Christopher Gaul, Cord A. Müller
We study the problem of disordered interacting bosons within grand-canonical thermodynamics and Bogoliubov theory. We compute the fractions of condensed and non-condensed particles and corrections to the compressibility and the speed of sound due to interaction and disorder. There are two small parameters, the disorder strength compared to the chemical potential and the dilute-gas parameter.
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We investigate the superfluid-insulator quantum phase transition in a disordered 1D Bose gas in the mean field limit, by studying the probability distribution of the density. The superfluid phase is characterized by a vanishing probability to have zero density, whereas a nonzero probability marks the insulator phase. This relation is derived analytically, and confirmed by a numerical study. This fragmentation criterion is particularly suited for detecting the phase transition in experiments. When a harmonic trap is included, the transition to the insulating phase can be extracted from the stat…
We discuss the kinetics of the disordered interacting Bose gas using the Boltzmann transport equation. The theory may serve as a unifying framework for studying questions of dynamics of the expanding Bose gas at different stages of the expansion. We show that the transport theory allows us to straightforwardly reproduce and generalize a number of results previously obtained from microscopic models in different formalisms. Based on estimates for the interparticle scattering rates, we discuss the relevance of interaction effects for the localization problem in the interacting disordered Bose gas…
We report measurements of particle number correlations and fluctuations of a photon Bose-Einstein condensate in a dye microcavity using a Hanbury Brown-Twiss experiment. The photon gas is coupled to a reservoir of molecular excitations, which serve both as heat bath and particle reservoir to realize grand-canonical conditions. For large reservoirs, we observe strong number fluctuations of order of the total particle number extending deep into the condensed phase. Our results demonstrate that Bose-Einstein condensation under grand-canonical ensemble conditions does not imply second-order cohere…
We describe interacting bosons at low temperature in spatially correlated random potentials. By a Bogoliubov expansion around the deformed mean-field condensate, the fundamental Hamiltonian for elementary excitations is derived, achieving an analytical formulation in the case of weak disorder. From this, we calculate the sound velocity and true zero-temperature condensate depletion in correlated disorder and all dimensions.
Grand-canonical fluctuations of Bose-Einstein condensates of light are accessible to state-of-the-art experiments [J. Schmitt et al., Phys. Rev. Lett. 112, 030401 (2014).]. We phenomenologically describe these fluctuations by using the grand-canonical ensemble for a weakly interacting Bose gas at thermal equilibrium. For a two-dimensional harmonic trap, we use two models for which the canonical partition functions of the weakly interacting Bose gas are given by exact recurrence relations. We find that the grand-canonical condensate fluctuations for weakly interacting Bose gases vanish at zero …
Recently, Nattermann and Pokrovsky [PRL 100, 060402 (2008)] have proposed a scaling approach for studying Bose-Einstein condensates in strongly disordered traps. In this paper we implement their scaling argument in the framework of the variational method for solving the time dependent Gross-Pitaevskii equation. We consider atomic gases with both short range s-wave interaction and long range anisotropic dipolar interaction. The theory is addressed to the regime of strong disorder and weak interactions where the physics is dominated by the collective pinning due to the disorder. The phenomenon o…
We investigate the momentum-dependent transport of 1D quasi-condensates in quasiperiodic optical lattices. We observe a sharp crossover from a weakly dissipative regime to a strongly unstable one at a disorder-dependent critical momentum. In the limit of non-disordered lattices the observations indicate a contribution of quantum phase slips to the dissipation. We identify a set of critical disorder and interaction strengths for which such critical momentum vanishes, separating a fluid regime from an insulating one. We relate our observation to the predicted zero-temperature superfluid-Bose gla…
Observations of center of mass dynamics offer a straightforward method to identify strongly interacting quantum phases of atoms placed in optical lattices. We theoretically study the dynamics of states derived from the disordered Bose-Hubbard model in a trapping potential. We find that the edge states in the trap allow center of mass motion even with insulating states in the center. We identify short and long-time scale mechanisms for edge state transport in insulating phases. We also argue that the center of mass velocity can aid in identifying a Bose-glass phase. Our zero temperature results…
We study the ground state of the disordered Bose-Hubbard model for spin-1 particles by means of the stochastic mean-field theory. This approach enables the determination of the probability distributions of various physical quantities, such as the superfluid order parameter, the average site occupation number, the standard deviation of the occupation per site and the square of the spin operator per site. We show how a stochastic method, previously used in the study of localization, can be flexibly used to solve the relevant equations with great accuracy. We have determined the phase diagram, wh…
Phase diagram of disordered Bose-Hubbard model based on mean-field and percolation analysis in two dimensions and at fixed $n=1$ filling
本文基于平均场理论，研究二维无序玻色-哈伯德模型在固定填充下的相图，发现超流相在玻色玻璃相之间重入，并通过渗流分析论证其鲁棒性。
We explore the quench dynamics of a two-dimensional, weakly interacting disordered Bose gas for various relative strengths of interactions and disorder. This allows us to identify two well distinct out-of-equilibrium regimes. When interactions are smaller than the disorder, the gas experiences multiple scattering and exhibits a short-range spatial coherence. At short time this coherence is only smoothly affected by interactions, via a diffusion process of the particles' energies. When interactions are larger than the disorder, scattering ceases and the gas behaves more and more like a fluid, u…
The disordered Bose-Hubbard model in two dimensions at non-integer filling admits a superfluid to Bose-glass transition at weak disorder. Less understood are the properties of this system at strong disorder and energy densities corresponding to excited states. In this work we study the Bose-glass transition of the ground state and the related finite energy localization transition, the mobility edge of the quasiparticle spectrum, a critical energy separating extended from localized quasiparticle excitations. To study these the fluctuation operator expansion is used. The level spacing statistics…
We discuss the stochastic mean-field theory (SMFT) method which is a new approach for describing disordered Bose systems in the thermodynamic limit including localization and dimensional effects. We explicate the method in detail and apply it to the disordered Bose-Hubbard model at finite temperature, with on-site box disorder, as well as experimentally relevant unbounded speckle disorder. We find that disorder-induced condensation and reentrant behavior at constant filling are only possible at low temperatures, beyond the reach of current experiments [Pasienski et al., arXiv:0908.1182]. Inclu…
We study the dynamic structure factor of a one-dimensional Bose gas confined in an optical lattice and modeled by the Bose-Hubbard Hamiltonian, using a variety of numerical and analytical approaches. The dynamic structure factor, experimentally measurable by Bragg spectroscopy, is studied in three relevant cases: in the clean regime, featuring either a superfluid or a Mott phase; and in the presence of two types of (quasi-)disordered external potentials: a quasi-periodic potential obtained from a bichromatic superlattice and a random-box disorder - both featuring a Bose glass phase. In the cle…
We review recent experiments on the Bose-Einstein condensation of photons in a dye-filled optical microresonator. The most well-known example of a photon gas, photons in blackbody radiation, does not show Bose-Einstein condensation. Instead of massively populating the cavity ground mode, photons vanish in the cavity walls when they are cooled down. The situation is different in an ultrashort optical cavity imprinting a low-frequency cutoff on the photon energy spectrum that is well above the thermal energy. The latter allows for a thermalization process in which both temperature and photon num…
Contour-time approach to the disordered Bose-Hubbard model in the strong coupling regime
本文开发了一种针对无序 Bose-Hubbard 模型的双粒子不可约强耦合方法，可处理平衡与非平衡情况，研究了平衡相图，并发现实验中非遍历动力学出现的无序强度对应于 Mott 绝缘体与 Bose 玻璃的相边界。
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…
Upper bound for the grand canonical free energy of the Bose gas in the Gross-Pitaevskii limit
本文在Gross-Pitaevskii极限和接近Bose-Einstein凝聚临界温度的条件下，通过粒子数涨落有效理论和温度依赖的Bogoliubov哈密顿量，给出了均匀玻色气体巨正则自由能的上界。
Anderson localization of elementary excitations in disordered binary Bose mixtures: Effects of the Lee-Huang-Yang quantum and thermal corrections
该研究结合解析与数值方法，探究含Lee-Huang-Yang量子与热修正的无序二元玻色混合物准粒子安德森局域化，分析两相下的局域化特征及热涨落、液滴态平顶区的相关效应。
In an equilibrium three-dimensional (3D) disordered condensate, it's well established that disorder can generate an amount of normal fluid equaling to $\frac{4}{3}$ of the condensate depletion. The concept that the superfluid is more volatile to the existence of disorder than the condensate is crucial to the understanding of Bose glass phase. In this Letter, we show that, by bringing a weakly disordered 3D condensate to nonequilibrium regime via a quantum quench in the interaction, disorder can destroy superfluid significantly more, leading to a steady state in which the normal fluid density f…
We study the superfluid transitions in bidimensional (2D) and tridimensional (3D) disordered and interacting Bose gases. We work in the limit of long-range correlated disorder such that it can be treated in the local density approximation. We present the superfluid transition curves both in the disorder-temperature plane well as in the disorder-entropy plane in 2D and 3D Bose gases. Surprisingly, we find that a small amount of disorder is always favorable to the apparition of a superfluid. Our results offer a quantitative comparison with recent experiments in 2D disordered ultra-cold gases, fo…
We study a one-dimensional disordered Bose fluid using bosonization, the replica method and a nonperturbative functional renormalization-group approach. The Bose-glass phase is described by a fully attractive strong-disorder fixed point characterized by a singular disorder correlator whose functional dependence assumes a cuspy form that is related to the existence of metastable states. At nonzero momentum scale, quantum tunneling between these metastable states leads to a rounding of the nonanalyticity in a quantum boundary layer that encodes the existence of rare superfluid regions responsibl…
We present a multi-site formulation of mean-field theory applied to the disordered Bose-Hubbard model. In this approach the lattice is partitioned into clusters, each isolated cluster being treated exactly, with inter-cluster hopping being treated approximately. The theory allows for the possibility of a different superfluid order parameter at every site in the lattice, such as what has been used in previously published site-decoupled mean-field theories, but a multi-site formulation also allows for the inclusion of spatial correlations allowing us, e.g., to calculate the correlation length (o…
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…
Disordered solid to Bose-glass transition in Bose-Hubbard model with disorder and long-range interactions
本文利用单格点与团簇Gutzwiller平均场理论和强耦合微扰展开，系统研究了含最近邻及次近邻长程相互作用的无序Bose-Hubbard模型的量子相图，揭示了无序固体到Bose玻璃的相变机制，并从渗流理论视角进行了分析。
We study the phase transition from Mott insulator (MI) to Bose glass (BG) of a disordered Bose-Hubbard model within the framework of Ginzburg-Landau effective action approach. By treating MI as unperturbed ground state and performing a systematic expansion with respect to tunneling matrix element, we extend such a field-theoretic method into the disordered lattice Bose systems. To the lowest order, a second order phase transition is confirmed to happen here and the corresponding phase boundary equation coincides with the previous mean-field approximation result. Keeping all the terms second or…
We investigate the isobar of an ideal Bose gas confined in a cubic box within the grand canonical ensemble, for a large yet finite number of particles, N. After solving the equation of the spinodal curve, we derive precise formulae for the supercooling and the superheating temperatures which reveal an N^{-1/3} or N^{-1/4} power correction to the known Bose-Einstein condensation temperature in the thermodynamic limit. Numerical computations confirm the accuracy of our analytical approximation, and further show that the isobar zigzags on the temperature-volume plane if N is greater than or equal…
We analyze an interacting Bose-Fermi mixture in a 1D disordered potential using a combination of renormalization group and variational methods. We obtain the complete phase diagram in the incommensurate case as a function of bosonic and inter-species interaction strengths, in the weak disorder limit. We find that the system is characterized by several phase transitions between superfluid and various glassy insulating states, including a new Bose-Fermi glass phase, where both species are coupled and localized. We show that the dynamical structure factor, as measured through Bragg scattering exp…
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 disorder effect on coherent fraction and the quantum phase transition of ultracold dilute Bose gases trapped in disordered optical lattices. Within the framework of Bogoliubov theory, an analytical expression for the particle density is derived and the dependence of coherent fraction on disorder strength as well as on lattice depth is discussed. In weak disorder regime, we find a decreased sensitivity of coherent fraction to disorder with the increase of on-site interaction strength. For strong disorder, the quantum phase boundary between superfluid phase and Bose glass phas…
We study the two-dimensional weakly repulsive Bose gas at zero temperature in the presence of correlated disorder. Using large-scale simulations, we show that the low-energy Bogoliubov cumulative density of states remains quadratic up to a critical disorder strength, beyond which a power law with disorder-dependent exponent $β<2$ sets in. We associate this threshold behavior with the transition from superfluid to Bose glass, and compare the resulting mean-field phase diagram with scaling laws and the Thomas-Fermi percolation threshold of the mean-field density profile.
We show that the Bose-glass phase of a one-dimensional disordered Bose fluid exhibits a chaotic behavior, i.e., an extreme sensitivity to external parameters. Using bosonization, the replica formalism and the nonperturbative functional renormalization group, we find that the ground state is unstable to any modification of the disorder configuration ("disorder" chaos) or variation of the Luttinger parameter ("quantum" chaos, analog to the "temperature" chaos in classical disordered systems). This result is obtained by considering two copies of the system, with slightly different disorder config…
We study the effects of an on-site disorder potential in a gas of spinor (spin-1) ultracold atoms loaded in an optical lattice corresponding to both ferromagnetic and antiferromagnetic spin dependent interactions. Starting with a disordered spinor Bose-Hubbard model (SBHM) on a two dimensional square lattice, we observe the appearance of a Bose glass phase using the fraction of the lattice sites having finite superfluid order parameter and non integer local densities as an indicator. A precise distinction between three different types of phases namely, superfluid (SF), Mott insulator (MI) and …
Motivated by a recent experiment, we study the dynamics of bosons in a disordered optical lattice, interacting with a variably sized bath of disorder free atoms. As the number of particles in the bath is increased, there is a transition between "localized" and "ergodic" behavior, which are characterized by the long-time behavior of an initial density wave. We model the dynamics with a stochastic mean field theory, reproducing the central observations of the experiment. A key conclusion from our study is that particle loss plays an important role.
An iterative scheme based on the kernel polynomial method is devised for the efficient computation of the one-body density matrix of weakly interacting Bose gases within Bogoliubov theory. This scheme is used to analyze the coherence properties of disordered bosons in one and two dimensions. In the one-dimensional geometry, we examine the quantum phase transition between superfluid and Bose glass at weak interactions, and we recover the scaling of the phase boundary that was characterized using a direct spectral approach by Fontanesi et al. [Phys. Rev. A 81, 053603 (2010)]. The kernel polynomi…
We numerically simulate an oscillating Bose-Einstein condensate in a disordered trap [Phys. Rev. A 82, 033603 (2010)] and the results are in good agreement with the experiment. It allows us to verify that total energy and particle number are conserved in this quantum system. The disorder acts as a medium, which results in a relaxation from nonequilibrium to equilibrium, i.e., thermalization. An algebraic localization is realized when the system approaches the equilibrium, and if the system falls into the regime when the healing length of the condensate exceeds the correlation length of the dis…
The understanding of disordered quantum systems is still far from being complete, despite many decades of research on a variety of physical systems. In this review we discuss how Bose-Einstein condensates of ultracold atoms in disordered potentials have opened a new window for studying fundamental phenomena related to disorder. In particular, we point our attention to recent experimental studies on Anderson localization and on the interplay of disorder and weak interactions. These realize a very promising starting point for a deeper understanding of the complex behaviour of interacting, disord…
We theoretically study the out-of-equilibrium dynamics in momentum space of a weakly interacting disordered Bose gas launched with a finite velocity. In the absence of interactions, coherent multiple scattering gives rise to a background of diffusive particles, on top of which a coherent backscattering interference emerges. We revisit this scenario in the presence of interactions, using a diagrammatic quantum transport theory. We find that the dynamics is governed by coupled kinetic equations describing the thermalization of the diffusive and coherent components of the gas. This phenomenon lea…
The question of how the low-energy properties of disordered quantum systems may be connected to exotic localization phenomena at high energy is a key open question in the context of quantum glasses and many-body localization. In arXiv:2105.05774 we have shown that key features of the excitation spectrum of a disordered system can be efficiently probed from out-of-equilibrium dynamics following a quantum quench, providing distinctive signatures of the various phases. Here, we extend this work by providing a more in-depth study of the behavior of the quench spectral functions associated to diffe…
Particle fluctuations in systems with Bose-Einstein condensate
本文澄清了玻色-爱因斯坦凝聚系统中的粒子涨落问题，指出“巨正则灾难”源于对巨正则系综的不当使用，强调规范对称性破缺是正确描述凝聚相的必要条件，并证明理想玻色气体与相互作用粒子系统在规范对称性破缺后均无异常涨落。
We investigate the properties of the superfluid phase in the three-dimensional disordered Bose-Hubbard model using Quantum Monte-Carlo simulations. The phase diagram is generated using Gaussian disorder on the on-site potential. Comparisons with box and speckle disorder show qualitative similarities leading to the re-entrant behavior of the superfluid. Quantitative differences that arise are controlled by the specific shape of the disorder. Statistics pertaining to disorder distributions are studied for a range of interaction strengths and system sizes, where strong finite-size effects are obs…
From Bose glass to many-body localization in a one-dimensional disordered Bose gas
利用玻色化与非微扰泛函重整化群，研究一维无序玻色气体的有限温度相图，提出两种场景：一种在有限温度下玻色玻璃失稳，另一种在低温下出现局域相，并探讨其与多体局域化相的相似性。
We study a one-dimensional disordered Bose fluid using bosonization, the replica method and a nonperturbative functional renormalization-group approach. We find that the Bose-glass phase is described by a fully attractive strong-disorder fixed point characterized by a singular disorder correlator whose functional dependence assumes a cuspy form that is related to the existence of metastable states. At nonzero momentum scale $k$, quantum tunneling between the ground state and low-lying metastable states leads to a rounding of the cusp singularity into a quantum boundary layer (QBL). The width o…
We study the weakly disordered Bose-Hubbard model on a cubic lattice through a one-loop renormalization group analysis of the corresponding effective field theory which is explicitly derived by combining a strong-coupling expansion with a replica average over the disorder. The method is applied not only to generic uncorrelated on-site disorder but also to simultaneous hopping disorder correlated with the differences of adjacent disorder potentials. Such correlations are inherent in fine-grained optical speckle potentials used as a source of disorder in optical lattice experiments. As a result …
We investigate the properties of a three-dimensional homogeneous dipolar Bose gas in a weak random potential with a Gaussian correlation function at finite temperature. Using the Bogoliubov theory (beyond the mean field), we calculate the superfluid and the condensate fractions in terms of the interaction strength on the one hand and in terms of the width and the strength of the disorder on the other. The influence of the disordered potential on the second order correlation function, the ground state energy and the chemical potential is also analyzed. We find that for fixed strength and correl…
The Casimir effect in a dilute Bose gas confined between two planar walls is investigated in the canonical ensemble at zero temperature by means of Cornwall-Jackiw-Tomboulis effective action approach within the improved Hartree-Fock approximation. Our results show that: (i) the Casimir energy and the resulting Casimir force in the canonical ensemble remarkably differ from those in the grand canonical ensemble; (ii) when the distance between two planar walls increases, the Casimir energy and Casimir force decay in accordance with a half-integer power law in the canonical ensemble instead of an …
The Bose glass (BG) phase is the Griffiths region of the disordered Bose Hubbard model (BHM), characterized by finite, quasi-superfluid clusters within a Mott insulating background. We propose to utilize this characterization to identify the complete zero-temperature phase diagram of the disordered BHM in $d\ge2$ dimensions by analyzing the geometric properties of what we call superfluid (SF) clusters, which are defined to be clusters of sites with non-integer expectation values for the local boson occupation number. The Mott insulator (MI) phase then is the region in the phase diagram where n…
Upper bound for the grand canonical free energy of the Bose gas in the Gross-Pitaevskii limit for general interaction potentials
本文将 Gross-Pitaevskii 极限下玻色气体巨正则自由能上界的结果推广到含硬核的一般相互作用势，利用 Jastrow 因子建模微观关联并利用不同长度尺度导致的能量抵消完成证明。
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 …
Anderson localization was first investigated in the context of electrons in solids. One of the successes was in explaining the puzzle of negative magneto-resistance - as early as the 1940s it had been observed that electron diffusion rates in some materials can increase with the application of a magnetic field. Anderson localization has now been demonstrated in ultra-cold atomic gases. We present a theoretical study of the two-dimensional ultra-cold Bose gas in the presence of disorder, to which we apply a synthetic magnetic field. We demonstrate that, in the ballistic transport regime this le…
Finite-temperature superfluid depletion of disordered Bose gases
该研究通过非均匀博格里乌夫理论，计算了有限温度下无序玻色气体的正常流体密度，并给出了无序修正的解析表达式。
The full statistical distribution of the superfluid fraction characterizing one-dimensional Bose gases in random potentials is discussed. Rare configurations with extreme fluctuations of the disorder potential can fragment the condensate and reduce the superfluid fraction to zero. The resulting bimodal probability distribution for the superfluid fraction is calculated numerically in the quasi-1D mean-field regime of ultracold atoms in laser speckle potentials. Using extreme-value statistics, an analytical scaling of the zero-superfluid probability as function of disorder strength, disorder cor…
Disorder modifies the sound-wave excitation spectrum of Bose-Einstein condensates. We consider the classical hydrodynamic limit, where the disorder correlation length is much longer than the condensate healing length. By perturbation theory, we compute the phonon lifetime and correction to the speed of sound. This correction is found to be negative in all dimensions, with universal asymptotics for smooth correlations. Considering in detail optical speckle potentials, we find a quite rich intermediate structure. This has consequences for the average density of states, particularly in one dimens…
We study the transport of an interacting Bose--Einstein condensate through a 1D correlated disorder potential. We use for this purpose the truncated Wigner method, which is, as we show, corresponding to the diagonal approximation of a semiclassical van Vleck-Gutzwiller representation of this many-body transport process. We also argue that semiclassical corrections beyond this diagonal approximation are vanishing under disorder average, thus confirming the validity of the truncated Wigner method in this context. Numerical calculations show that, while for weak atom-atom interaction strength And…
We present an approach to induce localization of a Bose-Einstein condensate in a one-dimensional lattice under the influence of unitary quantum walk evolution using disordered quantum coin operation. We introduce a discrete-time quantum walk model in which the interference effect is modified to diffuse or strongly localize the probability distribution of the particle by assigning a different set of coin parameters picked randomly for each step of the walk, respectively. Spatial localization of the particle/state is explained by comparing the variance of the probability distribution of the quan…
Previously we numerically showed that thermalization can occur in an oscillating Bose-Einstein condensate (BEC) with a disordered harmonic trap when healing length $ξ$ of the condensate is shorter than the correlation length $σ_{D}$ of the disorder [see, for example, the experiment reported in Phys. Rev. A \textbf{82}, 033603 (2010)]. In this work, we investigate the weakly interacting or Anderson localization regime $ξ>σ_{D}$ and show that the oscillating BEC can also exhibit a relaxation process from nonequilibrium to equilibrium. In such an isolated quantum system, energy and particle numbe…
Disorder effects in the thermodynamic properties of a ideal Bose gas confined in a semi-infinite multi-layer structure %described by $M$ permeable barriers within a box of thickness $L$ and infinite lateral extent, are analyzed. The layers are first modeled by a periodic array of $M$ Dirac delta-functions of equal intensity. Then, we introduce structural and compositional disorder, as well as a random set of layer vacancies in the system to calculate the internal energy, chemical potential and the specific heat for different configurations. Whereas structural and compositional disorder does no…
We simulate ultra-cold interacting Bosons in quasi-one-dimensional, incommensurate optical lattices. In the tight-binding limit, these lattices have pseudo-random on-site energies and thus can potentially lead to Anderson localization. We explore the parameter regimes that lead to Anderson localization and investigate the role of repulsive interactions, harmonic confinement and finite temperature. We find that interactions can obscure the exponential localization characteristic of Anderson localization, thus impeding the direct observation of this phenomenon when interactions are present.
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…
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…
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