Bose-Einstein quantum phase transition in an optical lattice model

Michael Aizenman; Elliott H. Lieb; Robert Seiringer; Jan Philip Solovej; Jakob Yngvason

doi:10.1103/PhysRevA.70.023612

Bose-Einstein quantum phase transition in an optical lattice model

Michael Aizenman, Elliott H. Lieb, Robert Seiringer, Jan Philip Solovej, Jakob Yngvason

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Abstract

An optical lattice model developed that is similar to the Bose-Hubbard model to describe the transition between Bose-Einstein condensation (BEC) and a Mott insulator state was analyzed. It was found that the system was a hard core lattice gas at half of the maximum density and the optical lattice was modeled by a periodic potential of strength λ. It was also observed that the interparticle interaction was essential for this transition that occurred even in the ground state. The results show that all the essential features could be proved rigorously such as the existence of BEC for small λ and its suppression for a large λ.

Original language	English (US)
Article number	023612
Pages (from-to)	023612-1-0236121-2
Journal	Physical Review A - Atomic, Molecular, and Optical Physics
Volume	70
Issue number	2
DOIs	https://doi.org/10.1103/PhysRevA.70.023612
State	Published - Aug 2004

All Science Journal Classification (ASJC) codes

Atomic and Molecular Physics, and Optics

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10.1103/PhysRevA.70.023612

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title = "Bose-Einstein quantum phase transition in an optical lattice model",

abstract = "An optical lattice model developed that is similar to the Bose-Hubbard model to describe the transition between Bose-Einstein condensation (BEC) and a Mott insulator state was analyzed. It was found that the system was a hard core lattice gas at half of the maximum density and the optical lattice was modeled by a periodic potential of strength λ. It was also observed that the interparticle interaction was essential for this transition that occurred even in the ground state. The results show that all the essential features could be proved rigorously such as the existence of BEC for small λ and its suppression for a large λ.",

author = "Michael Aizenman and Lieb, {Elliott H.} and Robert Seiringer and Solovej, {Jan Philip} and Jakob Yngvason",

note = "Funding Information: We are grateful to Letizzia Wastavino for help with Figs. . The work was supported in part by NSF Grants Nos. PHY 9971149 (M.A.), PHY 0139984-A01 (E.H.L.), and DMS-0111298 (J.P.S.); by EU Grant No. HPRN-CT-2002-00277 (J.P.S. and J.Y.); by MaPhySto—A Network in Mathematical Physics and Stochastics funded by The Danish National Research Foundation (J.P.S.); and by grants from the Danish research council (J.P.S.).",

year = "2004",

month = aug,

doi = "10.1103/PhysRevA.70.023612",

language = "English (US)",

volume = "70",

pages = "023612--1--0236121--2",

journal = "Physical Review A - Atomic, Molecular, and Optical Physics",

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T1 - Bose-Einstein quantum phase transition in an optical lattice model

AU - Aizenman, Michael

AU - Lieb, Elliott H.

AU - Seiringer, Robert

AU - Solovej, Jan Philip

AU - Yngvason, Jakob

N1 - Funding Information: We are grateful to Letizzia Wastavino for help with Figs. . The work was supported in part by NSF Grants Nos. PHY 9971149 (M.A.), PHY 0139984-A01 (E.H.L.), and DMS-0111298 (J.P.S.); by EU Grant No. HPRN-CT-2002-00277 (J.P.S. and J.Y.); by MaPhySto—A Network in Mathematical Physics and Stochastics funded by The Danish National Research Foundation (J.P.S.); and by grants from the Danish research council (J.P.S.).

PY - 2004/8

Y1 - 2004/8

N2 - An optical lattice model developed that is similar to the Bose-Hubbard model to describe the transition between Bose-Einstein condensation (BEC) and a Mott insulator state was analyzed. It was found that the system was a hard core lattice gas at half of the maximum density and the optical lattice was modeled by a periodic potential of strength λ. It was also observed that the interparticle interaction was essential for this transition that occurred even in the ground state. The results show that all the essential features could be proved rigorously such as the existence of BEC for small λ and its suppression for a large λ.

AB - An optical lattice model developed that is similar to the Bose-Hubbard model to describe the transition between Bose-Einstein condensation (BEC) and a Mott insulator state was analyzed. It was found that the system was a hard core lattice gas at half of the maximum density and the optical lattice was modeled by a periodic potential of strength λ. It was also observed that the interparticle interaction was essential for this transition that occurred even in the ground state. The results show that all the essential features could be proved rigorously such as the existence of BEC for small λ and its suppression for a large λ.

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JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 2

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ER -

Bose-Einstein quantum phase transition in an optical lattice model

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