Atomic diffusion in an optical quasicrystal with five-fold symmetry

Guidoni, L.; Dépret, B.; Stefano, A. Di; Verkerk, P.

doi:10.1103/physreva.60.r4233

Cited by 53 publications

(45 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, it is important to note that controlled disorder (or quasi-disorder) may also be created by means of different techniques. These include the use of two-color superlattice potentials [471][472][473], the employment of so-called quasi-crystal (i.e., quasi-periodic) optical lattices in 2D or 3D [474][475][476], the use of impurity atoms trapped at random positions in the nodes of a periodic optical lattice [477], random phase masks [478], or optical speckle patterns [479][480][481]. The latter is a random intensity pattern which is produced by the scattering of a coherent laser beam from a rough surface (see, e.g., Ref.…”

Section: Matter-waves In Disordered Potentialsmentioning

confidence: 99%

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

2008

View full text Add to dashboard Cite

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...

show abstract

Section: Matter-waves In Disordered Potentialsmentioning

confidence: 99%

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

2008

View full text Add to dashboard Cite

show abstract

“…Indeed, these have proved to be highly controllable and versatile systems [7,8]. Hence, dissipative optical lattices have been used recently to study several effects, such as mechanical bistability [9,10], spatial diffusion in random or quasi-periodic structures [11,12,13,14], and stochastic resonance [15,16,17]. Ratchet effects have also been investigated in dissipative optical lattices with either a spatial [18,19], or a temporal asymmetry [20,21,22,23].…”

Section: Introductionmentioning

confidence: 99%

Controllable 3D atomic Brownian motor in optical lattices

Dion

Sjölund

Petra

et al. 2008

Eur. Phys. J. Spec. Top.

View full text Add to dashboard Cite

Abstract. We study a Brownian motor, based on cold atoms in optical lattices, where atomic motion can be induced in a controlled manner in an arbitrary direction, by rectification of isotropic random fluctuations. In contrast with ratchet mechanisms, our Brownian motor operates in a potential that is spatially and temporally symmetric, in apparent contradiction to the Curie principle. Simulations, based on the Fokker-Planck equation, allow us to gain knowledge on the qualitative behaviour of our Brownian motor. Studies of Brownian motors, and in particular ones with unique control properties, are of fundamental interest because of the role they play in protein motors and their potential applications in nanotechnology. In particular, our system opens the way to the study of quantum Brownian motors.

show abstract

“…• with its neighbours, and polarized in-plane [26,27]. The resultant potential landscape produced by equations (2.1) and (2.2) resembles Penrose tilings.…”

Section: Quasi-crystalline Structurementioning

confidence: 99%

“…On the other hand, in real space, particles experience a complete absence of translational symmetry; quasi-periodic lattices have been proposed as a means of simulating disorder [30]. The nature of the eigenstates [30,31] and transport properties [26,27,30] of particles in quasi-periodic lattices, be they bosons or fermions, are expected to resemble those of particles in a random medium, which is the topic of §6.…”

Section: Quasi-crystalline Structurementioning

confidence: 99%

A glimpse of quantum phenomena in optical lattices

Vishveshwara

2012

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

Optical lattices in cold atomic systems offer an excellent setting for realizing quantum condensed matter phenomena. Here, a glimpse of such a setting is provided for the nonspecialist. Some basic aspects of cold atomic gases and optical lattices are reviewed. Quantum many-body physics is explored in the case of interacting bosons on a lattice. Quantum behaviour in the presence of a potential landscape is examined for three different cases: a hexagonal lattice potential, a quasi-periodic potential and a disorder potential.

show abstract

Atomic diffusion in an optical quasicrystal with five-fold symmetry

Cited by 53 publications

References 9 publications

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

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

Controllable 3D atomic Brownian motor in optical lattices

A glimpse of quantum phenomena in optical lattices

Contact Info

Product

Resources

About