NDLI: Generalized Bose–Einstein Condensation

Content Provider	Springer Nature Link
Author	Mullin, William J. Sakhel, Asaad R.
Copyright Year	2011
Abstract	Generalized Bose–Einstein condensation (GBEC) involves condensates appearing simultaneously in multiple states. We review examples of the three types in an ideal Bose gas with different geometries. In Type I there is a discrete number of quantum states each having macroscopic occupation; Type II has condensation into a continuous band of states, with each state having macroscopic occupation; in Type III each state is microscopically occupied while the entire condensate band is macroscopically occupied. We begin by discussing Type I or “normal” BEC into a single state for an isotropic harmonic oscillator potential. Other geometries and external potentials are then considered: the “channel” potential (harmonic in one dimension and hard-wall in the other), which displays Type II, the “cigar trap” (anisotropic harmonic potential), and the “Casimir prism” (an elongated box), the latter two having Type III condensations. General box geometries are considered in an appendix. We particularly focus on the cigar trap, which Van Druten and Ketterle first showed had a two-step condensation: a GBEC into a band of states at a temperature T $_{ c }$ and another “one-dimensional” transition at a lower temperature T $_{1}$ into the ground state. In a thermodynamic limit in which the ratio of the dimensions of the anisotropic harmonic trap is kept fixed, T $_{1}$ merges with the upper transition, which then becomes a normal BEC. However, in the thermodynamic limit of Beau and Zagrebnov, in which the ratio of the boundary lengths increases exponentially, T $_{1}$ becomes fixed at the temperature of a true Type I phase transition. The effects of interactions on GBEC are discussed and we show that there is evidence that Type III condensation may have been observed in the cigar trap.
Starting Page	125
Ending Page	150
Page Count	26
File Format	PDF
ISSN	00222291
Journal	Journal of Low Temperature Physics
Volume Number	166
Issue Number	3-4
e-ISSN	15737357
Language	English
Publisher	Springer US
Publisher Date	2011-10-25
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Generalized Bose–Einstein condensation Bose–Einstein condensation Ultracold gases Trapped gases Phase transitions Bose gas Magnetism, Magnetic Materials Characterization and Evaluation of Materials Condensed Matter Physics
Content Type	Text
Resource Type	Article
Subject	Atomic and Molecular Physics, and Optics Condensed Matter Physics Materials Science

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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