© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Acta Physica Polonica A

Bose-Einstein Condensates in Optical Lattices

Wojciech Wasilewski, Marek Trippenbach, Kazimierz Rza̧żewski

Published Jan 1, 2002• 5 citations

Abstract

c h a and K. R z¨âew ski b a I nst i t ut e of E xp eri m ental P hysi cs, Opti cs D i vi sion W arsaw Uni versi ty , Hoâa 69, 00-681 W arsaw, Pol an d b Center for Theo reti cal Physi cs, Pol ish Aca dem y of Sciences al .Lo tni k §w 32/ 46, 02-668 W arsaw, Po l and W e st udy an ult ra cold dilute gas of bosonic ato ms in an optical lattice induced by intersecting laser b eams.A s a Ùrst appro ximation w e neglect conÙning p otential and atom {atom interactions.In t his case the Gross{ Pitae vs ki j equation reduces to simple Mathieu equation.U pon cho osing p erio dic boundary conditions this problem has well know n perio dic solution.T his simple picture allow s to demonstrate lo cali zation of the w ave packet and formation of the band structure.W e calcula te spectrum of the excited states as a function of the strength of mo dulati ng p otential and using a standard adiabatici ty criterion w e predict the most e£cient w ay to ramp up optical lattice , w ithout higher state excitation.Finall y, we discuss the in Ûuence of the atom{atom interaction (nonlinea rity ) on the adiabatic ity of the pro cess.

DOI: 10.12693/aphyspola.101.47

Related papers

Interacting bosons in an optical lattice

Ch. Moseley, Oleksandr Fialko, K. Ziegler

Several models of a strongly interacting Bose gas in an optical lattice are studied within the functionalintegral approach. The one-dimensional Bose gas is briefly discussed. Then the Bose-Einstein condensate and the Mott insulator of a three-dimensional Bose gas are described in mean-field approximation, and the corresponding phase diagrams are evaluated. Other characteristic quantities, like the spectrum of quasiparticle excitations and the static structure factor, are obtained from Gaussian fluctuations around the mean-field solutions. We discuss the role of quantum and thermal fluctuations, and determine the behavior of physical quantities in terms of density and temperature of the Bose gas. In particular, we study the dilute limit, where the mean-field equation becomes the Gross-Pitaevskii equation. This allows us to extend the Gross-

•Nov 27, 2012•17 citations

Statistical Physics of Bose-Einstein Condensation

Mariusz Gajda, Kazimierz Rza̧żewski

cs, Po l i sh Ac ademy of Sciences al .Lo tni k §w 32/ 46, 02-668 W arsaw, Po l and b Center for Theo reti cal Physi cs, Po l ish Aca demy of Sciences al .Lo tni k §w 32/ 46, 02-668 W arsaw, Po l and ( Recei ved Novem ber 15, 2001)W e rev iew a pr ogress i n un derstandi ng of statisti cal prop erties of a quantu m degenerate Bose gas.W e show how the Ma xw ell demon ensem ble helps to compute Ûuctuations of the Bose{ Eins tein condensate of an ideal Bose gas according to the micro canoni cal ensemble.T hen, we review a metho d of measuring these Ûuctuations.U sing a solubl e mo del of interacting Bose gas w e also stress the imp ortance of higher-order correlation functions.Finall y, w e review our no vel computational metho d of studying an interacting Bose gas near its critical temp erature.

Acta Physica Polonica A•Dec 1, 2001•2 citations

Bose-Einstein condensates in optical lattices: band-gap structure, solitons, and vortices

Elena A. Ostrovskaya

We give an overview of localization effects of Bose-Einstein condensates in optical lattices. In particular, we discuss the structure, dynamics, and feasibility of generation and detection of matter-wave solitons and vortices in two-dimensional lattices

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jan 25, 2006•0 citations

Vortex Lines in Motion

Iwo Białynicki‐Birula, Tomasz Mloduchowski, Tomasz Radożycki +1 more

bl ¨ska 51, 01-737 W arsaw, Po l and T. Rado ây ck i Departm ent of Physi cs, W arsaw Uni versi ty , Ho âa 69, 00 -681 W arsaw, Po l and and C. Ïl iw a Center f or Theo reti cal Physi cs, al .Lo tni k §w 32/ 46, 02-668 Warsaw, Po la nd ( Recei ved Novem ber 15, 2001) W e ex tend our pre viou s analysi s of the motion of vortex lines in wave me chanics to the case of more ela borate vortex patterns and to a rotatin g harmonic trap .PAC S numb ers: 03.65.

Acta Physica Polonica A•Dec 1, 2001•15 citations

Bose-Einstein Condensates in Optical Lattices with Higher-Order Interactions

张爱霞, 薛具奎

在多维的光格子的 Bose 爱因斯坦冷凝物的高顺序的相互作用被讨论经分解并且数字地。健全速度和 Bloch 波浪的稳定性上的高顺序的原子相互作用的效果强烈取决于格子力量，这被表明。面对高顺序的效果，更紧密、高度维的格子被证实是为维持系统的精力充沛的稳定性的二个积极因素，并且 Bloch 的动态不稳定性飘动能与精力充沛的不稳定性同时发生。另外，我们发现高顺序的相互作用展出远程的行为，在一个倾斜的光格子的长寿协调 Bloch 摆动存在。我们的结果提供一个有效方法在光格子探查高顺序的相互作用。

理论物理通讯：英文版•Apr 15, 2012•0 citations

Dynamics of Bose-Einstein condensates in optical lattices

O. Morsch, Markus K. Oberthaler

Matter waves inside periodic potentials are well known from solid-state physics, where electrons interacting with a crystal lattice are considered. Atomic Bose-Einstein condensates inside light-induced periodic potentials (optical lattices) share many features with electrons in solids, but also with light waves in nonlinear materials and other nonlinear systems. Generally, atom-atom interactions in Bose-Einstein condensates lead to rich and interesting nonlinear effects. Furthermore, the experimental control over the parameters of the periodic potential and the condensate make it possible to enter regimes inaccessible in other systems. In this review, an introduction to the physics of ultracold bosonic atoms in optical lattices is given and an overview of the theoretical and experimental advances to date.

Reviews of Modern Physics•Feb 27, 2006•1,650 citations

c h a and K. R z¨âew ski b a I nst i t ut e of E xp eri m ental P hysi cs, Opti cs D i vi sion W arsaw Uni versi ty , Hoâa 69, 00-681 W arsaw, Pol an d b Center for Theo reti cal Physi cs, Pol ish Aca dem y of Sciences al .Lo tni k §w 32/ 46, 02-668 W arsaw, Po l and W e st udy an ult ra cold dilute gas of bosonic ato ms in an optical lattice induced by intersecting laser b eams.A s a Ùrst appro ximation w e neglect conÙning p otential and atom {atom interactions.In t his case the Gross{ Pitae vs ki j equation reduces to simple Mathieu equation.U pon cho osing p erio dic boundary conditions this problem has well know n perio dic solution.T his simple picture allow s to demonstrate lo cali zation of the w ave packet and formation of the band structure.W e calcula te spectrum of the excited states as a function of the strength of mo dulati ng p otential and using a standard adiabatici ty criterion w e predict the most e£cient w ay to ramp up optical lattice , w ithout higher state excitation.Finall y, we discuss the in Ûuence of the atom{atom interaction (nonlinea rity ) on the adiabatic ity of the pro cess.

Several models of a strongly interacting Bose gas in an optical lattice are studied within the functionalintegral approach. The one-dimensional Bose gas is briefly discussed. Then the Bose-Einstein condensate and the Mott insulator of a three-dimensional Bose gas are described in mean-field approximation, and the corresponding phase diagrams are evaluated. Other characteristic quantities, like the spectrum of quasiparticle excitations and the static structure factor, are obtained from Gaussian fluctuations around the mean-field solutions. We discuss the role of quantum and thermal fluctuations, and determine the behavior of physical quantities in terms of density and temperature of the Bose gas. In particular, we study the dilute limit, where the mean-field equation becomes the Gross-Pitaevskii equation. This allows us to extend the Gross-

cs, Po l i sh Ac ademy of Sciences al .Lo tni k §w 32/ 46, 02-668 W arsaw, Po l and b Center for Theo reti cal Physi cs, Po l ish Aca demy of Sciences al .Lo tni k §w 32/ 46, 02-668 W arsaw, Po l and ( Recei ved Novem ber 15, 2001)W e rev iew a pr ogress i n un derstandi ng of statisti cal prop erties of a quantu m degenerate Bose gas.W e show how the Ma xw ell demon ensem ble helps to compute Ûuctuations of the Bose{ Eins tein condensate of an ideal Bose gas according to the micro canoni cal ensemble.T hen, we review a metho d of measuring these Ûuctuations.U sing a solubl e mo del of interacting Bose gas w e also stress the imp ortance of higher-order correlation functions.Finall y, w e review our no vel computational metho d of studying an interacting Bose gas near its critical temp erature.

在多维的光格子的 Bose 爱因斯坦冷凝物的高顺序的相互作用被讨论经分解并且数字地。健全速度和 Bloch 波浪的稳定性上的高顺序的原子相互作用的效果强烈取决于格子力量，这被表明。面对高顺序的效果，更紧密、高度维的格子被证实是为维持系统的精力充沛的稳定性的二个积极因素，并且 Bloch 的动态不稳定性飘动能与精力充沛的不稳定性同时发生。另外，我们发现高顺序的相互作用展出远程的行为，在一个倾斜的光格子的长寿协调 Bloch 摆动存在。我们的结果提供一个有效方法在光格子探查高顺序的相互作用。

Matter waves inside periodic potentials are well known from solid-state physics, where electrons interacting with a crystal lattice are considered. Atomic Bose-Einstein condensates inside light-induced periodic potentials (optical lattices) share many features with electrons in solids, but also with light waves in nonlinear materials and other nonlinear systems. Generally, atom-atom interactions in Bose-Einstein condensates lead to rich and interesting nonlinear effects. Furthermore, the experimental control over the parameters of the periodic potential and the condensate make it possible to enter regimes inaccessible in other systems. In this review, an introduction to the physics of ultracold bosonic atoms in optical lattices is given and an overview of the theoretical and experimental advances to date.