Disordered Bose-Einstein Condensates in Quasi-One-Dimensional Magnetic Microtraps

Wang, Daw-Wei; Lukin, Mikhail D.; Demler, Eugene

doi:10.1103/physrevlett.92.076802

Cited by 99 publications

(127 citation statements)

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“…Generally speaking, disorder in quantum systems has been a subject of intense theoretical and experimental studies. In the context of ultracold atomic gases disorder may result from the roughness of a magnetic trap [469] or a magnetic microtrap [470]. However, it is important to note that controlled disorder (or quasi-disorder) may also be created by means of different techniques.…”

Section: Matter-waves In Disordered Potentialsmentioning

confidence: 99%

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

2008

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Abstract. The aim of the present review is to introduce the reader to some of the physical notions and of the mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the general framework, we discuss the prototypical models that are relevant to this setting for different dimensions and different potentials confining the atoms. We analyze some of the model properties and explore their typical wave solutions (plane wave solutions, bright, dark, gap solitons, as well as vortices). We then offer a collection of mathematical methods that can be used to understand the existence, stability and dynamics of nonlinear waves in such BECs, either directly or starting from different types of limits (e.g., the linear or the nonlinear limit, or the discrete limit of the corresponding equation). Finally, we consider some special topics involving more recent developments, and experimental setups in which there is still considerable need for developing mathematical as well as computational tools.PACS numbers: 03.75. Kk, 03.75.Lm, 05.45 • EP: Ermakov-Pinney (Equation)• GP: Gross-Pitaevskii (Equation)• KdV: Korteweg-de Vries (Equation)• LS: Lyapunov-Schmidt (Technique)• MT: Magnetic Trap• NLS: Nonlinear Schrödinger (Equation)• NPSE: Non-polynomial Schrödinger Equation IntroductionThe phenomenon of Bose-Einstein condensation is a quantum phase transition originally predicted by Bose [1] and Einstein [2,3] in 1924. In particular, it was shown that below a critical transition temperature T c , a finite fraction of particles of a boson gas (i.e., whose particles obey the Bose statistics) condenses into the same quantum state, known as the Bose-Einstein condensate (BEC). Although BoseEinstein condensation is known to be a fundamental phenomenon, connected, e.g., to superfluidity in liquid helium and superconductivity in metals (see, e.g., Ref.[4]), BECs were experimentally realized 70 years after their theoretical prediction: this major achievement took place in 1995, when different species of dilute alkali vapors confined in a magnetic trap (MT) were cooled down to extremely low temperatures [5][6][7], and has already been recognized through the 2001 Nobel prize in Physics [8,9]. This first unambiguous manifestation of a macroscopic quantum state in a manybody system sparked an explosion of activity, as reflected by the publication of several thousand papers related to BECs since then. Nowadays there exist more than fifty experimental BEC groups around the world, while an enormous amount of theoretical work has followed and driven the experimental efforts, with an impressive impact on many branches of Physics.From a theoretical standpoint, and for experimentally relevant conditions, the static and dynamical properties of a BEC can be described by means of an effective mean-field equation known as the Gross-Pitaevskii (GP) equation [10,11]. This is a variant of the famous nonlinear Schrödinger (NLS) equation [12] (incorporating an external potential used to confine th...

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Section: Matter-waves In Disordered Potentialsmentioning

confidence: 99%

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

2008

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“…[1] It was shown that a quantum phase transition between the superfluid and the insulating Bose-Glass phase can be achieved under realistic experimental conditions. [2] Furthermore, recent transport measurements of vortex dynamics in hightemperature superconducting cuprates have shown evidence of a Bose-Glass transition. [3] In the context of quantum antiferromagnetism, recent measurements of the magnetization and the specific heat have suggested a glassy regime in proximity to a magnetic-field-induced triplon condensate.…”

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Bose-Glass Phases in Disordered Quantum Magnets

2005

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In disordered spin systems with antiferromagnetic Heisenberg exchange, transitions into and out of a magnetic-field-induced ordered phase pass through a unique regime. Using quantum Monte Carlo simulations to study the zero-temperature behavior, these intermediate regions are determined to be a Bose-Glass phase. The localization of field-induced triplons causes a finite compressibility and hence glassiness in the disordered phase.PACS numbers: 73.43. Nq, 75.10.Nr, 75.50.Lk, 75.50.Ee Bose-Glass phenomena have recently been reported in a variety of disordered quantum many-body systems, including trapped atoms, vortex lattices, and Heisenberg antiferromagnets. These experiments have in common signatures of finite compressibility in proximity to a BoseEinstein condensate. In atomic waveguides, the fragmentation of such a condensate is caused by a random modulation of the local atomic density.[1] It was shown that a quantum phase transition between the superfluid and the insulating Bose-Glass phase can be achieved under realistic experimental conditions.[2] Furthermore, recent transport measurements of vortex dynamics in hightemperature superconducting cuprates have shown evidence of a Bose-Glass transition. [3] In the context of quantum antiferromagnetism, recent measurements of the magnetization and the specific heat have suggested a glassy regime in proximity to a magnetic-field-induced triplon condensate. [4,5] However, a theoretical understanding of the Bose-Glass phenomena in quantum spin systems based on a microscopic Hamiltonian is still lacking.In this letter, we study how disorder affects the quantum phase transition between a valence bond solid and a magnetic-field-induced Néel-ordered phase in an antiferromagnetic Heisenberg spin system. Using largescale quantum Monte Carlo simulations down to ultralow temperatures, we observe that in cubic dimer systems with bond randomness, there is an intermediate Bose-Glass regime, separating an antiferromagnetically ordered phase of condensed triplons from a spin liquid phase of localized triplons at low magnetic fields. For weak inter-dimer couplings, this model can be mapped onto a lattice boson model with random potential.[6] The Néel-ordered phase of delocalized triplons corresponds to the superfluid regime in the bosonic language. It is characterized by a finite staggered magnetization perpendicular to the applied magnetic field m ⊥ s , analogous to the superfluid order parameter in a bosonic system. The Bose-Glass phase is distinguished by a finite slope of the uniform magnetization m u as a function of the applied magnetic field, i.e., compressible bosons, whereas the order parameter m ⊥ s vanishes.In order to probe these observables and thus study emerging quantum phase transitions in such disordered quantum magnets, we apply the stochastic series expansion (SSE) quantum Monte Carlo (QMC) method. [7] In particular, the directed-loop algorithm is used to minimize bounce probabilities in the loop construction when magnetic fields are applied to the system.[8...

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“…(see, e.g., [1,2,3,4,5,6], and references therein). Recently, research on disordered bosons is strongly stimulated by the possibility of controlled experiments with ultracold atomic systems [7,8].Commensurability is relevant for the system of lattice bosons with the off-diagonal disorder (random hopping amplitude or on-site repulsion) and exact particlehole symmetry (taking place in the limit of large filling factor) [9]. It leads to a new type of insulator, incompressible and gapless Mott glass (MG) [10] in place of incompressible gapped Mott insulator (MI).…”

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Superfluid-Insulator Transition in a Commensurate One-Dimensional Bosonic System with Off-Diagonal Disorder

2005

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We study the nature of the superfluid-insulator quantum phase transition in a one-dimensional system of lattice bosons with off-diagonal disorder in the limit of large integer filling factor. Monte Carlo simulations of two strongly disordered models show that the universality class of the transition in question is the same as that of the superfluid-Mott-insulator transition in a pure system. This result can be explained by disorder self-averaging in the superfluid phase and applicability of the standard quantum hydrodynamic action. We also formulate the necessary conditions which should be satisfied by the stong-randomness universality class, if one exists.PACS numbers: 64.60. Cn, 03.75.Hh, 05.30.Jp, An interplay between commensurability, interactions, and disorder in the superfluid-insulator quantum phase transition is a challenging theoretical problem with applications to such diverse physical systems as 4 He in porous media and aerogels, superfluid films on various substrates, Josephson junction arrays, granular superconductors, disordered magnets, etc. (see, e.g., [1,2,3,4,5,6], and references therein). Recently, research on disordered bosons is strongly stimulated by the possibility of controlled experiments with ultracold atomic systems [7,8].Commensurability is relevant for the system of lattice bosons with the off-diagonal disorder (random hopping amplitude or on-site repulsion) and exact particlehole symmetry (taking place in the limit of large filling factor) [9]. It leads to a new type of insulator, incompressible and gapless Mott glass (MG) [10] in place of incompressible gapped Mott insulator (MI). In twodimensional (2D) systems, changing the nature of the insulating phase results in the new universality class of the superfluid-insulator (SF-I) transition. The SF-MG transition is characterized by the dynamical critical exponent 1 < z < 2 different from z = 1 for the SF-MI point in a perfect system [5]. A similar situation is expected in 3D.Surprisingly, very little is known for fact about the 1D case apart from perturbative renormalization group (RG) arguments. On the superfluid side of the transition, one can use the instanton language [11] in terms of which weak off-diagonal disorder does not seem to be relevant, leading only to the inhomogeneity of the microscopic stiffness in the equivalent (1+1)D classical XY model. Recently, Altman et al.[6] argued on the basis of the spatial RG analysis that while small off-diagonal disorder is indeed irrelevant for the SF-MG criticality, there should exist also the strong-randomness fixed point. We are not aware of any large-scale numerical simulations attempting to study the SF-MG criticality in the strongly disordered system.The main observable of interest in 1D systems is the Luttinger-liquid parameter g = π √ Λκ, where Λ is the superfluid stiffness and κ is the compressibility. There is a "smoking gun" signature in the behavior of g at the critical point which allows to discriminate between different scenarios of the phase transition. If the SF-MG transi...

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Disordered Bose-Einstein Condensates in Quasi-One-Dimensional Magnetic Microtraps

Cited by 99 publications

References 14 publications

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

Bose-Glass Phases in Disordered Quantum Magnets

Superfluid-Insulator Transition in a Commensurate One-Dimensional Bosonic System with Off-Diagonal Disorder

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