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Acta Physica Polonica A

Vortex Lines in Motion

Iwo Białynicki‐Birula, Tomasz Mloduchowski, Tomasz Radożycki, Cezary Śliwa

Published Dec 1, 2001• 15 citations
Publisher

Abstract

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.

DOI
10.12693/aphyspola.100.29

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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.
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.
eri ment al Ph ysi cs, W arsaw Uni versi ty Ho âa 69, 00-681 W arszawa, Pol an d b G ra m mar School No 3, Conra da 6, 01-922 W arszawa, Pol and c Insti tute of Physi cs, W arsaw Uni versi ty of Technol ogy Ko szykowa 75, 00-662 W arszawa, Po l and ( Recei ved Febr uar y 19, 2002) W e rep or t on ver y pre cise measurements of t he absorption pro Ùle of the 326.1 nm resonance line of cadmium broadened by interactions w ith the ground state C d atoms under thermal equilib riu m.T he exp erimental
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.