic systems. Our proposal relies on a background stationary field that consists of a Kagome vortex lattice, which breaks time-reversal symmetry and induces a periodic potential for Bogoliubov excitations. In analogy to the Haldane model, no external magnetic field or net flux is required. We construct a generic model based on the two-dimensional (2D) nonlinear Schrödinger equation and demonstrate the emergence of topological gaps crossed by chiral Bogoliubov edge modes. Our scheme can be rea…
