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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. https://resolver.caltech.edu/CaltechAUTHORS:20090817-144813522

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevB.80.024420DOIUNSPECIFIED
http://link.aps.org/doi/10.1103/PhysRevB.80.024420PublisherUNSPECIFIED
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
Funders:
Funding AgencyGrant Number
NSFPHY05-51164
Sherman Fairchild FoundationUNSPECIFIED
David and Lucile Packard FoundationUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
NSFPHY-0456720
NSFPHY-0803371
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
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20090817-144813522
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
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:08 Sep 2009 21:40
Last Modified:03 Oct 2019 00:54

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