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Resonant and antiresonant exciton-phonon coupling in quantum dot molecules

Michelle Lienhart1,*,†, Krzysztof Gawarecki2,*,‡, Markus Stöcker1, Frederik Bopp1, Charlotte Cullip1, Nadeem Akhlaq1, Christopher Thalacker1, Johannes Schall3, Sven Rodt3 et al.

Arne Ludwig4, Dirk Reuter5, Stephan Reitzenstein3, Kai Müller6, Paweł Machnikowski2, and Jonathan J. Finley1,§

  • *These authors contributed equally to this work.
  • †Contact author: michelle.lienhart@tum.de
  • ‡Contact author: krzysztof.gawarecki@pwr.edu.pl
  • §Contact author: jj.finley@tum.de
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Phys. Rev. B 112, 235305 – Published 8 December, 2025

DOI: https://doi.org/10.1103/xc25-1tph

Abstract

Spins confined in optically active quantum dot molecules (QDMs) can be used for the deterministic generation of photonic graph states with tailored entanglement structures. Their usefulness for the generation of such nonclassical states of light is determined by orbital and spin decoherence mechanisms, particularly phonon-mediated processes dominant at energy scales up to a few millielectronvolts. Here, we directly measure the spectral function of orbital phonon relaxation between the energy states of the neutral exciton in a QDM and benchmark our findings against microscopic k·p theory. Our results reveal pronounced resonances and antiresonances in the phonon-relaxation rates, ranging from tens of µs−1 up to tens of ns−1. Comparison with a kinetic model reveals the voltage (energy) dependent phonon coupling strength and fully explains the interplay between phonon-assisted relaxation and radiative recombination. The resonances and antiresonances enable further tunability of the exciton lifetime which can be leveraged to increase the lifetime of energetically unfavorable charge configurations needed for realizing efficient spin-photon interfaces and multidimensional cluster states.

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References (75)

  1. P.-L. Ardelt, K. Gawarecki, K. Müller, A. M. Waeber, A. Bechtold, K. Oberhofer, J. M. Daniels, F. Klotz, M. Bichler, T. Kuhn, H. J. Krenner, P. Machnikowski, and J. J. Finley, Coulomb mediated hybridization of excitons in coupled quantum dots, Phys. Rev. Lett. 116, 077401 (2016).
  2. F. Bopp, J. Schall, N. Bart, F. Vögl, C. Cullip, F. Sbresny, K. Boos, C. Thalacker, M. Lienhart, S. Rodt, D. Reuter, A. Ludwig, Andreas D. Wieck, S. Reitzenstein, K. Müller, and Jonathan J. Finley, Coherent driving of direct and indirect excitons in a quantum dot molecule, Phys. Rev. B 107, 165426 (2023).
  3. F. Bopp, J. Rojas, N. Revenga, H. Riedl, F. Sbresny, K. Boos, T. Simmet, A. Ahmadi, D. Gershoni, J. Kasprzak, A. Ludwig, S. Reitzenstein, A. Wieck, D. Reuter, K. Müller, and J. J. Finley, Quantum dot molecule devices with optical control of charge status and electronic control of coupling, Adv Quantum Tech 5, 2200049 (2022).
  4. Sophia E. Economou, N. Lindner, and T. Rudolph, Optically generated 2-dimensional photonic cluster state from coupled quantum dots, Phys. Rev. Lett. 105, 093601 (2010).
  5. Netanel H. Lindner and T. Rudolph, Proposal for pulsed on-demand sources of photonic cluster state strings, Phys. Rev. Lett. 103, 113602 (2009).
  6. A. Vezvaee, P. Hilaire, Matthew F. Doty, and Sophia E. Economou, Deterministic generation of entangled photonic cluster states from quantum dot molecules, Phys. Rev. Appl. 18, L061003 (2022).
  7. D. Cogan, Z.-E. Su, O. Kenneth, and D. Gershoni, Deterministic generation of indistinguishable photons in a cluster state, Nat. Photon. 17, 324 (2023).
  8. D. D. Awschalom, R. Hanson, J. Wrachtrup, and B. B. Zhou, Quantum technologies with optically interfaced solid-state spins, Nat. Photon. 12, 516 (2018).
  9. W. B. Gao, P. Fallahi, E. Togan, J. Miguel-Sanchez, and A. Imamoglu, Observation of entanglement between a quantum dot spin and a single photon, Nature (London) 491, 426 (2012).
  10. M. F. Doty, J. I. Climente, A. Greilich, M. Yakes, A. S. Bracker, and D. Gammon, Hole-spin mixing in inas quantum dot molecules, Phys. Rev. B 81, 035308 (2010).
  11. Kha X. Tran, Allan S. Bracker, Michael K. Yakes, Joel Q. Grim, and Samuel G. Carter, Enhanced spin coherence of a self-assembled quantum dot molecule at the optimal electrical bias, Phys. Rev. Lett. 129, 027403 (2022).
  12. R. Stockill, M. J. Stanley, L. Huthmacher, E. Clarke, M. Hugues, A. J. Miller, C. Matthiesen, C. Le Gall, and M. Atatüre, Phase-tuned entangled state generation between distant spin qubits, Phys. Rev. Lett. 119, 010503 (2017).
  13. T. Nakaoka, E. C. Clark, H. J. Krenner, M. Sabathil, M. Bichler, Y. Arakawa, G. Abstreiter, and J. J. Finley, Direct observation of acoustic phonon mediated relaxation between coupled exciton states in a single quantum dot molecule, Phys. Rev. B 74, 121305(R) (2006).
  14. P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, Ultralong dephasing time in InGaAs quantum dots, Phys. Rev. Lett. 87, 157401 (2001).
  15. K. Kawa, T. Kuhn, and P. Machnikowski, Coherence limitations in the optical control of the singlet-triplet qubit in a quantum dot molecule, Phys. Rev. B 106, 125308 (2022).
  16. J. Wiercinski, E. M. Gauger, and M. Cygorek, Phonon coupling versus pure dephasing in the photon statistics of cooperative emitters, Phys. Rev. Res. 5, 013176 (2023).
  17. A. J. Ramsay, A. V. Gopal, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, Damping of exciton Rabi rotations by acoustic phonons in optically excited InGaAs/GaAs quantum dots, Phys. Rev. Lett. 104, 017402 (2010).
  18. A. Vagov, V. M. Axt, T. Kuhn, W. Langbein, P. Borri, and U. Woggon, Nonmonotonous temperature dependence of the initial decoherence in quantum dots, Phys. Rev. B 70, 201305(R) (2004).
  19. S. Butscher and A. Knorr, Theory of strong electron–phonon coupling for ultrafast intersubband excitations, Phys. Status Solidi B 243, 2423 (2006).
  20. Kushal C. Wijesundara, Juan E. Rolon, Sergio E. Ulloa, Allan S. Bracker, D. Gammon, and Eric A. Stinaff, Tunable exciton relaxation in vertically coupled semiconductor inas quantum dots, Phys. Rev. B 84, 081404(R) (2011).
  21. Juan I. Climente, A. Bertoni, G. Goldoni, and E. Molinari, Phonon-induced electron relaxation in weakly confined single and coupled quantum dots, Phys. Rev. B 74, 035313 (2006).
  22. K. Gawarecki, M. Pochwała, A. Grodecka-Grad, and P. Machnikowski, Phonon-assisted relaxation and tunneling in self-assembled quantum dot molecules, Phys. Rev. B 81, 245312 (2010).
  23. K. Gawarecki and P. Machnikowski, Phonon-assisted relaxation between hole states in quantum dot molecules, Phys. Rev. B 85, 041305(R) (2012).
  24. M. Gawełczyk and K. Gawarecki, Tunneling-related electron spin relaxation in self-assembled quantum-dot molecules, Phys. Rev. B 103, 245422 (2021).
  25. K. Müller, A. Bechtold, C. Ruppert, M. Zecherle, G. Reithmaier, M. Bichler, H. J. Krenner, G. Abstreiter, A. W. Holleitner, J. M. Villas-Boas, M. Betz, and J. J. Finley, Electrical control of interdot electron tunneling in a double ingaas quantum-dot nanostructure, Phys. Rev. Lett. 108, 197402 (2012).
  26. K. Gawarecki, Spin-orbit coupling and magnetic-field dependence of carrier states in a self-assembled quantum dot, Phys. Rev. B 97, 235408 (2018).
  27. A. Grodecka-Grad and J. Förstner, Theory of phonon-mediated relaxation in doped quantum dot molecules, Phys. Rev. B 81, 115305 (2010).
  28. P. Zanardi and F. Rossi, Quantum information in semiconductors: Noiseless encoding in a quantum-dot array, Phys. Rev. Lett. 81, 4752 (1998).
  29. P. Zanardi and F. Rossi, Subdecoherent information encoding in a quantum-dot array, Phys. Rev. B 59, 8170 (1999).
  30. H. J. Krenner, M. Sabathil, E. C. Clark, A. Kress, D. Schuh, M. Bichler, G. Abstreiter, and J. J. Finley, Direct observation of controlled coupling in an individual quantum dot molecule, Phys. Rev. Lett. 94, 057402 (2005).
  31. F. Bopp, C. Cullip, C. Thalacker, M. Lienhart, J. Schall, N. Bart, F. Sbresny, K. Boos, S. Rodt, D. Reuter, A. Ludwig, Andreas D. Wieck, S. Reitzenstein, F. Troiani, G. Goldoni, E. Molinari, K. Müller, and Jonathan J. Finley, Magnetic tuning of the tunnel coupling in an optically active quantum dot molecule, Phys. Rev. B 112, L060404 (2025).
  32. H. J. Krenner, E. C. Clark, T. Nakaoka, M. Bichler, C. Scheurer, G. Abstreiter, and J. J. Finley, Optically probing spin and charge interactions in a tunable artificial molecule, Phys. Rev. Lett. 97, 076403 (2006).
  33. E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, Optical signatures of coupled quantum dots, Science 311, 636 (2006).
  34. M. Scheibner, I. V. Ponomarev, E. A. Stinaff, M. F. Doty, A. S. Bracker, C. S. Hellberg, T. L. Reinecke, and D. Gammon, Photoluminescence spectroscopy of the molecular biexciton in vertically stacked InAs-GaAs quantum dot pairs, Phys. Rev. Lett. 99, 197402 (2007).
  35. M. F. Doty, M. Scheibner, A. S. Bracker, I. V. Ponomarev, T. L. Reinecke, and D. Gammon, Optical spectra of doubly charged quantum dot molecules in electric and magnetic fields, Phys. Rev. B 78, 115316 (2008).
  36. M. Scheibner, A. S. Bracker, D. Kim, and D. Gammon, Essential concepts in the optical properties of quantum dot molecules, Solid State Commun. 149, 1427 (2009), Fundamental Phenomena and Applications of Quantum Dots.
  37. K. Müller, G. Reithmaier, E. C. Clark, V. Jovanov, M. Bichler, H. J. Krenner, M. Betz, G. Abstreiter, and J. J. Finley, Excited state quantum couplings and optical switching of an artificial molecule, Phys. Rev. B 84, 081302(R) (2011).
  38. K. Gawarecki, C. Spinnler, L. Zhai, Giang N. Nguyen, A. Ludwig, Richard J. Warburton, Matthias C. Löbl, Doris E. Reiter, and P. Machnikowski, Symmetry breaking via alloy disorder to explain radiative auger transitions in self-assembled quantum dots, Phys. Rev. B 108, 235410 (2023).
  39. M. C. Löbl, S. Scholz, I. Söllner, J. Ritzmann, T. Denneulin, A. Kovács, B. E. Kardynał, A. D. Wieck, A. Ludwig, and R. J. Warburton, Excitons in ingaas quantum dots without electron wetting layer states, Commun. Phys. 2, 93 (2019).
  40. C. Pryor, J. Kim, L. W. Wang, A. J. Williamson, and A. Zunger, Comparison of two methods for describing the strain profiles in quantum dots, J. Appl. Phys. 83, 2548 (1998).
  41. G. Bester, X. Wu, D. Vanderbilt, and A. Zunger, Importance of second-order piezoelectric effects in zinc-blende semiconductors, Phys. Rev. Lett. 96, 187602 (2006).
  42. Miguel A. Caro, S. Schulz, and E. P. O'Reilly, Origin of nonlinear piezoelectricity in III-V semiconductors: Internal strain and bond ionicity from hybrid-functional density functional theory, Phys. Rev. B 91, 075203 (2015).
  43. R. Winkler, Spin-Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems (Springer, Berlin, Heidelberg, 2003).
  44. H. R. Trebin, U. Rössler, and R. Ranvaud, Quantum resonances in the valence bands of zinc-blende semiconductors. I. Theoretical aspects, Phys. Rev. B 20, 686 (1979).
  45. J. Andrzejewski, G. Sęk, E. O'Reilly, A. Fiore, and J. Misiewicz, Eight-band k.P calculations of the composition contrast effect on the linear polarization properties of columnar quantum dots, J. Appl. Phys. 107, 073509 (2010).
  46. M. Gawełczyk, M. Syperek, A. Maryński, P. Mrowiński, L. Dusanowski, K. Gawarecki, J. Misiewicz, A. Somers, J. P. Reithmaier, S. Höfling, and G. Sęk, Exciton lifetime and emission polarization dispersion in strongly in-plane asymmetric nanostructures, Phys. Rev. B 96, 245425 (2017).
  47. R. P. Feynman, Forces in molecules, Phys. Rev. 56, 340 (1939).
  48. L. C. Lew Yan Voon and L. R. Ram-Mohan, Tight-binding representation of the optical matrix elements: Theory and applications, Phys. Rev. B 47, 15500 (1993).
  49. T. Eissfeller, Theory of the electronic structure of quantum dots in external fields, Ph.D. thesis, Technical University of Munich, 2012.
  50. M. Krzykowski, K. Gawarecki, and P. Machnikowski, Hole spin-flip transitions in a self-assembled quantum dot, Phys. Rev. B 102, 205301 (2020).
  51. L. M. Woods, T. L. Reinecke, and R. Kotlyar, Hole spin relaxation in quantum dots, Phys. Rev. B 69, 125330 (2004).
  52. Quantum Dot Molecules, Lecture Notes in Nanoscale Science and Technology, Vol. 14, edited by J. Wu and Z. M. Wang (Springer, New York, 2014).
  53. E. Stock, Matthias R. Dachner, T. Warming, A. Schliwa, A. Lochmann, A. Hoffmann, A. I. Toropov, Ashkat K. Bakarov, Ilya A. Derebezov, M. Richter, Vladimir A. Haisler, A. Knorr, and D. Bimberg, Acoustic and optical phonon scattering in a single In(Ga)As quantum dot, Phys. Rev. B 83, 041304(R) (2011).
  54. http://wcss.pl.
  55. Z. Wasilewski, S. Fafard, and J. McCaffrey, Size and shape engineering of vertically stacked self-assembled quantum dots, J. Cryst. Growth 201–202, 1131 (1999).
  56. A. S. Bracker, M. Scheibner, M. F. Doty, E. A. Stinaff, I. V. Ponomarev, J. C. Kim, L. J. Whitman, T. L. Reinecke, and D. Gammon, Engineering electron and hole tunneling with asymmetric inas quantum dot molecules, Appl. Phys. Lett. 89, 233110 (2006).
  57. J. Schall, M. Deconinck, N. Bart, M. Florian, M. von Helversen, C. Dangel, R. Schmidt, L. Bremer, F. Bopp, I. Hüllen, C. Gies, D. Reuter, A. D. Wieck, S. Rodt, J. J. Finley, F. Jahnke, A. Ludwig, and S. Reitzenstein, Bright electrically controllable quantum-dot-molecule devices fabricated by in situ electron-beam lithography, Adv. Quantum Technol. 4, 2100002 (2021).
  58. Gustavo A. Narvaez, G. Bester, and A. Zunger, Carrier relaxation mechanisms in self-assembled (In,Ga)AsGaAs quantum dots: Efficient p→s auger relaxation of electrons, Phys. Rev. B 74, 075403 (2006).
  59. Xin Q. Li, H. Nakayama, and Y. Arakawa, Phonon bottleneck in quantum dots: Role of lifetime of the confined optical phonons, Phys. Rev. B 59, 5069 (1999).
  60. J. Urayama, T. B. Norris, J. Singh, and P. Bhattacharya, Observation of phonon bottleneck in quantum dot electronic relaxation, Phys. Rev. Lett. 86, 4930 (2001).
  61. G. Bacher, R. Weigand, J. Seufert, V. D. Kulakovskii, N. A. Gippius, A. Forchel, K. Leonardi, and D. Hommel, Biexciton versus exciton lifetime in a single semiconductor quantum dot, Phys. Rev. Lett. 83, 4417 (1999).
  62. M. Van Den Zegel, N. Boens, D. Daems, and F. De Schryver, Possibilities and limitations of the time-correlated single photon counting technique: A comparative study of correction methods for the wavelength dependence of the instrument response function, Chem. Phys. 101, 311 (1986).
  63. M. Świderski and M. Zieliński, Exact diagonalization approach for atomistic calculation of piezoelectric effects in semiconductor quantum dots, Acta Phys. Pol. A 129, A-79 (2016).
  64. M. Bayer, G. Ortner, O. Stern, A. Kuther, A. A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. L. Reinecke, S. N. Walck, J. P. Reithmaier, F. Klopf, and F. Schäfer, Fine structure of neutral and charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots, Phys. Rev. B 65, 195315 (2002).
  65. A. Thränhardt, C. Ell, G. Khitrova, and H. M. Gibbs, Relation between dipole moment and radiative lifetime in interface fluctuation quantum dots, Phys. Rev. B 65, 035327 (2002).
  66. P. Amirtharaj and D. Seiler, Optical properties of semiconductors, in, Handbook of Optics, Vol. 2: Devices, Measurements, and Properties, 2nd ed. (McGraw-Hill Professional, New York, 1994).
  67. J. M. Daniels, P. Machnikowski, and T. Kuhn, Excitons in quantum dot molecules: Coulomb coupling, spin-orbit effects, and phonon-induced line broadening, Phys. Rev. B 88, 205307 (2013).
  68. See Supplemental Material at http://link.aps.org/supplemental/10.1103/xc25-1tph for details of the parameters.
  69. I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, Band parameters for III-V compound semiconductors and their alloys, J. Appl. Phys. 89, 5815 (2001).
  70. S. Birner, Modeling of semiconductor nanostructures and semiconductor–electrolyte interfaces, Ph.D. thesis, Technical University of Munich, Munich, Germany, 2011.
  71. W. Yi, V. Narayanamurti, H. Lu, M. A. Scarpulla, A. C. Gossard, Y. Huang, J.-H. Ryou, and R. D. Dupuis, Bandgap and band offsets determination of semiconductor heterostructures using three-terminal ballistic carrier spectroscopy, Appl. Phys. Lett. 95, 112102 (2009).
  72. M. Fox, Optical Properties of Solids, 2nd ed. (Oxford University Press, Oxford, 2010).
  73. Ioffe Institute, NSM Archive, Gallium arsenide (GaAs)—physical properties, http://www.ioffe.ru/SVA/NSM/Semicond/GaAs/ (1999), accessed Sept. 17, 2025.
  74. Handbook Series on Semiconductor Parameters, Vol. 2: Ternary and Quaternary III-V Compounds, edited by M. S. M. Levinshtein, S. L. Rumyantsev, and M. Shur (World Scientific, London, 1999).
  75. P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S. J. van der Walt, M. Brett, J. Wilson, K. J. Millman, N. Mayorov, A. R. J. Nelson, E. Jones, R. Kern, E. Larson, C. J. Carey et al., SciPy 1.0: Fundamental algorithms for scientific computing in python, Nat. Methods 17, 261 (2020).

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Phys. Rev. B 112, 235305– Published 8 December, 2025
  • Received 6 June 2025
  • Revised 6 November 2025
  • Accepted 12 November 2025
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