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

Nature Physics volume 6, pages 806–810 (2010)Cite this article

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.

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Figure 1: Effects of non-equilibrium noise on the localization quantum phase transition of a single shunted Josephson junction:
Figure 2: Effects of non-equilibrium noise on the response to Bragg spectroscopy.

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References

  1. Winkler, K. et al. Coherent optical transfer of Feshbach molecules to a lower vibrational state. Phys. Rev. Lett 98, 043201 (2007).

    Article  ADS  Google Scholar 

  2. Ni, K-K. et al. A high phase-space-density gas of polar molecules. Science 322, 231–235 (2008).

    Article  ADS  Google Scholar 

  3. Blatt, R. & Wineland, D. J. Entangled states of trapped atomic ions. Nature 453, 1008–1015 (2008).

    Article  ADS  Google Scholar 

  4. Lahaye, T., Menotti, C., Santos, L., Lewenstein, M. & Pfau, T. The physics of dipolar bosonic quantum gases. Rep. Prog. Phys. 72, 126401 (2009).

    Article  ADS  Google Scholar 

  5. Porras, D. & Cirac, J. I. Effective quantum spin systems with trapped ions. Phys. Rev. Lett. 92, 207901 (2004).

    Article  ADS  Google Scholar 

  6. García-Mata, I., Zhirov, O. & Shepelyansky, D. Frenkel–Kontorova model with cold trapped ions. Eur. Phys. J. D 41, 325–330 (2007).

    Article  ADS  Google Scholar 

  7. Deslauriers, L. et al. Scaling and suppression of anomalous heating in ion traps. Phys. Rev. Lett. 97, 103007 (2006).

    Article  ADS  Google Scholar 

  8. Labaziewicz, J. et al. Temperature dependence of electric field noise above gold surfaces. Phys. Rev. Lett. 101, 180602 (2008).

    Article  ADS  Google Scholar 

  9. Schmidt, A. Diffusion and localization in a dissipative quantum system. Phys. Rev. Lett. 51, 1506–1509 (1983).

    Article  ADS  Google Scholar 

  10. Chakravarty, S. Quantum fluctuations in the tunneling between superconductors. Phys. Rev. Lett. 49, 681–684 (1982).

    Article  ADS  Google Scholar 

  11. Leggett, A. J. et al. Dynamics of the dissipative two-state system. Rev. Mod. Phys. 59, 1–85 (1987).

    Article  ADS  Google Scholar 

  12. Clarke, J. & Wilhelm, F. K. Superconducting quantum bits. Nature 453, 1031–1042 (2008).

    Article  ADS  Google Scholar 

  13. Ithier, G. et al. Decoherence in a superconducting quantum bit circuit. Phys. Rev. B 72, 134519 (2005).

    Article  ADS  Google Scholar 

  14. Mitra, A., Takei, S., Kim, Y. B. & Millis, A. J. Nonequilibrium quantum criticality in open electronic systems. Phys. Rev. Lett. 97, 236808 (2006).

    Article  ADS  Google Scholar 

  15. Diehl, S. et al. Quantum states and phases in driven open quantum systems with cold atoms. Nature Phys. 4, 878–883 (2008).

    Article  ADS  Google Scholar 

  16. Sachdev, S. Quantum Phase Transitions (Cambridge Univ. Press, 1999).

    MATH  Google Scholar 

  17. Sondhi, S. L., Girvin, S. M., Carini, J. P. & Shahar, D. Continuous quantum phase transitions. Rev. Mod. Phys. 69, 315–333 (1997).

    Article  ADS  Google Scholar 

  18. Giamarchi, T. Quantum Physics in One Dimension (Oxford Univ. Press, 2004).

    MATH  Google Scholar 

  19. Morigi, G. & Fishman, S. Eigenmodes and thermodynamics of a Coulomb chain in a harmonic potential. Phys. Rev. Lett. 93, 170602 (2004).

    Article  ADS  Google Scholar 

  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, 167–170 (1997).

    Article  ADS  Google Scholar 

  21. Feldman, D. E. Nonequilibrium quantum phase transition in itinerant electron systems. Phys. Rev. Lett. 95, 177201 (2005).

    Article  ADS  Google Scholar 

  22. Zimmerli, G., Eiles, T. M., Kautz, R. L. & Martinis, J. M. Noise in the coulomb blockade electrometer. Appl. Phys. Lett. 61, 237–239 (1992).

    Article  ADS  Google Scholar 

  23. Cladeira, A. O. & Leggett, A. J. Path integral approach to quantum Brownian motion. Physica A 121, 587–616 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  24. Fisher, M. P. A. & Zwerger, W. Quantum Brownian motion in a periodic potential. Phys. Rev. B 32, 6190–6206 (1985).

    Article  ADS  Google Scholar 

  25. Haldane, F. D. M. Effective harmonic-fluid approach to low-energy properties of one-dimensional quantum fluids. Phys. Rev. Lett. 47, 1840–1843 (1981).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  27. Polkovnikov, A., Altman, E. & Demler, E. Interference between independent fluctuating condensates. Proc. Natl Acad. Sci. USA 103, 6125–6129 (2006).

    Article  ADS  Google Scholar 

  28. Stenger, J. et al. Bragg spectroscopy of a Bose–Einstein condensate. Phys. Rev. Lett. 82, 4569–4573 (1999).

    Article  ADS  Google Scholar 

  29. Steinhauer, J. et al. Bragg spectroscopy of the multibranch Bogoliubov spectrum of elongated Bose–Einstein condensates. Phys. Rev. Lett. 90, 060404 (2002).

    Article  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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, 15233–15262 (1992).

    Article  ADS  Google Scholar 

  32. Kollath, C., Meyer, J. S. & Giamarchi, T. Dipolar bosons in a planar array of one-dimensional tubes. Phys. Rev. Lett. 100, 130403 (2008).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  34. Kamenev, A. & Levchenko, A. Keldysh technique and non-linear sigma-model: Basic principles and applications. Adv. Phys. 58, 197–319 (2009).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank E. Berg, S. Huber, S. Kivelson, A. Lamacraft, K. Moler and E. Zeldov for stimulating discussions. This work was partially supported by the US–Israel BSF (E.A. and E.D.), ISF (E.A.) and Swiss SNF under MaNEP and division II (T.G.). E.D. acknowledges support from NSF DMR-0705472, CUA, DARPA-OLE and AFOSR-MURI. E.G.D.T. is supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities.

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Authors and 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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  1. Emanuele G. Dalla Torre
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All authors contributed equally to this work.

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Correspondence to Ehud Altman.

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Dalla Torre, E., Demler, E., Giamarchi, T. et al. Quantum critical states and phase transitions in the presence of non-equilibrium noise. Nature Phys 6, 806–810 (2010). https://doi.org/10.1038/nphys1754

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