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

Out-of-equilibrium steady states of a locally driven lossy qubit array

Shovan Dutta* and Nigel R. Cooper†

  • T.C.M. Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom

  • *sd843@cam.ac.uk
  • †nrc25@cam.ac.uk

Phys. Rev. Research 3, L012016 – Published 16 February, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L012016

Abstract

We find a rich variety of counterintuitive features in the steady states of a qubit array coupled to a dissipative source and sink at two arbitrary sites, using a master equation approach. We show there are setups where increasing the pump and loss rates establishes long-range coherence. At sufficiently strong dissipation, the source or sink effectively generates correlation between its neighboring sites, leading to a striking density-wave order for a class of “resonant” geometries. This effect can be used more widely to engineer nonequilibrium phases. We show the steady states are generically distinct for hard-core bosons and free fermions, and differ significantly from the ones found before in special cases. They are explained by generally applicable ansatzes for the long-time dynamics at weak and strong dissipation. Our findings are relevant for existing photonic setups.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (53)

  1. M. Schlosshauer, Quantum decoherence, Phys. Rep. 831, 1 (2019).
  2. M. Müller, S. Diehl, G. Pupillo, and P. Zoller, Engineered open systems and quantum simulations with atoms and ions, Adv. At. Mol. Opt. Phys. 61, 1 (2012).
  3. S. Diehl, E. Rico, M. A. Baranov, and P. Zoller, Topology by dissipation in atomic quantum wires, Nat. Phys. 7, 971 (2011).
  4. Y. Lin, J. P. Gaebler, F. Reiter, T. R. Tan, R. Bowler, A. S. Sørensen, D. Leibfried, and D. J. Wineland, Dissipative production of a maximally entangled steady state of two quantum bits, Nature (London) 504, 415 (2013).
  5. A. W. Carr and M. Saffman, Preparation of Entangled and Antiferromagnetic States by Dissipative Rydberg Pumping, Phys. Rev. Lett. 111, 033607 (2013).
  6. L. M. Sieberer, M. Buchhold, and S. Diehl, Keldysh field theory for driven open quantum systems, Rep. Prog. Phys. 79, 096001 (2016).
  7. G. Kordas, D. Witthaut, P. Buonsante, A. Vezzani, R. Burioni, A. I. Karanikas, and S. Wimberger, The dissipative Bose-Hubbard model, Eur. Phys. J. Spec. Top. 224, 2127 (2015).
  8. F. Verstraete, M. M. Wolf, and J. I. Cirac, Quantum computation and quantum-state engineering driven by dissipation, Nat. Phys. 5, 633 (2009).
  9. M. A. Cazalilla, R. Citro, T. Giamarchi, E. Orignac, and M. Rigol, One dimensional bosons: From condensed matter systems to ultracold gases, Rev. Mod. Phys. 83, 1405 (2011).
  10. R. Ma, B. Saxberg, C. Owens, N. Leung, Y. Lu, J. Simon, and D. I. Schuster, A dissipatively stabilized Mott insulator of photons, Nature (London) 566, 51 (2019).
  11. T. Prosen, Third quantization: a general method to solve master equations for quadratic open Fermi systems, New J. Phys. 10, 043026 (2008).
  12. T. Prosen and M. Žnidarič, Matrix product simulations of non-equilibrium steady states of quantum spin chains, J. Stat. Mech. (2009) P02035.
  13. M. Žnidarič, Exact solution for a diffusive nonequilibrium steady state of an open quantum chain, J. Stat. Mech. (2010) L05002.
  14. M. Žnidarič, Spin Transport in a One-Dimensional Anisotropic Heisenberg Model, Phys. Rev. Lett. 106, 220601 (2011).
  15. T. Prosen, Open XXZ Spin Chain: Nonequilibrium Steady State and a Strict Bound on Ballistic Transport, Phys. Rev. Lett. 106, 217206 (2011).
  16. M. Žnidarič, B. Žunkovič, and T. Prosen, Transport properties of a boundary-driven one-dimensional gas of spinless fermions, Phys. Rev. E 84, 051115 (2011).
  17. P. Kos and T. Prosen, Time-dependent correlation functions in open quadratic fermionic systems, J. Stat. Mech. (2017) 123103.
  18. T. Prosen and I. Pižorn, Quantum Phase Transition in a Far-from-Equilibrium Steady State of an XY Spin Chain, Phys. Rev. Lett. 101, 105701 (2008).
  19. M. Žnidarič, Solvable quantum nonequilibrium model exhibiting a phase transition and a matrix product representation, Phys. Rev. E 83, 011108 (2011).
  20. L. Banchi, P. Giorda, and P. Zanardi, Quantum information-geometry of dissipative quantum phase transitions, Phys. Rev. E 89, 022102 (2014).
  21. M. Žnidarič, A matrix product solution for a nonequilibrium steady state of an XX chain, J. Phys. A 43, 415004 (2010).
  22. S. Dutta and N. R. Cooper, Long-Range Coherence and Multiple Steady States in a Lossy Qubit Array, Phys. Rev. Lett. 125, 240404 (2020).
  23. B. Buča and T. Prosen, Exactly Solvable Counting Statistics in Open Weakly Coupled Interacting Spin Systems, Phys. Rev. Lett. 112, 067201 (2014).
  24. J. Yago Malo, E. P. L. van Nieuwenburg, M. H. Fischer, and A. J. Daley, Particle statistics and lossy dynamics of ultracold atoms in optical lattices, Phys. Rev. A 97, 053614 (2018).
  25. B. Paredes, A. Widera, V. Murg, O. Mandel, S. Fölling, I. Cirac, G. V. Shlyapnikov, T. W. Hänsch, and I. Bloch, Tonks–Girardeau gas of ultracold atoms in an optical lattice, Nature (London) 429, 277 (2004).
  26. T. Stöferle, H. Moritz, C. Schori, M. Köhl, and T. Esslinger, Transition from a Strongly Interacting 1D Superfluid to a Mott Insulator, Phys. Rev. Lett. 92, 130403 (2004).
  27. P. M. Preiss, R. Ma, M. E. Tai, A. Lukin, M. Rispoli, P. Zupancic, Y. Lahini, R. Islam, and M. Greiner, Strongly correlated quantum walks in optical lattices, Science 347, 1229 (2015).
  28. G. Barontini, R. Labouvie, F. Stubenrauch, A. Vogler, V. Guarrera, and H. Ott, Controlling the Dynamics of an Open Many-Body Quantum System with Localized Dissipation, Phys. Rev. Lett. 110, 035302 (2013).
  29. H. Schwager, J. I. Cirac, and G. Giedke, Dissipative spin chains: Implementation with cold atoms and steady-state properties, Phys. Rev. A 87, 022110 (2013).
  30. T. Fukuhara et al., Quantum dynamics of a mobile spin impurity, Nat. Phys. 9, 235 (2013).
  31. A. J. Daley, Quantum trajectories and open many-body quantum systems, Adv. Phys. 63, 77 (2014).
  32. G. Lindblad, On the generators of quantum dynamical semigroups, Commun. Math. Phys. 48, 119 (1976).
  33. V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, Completely positive dynamical semigroups of N-level systems, J. Math. Phys. 17, 821 (1976).
  34. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002).
  35. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L012016, which includes Refs. [ [50, 51, 52, 53]], for analytic and perturbative solution for steady states, derivation of effective dynamics and rate equations at weak and strong dissipation, and examples of dissipation-induced long-range coherence in resonant “dipole” geometries.
  36. I. Pižorn, One-dimensional Bose-Hubbard model far from equilibrium, Phys. Rev. A 88, 043635 (2013).
  37. B. Buča and T. Prosen, A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains, New J. Phys. 14, 073007 (2012).
  38. V. Popkov, S. Essink, C. Presilla, and G. Schütz, Effective quantum Zeno dynamics in dissipative quantum systems, Phys. Rev. A 98, 052110 (2018).
  39. B Misra and E. C. G. Sudarshan, The Zeno's paradox in quantum theory, J. Math. Phys. 18, 756 (1977).
  40. H. Fröml, C. Muckel, C. Kollath, A. Chiocchetta, and S. Diehl, Ultracold quantum wires with localized losses: Many-body quantum Zeno effect, Phys. Rev. B 101, 144301 (2020).
  41. I. Carusotto, A. A. Houck, A. J. Kollár, P. Roushan, D. I. Schuster, and J. Simon, Photonic materials in circuit quantum electrodynamics, Nat. Phys. 16, 268 (2020).
  42. V. Popkov, S. Essink, C. Kollath, and C. Presilla, Dissipative generation of pure steady states and a gambler's ruin problem, Phys. Rev. A 102, 032205 (2020).
  43. T. Prosen and M. Žnidarič, Long-Range Order in Nonequilibrium Interacting Quantum Spin Chains, Phys. Rev. Lett. 105, 060603 (2010).
  44. M. F. Maghrebi and A. V. Gorshkov, Nonequilibrium many-body steady states via Keldysh formalism, Phys. Rev. B 93, 014307 (2016).
  45. E. Fradkin, Jordan-Wigner Transformation for Quantum-Spin Systems in Two Dimensions and Fractional Statistics, Phys. Rev. Lett. 63, 322 (1989).
  46. R. O. Umucalılar and I. Carusotto, Generation and spectroscopic signatures of a fractional quantum Hall liquid of photons in an incoherently pumped optical cavity, Phys. Rev. A 96, 053808 (2017).
  47. L. Corman, P. Fabritius, S. Häusler, J. Mohan, L. H. Dogra, D. Husmann, M. Lebrat, and T. Esslinger, Quantized conductance through a dissipative atomic point contact, Phys. Rev. A 100, 053605 (2019).
  48. S. Maity, S. Bandyopadhyay, S. Bhattacharjee, and A. Dutta, Growth of mutual information in a quenched one-dimensional open quantum many-body system, Phys. Rev. B 101, 180301(R) (2020).
  49. V. Alba and F. Carollo, Spreading of correlations in Markovian open quantum systems, Phys. Rev. B 103, L020302 (2021).
  50. T. Prosen, Comments on a boundary-driven open XXZ chain: asymmetric driving and uniqueness of steady states, Phys. Scr. 86, 058511 (2012).
  51. H. Umezawa, Advanced Field Theory: Micro, Macro, and Thermal Physics (AIP, New York, 1993).
  52. M. V. Medvedyeva, F. H. L. Essler, and T. Prosen, Exact Bethe Ansatz Spectrum of a Tight-Binding Chain with Dephasing Noise, Phys. Rev. Lett. 117, 137202 (2016).
  53. D. Karevski, V. Popkov, and G. M. Schütz, Exact Matrix Product Solution for the Boundary-Driven Lindblad XXZ Chain, Phys. Rev. Lett. 110, 047201 (2013).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation