Skip to main content
SpringerLink
Log in

Introduction to Amplitude and Phase Modes

  • Chapter
  • First Online:
Probing Correlated Quantum Many-Body Systems at the Single-Particle Level

Part of the book series: Springer Theses ((Springer Theses))

  • 1004 Accesses

Abstract

Higgs modes are amplitude oscillations of a quantum field and appear as collective excitations in quantum many-body systems as a consequence of spontaneous breaking of a continuous symmetry.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Depening on the author, also Eq. 8.54 is sometimes called fluctuation-dissipation theorem

References

  1. Weinberg S (1996) The quantum theory of fields, vol 2. Cambridge University Press, Cambridge. ISBN 0521670543

    Google Scholar 

  2. Sachdev S (2011) Quantum phase transitions, 2nd edn. Cambridge University Press, Cambridge. ISBN 0521514681

    Google Scholar 

  3. Chubukov AV, Sachdev S, Ye J (1994) Theory of two-dimensional quantum Heisenberg antiferromagnets with a nearly critical ground state. Phys Rev B 49:11919–11961

    Article  ADS  Google Scholar 

  4. Sachdev S (1999) Universal relaxational dynamics near two-dimensional quantum critical points. Phys Rev B 59:14054–14073

    Article  ADS  Google Scholar 

  5. Altman E, Auerbach A (2002) Oscillating superfluidity of bosons in optical lattices. Phys Rev Lett 89:250404

    Article  ADS  Google Scholar 

  6. Zwerger W (2004) Anomalous fluctuations in phases with a broken continuous symmetry. Phys Rev Lett 92:027203

    Article  ADS  Google Scholar 

  7. Podolsky D, Auerbach A, Arovas DP (2011) Visibility of the amplitude (Higgs) mode in condensed matter. Phys Rev B 84:174522

    Article  ADS  Google Scholar 

  8. Pollet L (2012) Recent developments in Quantum Monte-Carlo simulations with applications for cold gases. arXiv:1206.0781

    Google Scholar 

  9. Podolsky D, Sachdev S (2012) Spectral functions of the Higgs mode near two-dimensional quantum critical points. Phys Rev B 86:054508

    Article  ADS  Google Scholar 

  10. Lindner NH, Auerbach A (2010) Conductivity of hard core bosons: a paradigm of a bad metal. Phys Rev B 81:054512

    Article  ADS  Google Scholar 

  11. Sooryakumar R, Klein M (1980) Raman scattering by superconducting-gap excitations and their coupling to charge-density waves. Phys Rev Lett 45:660–662

    Article  ADS  Google Scholar 

  12. Littlewood P, Varma C (1981) Gauge-invariant theory of the dynamical interaction of charge density waves and superconductivity. Phys Rev Lett 47:811–814

    Article  ADS  Google Scholar 

  13. Rüegg C, Normand B, Matsumoto M, Furrer A, McMorrow D, Krämer K, Güdel H, Gvasaliya S, Mutka H, Boehm M (2008) Quantum magnets under pressure: controlling elementary excitations in TlCuCl3. Phys Rev Lett 100:205701

    Article  ADS  Google Scholar 

  14. Bloch I, Dalibard J, Zwerger W (2008) Many-body physics with ultracold gases. Rev Mod Phys 80:885–964

    Article  ADS  Google Scholar 

  15. Polkovnikov A, Altman E, Demler E, Halperin B (2005) Decay of superfluid currents in a moving system of strongly interacting bosons. Phys Rev A 71:063613

    Article  ADS  Google Scholar 

  16. Polkovnikov A, Sachdev S, Girvin S (2002) Nonequilibrium Gross-Pitaevskii dynamics of boson lattice models. Phys Rev A 66:53607

    Article  ADS  Google Scholar 

  17. Sengupta K, Dupuis N (2005) Mott-insulator-to-superfluid transition in the Bose-Hubbard model: a strong-coupling approach. Phys Rev A 71:033629

    Article  ADS  Google Scholar 

  18. Huber SD, Altman E, Buchler HP, Blatter G (2007) Dynamical properties of ultracold bosons in an optical lattice. Phys Rev B 75:85106

    Article  ADS  Google Scholar 

  19. Huber S, Theiler B, Altman E, Blatte G (2008) Amplitude mode in the quantum phase model. Phys Rev Lett 100:050404

    Article  ADS  Google Scholar 

  20. Menotti C (2008) Spectral weight redistribution in strongly correlated bosons in optical lattices. Phys Rev B 77:235120

    Article  ADS  Google Scholar 

  21. Graß TD, Santos FEA (2011) Real-time Ginzburg-Landau theory for bosons in optical lattices. Laser Phys 21:1459–1463

    Article  ADS  Google Scholar 

  22. Stöferle T, Moritz H, Schori C, Köhl M, Esslinger T (2004) Transition from a strongly interacting 1D superfluid to a Mott insulator. Phys Rev Lett 92:130403

    Article  ADS  Google Scholar 

  23. Schori C, Stöferle T, Moritz H, Köhl M, Esslinger T (2004) Excitations of a superfluid in a three-dimensional optical lattice. Phys Rev Lett 93:240402

    Article  ADS  Google Scholar 

  24. Kollath C, Iucci A, Giamarchi T, Hofstetter W, Schollwöck U (2006) Spectroscopy of ultracold atoms by periodic lattice modulations. Phys Rev Lett 97:050402

    Article  ADS  Google Scholar 

  25. Bissbort U, Götze S, Li Y, Heinze J, Krauser JS, Weinberg M, Becker C, Sengstock K, Hofstetter W (2011) Detecting the amplitude mode of strongly interacting lattice bosons by Bragg scattering. Phys Rev Lett 106:205303

    Article  ADS  Google Scholar 

  26. Fisher MPA, Weichman PB, Grinstein G, Fisher DS (1989) Boson localization and the superfluid-insulator transition. Phys Rev B 40:546–570

    Article  ADS  Google Scholar 

  27. Schachenmayer J, Pupillo G, Daley AJ (2010) Time-dependent currents of one-dimensional bosons in an optical lattice. New J Phys 12:025014

    Article  Google Scholar 

  28. Nambu Y (1960) Quasi-particles and gauge invariance in the theory of superconductivity. Phys Rev 117:648–663

    Article  MathSciNet  ADS  Google Scholar 

  29. Goldstone J (1961) Field theories with superconductor solutions. Il Nuovo Cimento 19: 154–164

    Google Scholar 

  30. Higgs P (1964) Broken symmetries and the masses of gauge bosons. Phys Rev Lett 13:508–509

    Article  MathSciNet  ADS  Google Scholar 

  31. Cottingham WN, Greenwood D (2007) An introduction to the standard model of particle physics, 2nd edn. Cambridge University Press, Cambridge. ISBN 0521852498

    Google Scholar 

  32. Pethick CJ, Smith H (2001) Bose-Einstein condensation in dilute gases. Cambridge University Press, Cambridge. ISBN 0521665809

    Google Scholar 

  33. Chaikin PM, Lubensky TC (1995) Principles of condensed matter physics. Cambridge University Press, Cambridge

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max-Planck-Institute of Quantum Optics, Garching, Germany

    Manuel Endres

Authors
  1. Manuel Endres
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Manuel Endres .

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Endres, M. (2014). Introduction to Amplitude and Phase Modes . In: Probing Correlated Quantum Many-Body Systems at the Single-Particle Level. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-05753-8_8

Download citation

Publish with us

Policies and ethics

Search

Navigation