The Question of Spontaneous Symmetry Breaking in Condensates

D. W. Snoke; A. J. Daley

doi:10.1017/9781316084366.007

5 - The Question of Spontaneous Symmetry Breaking in Condensates

from Part II - General Topics

Published online by Cambridge University Press: 18 May 2017

D. W. Snoke and

Edited by

David W. Snoke and

D. W. Snoke: Affiliation:
Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA
A. J. Daley: Affiliation:
Department of Physics and Scottish Universities Physics Alliance, University of Strathclyde, Glasgow G4 0NG, Scotland, UK
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

The question of whether Bose-Einstein condensation involves spontaneous symmetry breaking is surprisingly controversial. We review the theory of spontaneous symmetry breaking in ferromagnets, compare it with the theory of symmetry breaking in condensates, and discuss the different viewpoints on the correspondence to experiments. These viewpoints include alternative perspectives in which we can treat condensates with fixed particle numbers, and where coherence arises from measurements. This question relates to whether condensates of quasiparticles such as polaritons can be viewed as “real” condensates.

Introduction

Spontaneous symmetry breaking is a deep subject in physics with long historical roots. At the most basic level, it arises in the field of cosmology. Physicists have long had an aesthetic principle that leads us to expect symmetry in the all of the basic equations of physical law. Yet the universe is manifestly full of asymmetries. How does a symmetric system acquire asymmetry merely by evolving in time? Starting in the 1950s, cosmologists began to borrow the ideas of spontaneous symmetry breaking from condensed matter physics, which were originally developed to explain spontaneous magnetization in ferromagnetic systems.

Spontaneous coherence in all its forms (e.g., Bose-Einstein condensation [BEC], superconductivity, and lasing) can be viewed as another type of symmetry breaking. The Hamiltonian of the system is symmetric, yet under some conditions, the energy of the system can be reduced by putting the system into a state with asymmetry, namely, a state with a common phase for a macroscopic number of particles. The symmetry of the system implies that it does not matter what the exact choice of that phase is, as long as it is the same for all the particles.

It is not obvious, however, whether the symmetry breaking which occurs in spontaneous coherence of the type seen in lasers or in Bose-Einstein condensation is the same as that seen in ferromagnetic systems. There are similarities in the systems which encourage the same view of all types of symmetry breaking, but there are also differences. In fact, there is a substantial school of thought that symmetry breaking in Bose-Einstein condensates with ultracold atoms is a “convenient fiction” (a term applied to optical coherence by Mølmer [1]).

Type: Chapter
Information: Universal Themes of Bose-Einstein Condensation , pp. 79 - 98

DOI: https://doi.org/10.1017/9781316084366.007 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2017

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References

[1] Mølmer, K. 1997. Optical coherence: a convenient fiction. Phys. Rev. A, 55, 3195–3203.Google Scholar

[2] Castin, Y., and Dalibard, J. 1997. Relative phase of two Bose-Einstein condensates. Phys. Rev. A, 55, 4330–4337.Google Scholar

[3] Gardiner, C.W. 1997. Particle-number-conserving Bogoliubov method which demonstrates the validity of the time-dependent Gross-Pitaevskii equation for a highly condensed Bose gas. Phys. Rev. A, 56, 1414–1423.Google Scholar

[4] Castin, Y., and Dum, R. 1998. Low-temperature Bose-Einstein condensates in timedependent traps: beyond the U(1) symmetry-breaking approach. Phys. Rev. A, 57, 3008–3021.Google Scholar

[5] Leggett, A.J. 2001. Bose-Einstein condensation in the alkali gases: some fundamental concepts. Rev. Mod. Phys., 73, 307–356.Google Scholar

[6] Leggett, A.J., and Sols, F. 1991. On the concept of spontaneously broken gauge symmetry in condensed matter physics. Foundations of Physics, 21(3), 353–364.Google Scholar

[7] Javanainen, J., and Yoo, S.M. 1996. Quantum phase of a Bose-Einstein condensate with an arbitrary number of atoms. Phys. Rev. Lett., 76, 161–164.Google Scholar

[8] Naraschewski, M., Wallis, H., Schenzle, A., Cirac, J.I., and Zoller, P. 1996. Interference of Bose condensates. Phys. Rev. A, 54, 2185–2196.Google Scholar

[9] Wong, T., Collett, M.J., and Walls, D.F. 1996. Interference of two Bose-Einstein condensates with collisions. Phys. Rev. A, 54, R3718–R3721.Google Scholar

[10] Wright, E.M., Walls, D.F., and Garrison, J.C. 1996. Collapses and revivals of Bose-Einstein condensates formed in small atomic samples. Phys. Rev. Lett., 77, 2158–2161.Google Scholar

[11] Stenholm, S. 2002. The question of phase in a Bose-Einstein condensate. Physica Scripta, 2002(T102), 89.Google Scholar

[12] Schachenmayer, J., Daley, A.J., and Zoller, P. 2011. Atomic matter-wave revivals with definite atom number in an optical lattice. Phys. Rev. A, 83, 043614.Google Scholar

[13] Snoke, D.W. 2009. Essential Concepts of Solid State Physics. Pearson, section 10.2.1.

[14] Ibid., section 11.3.1.

[15] Kazanas, D. 1980. Dynamics of the universe and spontaneous symmetry breaking. Astrophysical J., 241, L59–L63.Google Scholar

[16] Kibble, T.W, B. 1980. Some implications of a cosmological phase transition. Physics Reports, 67, 183–199.Google Scholar

[17] Zurek, W.H. 1996. Cosmological experiments in condensed matter systems. Physics Reports, 276, 177–221.Google Scholar

[18] Einstein, A. 1924. Quantum theory of the single-atom ideal gas. Absitz. Pruss. Akad. Wiss. Berlin, Kl. Math., 22, 261.

[19] Noziéres, P. 1995. Some comments on Bose-Einstein condensation. Pages 16–21 of: Bose-Einstein Condensation. Cambridge University Press, Griffin, A., Snoke, D, W., and Stringari, S., eds.

[20] Combescot, M., and Snoke, D.W. 2008. Stability of a Bose-Einstein condensate revisited for composite bosons. Phys. Rev. B, 78, 144303.Google Scholar

[21] Band, W. 1955. An Introduction to Quantum Statistics. D. Van Nostrand, pp. 154, 162.

[22] Snoke, D.W., Liu, G., and Girvin, S.M. 2012. The basis of the second law of thermodynamics in quantum field theory. Annals of Physics, 327, 1825–1851.Google Scholar

[23] Snoke, D.W., and Girvin, S.M. 2013. Dynamics of phase coherence onset in Bose condensates of photons by incoherent phonon emission. J. Low Temperature Phys., 171, 1.Google Scholar

[24] Snoke, D., Wolfe, J.P., and Mysyrowicz, A. 1987. Quantum saturation of a Bose gas: excitons in Cu2O. Phys. Rev. Lett., 59, 827.Google Scholar

[25] Semikoz, D.V., and Tkachev, I.I. 1995. Kinetics of Bose condensation. Phys. Rev. Lett., 74, 3093–3097.Google Scholar

[26] Andrews, M.R., Townsend, C.G., Miesner, H.-J., Durfee, D.S., Kurn, D.M., and Ketterle, W. 1997. Observation of interference between two Bose condensates. Science, 275(5300), 637–641.Google Scholar

[27] Mandel, L., and Wolf, E. 1995. Optical Coherence and Quantum Optics. Cambridge University Press.

[28] Imamoglu, A., Lewenstein, M., and You, L. 1997. Inhibition of coherence in trapped Bose-Einstein condensates. Phys. Rev. Lett., 78, 2511–2514.Google Scholar

[29] Javanainen, J., and Wilkens, M. 1997. Phase and phase diffusion of a split Bose- Einstein condensate. Phys. Rev. Lett., 78, 4675–4678.Google Scholar

[30] Milburn, G.J., Corney, J., Wright, E.M., and Walls, D.F. 1997. Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential. Phys. Rev. A, 55, 4318–4324.Google Scholar

[31] Cirac, J.I., Gardiner, C.W., Naraschewski, M., and Zoller, P. 1996. Continuous observation of interference fringes from Bose condensates. Phys. Rev. A, 54, R3714–R3717.Google Scholar

[32] Mølmer, K. 1997. Quantum entanglement and classical behaviour. Journal of Modern Optics, 44(10), 1937–1956.Google Scholar

[33] Siegman, A.E. 1986. Lasers. University Science Books.

[34] Greiner, M., Mandel, O., Hansch, T.W., and Bloch, I. 2002. Collapse and revival of the matter wave field of a Bose-Einstein condensate. Nature, 419(6902), 51–54.Google Scholar

[35] Will, S., Best, T., Schneider, U., Hackermuller, L., Luhmann, D.-S., and Bloch, I. 2010. Time-resolved observation of coherent multi-body interactions in quantum phase revivals. Nature, 465(7295), 197–201.Google Scholar

[36] Klaers, J., Schmitt, J., Vewinger, F., and Weitz, M. 2010. Bose-Einstein condensation of photons in an optical microcavity. Nature, 468, 548.Google Scholar

[37] Kasprzak, J., Richard, M., Kundermann, S., Baas, A., Jeanbrun, P., Keeling, J.M.J., André, R., Staehli, J.L., Savona, V., Littlewood, P.B., Deveaud, B., and Dang, L.S. 2006. Bose-Einstein condensation of exciton polaritons. Nature, 443, 409.Google Scholar

[38] Balili, R., Hartwell, V., Snoke, D.W., Pfeiffer, L., and West, K. 2007. Bose-Einstein condensation of microcavity polaritons in a trap. Science, 316, 1007.Google Scholar

[39] Liu, G., Snoke, D.W., Daley, A.J., Pfeiffer, L.N., and West, K. 2015. A new type of half-quantum circulation in a macroscopic polariton spinor ring condensate. Proc. National Acad. Sci. (USA), 112, 2676.Google Scholar

[40] Baumberg, J.J., Kavokin, A.V., Christopoulos, S., Grundy, A.J. D., Butte, R., Christmann, G., Solnyshkov, D.D., Malpuech, G., von Hogersthal, G. B. H., Feltin, E., Carlin, J.F., and Grandjean, N. 2008. Spontaneous polarization buildup in a roomtemperature polariton laser. Phys. Rev. Lett., 101, 136409.Google Scholar

[41] Abbarchi, M., Amo, A., Sala, V.G., Solnyshkov, D.D., Flayac, H., Ferrier, L., Sagnes, I., Galopin, E., LemaÎtre, A., Malpuech, G., and Bloch, J. 2013. Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons. Nature Phys., 9, 275.Google Scholar

[42] Wouters, M., and Carusotto, I. 2010. Superfluidity and critical velocities in nonequilibrium Bose-Einstein condensates. Phys. Rev. Lett., 105, 020602.Google Scholar

[43] Keeling, J. 2011. Superfluid density of an open dissipative condensate. Phys. Rev. Lett., 107, 080402.Google Scholar

[44] Demidov, V.E., Dzyapko, O., Demokritov, S.O., Melkov, G.A., and Slavin, A.N. 2008. Observation of spontaneous coherence in Bose-Einstein condensate of magnons. Phys. Rev. Lett., 100, 047205.Google Scholar

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