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Thermometry of strongly correlated fermionic quantum systems using impurity probes

George Mihailescu*, Steve Campbell†, and Andrew K. Mitchell‡

  • School of Physics, University College Dublin, Belfield, Dublin 4, Ireland and Centre for Quantum Engineering, Science, and Technology, University College Dublin, Dublin 4, Ireland

  • *george.mihailescu@ucdconnect.ie
  • †steve.campbell@ucd.ie
  • ‡andrew.mitchell@ucd.ie
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Phys. Rev. A 107, 042614 – Published 18 April, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.042614

Abstract

We study quantum-impurity models as a platform for quantum thermometry. A single quantum spin-12 impurity is coupled to an explicit, structured, fermionic thermal sample system, which we refer to as the environment or bath. We critically assess the thermometric capabilities of the impurity as a probe, when its coupling to the environment is of Ising or Kondo exchange type. In the Ising case, we find sensitivity equivalent to that of an idealized two-level system, with peak thermometric performance obtained at a temperature that scales linearly in the applied control field, independent of the coupling strength and environment spectral features. By contrast, a richer thermometric response can be realized for Kondo impurities, since strong probe-environment entanglement can then develop. At low temperatures, we uncover a regime with a universal thermometric response that is independent of microscopic details, controlled only by the low-energy spectral features of the environment. The many-body entanglement that develops in this regime means that low-temperature thermometry with a weakly applied control field is inherently less sensitive, while optimal sensitivity is recovered by suppressing the entanglement with stronger fields.

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References (92)

  1. A. Puglisi, A. Sarracino, and A. Vulpiani, Temperature in and out of equilibrium: A review of concepts, tools and attempts, Phys. Rep. 709, 1 (2017).
  2. M. Campisi, P. Hänggi, and P. Talkner, Colloquium: Quantum fluctuation relations: Foundations and applications, Rev. Mod. Phys. 83, 771 (2011).
  3. M. Perarnau-Llobet, E. Bäumer, K. V. Hovhannisyan, M. Huber, and A. Acin, No-Go Theorem for the Characterization of Work Fluctuations in Coherent Quantum Systems, Phys. Rev. Lett. 118, 070601 (2017).
  4. M. Esposito, K. Lindenberg, and C Van den Broeck, Entropy production as correlation between system and reservoir, New J. Phys. 12, 013013 (2010).
  5. R. Alicki and R. Kosloff, in Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions, edited by F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso, Fundamental Theories of Physics Vol. 195 (Springer, Cham, 2018), p. 1.
  6. M. G. A. Paris, Quantum estimation for quantum technology, Int. J. Quantum Inf. 07, 125 (2009).
  7. V. Giovannetti, S. Lloyd, and L. Maccone, Quantum Metrology, Phys. Rev. Lett. 96, 010401 (2006).
  8. C. W. Helstrom, Quantum detection and estimation theory, J. Stat. Phys. 1, 231 (1969).
  9. K. V. Hovhannisyan and L. A. Correa, Measuring the temperature of cold many-body quantum systems, Phys. Rev. B 98, 045101 (2018).
  10. S. Campbell, M. G. Genoni, and S. Deffner, Precision thermometry and the quantum speed limit, Quantum Sci. Technol. 3, 025002 (2018).
  11. M. Mehboudi, M. Moreno-Cardoner, G. De Chiara, and A. Sanpera, Thermometry precision in strongly correlated ultracold lattice gases, New J. Phys. 17, 055020 (2015).
  12. M. Mehboudi, A. Sanpera, and L. A. Correa, Thermometry in the quantum regime: Recent theoretical progress, J. Phys. A: Math. Theor. 52, 303001 (2019).
  13. M. T. Mitchison, T. Fogarty, G. Guarnieri, S. Campbell, T. Busch, and J. Goold, In Situ Thermometry of a Cold Fermi Gas via Dephasing Impurities, Phys. Rev. Lett. 125, 080402 (2020).
  14. V. Cavina, L. Mancino, A. De Pasquale, I. Gianani, M. Sbroscia, R. I. Booth, E. Roccia, R. Raimondi, V. Giovannetti, and M. Barbieri, Bridging thermodynamics and metrology in nonequilibrium quantum thermometry, Phys. Rev. A 98, 050101(R) (2018).
  15. S. Razavian, C. Benedetti, M. Bina, Y. Akbari-Kourbolagh, and M. G. A. Paris, Quantum thermometry by single-qubit dephasing, Eur. Phys. J. Plus 134, 284 (2019).
  16. E. O'Connor, B. Vacchini, and S. Campbell, Stochastic collisional quantum thermometry, Entropy 23, 12 (2021).
  17. A. Shu, S. Seah, and V. Scarani, Surpassing the thermal Cramér-Rao bound with collisional thermometry, Phys. Rev. A 102, 042417 (2020).
  18. G. O. Alves and G. T. Landi, Bayesian estimation for collisional thermometry, Phys. Rev. A 105, 012212 (2022).
  19. J. Tabanera, I. Luque, S. L. Jacob, M. Esposito, F. Barra, and J. M. R. Parrondo, Quantum collisional thermostats, New J. Phys. 24, 023018 (2022).
  20. R. Román-Ancheyta, B. Çakmak, and Ö. E Müstecaplıoğlu, Spectral signatures of non-thermal baths in quantum thermalization, Quantum Sci. Technol. 5, 015003 (2020).
  21. W. K. Mok, K. Bharti, L. C. Kwek, and A. Bayat, Optimal probes for global quantum thermometry, Commun. Phys. 4, 62 (2021).
  22. L. Garbe, O. Abah, S. Felicetti, and R. Puebla, Exponential time-scaling of estimation precision by reaching a quantum critical point, Phys. Rev. Res. 4, 043061 (2022).
  23. L. Garbe, O. Abah, S. Felicetti, and R. Puebla, Critical quantum metrology with fully-connected models: From Heisenberg to Kibble-Zurek scaling, Quantum Sci. Technol. 7, 035010 (2022).
  24. G. Salvatori, A. Mandarino, and M. G. A. Paris, Quantum metrology in Lipkin-Meshkov-Glick critical systems, Phys. Rev. A 90, 022111 (2014).
  25. I. Frérot and T. Roscilde, Quantum Critical Metrology, Phys. Rev. Lett. 121, 020402 (2018).
  26. S. Wald, S. V. Moreira, and F. L. Semião, In- and out-of-equilibrium quantum metrology with mean-field quantum criticality, Phys. Rev. E 101, 052107 (2020).
  27. N. Zhang, C. Chen, S.-Y. Bai, W. Wu, and J.-H. An, Non-Markovian Quantum Thermometry, Phys. Rev. Appl. 17, 034073 (2022).
  28. C. Benedetti, F. Buscemi, P. Bordone, and M. G. A. Paris, Quantum probes for the spectral properties of a classical environment, Phys. Rev. A 89, 032114 (2014).
  29. C. Benedetti, F. Salari Sehdaran, M. H. Zandi, and M. G. A. Paris, Quantum probes for the cutoff frequency of Ohmic environments, Phys. Rev. A 97, 012126 (2018).
  30. L. A. Correa, M. Mehboudi, G. Adesso, and A. Sanpera, Individual Quantum Probes for Optimal Thermometry, Phys. Rev. Lett. 114, 220405 (2015).
  31. S. Jevtic, D. Newman, T. Rudolph, and T. M. Stace, Single-qubit thermometry, Phys. Rev. A 91, 012331 (2015).
  32. J. Kondo, Resistance minimum in dilute magnetic alloys, Prog. Theor. Phys. 32, 37 (1964).
  33. S. Campbell, M. Mehboudi, G. De Chiara, and M. Paternostro, Global and local thermometry schemes in coupled quantum systems, New J. Phys. 19, 103003 (2017).
  34. S. Campbell, M. Paternostro, S. Bose, and M. S. Kim, Probing the environment of an inaccessible system by a qubit ancilla, Phys. Rev. A 81, 050301(R) (2010).
  35. J. Goold, T. Fogarty, N. Lo Gullo, M. Paternostro, and T. Busch, Orthogonality catastrophe as a consequence of qubit embedding in an ultracold Fermi gas, Phys. Rev. A 84, 063632 (2011).
  36. V. Montenegro, M. G. Genoni, A. Bayat, and M. G. A. Paris, Probing of nonlinear hybrid optomechanical systems via partial accessibility, Phys. Rev. Res. 4, 033036 (2022).
  37. D. Hangleiter, M. T. Mitchison, T. H. Johnson, M. Bruderer, M. B. Plenio, and D. Jaksch, Nondestructive selective probing of phononic excitations in a cold Bose gas using impurities, Phys. Rev. A 91, 013611 (2015).
  38. T. M. Stace, Quantum limits of thermometry, Phys. Rev. A 82, 011611(R) (2010).
  39. L. A. Correa, M. Perarnau-Llobet, K. V. Hovhannisyan, S. Hernández-Santana, M. Mehboudi, and A. Sanpera, Enhancement of low-temperature thermometry by strong coupling, Phys. Rev. A 96, 062103 (2017).
  40. G. Planella, M. F. B. Cenni, A. Acín, and M. Mehboudi, Bath-Induced Correlations Enhance Thermometry Precision at Low Temperatures, Phys. Rev. Lett. 128, 040502 (2022).
  41. M. R. Jørgensen, P. P. Potts, M. G. A. Paris, and J. B. Brask, Tight bound on finite-resolution quantum thermometry at low temperatures, Phys. Rev. Res. 2, 033394 (2020).
  42. P. P. Potts, J. B. Brask, and N. Brunner, Fundamental limits on low-temperature quantum thermometry with finite resolution, Quantum 3, 161 (2019).
  43. A. D. Pasquale, D. Rossini, R. Fazio, and V. Giovannetti, Local quantum thermal susceptibility, Nat. Commun. 7, 12782 (2016).
  44. B. R. Frieden, Science from Fisher Information: A Unification (Cambridge University Press, Cambridge, 2004).
  45. S. L. Braunstein and C. M. Caves, Statistical Distance and the Geometry of Quantum States, Phys. Rev. Lett. 72, 3439 (1994).
  46. G. Tóth and I. Apellaniz, Quantum metrology from a quantum information science perspective, J. Phys. A: Math. Theor. 47, 424006 (2014).
  47. V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nat. Photon. 5, 222 (2011).
  48. W. J. De Haas, J. De Boer, and G. J. Van den Berg, The electrical resistance of gold, copper and lead at low temperatures, Physica 1, 1115 (1934).
  49. T. A. Costi, L. Bergqvist, A. Weichselbaum, J. von Delft, T. Micklitz, A. Rosch, P. Mavropoulos, P. H. Dederichs, F. Mallet, L. Saminadayar, and C. Bäuerle, Kondo Decoherence: Finding the Right Spin Model for Iron Impurities in Gold and Silver, Phys. Rev. Lett. 102, 056802 (2009).
  50. A. Hewson, The Kondo Problem to Heavy Fermions (Cambridge University Press, Cambridge, 1993).
  51. M. Ternes, A. J. Heinrich, and W.-D. Schneider, Spectroscopic manifestations of the Kondo effect on single adatoms, J. Phys.: Condens. Matter 21, 053001 (2009).
  52. J. E. Hoffman, K. McElroy, D.-H. Lee, K. M. Lang, H. Eisaki, S. Uchida, and J. C. Davis, Imaging quasiparticle interference in Bi2Sr2CaCu2O8+δ, Science 297, 1148 (2002).
  53. P. G. Derry, A. K. Mitchell, and D. E. Logan, Quasiparticle interference from magnetic impurities, Phys. Rev. B 92, 035126 (2015); A. K. Mitchell, P. G. Derry, and D. E. Logan, Multiple magnetic impurities on surfaces: Scattering and quasiparticle interference, ibid. 91, 235127 (2015).
  54. A. K. Mitchell and L. Fritz, Signatures of Weyl semimetals in quasiparticle interference, Phys. Rev. B 93, 035137 (2016).
  55. S. Yan, L. Malavolti, J. A. J. Burgess, A. Droghetti, A. Rubio, and S. Loth, Nonlocally sensing the magnetic states of nanoscale antiferromagnets with an atomic spin sensor, Sci. Adv. 3, e1603137 (2017).
  56. D. N. Zubarev, Double-time Green functions in statistical physics, Sov. Phys. Usp. 3, 320 (1960).
  57. C. Piquard, P. Glidic, C. Han, A. Aassime, A. Cavanna, U. Gennser, Y. Meir, E. Sela, A. Anthore, and F. Pierre, Observation of a Kondo impurity state and universal screening using a charge pseudospin, arXiv:2303.12039.
  58. P. W. Anderson, Localized magnetic states in metals, Phys. Rev. 124, 41 (1961).
  59. Z. Iftikhar, A. Anthore, A. K. Mitchell, F. D. Parmentier, U. Gennser, A. Ouerghi, A. Cavanna, C. Mora, P. Simon, and F. Pierre, Tunable quantum criticality and super-ballistic transport in a “charge” Kondo circuit, Science 360, 1315 (2018).
  60. A. K. Mitchell, M. Becker, and R. Bulla, Real-space renormalization group flow in quantum impurity systems: Local moment formation and the Kondo screening cloud, Phys. Rev. B 84, 115120 (2011).
  61. I. V. Borzenets, J. Shim, and J. C. H. Chen, Observation of the Kondo screening cloud, Nature (London) 579, 210 (2020).
  62. A. Bayat, P. Sodano, and S. Bose, Negativity as the entanglement measure to probe the Kondo regime in the spin-chain Kondo model, Phys. Rev. B 81, 064429 (2010).
  63. S.-S. B. Lee, J. Park, and H.-S. Sim, Macroscopic Quantum Entanglement of a Kondo Cloud at Finite Temperature, Phys. Rev. Lett. 114, 057203 (2015).
  64. J. Shim, H.-S. Sim, and S.-S. B. Lee, Numerical renormalization group method for entanglement negativity at finite temperature, Phys. Rev. B 97, 155123 (2018).
  65. D. Kim, J. Shim, and H.-S. Sim, Universal Thermal Entanglement of Multichannel Kondo Effects, Phys. Rev. Lett. 127, 226801 (2021).
  66. T. A. Costi, Kondo Effect in a Magnetic Field and the Magnetoresistivity of Kondo Alloys, Phys. Rev. Lett. 85, 1504 (2000).
  67. K. G. Wilson, The renormalization group: Critical phenomena and the Kondo problem, Rev. Mod. Phys. 47, 773 (1975).
  68. R. Bulla, T. A. Costi, and T. Pruschke, Numerical renormalization group method for quantum impurity systems, Rev. Mod. Phys. 80, 395 (2008).
  69. D. Goldhaber-Gordon, H. Shtrikman, D. Mahalu, D. Abusch-Magder, U. Meirav, and M. A. Kastner, Kondo effect in a single-electron transistor, Nature (London) 391, 156 (1998).
  70. W. Liang, M. P. Shores, M. Bockrath, J. R. Long, and H. Park, Kondo resonance in a single-molecule transistor, Nature (London) 417, 725 (2002).
  71. A. K. Mitchell, K. G. L. Pedersen, P. Hedegård, and J. Paaske, Kondo blockade due to quantum interference in single-molecule junctions, Nat. Commun. 8, 15210 (2017).
  72. L. Fritz and M. Vojta, The physics of Kondo impurities in graphene, Rep. Prog. Phys. 76, 032501 (2013).
  73. C. Gonzalez-Buxton and K. Ingersent, Renormalization-group study of Anderson and Kondo impurities in gapless Fermi systems, Phys. Rev. B 57, 14254 (1998).
  74. A. K. Mitchell and L. Fritz, Kondo effect with diverging hybridization: Possible realization in graphene with vacancies, Phys. Rev. B 88, 075104 (2013); A. K. Mitchell, M. Vojta, R. Bulla, and L. Fritz, Quantum phase transitions and thermodynamics of the power-law Kondo model, ibid. 88, 195119 (2013).
  75. M. R. Galpin and D. E. Logan, Anderson impurity model in a semiconductor, Phys. Rev. B 77, 195108 (2008).
  76. A. N. Pasupathy, R. C. Bialczak, J. Martinek, J. E. Grose, L. A. K. Donev, P. L. McEuen, and D. C. Ralph, The Kondo effect in the presence of ferromagnetism, Science 306, 86 (2004); A. K. Mitchell, D. Schuricht, M. Vojta, and L. Fritz, Kondo effect on the surface of three-dimensional topological insulators: Signatures in scanning tunneling spectroscopy, Phys. Rev. B 87, 075430 (2013); A. K. Mitchell and L. Fritz, Kondo effect in three-dimensional Dirac and Weyl systems, ibid. 92, 121109(R) (2015).
  77. A. Polkovnikov, S. Sachdev, and M. Vojta, Impurity in a d-Wave Superconductor: Kondo Effect and STM Spectra, Phys. Rev. Lett. 86, 296 (2001).
  78. A. Bayat, Scaling of Tripartite Entanglement at Impurity Quantum Phase Transitions, Phys. Rev. Lett. 118, 036102 (2017).
  79. A. Weichselbaum and J. von Delft, Sum-Rule Conserving Spectral Functions from the Numerical Renormalization Group, Phys. Rev. Lett. 99, 076402 (2007).
  80. M. G. A. Paris, Achieving the Landau bound to precision of quantum thermometry in systems with vanishing gap, J. Phys. A: Math. Theor. 49, 03LT02 (2016).
  81. P. Zanardi, M. G. A. Paris, and L. Campos Venuti, Quantum criticality as a resource for quantum estimation, Phys. Rev. A 78, 042105 (2008).
  82. A. De Pasquale, K. Yuasa, and V. Giovannetti, Estimating temperature via sequential measurements, Phys. Rev. A 96, 012316 (2017).
  83. C. Han, Y. Meir, and E. Sela, Realistic Protocol to Measure Entanglement at Finite Temperatures, Phys. Rev. Lett. 130, 136201 (2023).
  84. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81, 109 (2009).
  85. G. Tarnopolsky, A. J. Kruchkov, and A. Vishwanath, Origin of Magic Angles in Twisted Bilayer Graphene, Phys. Rev. Lett. 122, 106405 (2019).
  86. S. Lisi, X. Lu, T. Benschop et al., Observation of flat bands in twisted bilayer graphene, Nat. Phys. 17, 189 (2021).
  87. N. F. Q. Yuan, H. Isobe, and L. Fu, Magic of high-order van Hove singularity, Nat. Commun. 10, 5769 (2019).
  88. I. Bashir, D. Leipold, E. Blokhina, M. Asker, D. Redmond, A. Esmailiyan, P. Giounanlis, H. Haenlein, X. Wu, A. Sokolov et al., Monolithic integration of quantum resonant tunneling gate on a 22nm FD-SOI CMOS process, arXiv:2112.04586; E. Blokhina, P. Giounanlis, A. K. Mitchell, D. R. Leipold, and R. B. Staszewski, CMOS position-based charge qubits: Theoretical analysis of control and entanglement, IEEE Access 8, 4182 (2019).
  89. W. Pouse, L. Peeters, C. L. Hsueh, U. Gennser, A. Cavanna, M. A. Kastner, A. K. Mitchell, and D. Goldhaber-Gordon, Quantum simulation of an exotic quantum critical point in a two-site charge Kondo circuit, Nat. Phys. 19, 492 (2023).
  90. A. Bayat, T. J. G. Apollaro, S. Paganelli, G. De Chiara, H. Johannesson, S. Bose, and P. Sodano, Nonequilibrium critical scaling in quantum thermodynamics, Phys. Rev. B 93, 201106(R) (2016).
  91. A. S. Shankar, D. O. Oriekhov, A. K. Mitchell, and L. Fritz, Kondo effect in twisted bilayer graphene, arXiv:2303.02492.
  92. K. Chen and C. Jayaprakash, The Kondo effect in pseudo-gap Fermi systems: A renormalization group study, J. Phys.: Condens. Matter 7, L491 (1995); R. Bulla, T. Pruschke, and A. C. Hewson, Anderson impurity in pseudo-gap fermi systems, ibid. 9, 10463 (1997).

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Phys. Rev. A 107, 042614– Published 18 April, 2023
  • Received 5 January 2023
  • Accepted 31 March 2023
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