- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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
  • Open Access

Non-Markovian dynamics of generation of bound states in the continuum via single-photon scattering

Giuseppe Magnifico, Maria Maffei*, Domenico Pomarico, Debmalya Das, Paolo Facchi, Saverio Pascazio, and Francesco V. Pepe

  • *Contact author: maria.maffei@uniba.it
PDF

Phys. Rev. Research 7, 033249 – Published 15 September, 2025

DOI: https://doi.org/10.1103/gtf6-zb57

Abstract

The excitation of bound states in the continuum (BICs) in two- or multiqubit systems lies at the heart of entanglement generation and harnessing in waveguide quantum electrodynamics platforms. However, the generation of qubit pair BICs through single-photon scattering is hindered by the fact that these states are effectively decoupled from propagating photons. We prove that scattering of a parity-invariant single photon on a qubit pair, combined with a properly engineered time variation of the qubit detuning, is not only feasible, but also more effective than strategies based on the relaxation of the excited states of the qubits when the distance between the qubits gives rise to non-negligible photon delays (non-Markovian regime). The use of tensor network methods to simulate the proposed scheme enables us to include such photon delays in collision models, thus opening the possibility to follow the time evolution of the full quantum system, including qubits and field, and to efficiently implement and characterize the dynamics, hence identifying optimal working points for the BIC generation.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (74)

  1. F. Ciccarello, P. Lodahl, and D. Schneble, Waveguide quantum electrodynamics, Opt. Photon. News 35, 34 (2024).
  2. C. M. Roy, D. Wilson, and O. Firstenberg, Colloquium: Strongly interacting photons in one-dimensional continuum, Rev. Mod. Phys. 89, 021001 (2017).
  3. D. Lonigro, P. Facchi, S. Pascazio, F. V. Pepe, and D. Pomarico, Stationary excitation waves and multimerization in arrays of quantum emitters, New J. Phys. 23, 103033 (2021).
  4. A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation, Phys. Rev. A 69, 062320 (2004).
  5. J. Q. You and F. Nori, Atomic physics and quantum optics using superconducting circuits, Nature (London) 474, 589 (2011).
  6. A. Faraon, E. Waks, D. Englund, I. Fushman, and J. Vučković, Efficient photonic crystal cavity-waveguide couplers, Appl. Phys. Lett. 90, 073102 (2007).
  7. B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, A photon turnstile dynamically regulated by one atom, Science 319, 1062 (2008).
  8. E. Vetsch, D. Reitz, G. Sague, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber, Phys. Rev. Lett. 104, 203603 (2010).
  9. M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, Efficient all-optical switching using slow light within a hollow fiber, Phys. Rev. Lett. 102, 203902 (2009).
  10. A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics, Nature (London) 431, 162 (2004).
  11. O. Astafiev, A. M. Zagoskin, A. A. Abdumalikov, Y. A. Pashkin, T. Yamamoto, K. Inomata, Y. Nakamura, and J. S. Tsai, Resonance fluorescence of a single artificial atom, Science 327, 840 (2010).
  12. J. S. Douglas, H. Habibian, C. L. Hung, A. V. Gorshkov, H. J. Kimble, and D. E. Chang, Quantum many-body models with cold atoms coupled to photonic crystals, Nat. Photon. 9, 326 (2015).
  13. U. Dorner and P. Zoller, Laser-driven atoms in half-cavities, Phys. Rev. A 66, 023816 (2002).
  14. G. Zumofen, N. M. Mojarad, V. Sandoghdar, and M. Agio, Perfect reflection of light by an oscillating dipole, Phys. Rev. Lett. 101, 180404 (2008).
  15. N. Lindlein, R. Maiwald, H. Konermann, M. Sondermann, U. Peschel, and G. Leuchs, A new 4π geometry optimized for focusing on an atom with a dipole-like radiation pattern, Laser Phys. 17, 927 (2007).
  16. H. Dong, Z. R. Gong, H. Ian, L. Zhou, and C. P. Sun, Intrinsic cavity QED and emergent quasinormal modes for a single photon, Phys. Rev. A 79, 063847 (2009).
  17. T. Tufarelli, F. Ciccarello, and M. S. Kim, Dynamics of spontaneous emission in a single-end photonic waveguide, Phys. Rev. A 87, 013820 (2013).
  18. J. T. Shen and S. Fan, Coherent single photon transport in a one-dimensional waveguide coupled with superconducting quantum bits, Phys. Rev. Lett. 95, 213001 (2005).
  19. V. I. Yudson, Dynamics of the integrable one-dimensional system “photons + two-level atoms”, Phys. Lett. A 129, 17 (1988).
  20. M. Weng, H. Yu, and Z. Wang, High-fidelity generation of Bell and w states in a giant-atom system via bound states in the continuum, Phys. Rev. A 111, 053711 (2025).
  21. S. Mahmoodian, G. Calajó, D. E. Chang, K. Hammerer, and A. S. Sørensen, Dynamics of many-body photon bound states in chiral waveguide QED, Phys. Rev. X 10, 031011 (2020).
  22. P. Facchi, D. Lonigro, S. Pascazio, F. V. Pepe, and D. Pomarico, Bound states in the continuum for an array of quantum emitters, Phys. Rev. A 100, 023834 (2019).
  23. S. Tirone, G. M. Andolina, G. Calajò, V. Giovannetti, and D. Rossini, Many-body enhancement of energy storage in a waveguide-QED quantum battery, Phys. Rev. A 112, 013717 (2025).
  24. A. Asenjo-Garcia, M. Moreno-Cardoner, A. Albrecht, H. J. Kimble, and D. E. Chang, Exponential improvement in photon storage fidelities using subradiance and “selective radiance” in atomic arrays, Phys. Rev. X 7, 031024 (2017).
  25. P. C. Cárdenas, M. Paternostro, and F. L. Semião, Non-Markovian qubit dynamics in a circuit-QED setup, Phys. Rev. A 91, 022122 (2015).
  26. H. Pichler, S. Choi, P. Zoller, and M. D. Lukin, Universal photonic quantum computation via time-delayed feedback, Proc. Natl. Acad. Sci. USA 114, 11362 (2017).
  27. I. Papaefstathiou, D. Malz, J. I. Cirac, and M. C. Bañuls, Efficient tensor network simulation of multi-emitter non-Markovian systems, Phys. Rev. A 112, 013721 (2025).
  28. D. Cilluffo, M. Kost, N. Lorenzoni, and M. B. Plenio, Operator-basis matrix product state formalism for optical circuits, arXiv:2502.01737.
  29. A. Gonzalez-Tudela, D. Martin-Cano, E. Moreno, L. Martin-Moreno, C. Tejedor, and F. J. Garcia-Vidal, Entanglement of two qubits mediated by one-dimensional plasmonic waveguides, Phys. Rev. Lett. 106, 020501 (2011).
  30. E. Shahmoon and G. Kurizki, Nonradiative interaction and entanglement between distant atoms, Phys. Rev. A 87, 033831 (2013).
  31. P. Facchi, M. S. Kim, S. Pascazio, F. V. Pepe, D. Pomarico, and T. Tufarelli, Bound states and entanglement generation in waveguide quantum electrodynamics, Phys. Rev. A 94, 043839 (2016).
  32. X. H. H. Zhang and H. U. Baranger, Heralded bell state of dissipative qubits using classical light in a waveguide, Phys. Rev. Lett. 122, 140502 (2019).
  33. H. Zheng and H. U. Baranger, Persistent quantum beats and long-distance entanglement from waveguide-mediated interactions, Phys. Rev. Lett. 110, 113601 (2013).
  34. C. Gonzalez-Ballestero, F. J. Garcia-Vidal, and E. Moreno, Non-Markovian effects in waveguide-mediated entanglement, New J. Phys. 15, 073015 (2013).
  35. E. S. Redchenko and V. I. Yudson, Decay of metastable excited states of two qubits in a waveguide, Phys. Rev. A 90, 063829 (2014).
  36. M. Laakso and M. Pletyukhov, Scattering of two photons from two distant qubits: Exact solution, Phys. Rev. Lett. 113, 183601 (2014).
  37. A. F. van Loo, A. Fedorov, K. Lalumière, B. C. Sanders, A. Blais, and A. Wallraff, Photon-mediated interactions between distant artificial atoms, Science 342, 1494 (2013).
  38. A. Rosario Hamann, C. Müller, M. Jerger, M. Zanner, J. Combes, M. Pletyukhov, M. Weides, T. M. Stace, and A. Fedorov, Nonreciprocity realized with quantum nonlinearity, Phys. Rev. Lett. 121, 123601 (2018).
  39. E. Mascarenhas, M. F. Santos, A. Auffèves, and D. Gerace, Quantum rectifier in a one-dimensional photonic channel, Phys. Rev. A 93, 043821 (2016).
  40. G. Calajó, Y.-L. L. Fang, H. U. Baranger, and F. Ciccarello, Exciting a bound state in the continuum through multiphoton scattering plus delayed quantum feedback, Phys. Rev. Lett. 122, 073601 (2019).
  41. D. Lonigro, P. Facchi, A. D. Greentree, S. Pascazio, F. V. Pepe, and D. Pomarico, Photon-emitter dressed states in a closed waveguide, Phys. Rev. A 104, 053702 (2021).
  42. P.-O. Guimond, B. Vermersch, M. Juan, A. Sharafiev, G. Kirchmair, and P. Zoller, A unidirectional on-chip photonic interface for superconducting circuits, npj Quantum Inf. 6, 32 (2020).
  43. M. Scigliuzzo, G. Calajó, F. Ciccarello, D. P. Lozano, A. Bengtsson, P. Scarlino, A. Wallraff, D. Chang, P. Delsing, and S. Gasparinetti, Controlling atom-photon bound states in an array of Josephson-junction resonators, Phys. Rev. X 12, 031036 (2022).
  44. S. Gasparinetti, Photons go one way or another, Nat. Phys. 19, 310 (2023).
  45. P. Facchi, S. Pascazio, F. V. Pepe, and D. Pomarico, Correlated photon emission by two excited atoms in a waveguide, Phys. Rev. A 98, 063823 (2018).
  46. M. Maffei, D. Pomarico, P. Facchi, G. Magnifico, S. Pascazio, and F. Pepe, Directional emission and photon bunching from a qubit pair in waveguide, Phys. Rev. Res. 6, L032017 (2024).
  47. F. H. Stillinger and D. R. Herrick, Bound states in the continuum, Phys. Rev. A 11, 446 (1975).
  48. H. Friedrich and D. Wintgen, Interfering resonances and bound states in the continuum, Phys. Rev. A 32, 3231 (1985).
  49. M. Gullans, T. G. Tiecke, D. E. Chang, J. Feist, J. D. Thompson, J. I. Cirac, P. Zoller, and M. D. Lukin, Nanoplasmonic lattices for ultracold atoms, Phys. Rev. Lett. 109, 235309 (2012).
  50. A. Tiranov, V. Angelopoulou, C. J. van Diepen, B. Schrinski, O. A. Dall’Alba Sandberg, Y. Wang, L. Midolo, S. Scholz, A. D. Wieck, A. Ludwig, A. S. Sørensen, and P. Lodahl, Collective super- and subradiant dynamics between distant optical quantum emitters, Science 379, 389 (2023).
  51. K. Sinha, A. González-Tudela, Y. Lu, and P. Solano, Collective radiation from distant emitters, Phys. Rev. A 102, 043718 (2020).
  52. K. Sinha, P. Meystre, E. A. Goldschmidt, F. K. Fatemi, S. L. Rolston, and P. Solano, Non-Markovian collective emission from macroscopically separated emitters, Phys. Rev. Lett. 124, 043603 (2020).
  53. Z. Hayran and F. Monticone, Capturing broadband light in a compact bound state in the continuum, ACS Photon. 8, 813 (2021).
  54. R. Trivedi, D. Malz, S. Sun, S. Fan, and J. Vučković, Optimal two-photon excitation of bound states in non-Markovian waveguide QED, Phys. Rev. A 104, 013705 (2021).
  55. W. Alvarez-Giron, P. Solano, K. Sinha, and B. Barberis-Blostein, Delay-induced spontaneous dark state generation from two distant excited atoms, Phys. Rev. Res. 6, 023213 (2024).
  56. M. Pechal, J.-C. Besse, M. Mondal, M. Oppliger, S. Gasparinetti, and A. Wallraff, Superconducting switch for fast on-chip routing of quantum microwave fields, Phys. Rev. Appl. 6, 024009 (2016).
  57. C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature (London) 479, 376 (2011).
  58. C. M. Wilson, T. Duty, M. Sandberg, F. Persson, V. Shumeiko, and P. Delsing, Photon generation in an electromagnetic cavity with a time-dependent boundary, Phys. Rev. Lett. 105, 233907 (2010).
  59. H. Pichler and P. Zoller, Photonic circuits with time delays and quantum feedback, Phys. Rev. Lett. 116, 093601 (2016).
  60. P.-O. Guimond, M. Pletyukhov, H. Pichler, and P. Zoller, Delayed coherent quantum feedback from a scattering theory and a matrix product state perspective, Quantum Sci. Technol. 2, 044012 (2017).
  61. D. Cilluffo, N. Lorenzoni, and M. B. Plenio, Simulating Gaussian boson sampling with tensor networks in the Heisenberg picture, arXiv:2305.11215.
  62. K. Vodenkova and H. Pichler, Continuous coherent quantum feedback with time delays: Tensor network solution, Phys. Rev. X 14, 031043 (2024).
  63. C. W. Gardiner and M. J. Collett, Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation, Phys. Rev. A 31, 3761 (1985).
  64. C. W. Gardiner and P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Springer, Berlin, 2000).
  65. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley-VCH Verlag GmbH, Weinheim, 1998).
  66. D. Burgarth, P. Facchi, R. Hillier, and M. Ligabò, Taming the rotating wave approximation, Quantum 8, 1262 (2024).
  67. J. Combes, J. Kerckhoff, and M. Sarovar, The SLH framework for modeling quantum input-output networks, Adv. Phys. X 2, 784 (2017).
  68. V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, Completely positive dynamical semigroups of N-level systems, J. Math. Phys. 17, 821 (1976).
  69. G. Lindblad, On the generators of quantum dynamical semigroups, Commun. Math. Phys. 48, 119 (1976).
  70. F. Ciccarello, Collision models in quantum optics, Quantum Meas. Quantum Metrol. 4, 53 (2017).
  71. D. Cilluffo, A. Carollo, S. Lorenzo, J. A. Gross, G. M. Palma, and F. Ciccarello, Collisional picture of quantum optics with giant emitters, Phys. Rev. Res. 2, 043070 (2020).
  72. F. Ciccarello, S. Lorenzo, V. Giovannetti, and G. M. Palma, Quantum collision models: Open system dynamics from repeated interactions, Phys. Rep. 954, 1 (2022).
  73. I.-C. Hoi, A. F. Kockum, L. Tornberg, A. Pourkabirian, G. Johansson, P. Delsing, and C. M. Wilson, Probing the quantum vacuum with an artificial atom in front of a mirror, Nat. Phys. 11, 1045 (2015).
  74. H.-P. Breuer, E.-M. Laine, and J. Piilo, Measure for the degree of non-Markovian behavior of quantum processes in open systems, Phys. Rev. Lett. 103, 210401 (2009).

Outline

Information

Phys. Rev. Research 7, 033249– Published 15 September, 2025
  • Received 14 January 2025
  • Revised 4 June 2025
  • Accepted 18 July 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation