Quantum critical states and phase transitions in the presence of non-equilibrium noise

Journal name:
Nature Physics
Volume:
6,
Pages:
806–810
Year published:
DOI:
doi:10.1038/nphys1754
Received
Accepted
Published online

Abstract

Quantum critical points are characterized by scale-invariant correlations and therefore by long-range entanglement. As such, they present fascinating examples of quantum states of matter and their study is an important theme in modern physics. However, little is known about the fate of quantum criticality under non-equilibrium conditions. Here we investigate the effect of external noise sources on quantum critical points. It is natural to expect that noise will have a similar effect to finite temperature, that is, destroying the subtle correlations underlying the quantum critical behaviour. Surprisingly, we find that the ubiquitous 1/f noise does preserve the critical correlations. The emergent states show an intriguing interplay of intrinsic quantum critical and external-noise-driven fluctuations. We illustrate this general phenomenon with specific examples describing solid-state and ultracold-atoms systems. Moreover, our approach shows that genuine quantum phase transitions can exist even under non-equilibrium conditions.

At a glance

Figures

  1. Effects of non-equilibrium noise on the localization quantum phase transition of a single shunted Josephson junction:
    Figure 1: Effects of non-equilibrium noise on the localization quantum phase transition of a single shunted Josephson junction:

    a, Electronic circuit relevant to a resistively shunted Josephson junction with charging noise. b, Critical resistance R/RQ as a function of the noise strength F0, in the weak coupling limit. c, Critical conductance R/RQ as a function of the noise strength F0, in the strong-coupling limit. b and c are related by the duality transformation R/RQ RQ/R and ‘superconductor’ ‘normal’. d, Schematic phase diagram at equilibrium (dotted line) and in the presence of non-equilibrium 1/f noise (dashed line).

  2. Effects of non-equilibrium noise on the response to Bragg spectroscopy.
    Figure 2: Effects of non-equilibrium noise on the response to Bragg spectroscopy.

    a, Imaginary part of the response function χ′′(q,ω) in a one-dimensional system with K=0.5, at equilibrium (F0=0). b, The same plot as in a, in the presence of a strong 1/f noise with F0/η=4π2.

References

  1. Winkler, K. et al. Coherent optical transfer of Feshbach molecules to a lower vibrational state. Phys. Rev. Lett 98, 043201 (2007).
  2. Ni, K-K. et al. A high phase-space-density gas of polar molecules. Science 322, 231235 (2008).
  3. Blatt, R. & Wineland, D. J. Entangled states of trapped atomic ions. Nature 453, 10081015 (2008).
  4. Lahaye, T., Menotti, C., Santos, L., Lewenstein, M. & Pfau, T. The physics of dipolar bosonic quantum gases. Rep. Prog. Phys. 72, 126401 (2009).
  5. Porras, D. & Cirac, J. I. Effective quantum spin systems with trapped ions. Phys. Rev. Lett. 92, 207901 (2004).
  6. García-Mata, I., Zhirov, O. & Shepelyansky, D. Frenkel–Kontorova model with cold trapped ions. Eur. Phys. J. D 41, 325330 (2007).
  7. Deslauriers, L. et al. Scaling and suppression of anomalous heating in ion traps. Phys. Rev. Lett. 97, 103007 (2006).
  8. Labaziewicz, J. et al. Temperature dependence of electric field noise above gold surfaces. Phys. Rev. Lett. 101, 180602 (2008).
  9. Schmidt, A. Diffusion and localization in a dissipative quantum system. Phys. Rev. Lett. 51, 15061509 (1983).
  10. Chakravarty, S. Quantum fluctuations in the tunneling between superconductors. Phys. Rev. Lett. 49, 681684 (1982).
  11. Leggett, A. J. et al. Dynamics of the dissipative two-state system. Rev. Mod. Phys. 59, 185 (1987).
  12. Clarke, J. & Wilhelm, F. K. Superconducting quantum bits. Nature 453, 10311042 (2008).
  13. Ithier, G. et al. Decoherence in a superconducting quantum bit circuit. Phys. Rev. B 72, 134519 (2005).
  14. Mitra, A., Takei, S., Kim, Y. B. & Millis, A. J. Nonequilibrium quantum criticality in open electronic systems. Phys. Rev. Lett. 97, 236808 (2006).
  15. Diehl, S. et al. Quantum states and phases in driven open quantum systems with cold atoms. Nature Phys. 4, 878883 (2008).
  16. Sachdev, S. Quantum Phase Transitions (Cambridge Univ. Press, 1999).
  17. Sondhi, S. L., Girvin, S. M., Carini, J. P. & Shahar, D. Continuous quantum phase transitions. Rev. Mod. Phys. 69, 315333 (1997).
  18. Giamarchi, T. Quantum Physics in One Dimension (Oxford Univ. Press, 2004).
  19. Morigi, G. & Fishman, S. Eigenmodes and thermodynamics of a Coulomb chain in a harmonic potential. Phys. Rev. Lett. 93, 170602 (2004).
  20. Antal, T., Rácz, Z. & Sasvári, L. Nonequilibrium steady state in a quantum system: One-dimensional transverse Ising model with energy current. Phys. Rev. Lett. 78, 167170 (1997).
  21. Feldman, D. E. Nonequilibrium quantum phase transition in itinerant electron systems. Phys. Rev. Lett. 95, 177201 (2005).
  22. Zimmerli, G., Eiles, T. M., Kautz, R. L. & Martinis, J. M. Noise in the coulomb blockade electrometer. Appl. Phys. Lett. 61, 237239 (1992).
  23. Cladeira, A. O. & Leggett, A. J. Path integral approach to quantum Brownian motion. Physica A 121, 587616 (1983).
  24. Fisher, M. P. A. & Zwerger, W. Quantum Brownian motion in a periodic potential. Phys. Rev. B 32, 61906206 (1985).
  25. Haldane, F. D. M. Effective harmonic-fluid approach to low-energy properties of one-dimensional quantum fluids. Phys. Rev. Lett. 47, 18401843 (1981).
  26. Daley, A. J., Fedichev, P. O. & Zoller, P. Single-atom cooling by superfluid immersion: A nondestructive method for qubits. Phys. Rev. A 69, 022306 (2004).
  27. Polkovnikov, A., Altman, E. & Demler, E. Interference between independent fluctuating condensates. Proc. Natl Acad. Sci. USA 103, 61256129 (2006).
  28. Stenger, J. et al. Bragg spectroscopy of a Bose–Einstein condensate. Phys. Rev. Lett. 82, 45694573 (1999).
  29. Steinhauer, J. et al. Bragg spectroscopy of the multibranch Bogoliubov spectrum of elongated Bose–Einstein condensates. Phys. Rev. Lett. 90, 060404 (2002).
  30. Clément, D., Fabbri, N., Fallani, L., Fort, C. & Inguscio, M. Exploring correlated 1d Bose gases from the superfluid to the Mott-insulator state by inelastic light scattering. Phys. Rev. Lett. 102, 155301 (2009).
  31. Kane, C. L. & Fisher, M. P. A. Transmission through barriers and resonant tunneling in an interacting one-dimensional electron gas. Phys. Rev. B 46, 1523315262 (1992).
  32. Kollath, C., Meyer, J. S. & Giamarchi, T. Dipolar bosons in a planar array of one-dimensional tubes. Phys. Rev. Lett. 100, 130403 (2008).
  33. Refael, G., Demler, E., Oreg, Y. & Fisher, D. S. Superconductor-to-normal transitions in dissipative chains of mesoscopic grains and nanowires. Phys. Rev. B 75, 014522 (2007).
  34. Kamenev, A. & Levchenko, A. Keldysh technique and non-linear sigma-model: Basic principles and applications. Adv. Phys. 58, 197319 (2009).

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Author information

Affiliations

  1. Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel

    • Emanuele G. Dalla Torre &
    • Ehud Altman
  2. Department of Physics, Harvard University, Cambridge Massachusetts 02138, USA

    • Eugene Demler
  3. DPMC-MaNEP, University of Geneva, 24 Quai Ernest-Ansermet, 1211 Geneva, Switzerland

    • Thierry Giamarchi

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All authors contributed equally to this work.

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The authors declare no competing financial interests.

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