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Geometrical approach to hydrodynamics and low-energy excitations of spinor condensates

Barnett, Ryan and Podolsky, Daniel and Refael, Gil (2009) Geometrical approach to hydrodynamics and low-energy excitations of spinor condensates. Physical Review B, 80 (2). 024420. ISSN 1098-0121. doi:10.1103/PhysRevB.80.024420.

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In this work, we derive the equations of motion governing the dynamics of spin-F spinor condensates. We pursue a description based on standard physical variables (total density and superfluid velocity), alongside 2F “spin nodes:” unit vectors that describe the spin-F state and also exhibit the point-group symmetry of a spinor condensate's mean-field ground state. In the first part of our analysis, we derive the hydrodynamic equations of motion, which consist of a mass continuity equation, 2F Landau-Lifshitz equations for the spin nodes, and a modified Euler equation. In particular, we provide a generalization of the Mermin-Ho relation to spin one and find an analytic solution for the skyrmion texture in the incompressible regime of a spin-half condensate. In the second part, we study the linearized dynamics of spinor condensates. We provide a general method to linearize the equations of motion based on the symmetry of the mean-field ground state using the local stereographic projection of the spin nodes. We also provide a simple construction to extract the collective modes from symmetry considerations alone akin to the analysis of vibrational excitations of polyatomic molecules. Finally, we present a mapping between the spin-wave modes, and the wave functions of electrons in atoms, where the spherical symmetry is degraded by a crystal field. These results demonstrate the beautiful geometrical structure that underlies the dynamics of spinor condensates.

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Additional Information:© 2009 The American Physical Society. Received 12 March 2009; revised 10 June 2009; published 21 July 2009. It is a pleasure to acknowledge useful conversations with E. Demler, T.-L. Ho, I. Klich, A. Lamacraft, and especially A. Turner. We would like to acknowledge the hospitality of the KITP, supported by NSF under Grant No. PHY05-51164. We are also grateful for support from the Sherman Fairchild Foundation (RB); the Packard and Sloan Foundations, the Institute for Quantum Information under NSF under Grants No. PHY-0456720 and No. PHY-0803371, and The Research Corporation Cottrell Scholars program (GR); and CIFAR, NSERC, and CRC (DP). 05.30.Jp Boson systems (quantum statistical mechanics) 03.75.Hh Static properties of Bose-Einstein condensates 03.75.Kk Dynamic properties of Bose-Einstein condensates 03.75.Mn Multicomponent condensates; spinor condensates
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
David and Lucile Packard FoundationUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Research CorporationUNSPECIFIED
Canadian Institute for Advanced ResearchUNSPECIFIED
Natural Sciences and Engineering Research Council of CanadaUNSPECIFIED
Canada Research ChairsUNSPECIFIED
Subject Keywords:Bose-Einstein condensation; crystal field interactions; ground states; hydrodynamics; molecular configurations; spin waves; vibrational states; wave functions
Issue or Number:2
Record Number:CaltechAUTHORS:20090817-144813522
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Official Citation:Geometrical approach to hydrodynamics and low-energy excitations of spinor condensates Ryan Barnett, Daniel Podolsky, and Gil Refael, Phys. Rev. B 80, 024420 (2009), DOI:10.1103/PhysRevB.80.024420
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15091
Deposited By: George Porter
Deposited On:08 Sep 2009 21:40
Last Modified:08 Nov 2021 23:16

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