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  • Letter
  • Open Access

Signatures of non-Markovianity in cavity QED with color centers in two-dimensional materials

Mark Kamper Svendsen1, Sajid Ali1,2, Nicolas Stenger3,4,5, Kristian Sommer Thygesen1,4, and Jake Iles-Smith6,7,*

  • 1CAMD, Department of Physics, Technical University of Denmark, 2800 Kongens Lyngby, Denmark
  • 2School of Physics and Astronomy, Monash University, Victoria 3800, Australia
  • 3Department of electrical and photonics engineering, Technical University of Denmark, 2800 Kongens Lyngby, Denmark
  • 4Center for Nanostructured Graphene, Technical University of Denmark, 2800 Kongens Lyngby, Denmark
  • 5NanoPhoton–Center for Nanophotonics, Technical University of Denmark, 2800 Kongens Lyngby, Denmark
  • 6Department of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
  • 7Department of Electrical and Electronic Engineering, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom

  • *jake.iles-smith@manchester.ac.uk

Phys. Rev. Research 5, L032037 – Published 15 September, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L032037

Abstract

Light-matter interactions of defects in two-dimensional materials are expected to be profoundly impacted by strong coupling to phonons. In this work, we combine ab initio calculations of a defect in hBN with a fully quantum mechanical and numerically exact description of a cavity-defect system to elucidate this impact. We show that, even at weak light-matter coupling, the dynamical evolution of the cavity-defect system has clear signatures of non-Markovian phonon effects, and that linear absorption spectra show the emergence of hybridized light-matter-phonon states in regimes of strong light-matter coupling. We emphasise that our methodology is general, and can be applied to a wide variety of material-defect systems.

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References (60)

  1. C. Chakraborty, L. Kinnischtzke, K. M. Goodfellow, R. Beams, and A. N. Vamivakas, Voltage-controlled quantum light from an atomically thin semiconductor, Nat. Nanotechnol. 10, 507 (2015).
  2. Y.-M. He, G. Clark, J. R. Schaibley, Y. He, M.-C. Chen, Y.-J. Wei, X. Ding, Q. Zhang, W. Yao, X. Xu, C.-Y. Lu, and J.-W. Pan, Single quantum emitters in monolayer semiconductors, Nat. Nanotechnol. 10, 497 (2015).
  3. M. Koperski, K. Nogajewski, A. Arora, V. Cherkez, P. Mallet, J.-Y. Veuillen, J. Marcus, P. Kossacki, and M. Potemski, Single photon emitters in exfoliated WSe2 structures, Nat. Nanotechnol. 10, 503 (2015).
  4. A. Srivastava, M. Sidler, A. V. Allain, D. S. Lembke, A. Kis, and A. Imamolu, Optically active quantum dots in monolayer WSe2, Nat. Nanotechnol. 10, 491 (2015).
  5. J. Klein, M. Lorke, M. Florian, F. Sigger, L. Sigl, S. Rey, J. Wierzbowski, J. Cerne, K. Müller, E. Mitterreiter et al., Site-selectively generated photon emitters in monolayer MoS2 via local helium ion irradiation, Nat. Commun. 10, 2755 (2019).
  6. S. Michaelis de Vasconcellos, D. Wigger, U. Wurstbauer, A. W. Holleitner, R. Bratschitsch, and T. Kuhn, Single-photon emitters in layered van der Waals materials, Phys. Status Solidi B 259, 2100566 (2022).
  7. M. Kianinia, Z.-Q. Xu, M. Toth, and I. Aharonovich, Quantum emitters in 2D materials: Emitter engineering, photophysics, and integration in photonic nanostructures, Appl. Phys. Rev. 9, 011306 (2022).
  8. T. T. Tran, K. Bray, M. J. Ford, M. Toth, and I. Aharonovich, Quantum emission from hexagonal boron nitride monolayers, Nat. Nanotechnol. 11, 37 (2016).
  9. I. Aharonovich and M. Toth, Quantum emitters in two dimensions, Science 358, 170 (2017).
  10. M. Fischer, J. M. Caridad, A. Sajid, S. Ghaderzadeh, M. Ghorbani-Asl, L. Gammelgaard, P. Bøggild, K. S. Thygesen, A. V. Krasheninnikov, S. Xiao et al., Controlled generation of luminescent centers in hexagonal boron nitride by irradiation engineering, Sci. Adv. 7, eabe7138 (2021).
  11. N. Mendelson, D. Chugh, J. R. Reimers, T. S. Cheng, A. Gottscholl, H. Long, C. J. Mellor, A. Zettl, V. Dyakonov, P. H. Beton et al., Identifying carbon as the source of visible single-photon emission from hexagonal boron nitride, Nat. Mater. 20, 321 (2021).
  12. A. Gottscholl, M. Kianinia, V. Soltamov, S. Orlinskii, G. Mamin, C. Bradac, C. Kasper, K. Krambrock, A. Sperlich, M. Toth et al., Initialization and read-out of intrinsic spin defects in a van der Waals crystal at room temperature, Nat. Mater. 19, 540 (2020).
  13. M. Hoese, P. Reddy, A. Dietrich, M. K. Koch, K. G. Fehler, M. W. Doherty, and A. Kubanek, Mechanical decoupling of quantum emitters in hexagonal boron nitride from low-energy phonon modes, Sci. Adv. 6, eaba6038 (2020).
  14. G. Cassabois, P. Valvin, and B. Gil, Hexagonal boron nitride is an indirect bandgap semiconductor, Nat. Photonics 10, 262 (2016).
  15. T. T. Tran, C. Bradac, A. S. Solntsev, M. Toth, and I. Aharonovich, Suppression of spectral diffusion by anti-stokes excitation of quantum emitters in hexagonal boron nitride, Appl. Phys. Lett. 115, 071102 (2019).
  16. K. Li, T. Smart, and Y. Ping, C2CN as a 2 eV single-photon emitter candidate in hexagonal boron nitride, arXiv:2110.01787.
  17. T. Vogl, R. Lecamwasam, B. C. Buchler, Y. Lu, and P. K. Lam, Compact cavity-enhanced single-photon generation with hexagonal boron nitride, ACS Photonics 6, 1955 (2019).
  18. S. Häußler, G. Bayer, R. Waltrich, N. Mendelson, C. Li, D. Hunger, I. Aharonovich, and A. Kubanek, Tunable fiber-cavity enhanced photon emission from defect centers in hBn, Adv. Opt. Mater. 9, 2002218 (2021).
  19. E. V. Denning, J. Iles-Smith, N. Gregersen, and J. Mork, Phonon effects in quantum dot single-photon sources, Opt. Mater. Express 10, 222 (2020).
  20. A. Nazir and D. P. S. McCutcheon, Modelling exciton–phonon interactions in optically driven quantum dots, J. Phys.: Condens. Matter 28, 103002 (2016).
  21. T. Q. P. Vuong, G. Cassabois, P. Valvin, A. Ouerghi, Y. Chassagneux, C. Voisin, and B. Gil, Phonon-Photon Mapping in a Color Center in Hexagonal Boron Nitride, Phys. Rev. Lett. 117, 097402 (2016).
  22. M. A. Feldman, A. Puretzky, L. Lindsay, E. Tucker, D. P. Briggs, P. G. Evans, R. F. Haglund, and B. J. Lawrie, Phonon-induced multicolor correlations in hBn single-photon emitters, Phys. Rev. B 99, 020101(R) (2019).
  23. P. Khatri, I. J. Luxmoore, and A. J. Ramsay, Phonon sidebands of color centers in hexagonal boron nitride, Phys. Rev. B 100, 125305 (2019).
  24. G. Grosso, H. Moon, C. J. Ciccarino, J. Flick, N. Mendelson, L. Mennel, M. Toth, I. Aharonovich, P. Narang, and D. R. Englund, Low-temperature electronphonon interaction of quantum emitters in hexagonal boron nitride, ACS Photonics 7, 1410 (2020).
  25. A. Sajid and K. S. Thygesen, VNCB defect as source of single photon emission from hexagonal boron nitride, 2D Mater. 7, 031007 (2020).
  26. C. Jara, T. Rauch, S. Botti, M. A. L. Marques, A. Norambuena, R. Coto, J. E. Castellanos-Águila, J. R. Maze, and F. Munoz, First-principles identification of single photon emitters based on carbon clusters in hexagonal boron nitride, J. Phys. Chem. A 125, 1325 (2021).
  27. K. Li, T. J. Smart, and Y. Ping, Carbon trimer as a 2 eV single-photon emitter candidate in hexagonal boron nitride: A first-principles study, Phys. Rev. Mater. 6, L042201 (2022).
  28. A. Strathearn, P. Kirton, D. Kilda, J. Keeling, and B. W. Lovett, Efficient non-Markovian quantum dynamics using time-evolving matrix product operators, Nat. Commun. 9, 3322 (2018).
  29. M. R. Jørgensen and F. A. Pollock, Exploiting the Causal Tensor Network Structure of Quantum Processes to Efficiently Simulate Non-Markovian Path Integrals, Phys. Rev. Lett. 123, 240602 (2019).
  30. D. Gribben, A. Strathearn, J. Iles-Smith, D. Kilda, A. Nazir, B. W. Lovett, and P. Kirton, Exact quantum dynamics in structured environments, Phys. Rev. Res. 2, 013265 (2020).
  31. D. Gribben, D. M. Rouse, J. Iles-Smith, A. Strathearn, H. Maguire, P. Kirton, A. Nazir, E. M. Gauger, and B. W. Lovett, Exact dynamics of nonadditive environments in non-Markovian open quantum systems, PRX Quantum 3, 010321 (2022).
  32. M. K. Svendsen, Y. Kurman et al., Combining density functional theory with macroscopic QED for quantum light-matter interactions in 2D materials, Nat. Commun. 12, 2778 (2021).
  33. S. Latini, U. De Giovannini, E. J. Sie, N. Gedik, H. Hübener, and A. Rubio, Phonoritons as Hybridized Exciton-Photon-Phonon Excitations in a Monolayer h-BN Optical Cavity, Phys. Rev. Lett. 126, 227401 (2021).
  34. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.5.L032037 for a detailed derivation of the model, methods used, and the C2CN defect.
  35. A. Sajid, J. R. Reimers, and M. J. Ford, Defect states in hexagonal boron nitride: Assignments of observed properties and prediction of properties relevant to quantum computation, Phys. Rev. B 97, 064101 (2018).
  36. This analysis is repeated in the Supplemental Material [34] for the C2CN defect.
  37. B. M. Garraway, Nonperturbative decay of an atomic system in a cavity, Phys. Rev. A 55, 2290 (1997).
  38. G. Pleasance, B. M. Garraway, and F. Petruccione, Generalized theory of pseudomodes for exact descriptions of non-Markovian quantum processes, Phys. Rev. Res. 2, 043058 (2020).
  39. E. V. Denning, J. Iles-Smith, A. D. Osterkryger, N. Gregersen, and J. Mork, Cavity-waveguide interplay in optical resonators and its role in optimal single-photon sources, Phys. Rev. B 98, 121306(R) (2018).
  40. H. J. Carmichael, Statistical Methods in Quantum Optics 1: Master Equations and Fokker-Planck Equations (Springer, Berlin, 1999), Vol. 1.
  41. H. Maguire, J. Iles-Smith, and A. Nazir, Environmental Nonadditivity and Franck-Condon physics in Nonequilibrium Quantum Systems, Phys. Rev. Lett. 123, 093601 (2019).
  42. G. D. Mahan, Many-Particle Physics (Springer, Berlin, 2013).
  43. F. Duschinsky, The importance of the electron spectrum in multi atomic molecules. Concerning the Franck-Condon principle, Acta Physicochim. URSS 7, 551 (1937).
  44. R. Borrelli, A. Capobianco, and A. Peluso, Franck–Condon factors—computational approaches and recent developments, Can. J. Chem. 91, 495 (2013).
  45. G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558 (1993).
  46. H.-P. Breuer, F. Petruccione et al., The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002).
  47. M. Popovic, M. T. Mitchison, A. Strathearn, B. W. Lovett, J. Goold, and P. R. Eastham, Quantum heat statistics with time-evolving matrix product operators, PRX Quantum 2, 020338 (2021).
  48. G. E. Fux, E. P. Butler, P. R. Eastham, B. W. Lovett, and J. Keeling, Efficient Exploration of Hamiltonian Parameter Space for Optimal Control of Non-Markovian Open Quantum Systems, Phys. Rev. Lett. 126, 200401 (2021).
  49. N. Makri and D. E. Makarov, Tensor propagator for iterative quantum time evolution of reduced density matrices. I. Theory, J. Chem. Phys. 102, 4600 (1995).
  50. N. Makri and D. E. Makarov, Tensor propagator for iterative quantum time evolution of reduced density matrices. II. Numerical methodology, J. Chem. Phys. 102, 4611 (1995).
  51. M. Cygorek, M. Cosacchi, A. Vagov, V. M. Axt, B. W. Lovett, J. Keeling, and E. M. Gauger, Simulation of open quantum systems by automated compression of arbitrary environments, Nat. Phys. 18, 662 (2022).
  52. H. F. Trotter, On the product of semi-groups of operators, Proc. Am. Math. Soc. 10, 545 (1959).
  53. A. Strathearn, B. W. Lovett, and P. Kirton, Efficient real-time path integrals for non-Markovian spin-boson models, New J. Phys. 19, 093009 (2017).
  54. R. Orús, A practical introduction to tensor networks: Matrix product states and projected entangled pair states, Ann. Phys. (NY) 349, 117 (2014).
  55. M. Ruggenthaler, N. Tancogne-Dejean, J. Flick, H. Appel, and A. Rubio, From a quantum-electrodynamical light–matter description to novel spectroscopies, Nat. Rev. Chem. 2, 0118 (2018).
  56. J. Flick, D. M. Welakuh, M. Ruggenthaler, H. Appel, and A. Rubio, Light–matter response in nonrelativistic quantum electrodynamics, ACS Photonics 6, 2757 (2019).
  57. S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford University Press, Oxford, 1999).
  58. J. Iles-Smith, D. P. S. McCutcheon, A. Nazir, and J. Mørk, Phonon scattering inhibits simultaneous near-unity efficiency and indistinguishability in semiconductor single-photon sources, Nat. Photonics 11, 521 (2017).
  59. J. Del Pino, F. A. Y. N. Schröder, A. W. Chin, J. Feist, and F. J. Garcia-Vidal, Tensor Network Simulation of Non-Markovian Dynamics in Organic Polaritons, Phys. Rev. Lett. 121, 227401 (2018).
  60. S. White, C. Stewart, A. S. Solntsev, C. Li, M. Toth, M. Kianinia, and I. Aharonovich, Phonon dephasing and spectral diffusion of quantum emitters in hexagonal boron nitride, Optica 8, 1153 (2021).

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