Pinning of Vortices in a Bose-Einstein Condensate by an Optical Lattice

Reijnders, J. W.; Duine, R. A.

doi:10.1103/physrevlett.93.060401

Cited by 84 publications

(99 citation statements)

References 34 publications

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“…3.6.2) becomes relevant, purely 3D discrete vortices can be constructed [463][464][465]. An interesting twist of the pinning of vortices (which has been observed experimentally [466]) is the case when a vortex lattice is induced to transition from a triangular Abrikosov vortex lattice to a square lattice by an optical lattice [467,468]. Another type of vortex lattice manipulation is the use of large-amplitude oscillations to induce structural phase transitions (e.g., from triangular to orthorhombic) [39].…”

Section: Periodic 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: Periodic Potentialsmentioning

confidence: 99%

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

2008

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“…Colloidal crystallization on periodic substrates may prove to be a useful method to create novel colloidal structures for photonic band gap device or filter applications [11]. Additionally, colloids are an ideal model system for studying collective particle states as well as topological defects generated on periodic substrates, which is relevant to a variety of other systems including atoms and molecules adsorbed on surfaces [12,13], superconducting vortices interacting with periodic pinning sites [14], or vortices in Bose-Einstein condensates interacting with periodic optical traps [15].An open question is what kind of ordering and melting transitions occur for CMCs that are not pure, but are composed of a mixture of n-mers and m-mers, where m = n + 1. In this work we show that when the number of colloids N c is a rational, noninteger multiple p of the number of substrate minima N s , a variety of novel crystalline and partially crystalline colloidal states form which cannot occur at integer fillings.…”

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confidence: 99%

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confidence: 99%

Ordering and melting in colloidal molecular crystal mixtures

Reichhardt

2005

Phys. Rev. E

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We show in simulations that a rich variety of novel orderings such as pinwheel and star states can be realized for colloidal molecular crystal mixtures at rational ratios of the number of colloids to the number of minima from an underlying periodic substrate. These states can have multi-step melting transitions and also show coexistence in which one species disorders while the other species remains orientationally ordered. For other mixtures, only partially ordered or frustrated states form. PACS numbers: 82.70.DdRecently a new type of colloidal state termed colloidal molecular crystals (CMCs) for colloids interacting with two-dimensional periodic substrates has been proposed in simulations [1,2], observed experimentally [3], and studied theoretically [4,5]. CMCs occur when the number of colloids is an integer multiple n of the number of substrate minima, and the n colloids residing in each minimum form a composite n-mer object such as a dimer or trimer. Neighboring n-mers can have an orientational ordering relative to one another in addition to the spatially periodic ordering imposed by the underlying substrate. The CMCs were named in analogy with molecular crystals, in which the molecules have orientational as well as crystalline ordering.CMCs exhibit interesting two-step melting transitions. The first stage of melting occurs when the n-mers begin to rotate and lose orientational ordering, while in the second stage, the n-mers dissolve and individual colloids begin to diffuse throughout the sample [1,3]. The orientational melting was shown to fall into an Ising-like transition class [4,5]. A reentrant disordering can also occur in which an orientationally ordered n-mer state disorders when the substrate strength is increased [2,3]. Recent theoretical work has shown that the orientational ordering arises due to the anisotropic multipole interactions between the n-mers [4]. The reentrant disordering occurs when the n-mer is compressed by the increasing substrate force, decreasing both the distance between the colloids and the multipole moment, until the multipole interaction energy drops below the thermal energy.When the substrate is varied, new states emerge. Studies of colloids interacting with arrays of small traps embedded in a smooth background have shown coexistence between an interstitial colloidal liquid and a pinned ordered solid [6]. In the case of colloids driven over twodimensional (2D) substrates, interesting locking effects occur when the colloids move preferentially along certain symmetry directions of the underlying lattice [7][8][9][10]. Colloidal crystallization on periodic substrates may prove to be a useful method to create novel colloidal structures for photonic band gap device or filter applications [11]. Additionally, colloids are an ideal model system for studying collective particle states as well as topological defects generated on periodic substrates, which is relevant to a variety of other systems including atoms and molecules adsorbed on surfaces [12,13], superconducting vortices int...

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“…Experimental evidence for a coexistence of a liquid and a solid has been obtained in a system where colloids located at pinning sites remain immobile while colloids in the unpinned interstitial regions are mobile [19]. Related systems that can be modeled as repulsive particles interacting with a periodic substrate include vortices in superconductors with artificial pinning sites [24,25] and vortices in BoseEinstein condensates interacting with optical traps [26].…”

Section: Introductionmentioning

confidence: 99%

Heterogeneities and topological defects in two-dimensional pinned liquids

Lin

Reichhardt²,

Nussinov³

et al. 2006

Phys. Rev. E

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We simulate a model of repulsively interacting colloids on a commensurate two-dimensional triangular pinning substrate where the amount of heterogeneous motion that appears at melting can be controlled systematically by turning off a fraction of the pinning sites. We correlate the amount of heterogeneous motion with the average topological defect number, time dependent defect fluctuations, colloid diffusion, and the form of the van Hove correlation function. When the pinning sites are all off or all on, the melting occurs in a single step. When a fraction of the sites are turned off, the melting becomes considerably broadened and signatures of a two-step melting process appear. The noise power associated with fluctuations in the number of topological defects reaches a maximum when half of the pinning sites are removed, and the noise spectrum has a pronounced 1/f α structure in the heterogeneous regime. We find that regions of high mobility are associated with regions of high dislocation densities.

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Pinning of Vortices in a Bose-Einstein Condensate by an Optical Lattice

Cited by 84 publications

References 34 publications

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

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

Ordering and melting in colloidal molecular crystal mixtures

Heterogeneities and topological defects in two-dimensional pinned liquids

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