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  • Letter
  • Open Access

Non-Markovian transient spectroscopy in cavity QED

Z. McIntyre* and W. A. Coish†

  • Department of Physics, McGill University, 3600 rue University, Montreal, Quebec H3A 2T8, Canada

  • *zoe.mcintyre@mail.mcgill.ca
  • †coish@physics.mcgill.ca
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Phys. Rev. Research 4, L042039 – Published 30 November, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L042039

Abstract

We theoretically analyze measurements of the transient field leaving a cavity as a tool for studying non-Markovian dynamics in cavity quantum electrodynamics (QED). Combined with a dynamical decoupling pulse sequence, transient spectroscopy can be used to recover spectral features that may be obscured in the stationary cavity transmission spectrum due to inhomogeneous broadening. The formalism introduced here can be leveraged to perform in situ noise spectroscopy, revealing a robust signature of quantum noise arising from noncommuting observables, a purely quantum effect.

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References (56)

  1. L. M. K. Vandersypen, H. Bluhm, J. S. Clarke, A. S. Dzurak, R. Ishihara, A. Morello, D. J. Reilly, L. R. Schreiber, and M. Veldhorst, Interfacing spin qubits in quantum dots and donors-hot, dense, and coherent, npj Quantum Inf. 3, 34 (2017).
  2. M. M. Desjardins, J. J. Viennot, M. C. Dartiailh, L. E. Bruhat, M. R. Delbecq, M. Lee, M.-S. Choi, A. Cottet, and T. Kontos, Observation of the frozen charge of a kondo resonance, Nature 545, 71 (2017).
  3. A. A. Clerk, K. W. Lehnert, P. Bertet, J. R. Petta, and Y. Nakamura, Hybrid quantum systems with circuit quantum electrodynamics, Nat. Phys. 16, 257 (2020).
  4. A. Stockklauser, P. Scarlino, J. V. Koski, S. Gasparinetti, C. K. Andersen, C. Reichl, W. Wegscheider, T. Ihn, K. Ensslin, and A. Wallraff, Strong Coupling Cavity QED with Gate-Defined Double Quantum Dots Enabled by a High Impedance Resonator, Phys. Rev. X 7, 011030 (2017).
  5. X. Mi, J. V. Cady, D. M. Zajac, P. W. Deelman, and J. R. Petta, Strong coupling of a single electron in silicon to a microwave photon, Science 355, 156 (2017).
  6. X. Mi, M. Benito, S. Putz, D. M. Zajac, J. M. Taylor, G. Burkard, and J. R. Petta, A coherent spin-photon interface in silicon, Nature 555, 599 (2018).
  7. N. Samkharadze, G. Zheng, N. Kalhor, D. Brousse, A. Sammak, U. C. Mendes, A. Blais, G. Scappucci, and L. M. K. Vandersypen, Strong spin-photon coupling in silicon, Science 359, 1123 (2018).
  8. A. J. Landig, J. V. Koski, P. Scarlino, U. C. Mendes, A. Blais, C. Reichl, W. Wegscheider, A. Wallraff, K. Ensslin, and T. Ihn, Coherent spin-photon coupling using a resonant exchange qubit, Nature 560, 179 (2018).
  9. T. Cubaynes, M. R. Delbecq, M. C. Dartiailh, R. Assouly, M. M. Desjardins, L. C. Contamin, L. E. Bruhat, Z. Leghtas, F. Mallet, A. Cottet, and T. Kontos, Highly coherent spin states in carbon nanotubes coupled to cavity photons, npj Quantum Inf. 5, 47 (2019).
  10. J. J. Viennot, M. C. Dartiailh, A. Cottet, and T. Kontos, Coherent coupling of a single spin to microwave cavity photons, Science 349, 408 (2015).
  11. D. J. van Woerkom, P. Scarlino, J. H. Ungerer, C. Müller, J. V. Koski, A. J. Landig, C. Reichl, W. Wegscheider, T. Ihn, K. Ensslin, and A. Wallraff, Microwave Photon-Mediated Interactions between Semiconductor Qubits, Phys. Rev. X 8, 041018 (2018).
  12. F. Borjans, X. G. Croot, X. Mi, M. J. Gullans, and J. R. Petta, Resonant microwave-mediated interactions between distant electron spins, Nature 577, 195 (2020).
  13. P. Harvey-Collard, J. Dijkema, G. Zheng, A. Sammak, G. Scappucci, and L. M. K. Vandersypen, Circuit Quantum Electrodynamics with Two Remote Electron Spins, Phys. Rev. X 12, 021026 (2022).
  14. C. J. Hood, M. S. Chapman, T. W. Lynn, and H. J. Kimble, Real-Time Cavity QED with Single Atoms, Phys. Rev. Lett. 80, 4157 (1998).
  15. J. Ye, D. W. Vernooy, and H. J. Kimble, Trapping of Single Atoms in Cavity QED, Phys. Rev. Lett. 83, 4987 (1999).
  16. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  17. 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).
  18. K. Jacobs, Quantum Measurement Theory and its Applications (Cambridge University Press, UK, 2014).
  19. G. Burkard, M. J. Gullans, X. Mi, and J. R. Petta, Superconductor–semiconductor hybrid-circuit quantum electrodynamics, Nat. Rev. Phys. 2, 129 (2020).
  20. S. Schlör, J. Lisenfeld, C. Müller, A. Bilmes, A. Schneider, D. P. Pappas, A. V. Ustinov, and M. Weides, Correlating Decoherence in Transmon Qubits: Low Frequency Noise by Single Fluctuators, Phys. Rev. Lett. 123, 190502 (2019).
  21. J. J. Burnett, A. Bengtsson, M. Scigliuzzo, D. Niepce, M. Kudra, P. Delsing, and J. Bylander, Decoherence benchmarking of superconducting qubits, npj Quantum Inf. 5, 54 (2019).
  22. V. Ranjan, S. Probst, B. Albanese, A. Doll, O. Jacquot, E. Flurin, R. Heeres, D. Vion, D. Esteve, J. J. L. Morton, and P. Bertet, Pulsed electron spin resonance spectroscopy in the Purcell regime, J. Magn. Reson. 310, 106662 (2020).
  23. M. Le Dantec, M. Rančić, S. Lin, E. Billaud, V. Ranjan, D. Flanigan, S. Bertaina, T. Chanelière, P. Goldner, A. Erb et al., Twenty-three–millisecond electron spin coherence of erbium ions in a natural-abundance crystal, Sci. Adv. 7, eabj9786 (2021).
  24. O. Černotík, A. Dantan, and C. Genes, Cavity Quantum Electrodynamics with Frequency-Dependent Reflectors, Phys. Rev. Lett. 122, 243601 (2019).
  25. M. Bundgaard-Nielsen, J. Mørk, and E. V. Denning, Non-Markovian perturbation theories for phonon effects in strong-coupling cavity quantum electrodynamics, Phys. Rev. B 103, 235309 (2021).
  26. A. Carmele and S. Reitzenstein, Non-Markovian features in semiconductor quantum optics: quantifying the role of phonons in experiment and theory, Nanophotonics 8, 655 (2019).
  27. 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).
  28. D. O. Krimer, S. Putz, J. Majer, and S. Rotter, Non-Markovian dynamics of a single-mode cavity strongly coupled to an inhomogeneously broadened spin ensemble, Phys. Rev. A 90, 043852 (2014).
  29. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.4.L042039 for detailed derivations of the results presented in the main text.
  30. F. Beaudoin and W. A. Coish, Enhanced hyperfine-induced spin dephasing in a magnetic-field gradient, Phys. Rev. B 88, 085320 (2013).
  31. L. M. Norris, G. A. Paz-Silva, and L. Viola, Qubit Noise Spectroscopy for Non-Gaussian Dephasing Environments, Phys. Rev. Lett. 116, 150503 (2016).
  32. Ł. Cywinśki, R. M. Lutchyn, C. P. Nave, and S. Das Sarma, How to enhance dephasing time in superconducting qubits, Phys. Rev. B 77, 174509 (2008).
  33. U. Gavish, Y. Levinson, and Y. Imry, Detection of quantum noise, Phys. Rev. B 62, R10637 (2000).
  34. N. Zhao, J. Honert, B. Schmid, M. Klas, J. Isoya, M. Markham, D. Twitchen, F. Jelezko, R.-B. Liu, H. Fedder, and J. Wrachtrup, Sensing single remote nuclear spins, Nat. Nanotechnol. 7, 657 (2012).
  35. G. A. Álvarez and D. Suter, Measuring the Spectrum of Colored Noise by Dynamical Decoupling, Phys. Rev. Lett. 107, 230501 (2011).
  36. T. Yuge, S. Sasaki, and Y. Hirayama, Measurement of the Noise Spectrum Using a Multiple-Pulse Sequence, Phys. Rev. Lett. 107, 170504 (2011).
  37. J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J.-S. Tsai, and W. D. Oliver, Noise spectroscopy through dynamical decoupling with a superconducting flux qubit, Nat. Phys. 7, 565 (2011).
  38. P. Szańkowski, G. Ramon, J. Krzywda, D. Kwiatkowski, and Ł. Cywiński, Environmental noise spectroscopy with qubits subjected to dynamical decoupling, J. Phys.: Condens. Matter 29, 333001 (2017).
  39. P. Szańkowski, Transition between continuous and discrete spectra in dynamical-decoupling noise spectroscopy, Phys. Rev. A 100, 052115 (2019).
  40. K. W. Chan, W. Huang, C. H. Yang, J. C. C. Hwang, B. Hensen, T. Tanttu, F. E. Hudson, K. M. Itoh, A. Laucht, A. Morello, and A. S. Dzurak, Assessment of a Silicon Quantum Dot Spin Qubit Environment via Noise Spectroscopy, Phys. Rev. Appl. 10, 044017 (2018).
  41. G. A. Paz-Silva, L. M. Norris, and L. Viola, Multiqubit spectroscopy of Gaussian quantum noise, Phys. Rev. A 95, 022121 (2017).
  42. D. Kwiatkowski, P. Szańkowski, and Ł. Cywiński, Influence of nuclear spin polarization on the spin-echo signal of an NV-center qubit, Phys. Rev. B 101, 155412 (2020).
  43. B. Hensen, W. W. Huang, C.-H. Yang, K. W. Chan, J. Yoneda, T. Tanttu, F. E. Hudson, A. Laucht, K. M. Itoh, T. D. Ladd, A. Morello, and A. S. Dzurak, A silicon quantum-dot-coupled nuclear spin, Nat. Nanotechnol. 15, 13 (2020).
  44. F. Beaudoin, D. Lachance-Quirion, W. A. Coish, and M. Pioro-Ladrière, Coupling a single electron spin to a microwave resonator: controlling transverse and longitudinal couplings, Nanotechnology 27, 464003 (2016).
  45. A. Shnirman, G. Schön, I. Martin, and Y. Makhlin, Low- and High-Frequency Noise from Coherent Two-Level Systems, Phys. Rev. Lett. 94, 127002 (2005).
  46. Y. M. Galperin, B. L. Altshuler, J. Bergli, and D. V. Shantsev, Non-Gaussian Low-Frequency Noise as a Source of Qubit Decoherence, Phys. Rev. Lett. 96, 097009 (2006).
  47. R. Zhao, T. Tanttu, K. Y. Tan, B. Hensen, K. W. Chan, J. C. C. Hwang, R. C. C. Leon, C. H. Yang, W. Gilbert, F. E. Hudson, K. M. Itoh, A. A. Kiselev, T. D. Ladd, A. Morello, A. Laucht, and A. S. Dzurak, Single-spin qubits in isotopically enriched silicon at low magnetic field, Nat. Commun. 10, 5500 (2019).
  48. F. K. Malinowski, F. Martins, P. D. Nissen, E. Barnes, Ł. Cywinśki, M. S. Rudner, S. Fallahi, C. Gardner, Geoffrey, M. J. Manfra, C. M. Marcus, and F. Kuemmeth, Notch filtering the nuclear environment of a spin qubit, Nat. Nanotechnol. 12, 16 (2017).
  49. J. Mielke, J. R. Petta, and G. Burkard, Nuclear spin readout in a cavity-coupled hybrid quantum dot-donor system, PRX Quantum 2, 020347 (2021).
  50. For h(t)=ei(HE−h/2)the−i(HE−h/2)t=∑αcα(t)Iα, the quantum-noise term produces a phase arising from 〈[h(t),h]〉=i∑αβεαβγcα(t)cβ(0)〈Iγ〉, which is nonzero for a polarized initial state, 〈Iγ〉=Tr(ρ¯EIγ)≠0. This analysis applies within the Gaussian approximation, which can be justified even for a single spin at short times.
  51. J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. Hemmer, A. Yacoby, R. Walsworth, and M. Lukin, High-sensitivity diamond magnetometer with nanoscale resolution, Nat. Phys. 4, 810 (2008).
  52. J. Gambetta, A. Blais, D. I. Schuster, A. Wallraff, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Qubit-photon interactions in a cavity: Measurement-induced dephasing and number splitting, Phys. Rev. A 74, 042318 (2006).
  53. A. N. Korotkov, Quantum Bayesian approach to circuit QED measurement with moderate bandwidth, Phys. Rev. A 94, 042326 (2016).
  54. D. P. DiVincenzo and D. Loss, Rigorous born approximation and beyond for the spin-boson model, Phys. Rev. B 71, 035318 (2005).
  55. W. A. Coish, J. Fischer, and D. Loss, Free-induction decay and envelope modulations in a narrowed nuclear spin bath, Phys. Rev. B 81, 165315 (2010).
  56. P. M. Mutter and G. Burkard, Fingerprints of Qubit Noise in Transient Cavity Transmission, Phys. Rev. Lett. 128, 236801 (2022).

Outline

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Phys. Rev. Research 4, L042039– Published 30 November, 2022
  • Received 4 June 2022
  • Revised 12 August 2022
  • Accepted 14 October 2022
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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.

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