- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

First order phase transition between two centro-symmetric superradiant crystals

Xiangliang Li1, Davide Dreon1, Philip Zupancic1, Alexander Baumgärtner1, Andrea Morales1, Wei Zheng2,3,4, Nigel R. Cooper2, Tobias Donner1,*, and Tilman Esslinger1

  • 1Institute for Quantum Electronics, Eidgenössische Technische Hochschule Zürich, Otto-Stern-Weg 1, 8093 Zurich, Switzerland
  • 2T.C.M. Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
  • 3Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
  • 4CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China

  • *donner@phys.ethz.ch
PDF

Phys. Rev. Research 3, L012024 – Published 5 March, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L012024

Abstract

We observe a structural phase transition between two configurations of a superradiant crystal by coupling a Bose-Einstein condensate to an optical cavity and applying imbalanced transverse pump fields. The transition can be interpreted as a transition between two nonpolar, centro-symmetric structures involving a change in polarization. We find that this first order phase transition is accompanied by transient dynamics of the order parameter which we measure in real time. The phase transition and the excitation spectrum can be derived from a microscopic Hamiltonian, in quantitative agreement with our experimental data.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (41)

  1. P. Beaud et al., A time-dependent order parameter for ultrafast photoinduced phase transitions, Nat. Mater. 13, 923 (2014).
  2. S. L. Johnson et al., Femtosecond Dynamics of the Collinear-to-Spiral Antiferromagnetic Phase Transition in CuO, Phys. Rev. Lett. 108, 037203 (2012).
  3. M. Eichberger, H. Schäfer, M. Krumova, M. Beyer, J. Demsar, H. Berger, G. Moriena, G. Sciaini, and R. J. D. Miller, Snapshots of cooperative atomic motions in the optical suppression of charge density waves, Nature (London) 468, 799 (2010).
  4. R. Yusupov, T. Mertelj, V. V. Kabanov, S. Brazovskii, P. Kusar, J.-H. Chu, I. R. Fisher, and D. Mihailovic, Coherent dynamics of macroscopic electronic order through a symmetry breaking transition, Nat. Phys. 6, 681 (2010).
  5. I. Waki, S. Kassner, G. Birkl, and H. Walther, Observation of Ordered Structures of Laser-Cooled Ions in a Quadrupole Storage Ring, Phys. Rev. Lett. 68, 2007 (1992).
  6. M. G. Raizen, J. M. Gilligan, J. C. Bergquist, W. M. Itano, and D. J. Wineland, Ionic crystals in a linear Paul trap, Phys. Rev. A 45, 6493 (1992).
  7. E. Shimshoni, G. Morigi, and S. Fishman, Quantum structural phase transition in chains of interacting atoms, Phys. Rev. A 83, 032308 (2011).
  8. M. Lewenstein, A. Sanpera, and V. Ahufinger, Ultracold Atoms in Optical Lattices (Oxford University Press, Oxford, 2012), p. 479.
  9. I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).
  10. H. Ritsch, P. Domokos, F. Brennecke, and T. Esslinger, Cold atoms in cavity-generated dynamical optical potentials, Rev. Mod. Phys. 85, 553 (2013).
  11. A. T. Black, H. W. Chan, and V. Vuletić, Observation of Collective Friction Forces due to Spatial Self-Organization of Atoms: From Rayleigh to Bragg Scattering, Phys. Rev. Lett. 91, 203001 (2003).
  12. K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, Dicke quantum phase transition with a superfluid gas in an optical cavity, Nature (London) 464, 1301 (2010).
  13. D. Schmidt, H. Tomczyk, S. Slama, and C. Zimmermann, Dynamical Instability of a Bose-Einstein Condensate in an Optical Ring Resonator, Phys. Rev. Lett. 112, 115302 (2014).
  14. J. Klinder, H. Keßler, M. Wolke, L. Mathey, and A. Hemmerich, Dynamical phase transition in the open Dicke model, Proc. Natl. Acad. Sci. USA 112, 3290 (2015).
  15. J. Léonard, A. Morales, P. Zupancic, T. Esslinger, and T. Donner, Supersolid formation in a quantum gas breaking a continuous translational symmetry, Nature (London) 543, 87 (2017).
  16. A. J. Kollár, A. T. Papageorge, V. D. Vaidya, Y. Guo, J. Keeling, and B. L. Lev, Supermode-density-wave-polariton condensation with a Bose-Einstein condensate in a multimode cavity, Nat. Commun. 8, 14386 (2017).
  17. N. Piovella, M. Gatelli, and R. Bonifacio, Quantum effects in the collective light scattering by coherent atomic recoil in a Bose-Einstein condensate, Opt. Commun. 194, 167 (2001).
  18. S. Slama, S. Bux, G. Krenz, C. Zimmermann, and P. W. Courteille, Superradiant Rayleigh Scattering and Collective Atomic Recoil Lasing in a Ring Cavity, Phys. Rev. Lett. 98, 053603 (2007).
  19. S. Gopalakrishnan, B. L. Lev, and P. M. Goldbart, Emergent crystallinity and frustration with Bose-Einstein condensates in multimode cavities, Nat. Phys. 5, 845 (2009).
  20. R. Resta, Macroscopic polarization in crystalline dielectrics: The geometric phase approach, Rev. Mod. Phys. 66, 899 (1994).
  21. R. Resta and D. Vanderbilt, Theory of Polarization: A Modern Approach, in Physics of Ferroelectrics, Topics in Applied Physics (Springer, Berlin, Heidelberg, 2007), Vol. 105, pp. 31–68.
  22. N. A. Spaldin, A beginner's guide to the modern theory of polarization, J. Solid State Chem. 195, 2 (2012).
  23. P. Domokos and H. Ritsch, Collective Cooling and Self-Organization of Atoms in a Cavity, Phys. Rev. Lett. 89, 253003 (2002).
  24. K. Baumann, R. Mottl, F. Brennecke, and T. Esslinger, Exploring Symmetry Breaking at the Dicke Quantum Phase Transition, Phys. Rev. Lett. 107, 140402 (2011).
  25. K. J. Arnold, M. P. Baden, and M. D. Barrett, Self-Organization Threshold Scaling for Thermal Atoms Coupled to a Cavity, Phys. Rev. Lett. 109, 153002 (2012).
  26. S. Bux, C. Gnahm, R. A. W. Maier, C. Zimmermann, and P. W. Courteille, Cavity-Controlled Collective Scattering at the Recoil Limit, Phys. Rev. Lett. 106, 203601 (2011).
  27. H. Keßler, J. Klinder, M. Wolke, and A. Hemmerich, Steering Matter Wave Superradiance with an Ultranarrow-Band Optical Cavity, Phys. Rev. Lett. 113, 070404 (2014).
  28. F. Mivehvar, H. Ritsch, and F. Piazza, Cavity-Quantum-Electrodynamical Toolbox for Quantum Magnetism, Phys. Rev. Lett. 122, 113603 (2019).
  29. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L012024 for experimental details and derivations Refs. [37, 38, 39, 40, 41].
  30. P. Zupancic, D. Dreon, X. Li, A. Baumgärtner, A. Morales, W. Zheng, N. R. Cooper, T. Esslinger, and T. Donner, P-Band Induced Self-Organization and Dynamics with Repulsively Driven Ultracold Atoms in an Optical Cavity, Phys. Rev. Lett. 123, 233601 (2019).
  31. C. Gerry and P. Knight, Introductory Quantum Optics (Cambridge University Press, Cambridge, 2004).
  32. K. Huang, Introduction to Statistical Physics (Wiley, New York, 1987).
  33. F. Piazza, P. Strack, and W. Zwerger, Bose-Einstein condensation versus Dicke-Hepp-Lieb transition in an optical cavity, Ann. Phys. (NY) 339, 135 (2013).
  34. R. Landig, L. Hruby, N. Dogra, M. Landini, R. Mottl, T. Donner, and T. Esslinger, Quantum phases from competing short- and long-range interactions in an optical lattice, Nature (London) 532, 476 (2016).
  35. F. Mivehvar, H. Ritsch, and F. Piazza, Superradiant Topological Peierls Insulator inside an Optical Cavity, Phys. Rev. Lett. 118, 073602 (2017).
  36. J. Fan, G. Chen, and S. Jia, Atomic self-organization emerging from tunable quadrature coupling, Phys. Rev. A 101, 063627 (2020).
  37. A. Morales, D. Dreon, X. Li, A. Baumgärtner, P. Zupancic, T. Donner, and T. Esslinger, Two-mode Dicke model from nondegenerate polarization modes, Phys. Rev. A 100, 013816 (2019).
  38. H. R. Carleton and W. T. Maloney, A balanced optical heterodyne detector, Appl. Opt. 7, 1241 (1968).
  39. H. P. Yuen and V. W. S. Chan, Noise in homodyne and heterodyne detection, Opt. Lett. 8, 177 (1983).
  40. R. Stierlin, R. Bättig, P.-D. Henchoz, and H. P. Weber, Excess-noise suppression in a fibre-optic balanced heterodyne detection system, Opt. Quantum Electron. 18, 445 (1986).
  41. J. F. Holmes and B. J. Rask, Optimum optical local-oscillator power levels for coherent detection with photodiodes, Appl. Opt. 34, 927 (1995).

Outline

Information

Phys. Rev. Research 3, L012024– Published 5 March, 2021
  • Received 16 April 2020
  • Accepted 31 January 2021
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation