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Optics Letters

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  • Editor: Anthony J. Campillo
  • Vol. 31, Iss. 4 — Feb. 15, 2006
  • pp: 519–521

Magic numbers and erratic level crossings of double-well Bose–Einstein condensates

Ying Wu and Xiaoxue Yang  »View Author Affiliations


Optics Letters, Vol. 31, Issue 4, pp. 519-521 (2006)
http://dx.doi.org/10.1364/OL.31.000519


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Abstract

By developing an approach by which we are able to quickly obtain spectra and eigenstates, we reveal for what is believed to be the first time the two novel phenomena of magic numbers and erratic level crossings in double-well Bose–Einstein condensates of N atoms. For N 27 and values of U J that are not too small (U is the two-body interaction strength, and J is the hopping parameter), systems with even atoms are shown to be much more stable than those with odd atoms, and hence even integers play a role in such systems as if they were the magic numbers of nuclei. For N 30 , erratic level crossings occur as N U J .

© 2006 Optical Society of America

OCIS Codes
(020.7010) Atomic and molecular physics : Laser trapping
(190.4180) Nonlinear optics : Multiphoton processes
(270.0270) Quantum optics : Quantum optics

ToC Category:
Quantum Optics

History
Original Manuscript: October 6, 2005
Revised Manuscript: November 2, 2005
Manuscript Accepted: November 6, 2005

Citation
Ying Wu and Xiaoxue Yang, "Magic numbers and erratic level crossings of double-well Bose-Einstein condensates," Opt. Lett. 31, 519-521 (2006)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-31-4-519


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  19. The Mathematica code is ⪡ Linear Algebra 'Tridiagonal'; n=to be designated; p[j−]≔j(j−1)(n+2−j)(n+1−j); q[j−]≔2j+un(n−1)+2j(n−j)u−lambda; k=Floor[n/2]+1; m=Floor[(n−1)/2]+1; a=Table[Switch[j−i,−1,up[2j],0,q[2j−2],1,u, −,0],i,k,j,k]; b=Table[Switch[j−i,−1,up[2j+1],0,q[2j−1],1,u, −,0],i,m,j,m]; Solve[Det[a]==0,lambda]; Solve[Det[b]==0,lambda] with the total atoms N denoted as n.
  20. The code {n=10,f[j−]≔Plot[Root[exp1&,j],{u,0,100}]; g[j−]≔Plot[Root[exp2&,j],{u,0,100}]; Show[f[1],...,f[6],g[1],...,g[5]]} plots in a single figure all 11 eigenvalues lambda versus u∊[0,100] for N=10. Root[exp1&,j] and Root[exp2&,j] are the solutions to Eqs. , respectively.

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