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Quantum Sensing of Time-Dependent Electromagnetic Fields with Single-Electron Excitations

H. Souquet-Basiège1, B. Roussel2, G. Rebora1, G. Ménard3, I. Safi4, G. Fève3, and P. Degiovanni1

Phys. Rev. X 15, 031043 – Published 14 August, 2025

DOI: https://doi.org/10.1103/1nfc-stxp

Abstract

In this study, we investigate the potential of electronic interferometers for probing the quantum state of electromagnetic radiation on a chip at subnanosecond timescales. We propose to use single-electron excitations propagating within an electronic Mach-Zehnder interferometer in the Aharonov-Bohm-dominated regime. We discuss how information about the quantum state of the electromagnetic radiation is encoded into the interference contribution to the average outgoing electrical current. By investigating squeezed radiation and single-edge magnetoplasmons probed by leviton pulses in a realistic setup, we show that single-electron interferometers have the potential to probe quantum radiation in the time domain with subnanosecond to picosecond time resolution. Our research could have significant implications for probing the fundamental properties of light in the microwave to terahertz domains at extremely short timescales.

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References (123)

  1. G. Fève, A. Mahé, J. Berroir, T. Kontos, B. Plaçais, D. C. Glattli, A. Cavanna, B. Etienne, and Y. Jin, An on-demand single electron source, Science 316, 1169 (2007).
  2. J. Dubois, T. Jullien, F. Portier, P. Roche, A. Cavanna, Y. Jin, W. Wegscheider, P. Roulleau, and D. C. Glattli, Minimal excitation states for electron quantum optics using levitons, Nature (London) 502, 659 (2013).
  3. E. Bocquillon, V. Freulon, F. Parmentier, J.-M. Berroir, B. Plaçais, C. Wahl, J. Rech, T. Jonckheere, T. Martin, C. Grenier, D. Ferraro, P. Degiovanni, and G. Fève, Electron quantum optics in ballistic chiral conductors, Ann. Phys. (Berlin) 526, 1 (2014).
  4. E. Bocquillon, F. D. Parmentier, C. Grenier, J.-M. Berroir, P. Degiovanni, D. C. Glattli, B. Plaçais, A. Cavanna, Y. Jin, and G. Fève, Electron quantum optics: Partitioning electrons one by one, Phys. Rev. Lett. 108, 196803 (2012).
  5. E. Bocquillon, V. Freulon, J.-M. Berroir, P. Degiovanni, B. Plaçais, A. Cavanna, Y. Jin, and G. Fève, Coherence and indistinguability of single electrons emitted by independent sources, Science 339, 1054 (2013).
  6. A. Marguerite, C. Cabart, C. Wahl, B. Roussel, V. Freulon, D. Ferraro, C. Grenier, J. M. Berroir, B. Placais, T. Jonckheere, J. Rech, T. Martin, P. Degiovanni, A. Cavanna, Y. Jin, and G. Fève, Decoherence and relaxation of a single electron in a one-dimensional conductor, Phys. Rev. B 94, 115311 (2016).
  7. P. Roulleau, F. Portier, D. C. Glattli, P. Roche, A. Cavanna, G. Faini, U. Gennser, and D. Mailly, Direct measurement of the coherence length of edge states in the integer quantum Hall regime, Phys. Rev. Lett. 100, 126802 (2008).
  8. P. Roulleau, F. Portier, P. Roche, A. Cavanna, G. Faini, U. Gennser, and D. Mailly, Tuning decoherence with a voltage probe, Phys. Rev. Lett. 102, 236802 (2009).
  9. S. Tewari, P. Roulleau, C. Grenier, F. Portier, A. Cavanna, U. Gennser, D. Mailly, and P. Roche, Robust quantum coherence above the Fermi sea, Phys. Rev. B 93, 035420 (2016).
  10. R. Rodriguez, F. Parmentier, D. Ferraro, P. Roulleau, U. Gensser, A. Cavanna, M. Sassetti, F. Portier, D. Mailly, and P. Roche, Relaxation and revival of quasiparticles injected in an interacting quantum Hall liquid, Nat. Commun. 11, 2426 (2020).
  11. M. Jo, J.-Y. M. Lee, A. Assouline, P. Brasseur, K. Watanabe, T. Taniguchi, P. Roche, D. C. Glattli, N. Kumada, F. D. Parmentier, H. S. Sim, and P. Roulleau, Scaling behavior of electron decoherence in a graphene Mach-Zehnder interferometer, Nat. Commun. 13, 5473 (2022).
  12. A. Assouline, L. Pugliese, H. Chakraborti, S. Lee, L. Bernabeu, M. Jo, K. Watanabe, T. Taniguchi, D. C. Glattli, N. Kumada, H.-S. Sim, F. D. Parmentier, and P. Roulleau, Emission and coherent control of levitons in graphene, Science 382, 1260 (2023).
  13. L. Levitov, H. Lee, and G. Lesovik, Electron counting statistics and coherent states of electric current, J. Math. Phys. (N.Y.) 37, 4845 (1996).
  14. T. Jullien, P. Roulleau, P. Roche, A. Cavanna, Y. Jin, and D. C. Glattli, Quantum tomography of an electron, Nature (London) 514, 603 (2014).
  15. R. Bisognin, A. Marguerite, B. Roussel, M. Kumar, C. Cabart, C. Chapdelaine, A. Mohammad-Djafari, J. M. Berroir, E. Bocquillon, B. Plaçais, A. Cavanna, U. Gennser, Y. Jin, P. Degiovanni, and G. Fève, Quantum tomography of electrical currents, Nat. Commun. 10, 3379 (2019).
  16. J. D. Fletcher, N. Johnson, E. Locane, P. See, J. P. Griffiths, I. Farrer, D. A. Ritchie, P. W. Brouwer, V. Kashcheyevs, and M. Kataoka, Continuous-variable tomography of solitary electrons, Nat. Commun. 10, 5298 (2019).
  17. B. Roussel, C. Cabart, G. Fève, and P. Degiovanni, Processing quantum signals carried by electrical currents, PRX Quantum 2, 020314 (2021).
  18. V. Kashcheyevs, P. Degiovanni, B. Roussel, M. Kataoka, J. D. Fletcher, L. Freise, N. Ubbelhode, G. Fève, H. Bartolomei, F. Couëdo, A. Kadykov, W. Poirier, P. Roulleau, F. D. Parmentier, and F. Hohls, Single-electron wave packets for quantum metrology: Concepts, implementations and applications (2021), SEQUOIA project (17FUN04) technical report.
  19. M. Aluffi, T. Vasselon, S. Ouacel, H. Edlbauer, C. Geffroy, P. Roulleau, D. C. Glattli, G. Georgiou, and C. Bäuerle, Ultrashort electron wave packets via frequency-comb synthesis, Phys. Rev. Appl. 20, 034005 (2023).
  20. K. Yoshioka, G. Bernard, T. Wakamura, M. Hashisaka, K. ichi Sasaki, S. Sasaki, K. Watanabe, T. Taniguchi, and N. Kumada, On-chip transfer of ultrashort graphene plasmon wavepackets using terahertz electronics, National electronics review 7, 537 (2024).
  21. D. C. Glattli, J. Nath, I. Taktak, P. Roulleau, C. Bauerle, and X. Waintal, Design of a single-shot electron detector with sub-electron sensitivity for electron flying qubit operation, arXiv:2002.03947.
  22. V. Thiney, P.-A. Mortemousque, K. Rogdakis, R. Thalineau, A. Ludwig, A. D. Wieck, M. Urdampilleta, C. Bäuerle, and T. Meunier, In-flight detection of few electrons using a singlet-triplet spin qubit, Phys. Rev. Res. 4, 043116 (2022).
  23. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  24. G. Burkard, T. D. Ladd, A. Pan, J. M. Nichol, and J. R. Petta, Semiconductor spin qubits, Rev. Mod. Phys. 95, 025003 (2023).
  25. H. Edlbauer et al., Semiconductor-based electron flying qubits: Review on recent progress accelerated by numerical modelling, Eur. Phys. J. Quantum Technol. 9, 21 (2022).
  26. L. Viti and M. S. Vitiello, Tailored nano-electronics and photonics with two-dimensional materials at terahertz frequencies, J. Appl. Phys. 130, 170903 (2021).
  27. P. Kruit, R. Hobbs, C.-S. Kim, Y. Yang, V. Manfrinato, J. Hammer, S. Thomas, P. Weber, B. Klopfer, C. Kohstall, T. Juffmann, M. Kasevich, P. Hommelhoff, and K. Berggren, Designs for a quantum electron microscope, Ultramicroscopy 164, 31 (2016).
  28. A. Feist, K. E. Echternkamp, J. Schauss, S. V. Yalunin, S. Schäfer, and C. Ropers, Quantum coherent optical phase modulation in an ultrafast transmission electron microscope, Nature (London) 521, 200 (2015).
  29. R. Ruimy, A. Gorlach, C. Mechel, N. Rivera, and I. Kaminer, Toward atomic-resolution quantum measurements with coherently shaped free electrons, Phys. Rev. Lett. 126, 233403 (2021).
  30. J. H. Gaida, H. Lourenço-Martins, M. Sivis, T. Rittmann, A. Feist, F. J. García de Abajo, and C. Ropers, Attosecond electron microscopy by free-electron homodyne detection, Nat. Photonics 18, 509 (2024).
  31. R. Ruimy, A. Karnieli, and I. Kaminer, Free-electron quantum optics, Nat. Phys. 21, 193 (2025).
  32. A. Facon, E.-K. Dietsche, D. Grosso, S. Haroche, J.-M. Raimond, M. Brune, and S. Gleyzes, A sensitive electrometer based on a Rydberg atom in a Schrödinger-cat state, Nature (London) 535, 262 (2016).
  33. V. Calero, M. A. Suarez, R. Salut, F. Baida, A. Caspar, F. Behague, N. Courjal, L. Galtier, L. Gillette, L. Duvillaret, G. Gaborit, and M. P. Bernal, An ultra wideband-high spatial resolution-compact electric field sensor based on lab-on-fiber technology, Sci. Rep. 9, 8058 (2019).
  34. G. Georgiou, C. Geffroy, C. Bäuerle, and J.-F. Roux, Efficient three-dimensional photonic–plasmonic photoconductive switches for picosecond THz pulses, ACS Photonics 7, 1444 (2020).
  35. A. N. Cleland and M. L. Roukes, A nanometre-scale mechanical electrometer, Nature (London) 392, 160 (1998).
  36. D. Chen, H. Zhang, J. Sun, M. Pandit, G. Sobreviela, Y. Wang, Q. Zhang, X. Chen, A. Seshia, and J. Xie, Ultrasensitive resonant electrometry utilizing micromechanical oscillators, Phys. Rev. Appl. 14, 014001 (2020).
  37. I. Ahmed, J. A. Haigh, S. Schaal, S. Barraud, Y. Zhu, C. M. Lee, M. Amado, J. W. A. Robinson, A. Rossi, J. J. L. Morton, and M. F. Gonzalez-Zalba, Radio-frequency capacitive gate-based sensing, Phys. Rev. Appl. 10, 014018 (2018).
  38. F. Dolde, M. W. Doherty, J. Michl, I. Jakobi, B. Naydenov, S. Pezzagna, J. Meijer, P. Neumann, F. Jelezko, N. B. Manson, and J. Wrachtrup, Nanoscale detection of a single fundamental charge in ambient conditions using the NV− center in diamond, Phys. Rev. Lett. 112, 097603 (2014).
  39. A. N. Vamivakas, Y. Zhao, S. Fält, A. Badolato, J. M. Taylor, and M. Atatüre, Nanoscale optical electrometer, Phys. Rev. Lett. 107, 166802 (2011).
  40. C. Arnold, V. Loo, A. Lemaître, I. Sagnes, O. Krebs, P. Voisin, P. Senellart, and L. Lanco, Cavity-enhanced real-time monitoring of single-charge jumps at the microsecond time scale, Phys. Rev. X 4, 021004 (2014).
  41. H. Brenning, S. Kafanov, T. Duty, S. Kubatkin, and P. Delsing, An ultrasensitive radio-frequency single-electron transistor working up to 4.2 K, J. Appl. Phys. 100, 114321 (2006).
  42. D. J. Reilly, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Fast single-charge sensing with a rf quantum point contact, Appl. Phys. Lett. 91, 162101 (2007).
  43. M. Hatridge, R. Vijay, D. H. Slichter, J. Clarke, and I. Siddiqi, Dispersive magnetometry with a quantum limited SQUID parametric amplifier, Phys. Rev. B 83, 134501 (2011).
  44. M. J. Biercuk, D. J. Reilly, T. M. Buehler, V. C. Chan, J. M. Chow, R. G. Clark, and C. M. Marcus, Charge sensing in carbon-nanotube quantum dots on microsecond timescales, Phys. Rev. B 73, 201402(R) (2006).
  45. Y. Ji, Y. Chung, D. Sprinzak, M. Heiblum, D. Mahalu, and H. Shtrikman, An electronic Mach-Zehnder interferometer, Nature (London) 422, 415 (2003).
  46. E. V. Sukhorukov and V. V. Cheianov, Resonant dephasing in the electronic Mach-Zehnder interferometer, Phys. Rev. Lett. 99, 156801 (2007).
  47. J. R. Souquet, M. J. Woolley, J. Gabelli, P. Simon, and A. A. Clerk, Photon-assisted tunnelling with nonclassical light, Nat. Commun. 5, 5562 (2014).
  48. C. Guerlin, J. Bernu, S. Deléglise, C. Sayrin, S. Gleyzes, S. Kuhr, M. Brune, J.-M. Raimond, and S. Haroche, Progressive field-state collapse and quantum non-demolition photon counting, Nature (London) 448, 889 (2007).
  49. V. B. Braginsky, Y. Vorontsov, and K. Thorne, Quantum nondemolition measurements, Science 209, 547 (1980).
  50. F. Hohls, A. C. Welker, C. Leicht, L. Fricke, B. Kaestner, P. Mirovsky, A. Müller, K. Pierz, U. Siegner, and H. W. Schumacher, Semiconductor quantized voltage source, Phys. Rev. Lett. 109, 056802 (2012).
  51. J. D. Fletcher, P. See, H. Howe, M. Pepper, S. P. Giblin, J. P. Griffiths, G. A. C. Jones, I. Farrer, D. A. Ritchie, T. J. B. M. Janssen, and M. Kataoka, Clock-controlled emission of single-electron wave packets in a solid-state circuit, Phys. Rev. Lett. 111, 216807 (2013).
  52. J. Waldie, P. See, V. Kashcheyevs, J. P. Griffiths, I. Farrer, G. A. C. Jones, D. A. Ritchie, T. J. B. M. Janssen, and M. Kataoka, Measurement and control of electron wave packets from a single-electron source, Phys. Rev. B 92, 125305 (2015).
  53. G. Roussely, E. Arrighi, G. Georgiou, S. Takada, M. Schalk, M. Urdampilleta, A. Ludwig, A. D. Wieck, P. Armagnat, T. Kloss, X. Waintal, T. Meunier, and C. Bäuerle, Unveiling the bosonic nature of an ultrashort few-electron pulse, Nat. Commun. 9, 2811 (2018).
  54. H. Bartolomei, E. Frigerio, M. Ruelle, G. Rebora, Y. Jin, U. Gennser, A. Cavanna, E. Baudin, J.-M. Berroir, I. Safi, P. Degiovanni, G. C. Ménard, and G. Fève, Time-resolved sensing of electromagnetic fields with single-electron interferometry, Nat. Nanotechnol. 20, 596 (2025).
  55. S. Ouacel et al., Electronic interferometry with ultrashort plasmonic pulses, Nat. Commun. 16, 4632 (2025).
  56. D. Ferraro, B. Roussel, C. Cabart, E. Thibierge, G. Fève, C. Grenier, and P. Degiovanni, Real-time decoherence of Landau and Levitov quasiparticles in quantum Hall edge channels, Phys. Rev. Lett. 113, 166403 (2014).
  57. C. Cabart, B. Roussel, G. Fève, and P. Degiovanni, Taming electronic decoherence in 1d chiral ballistic quantum conductors, Phys. Rev. B 98, 155302 (2018).
  58. E. Condon, A theory of intensity distribution in band systems, Phys. Rev. 28, 1182 (1926).
  59. I. Safi and H. J. Schulz, Transport in an inhomogeneous interacting one-dimensional system, Phys. Rev. B 52, R17040 (1995).
  60. I. Safi, A dynamic scattering approach for a gated interacting wire, Eur. Phys. J. D 12, 451 (1999).
  61. D. Ferraro, F. Ronetti, J. Rech, T. Jonckheere, M. Sassetti, and T. Martin, Enhancing photon squeezing one leviton at a time, Phys. Rev. B 97, 155135 (2018).
  62. G. Rebora, D. Ferraro, and M. Sassetti, Suppression of the radiation squeezing in interacting quantum Hall edge channels, New J. Phys. 23, 063018 (2021).
  63. H. Bartolomei, R. Bisognin, H. Kamata, J.-M. Berroir, E. Bocquillon, G. Ménard, B. Plaçais, A. Cavanna, U. Gennser, Y. Jin, P. Degiovanni, C. Mora, and G. Fève, Observation of edge magnetoplasmon squeezing in a quantum Hall conductor, Phys. Rev. Lett. 130, 106201 (2023).
  64. G. Gasse, C. Lupien, and B. Reulet, Observation of squeezing in the electron quantum shot noise of a tunnel junction, Phys. Rev. Lett. 111, 136601 (2013).
  65. U. Mendes and C. Mora, Cavity squeezing by a quantum conductor, New J. Phys. 17, 113014 (2015).
  66. M. Moskalets and M. Büttiker, Floquet scattering theory for current and heat noise in large amplitude adiabatic pumps, Phys. Rev. B 70, 245305 (2004).
  67. S. Bolduc Beaudoin, E. Pinsolle, and B. Reulet, Counting statistics of ultrabroadband microwave photons, Phys. Rev. Res. 6, 043238 (2024).
  68. J.-O. Simoneau, S. Jezouin, C. Lupien, and B. Reulet, Time-resolved quantum correlations in electronic noise, arXiv:2404.09068.
  69. N. Ubbelohde, L. Freise, E. Pavlovska, P. G. Silvestrov, P. Recher, M. Kokainis, G. Barinovs, F. Hohls, T. Weimann, K. Pierz, and V. Kashcheyevs, Two electrons interacting at a mesoscopic beam splitter, Nat. Nanotechnol. 18, 733 (2023).
  70. J. Wang, H. Edlbauer, A. Richard, S. Ota, W. Park, J. Shim, A. Ludwig, A. D. Wieck, H.-S. Sim, M. Urdampilleta, T. Meunier, T. Kodera, N.-H. Kaneko, H. Sellier, X. Waintal, S. Takada, and C. Bäuerle, Coulomb-mediated antibunching of an electron pair surfing on sound, Nat. Nanotechnol. 18, 721 (2023).
  71. J. D. Fletcher, W. Park, S. Ryu, P. See, J. P. Griffiths, G. A. C. Jones, I. Farrer, D. A. Ritchie, H. S. Sim, and M. Kataoka, Time-resolved Coulomb collision of single electrons, Nat. Nanotechnol. 18, 727 (2023).
  72. A. C. Elitzur and L. Vaidman, Quantum mechanical interaction-free measurements, Found. Phys. 23, 987 (1993).
  73. I. Safi and H. Schulz, Transport through a single band wire connected to measuring leads, in Quantum Transport in Semiconductor Submicron Structures, edited by B. Kramer (Kluwer Academic Press, Dordrecht, 1995), p. 159.
  74. P. Degiovanni, C. Grenier, and G. Fève, Decoherence and relaxation of single electron excitations in quantum Hall edge channels, Phys. Rev. B 80, 241307(R) (2009).
  75. P. Degiovanni, C. Grenier, G. Fève, C. Altimiras, H. le Sueur, and F. Pierre, Plasmon scattering approach to energy exchange and high-frequency noise in ν=2 quantum Hall edge channels, Phys. Rev. B 81, 121302(R) (2010).
  76. E. Bocquillon, V. Freulon, J.-M. Berroir, P. Degiovanni, B. Plaçais, A. Cavanna, Y. Jin, and G. Fève, Separation between neutral and charge modes in one dimensional chiral edge channels, Nat. Commun. 4, 1839 (2013).
  77. P. Woodward, Probability and Information Theory, with Applications to Radar (McGraw-Hill, New York, 1953).
  78. J. T. Chalker, Y. Gefen, and M. Y. Veillette, Decoherence and interactions in an electronic Mach-Zehnder interferometer, Phys. Rev. B 76, 085320 (2007).
  79. I. P. Levkivskyi and E. V. Sukhorukov, Dephasing in the electronic Mach-Zehnder interferometer at filling factor ν=2, Phys. Rev. B 78, 045322 (2008).
  80. C. Neuenhahn and F. Marquardt, Dephasing by electron-electron interactions in a ballistic interferometer, New J. Phys. 10, 115018 (2008).
  81. C. Neuenhahn and F. Marquardt, Universal dephasing in a chiral 1d interacting fermion system, Phys. Rev. Lett. 102, 046806 (2009).
  82. E. G. Idrisov, I. P. Levkivskyi, and E. V. Sukhorukov, Dephasing in a Mach-Zehnder interferometer by an ohmic contact, Phys. Rev. Lett. 121, 026802 (2018).
  83. C. Grenier, R. Hervé, G. Fève, and P. Degiovanni, Electron quantum optics in quantum Hall edge channels, Mod. Phys. Lett. B 25, 1053 (2011).
  84. G. Rebora, D. Ferraro, R. H. Rodriguez, F. D. Parmentier, P. Roche, and M. Sassetti, Electronic wave-packets in integer quantum Hall edge channels: Relaxation and dissipative effects, Entropy 23, 138 (2021).
  85. K. S. Singwi and A. Sjölander, Resonance absorption of nuclear gamma rays and the dynamics of atomic motions, Phys. Rev. 120, 1093 (1960).
  86. C. Tzara, Diffusion des photons sur les atomes et les noyaux dans les cristaux, J. Phys. Radium 22, 303 (1961).
  87. D. Dasenbrook and C. Flindt, Dynamical scheme for interferometric measurements of full-counting statistics, Phys. Rev. Lett. 117, 146801 (2016).
  88. J. Dubois, T. Jullien, C. Grenier, P. Degiovanni, P. Roulleau, and D. C. Glattli, Integer and fractional charge Lorentzian voltage pulses analyzed in the framework of photon-assisted shot noise, Phys. Rev. B 88, 085301 (2013).
  89. H. Duprez, E. Sivre, A. Anthore, A. Aassime, A. Cavanna, U. Gennser, and F. Pierre, Transmitting the quantum state of electrons across a metallic island with Coulomb interaction, Science 366, 1243 (2019).
  90. M. Misiorny, G. Fève, and J. Splettstoesser, Shaping charge excitations in chiral edge states with a time-dependent gate voltage, Phys. Rev. B 97, 075426 (2018).
  91. H. Duprez, E. Sivre, A. Anthore, A. Aassime, A. Cavanna, A. Ouerghi, U. Gennser, and F. Pierre, Macroscopic electron quantum coherence in a solid-state circuit, Phys. Rev. X 9, 021030 (2019).
  92. This is justified by observing that |Sba(ω0)|2/Q0 is significantly smaller than unity and experimentally achieved squeezing parameters are below z≃0.0719. Even a 3 dB noise reduction corresponds to z≃0.1733.

  93. The only hypothesis for deriving Eqs. (50) and (52) is that |Sba(ω)|2 does not vary significantly on the bandwidth of χ.

  94. C. Fabre and N. Treps, Modes and states in quantum optics, Rev. Mod. Phys. 92, 035005 (2020).
  95. M. Walschaers, C. Fabre, V. Parigi, and N. Treps, Entanglement and Wigner function negativity of multimode non-Gaussian states, Phys. Rev. Lett. 119, 183601 (2017).
  96. M. Walschaers, Non-Gaussian quantum states and where to find them, PRX Quantum 2, 030204 (2021).
  97. B. I. Halperin, A. Stern, I. Neder, and B. Rosenow, Theory of the Fabry-Pérot quantum Hall interferometer, Phys. Rev. B 83, 155440 (2011).
  98. G. A. Frigeri, D. D. Scherer, and B. Rosenow, Sub-periods and apparent pairing in integer quantum Hall interferometers, Europhys. Lett. 126, 67007 (2019).
  99. G. A. Frigeri and B. Rosenow, Electron pairing in the quantum Hall regime due to neutralon exchange, Phys. Rev. Res. 2, 043396 (2020).
  100. C. Bauerle, D. Glattli, T. Meunier, F. Portier, P. Roche, P. Roulleau, S. Takada, and X. Waintal, Coherent control of single electrons: A review of current progress, Rep. Prog. Phys. 81, 056503 (2018).
  101. H. Souquet-Basiège, B. Roussel, G. Rebora, G. Ménard, I. Safi, G. Fève, and P. Degiovanni, The electronic ambiguity function in single electron interferometry (to be published).
  102. J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, The theory and design of chirp radars, Bell Syst. Tech. J. 39, 745 (1960).
  103. J. Radon, On the determination of functions from their integral values along certain manifolds, IEEE Trans. Med. Imaging 5, 170 (1986).
  104. D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum, Phys. Rev. Lett. 70, 1244 (1993).
  105. A. I. Lvovsky and M. G. Raymer, Continuous-variable optical quantum-state tomography, Rev. Mod. Phys. 81, 299 (2009).
  106. M. Tsang, R. Nair, and X.-M. Lu, Quantum theory of superresolution for two incoherent optical point sources, Phys. Rev. X 6, 031033 (2016).
  107. M. Tsang, Subdiffraction incoherent optical imaging via spatial-mode demultiplexing, New J. Phys. 19, 023054 (2017).
  108. J. Řehaček, Z. Hradil, B. Stoklasa, M. Paúr, J. Grover, A. Krzic, and L. L. Sánchez-Soto, Multiparameter quantum metrology of incoherent point sources: Towards realistic superresolution, Phys. Rev. A 96, 062107 (2017).
  109. M. Paúr, B. Stoklasa, J. Grover, A. Krzic, L. L. Sánchez-Soto, Z. Hradil, and J. Řeháček, Tempering Rayleigh curse with PSF shaping, Optica 5, 1177 (2018).
  110. F. Benatti, R. Floreanini, and U. Marzolino, Entanglement in fermion systems and quantum metrology, Phys. Rev. A 89, 032326 (2014).
  111. V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nat. Photonics 5, 222 (2011).
  112. L. Freise, T. Gerster, D. Reifert, T. Weimann, K. Pierz, F. Hohls, and N. Ubbelohde, Trapping and counting ballistic nonequilibrium electrons, Phys. Rev. Lett. 124, 127701 (2020).
  113. M. Büttiker, A. Prêtre, and H. Thomas, Dynamic conductance and the scattering matrix of small conductors, Phys. Rev. Lett. 70, 4114 (1993).
  114. The radius 1 reflects the relaxation resistance Rq=RK/2 of the circuit predicted in Ref. [115].

  115. M. Büttiker, H. Thomas, and A. Prêtre, Mesoscopic capacitors, Phys. Lett. A 180, 364 (1993).
  116. A. Delgard, B. Chenaud, U. Gennser, A. Cavanna, D. Mailly, P. Degiovanni, and C. Chaubet, Coulomb interactions and effective quantum inertia of charge carriers in a macroscopic conductor, Phys. Rev. B 104, L121301 (2021).
  117. C. Grenier, R. Hervé, E. Bocquillon, F. Parmentier, B. Plaçais, J.-M. Berroir, G. Fève, and P. Degiovanni, Single electron quantum tomography in quantum Hall edge channels, New J. Phys. 13, 093007 (2011).
  118. We will discuss other cases later, but for the average current, any other contribution would be irrelevant.

  119. D. Ferraro, C. Wahl, J. Rech, T. Jonckheere, and T. Martin, Electronic Hong-Ou-Mandel interferometry in two-dimensional topological insulators, Phys. Rev. B 89, 075407 (2014).
  120. D. Dasenbrook, J. Bowles, J. B. Brask, P. P. Hofer, C. Flindt, and N. Brunner, Single-electron entanglement and nonlocality, New J. Phys. 18, 043036 (2016).
  121. The truncation for positive or negative energies can be neglected provided γe≪|ωe|.

  122. C. Grenier, J. Dubois, T. Jullien, P. Roulleau, D. C. Glattli, and P. Degiovanni, Fractionalization of minimal excitations in integer quantum Hall edge channels, Phys. Rev. B 88, 085302 (2013).
  123. Note that |Sq0⟩=|0⟩.

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