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18 - Spinor-Dipolar Aspects of Bose-Einstein Condensation

from Part III - Condensates in Atomic Physics

Published online by Cambridge University Press:  18 May 2017

By
M. Ueda
Edited by
Nick P. Proukakis ,
David W. Snoke  and
Peter B. Littlewood
M. Ueda
Affiliation:
Department of Physics, University of Tokyo
Nick P. Proukakis
Affiliation:
Newcastle University
David W. Snoke
Affiliation:
University of Pittsburgh
Peter B. Littlewood
Affiliation:
University of Chicago
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Summary

Selected topics on spinor-dipolar aspects of Bose-Einstein condensation are overviewed. Spinor aspects include spin correlations, fragmentation, dynamical symmetries, and quantum mass acquisition. Dipolar aspects include magnetostriction, d-wave collapse, roton-maxon spectrum, supersolidity, and ferrofluidity. Finally, spinor-dipolar aspects concern the Einstein–de Haas effect and spontaneous mass and spin currents in the ground state.

Introduction

Bose-Einstein condensation is a phenomenon in which a macroscopic number of particles occupy the same single-particle state as a consequence of symmetrization of a many-body wave function and thereby quantum effects are amplified to the macroscopic level. The amplified single-particle state serves as a complex order parameter whose phase behaves as an emergent thermodynamic quantity, with its temporal and spatial variations giving the chemical potential and the superfluid velocity, respectively. If the interparticle interaction is repulsive, a Bose-Einstein condensate (BEC) acquires stability against excitations out of the condensate because they would cost the Fock exchange energy. This rigidity of the order parameter or the condensate wave function endows a BEC with several remarkable transport properties which are collectively known as superfluidity. In particular, the superfluid fraction can be 100% at zero temperature even though the condensate fraction is depleted due to interparticle interactions. Interparticle interactions also make excited particles phase-locked to the condensate, leading to Bogoliubov quasiparticles, which are the manifestation of phase-coherent particle– hole excitations.

When constituent particles have spin degrees of freedom, a BEC features magnetism and spin nematicity which conspire with superfluidity to produce a rich phase diagram. In the absence of an external magnetic field, the mean-field groundstate phase diagram includes two [1, 2], five [3, 4, 5], and eleven phases [6, 7] for spin-1, 2, and 3 BECs, respectively. BECs with spin degrees of freedom are called spinor condensates. Moreover, the magnetic dipole–dipole interaction (MDDI) between atoms lends distinct twists to spinor condensates because it is long-ranged and anisotropic in sharp contrast with other interactions, which are short-ranged and isotropic. In this chapter, we will present a brief overview on the spinordipolar aspects of BEC. An early experimental work of spinor BECs is reviewed in Ref. [8]. Later developments with an emphasis on theoretical aspects are described in Ref. [9]. Many-body physics of polarized dipolar gases is reviewed in Ref. [10].

Type
Chapter
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Universal Themes of Bose-Einstein Condensation , pp. 371 - 386
Publisher: Cambridge University Press
Print publication year: 2017

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References

[1] Ohmi, T., and Machida, K. 1998. Bose-Einstein condensation with internal degrees of freedom in alkali atom gases. J. Phys. Soc. Jpn., 67, 1822.Google Scholar
[2] Ho, T.-L. 1998. Spinor Bose condensates in optical trap. Phys. Rev. Lett., 81, 742.Google Scholar
[3] Koashi, M., and Ueda, M. 2000. Exact eigenstates and magnetic response of spin-1 and spin-2 Bose-Einstein condensates. Phys. Rev. Lett., 84, 1066.Google Scholar
[4] Ciobanu, C. V., Yip, S.-K., and Ho, T.-L. 2000. Phase diagrams of F=2 spinor Bose- Einstein condensates. Phys. Rev. A, 61, 033607.Google Scholar
[5] Ueda, M., and Koashi, M. 2002. Theory of spin-2 Bose-Einstein condensates: spin correlations, magnetic response, and excitation spectra. Phys. Rev. A, 65, 063602.CrossRefGoogle Scholar
[6] Diener, R. B., and Ho, T.-L. 2006. 52Cr spinor condensate: a biaxial of uniaxial spin nematic. Phys. Rev. Lett., 96, 190405.Google Scholar
[7] Kawaguchi, Y., and Ueda, M. 2011. Symmetry classification of spinor Bose-Einstein condensates. Phys. Rev. A, 84, 053616.Google Scholar
[8] Stamper-Kurn, D. M., and Ketterle, W. 2001. Spinor Condensates and Light Scattering from Bose-Einstein Condensates. New York: Springer-Verlag. Chap. 2, pages 137–218.
[9] Kawaguchi, Y., and Ueda, M. 2012. Spinor Bose Einstein condensates. Phys. Rep., 520, 253–381.Google Scholar
[10] Baranov, M. A. 2008. Theoretical progress in many-body physics with ultracold dipolar gases. Phys. Rep., 464, 71.Google Scholar
[11] Ueda, M. 2012. Bose gases with nonzero spin. Annual Review of Condensed Matter Physics, 3, 263–283.Google Scholar
[12] Stamper-Kurn, D. M., and Ueda, M. 2013. Spinor Bose gases: symmetries, magnetism, and quantum dynamics. Rev. Mod. Phys., 85, 1191.Google Scholar
[13] Landau, L. D., and Lifshitz, E. M. 1981. Quantum Mechanics (Non-Relativistic Theory), 3rd Edition. Butterworth-Heinemann.
[14] Santos, L., and Pfau, T. 2006. Spin-3 chromium Bose-Einstein condensates. Phys. Rev. Lett., 96, 190404.Google Scholar
[15] Schmaljohann, H., Erhard, M., Kronj äger, J., Kottke, M., van Staa, S., Cacciapuoti, L., Arlt, J. J., Bongs, K., and Sengstock, K. 2004. Dynamics of F = 2 spinor Bose- Einstein condensates. Phys. Rev. Lett., 92, 040402.Google Scholar
[16] Kuwamoto, T., Araki, K., Eno, T., and Hirano, T. 2004. Magnetic field dependence of the dynamics of Rb 87 spin-2 Bose-Einstein condensates. Phys. Rev. A, 69, 063604.Google Scholar
[17] Chang, M.-S., Hamley, C. D., Barrett, M. D., Sauer, J. A., Fortier, K. M., Zhang, W., You, L., and Chapman, M. S. 2004. Observation of spinor dynamics in optically trapped 87Rb Bose-Einstein condensates. Phys. Rev. Lett., 92, 140403.Google Scholar
[18] Kronj äger, J., Becker, C., Brinkmann, M., Walser, R., Navez, P., Bongs, K., and Sengstock, K. 2005. Evolution of a spinor condensate: coherent dynamics, dephasing, and revivals. Phys. Rev. A, 72, 063619.Google Scholar
[19] Widera, A., Gerbier, F., Fölling, S., Gericke, T., Mandel, O., and Bloch, I. 2006. Precision measurement of spin-dependent interaction strengths for spin-1 and spin- 2 87Rb atoms. New J. Phys., 8, 152.Google Scholar
[20] Black, A. T., Gomez, E., Turner, L. D., Jung, S., and Lett, P. D. 2007. Spinor dynamics in an antiferromagnetic spin-1 condensate. Phys. Rev. Lett., 99, 070403.Google Scholar
[21] Uchino, S., Otsuka, T., and Ueda, M. 2008. Dynamical symmetry in spinor Bose- Einstein condensates. Phys. Rev. A, 78, 023609.Google Scholar
[22] Volovik, G. E., and Gorkov, L. P. 1985. Superconducting classes in heavy-fermion systems. Sov. Phys. JETP, 61, 843.Google Scholar
[23] Murata, K., Saito, H., and Ueda, M. 2007. Broken-axisymmetry phase of a spin-1 ferromagnetic Bose-Einstein condensate. Phys. Rev. A, 75, 013607.Google Scholar
[24] Saito, H., and Ueda, M. 2005. Diagnostics for the ground-state phase of a spin-2 Bose-Einstein condensate. Phys. Rev. A, 72, 053628.Google Scholar
[25] Griesmaier, A., Werner, J., Hensler, S., Stuhler, J., and Pfau, T. 2005. Bose-Einstein condensation of chromium. Phys. Rev. Lett., 94, 160401.Google Scholar
[26] Law, C. K., Pu, H., and Bigelow, N. P. 1998. Quantum spins mixing in spinor Bose- Einstein condensates. Phys. Rev. Lett., 81, 5257.Google Scholar
[27] Uchino, S., Kobayashi, M., and Ueda, M. 2010. Bogoliubov theory and Lee-Huang- Yang corrections in spin-1 and spin-2 Bose-Einstein condensates in the presence of the quadratic Zeeman effect. Phys. Rev. A, 81, 063632.CrossRefGoogle Scholar
[28] Nozières, P., and Saint James, D. Particle vs. pair condensation in attractive Bose liquids. J. Phys. (Paris), 43, 1133.
[29] Mueller, E. J., Ho, T.-L., Ueda, M., and Baym, G. 2006. Fragmentation of Bose- Einstein condensates. Phys. Rev. A, 74, 033612.Google Scholar
[30] Iachello, F. 2006. Lie Algebras and Applications. Berlin: Springer Verlag.
[31] Talmi, Igal. 2993. Simple Models of Complex Nuclei: The ShellModel and Interacting Boson Model. London: Harwood Acad. Publ.
[32] Rohoziński, S. G. 1978. The oscillator basis for octupole collective motion in nuclei. J. Phys. G, 4, 1075.Google Scholar
[33] Weinberg, S. 1972. Approximate symmetries and pseudo-Goldstone bosons. Phys. Rev. Lett., 29, 1698.Google Scholar
[34] Georgi, H., and Pais, A. 1975. Vacuum symmetry and the pseudo-Goldstone phenomenon. Phys. Rev. D, 12, 508.Google Scholar
[35] Uchino, S., Kobayashi, M., Nitta, M., and Ueda, M. 2010. Quasi-Nambu-Goldstone modes in Bose-Einstein condensates. Phys. Rev. Lett., 105, 230406.Google Scholar
[36] Phuc, N. T., Kawaguchi, Y, and Ueda, M. 2013a. Beliaev theory of spinor Bose- Einstein condensates. Ann. Phys. (Berlin), 328, 158.Google Scholar
[37] Phuc, N. T., Kawaguchi, Y, and Ueda, M. 2013b. Fluctuation-induced and symmetryprohibited metastabilities in spinor Bose-Einstein condensates. Phys. Rev. A, 88, 043629.Google Scholar
[38] Phuc, N. T., Kawaguchi, Y, and Ueda, M. 2014. Quantum mass acquisition in spinor Bose-Einstein condensates. Phys. Rev. Lett., 113, 230401.Google Scholar
[39] Santos, L., Shlyapnikov, G. V., Zoller, P., and Lewenstein, M. 2000. Bose-Einstein condensation in trapped dipolar gases. Phys. Rev. Lett., 85, 1791.Google Scholar
[40] Lahaye, T., Koch, T., Frohlich, B., Fattori, M., Metz, J., Griesmaier, A., Giovanazzi, S., and Pfau, T. 2007. Strong dipolar effects in a quantum ferrofluid. Nature, 448, 672.Google Scholar
[41] Pollack, S. E., Dries, D., Junker, M., Chen, Y. P., Corcovilos, T. A., and Hulet, R. G. 2009. Extreme tunability of interactions in a 7Li Bose-Einstein condensate. Phys. Rev. Lett., 102, 090402.Google Scholar
[42] Lahaye, T., Metz, J., Froehlich, B., Koch, T., Meister, M., Griesmaier, A., Pfau, T., Saito, H., Kawaguchi, Y., and Ueda, M. 2008. d-wave collapse and explosion of a dipolar Bose-Einstein condensate. Phys. Rev. Lett., 101, 080401.Google Scholar
[43] Santos, L., Shlyapnikov, G. V., and Lewenstein, M. 2003. Roton-maxon spectrum and stability of trapped dipolar Bose-Einstein condensates. Phys. Rev. Lett., 90, 250403.Google Scholar
[44] Pedri, P., and Santos, L. 2005. Two-dimensional bright solitons in dipolar Bose- Einstein condensates. Phys. Rev. Lett., 95, 200404.Google Scholar
[45] Góral, K., Santos, L., and Lewenstein, M. 2002. Quantum phases of dipolar bosons in optical lattices. Phys. Rev. Lett., 88, 170406.Google Scholar
[46] Yi, S., Li, T., and Sun, C. P. 2007. Novel quantum phases of dipolar Bose gases in optical lattices. Phys. Rev. Lett., 98, 260405.Google Scholar
[47] Saito, H., Kawaguchi, Y., and Ueda, M. 2009. Ferrofluidity in a two-component dipolar Bose-Einstein condensate. Phys. Rev. Lett., 102, 230403.Google Scholar
[48] Pu, H., Zhang, W., and Meystre, P. 2001. Ferromagnetism in a lattice of Bose-Einstein condensates. Phys. Rev. Lett., 87, 140405.Google Scholar
[49] Gross, K., Search, C. P., Pu, H., Zhang, W., and Meystre, P. 2002. Magnetism in a lattice of spinor Bose-Einstein condensates. Phys. Rev. A, 66, 033603.Google Scholar
[50] Zhang, W., Pu, H., Search, C., and Meystre, P. 2002. Spin waves in a Bose-Einstein condensed atomic spin chain. Phys. Rev. Lett., 88, 060401.Google Scholar
[51] Kawaguchi, Y., Saito, H., and Ueda, M. 2006. Einstein-de Haas effect in dipolar Bose- Einstein condensates. Phys. Rev. Lett., 96, 080405.Google Scholar
[52] Gawryluk, K., Brewczyk, M., Bongs, K., and Gajda, M. 2007. Resonant Einstein–de Haas effect in a rubidium condensate. Phys. Rev. Lett., 99, 130401.Google Scholar
[53] Gawryluk, K., Bongs, K., and Brewczyk, M. 2011. How to observe dipolar effects in spinor Bose-Einstein condensates. Phys. Rev. Lett., 106, 140403.Google Scholar
[54] Hensler, S., Werner, J., Griesmaier, A., Schmidt, P. O., Gorlitz, A., Pfau, T., Giovanazzi, S., and Rzazewski, K. 2003. Dipolar relaxation in an ultra-cold gas of magnetically trapped chromium atoms. Appl. Phys. B, 77, 765.Google Scholar
[55] Pasquiou, B., Bismut, G., Beaufils, Q., Crubellier, A., Maréchal, E., Pedri, P., Vernac, L., Gorceix, O., and Laburthe-Tolra, B. 2010. Control of dipolar relaxation in external fields. Phys. Rev. A, 81, 042716.Google Scholar
[56] Pasquiou, B., Maréchal, E., Bismut, G., Pedri, P., Vernac, L., Gorceix, O., and Laburthe-Tolra, B. 2011. Spontaneous demagnetization of a dipolar spinor Bose gas in an ultralow magnetic field. Phys. Rev. Lett., 106, 255303.Google Scholar
[57] Kawaguchi, Y., Saito, H., and Ueda, M. 2006. Spontaneous circulation in ground-state spinor dipolar Bose-Einstein condensates. Phys. Rev. Lett., 97, 130404.Google Scholar
[58] Yi, S., and Pu, H. 2006. Spontaneous spin textures in dipolar spinor condensates. Phys. Rev. Lett., 97, 020401.Google Scholar
[59] Kawaguchi, Y., Saito, H., and Ueda, M. 2007. Can spinor dipolar effects be observed in Bose-Einstein condensates? Phys. Rev. Lett., 98, 110406.Google Scholar
[60] Yujiro, E., Hiroki, S., and Hirano, T. 2014. Observation of dipole-induced spin texture in a 87Rb Bose-Einstein condensate. Phys. Rev. Lett., 112, 185301.Google Scholar
[61] Ueda, M. 2014. Topological aspects in spinor Bose-Einstein condensates (Key Issues Review). Reports on Progress in Physics, 77, 122401.Google Scholar
[62] Lewenstein, M., Sanpera, A., Ahufinger, V., Damski, B., Sen, A., and Sen, U. 2007. Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond. Adv. Phys, 56, 243–379.CrossRefGoogle Scholar
[63] Dalibard, J., Gerbier, F, Juzeliuūas, G., and Öhberg, P. 2011. Artificial gauge potentials for neutral atoms. Rev. Mod. Phys., 83, 1523.Google Scholar

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