Beyond-adiabatic Quantum Admittance of a Semiconductor Quantum Dot at High Frequencies: Rethinking Reflectometry as Polaron Dynamics

L. Peri1,2, G. A. Oakes1,2, L. Cochrane1,2, C. J. B. Ford1, and M. F. Gonzalez-Zalba2

1Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
2Quantum Motion, 9 Sterling Way, London N7 9HJ, United Kingdom

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Abstract

Semiconductor quantum dots operated dynamically are the basis of many quantum technologies such as quantum sensors and computers. Hence, modelling their electrical properties at microwave frequencies becomes essential to simulate their performance in larger electronic circuits. Here, we develop a self-consistent quantum master equation formalism to obtain the admittance of a quantum dot tunnel-coupled to a charge reservoir under the effect of a coherent photon bath. We find a general expression for the admittance that captures the well-known semiclassical (thermal) limit, along with the transition to lifetime and power broadening regimes due to the increased coupling to the reservoir and amplitude of the photonic drive, respectively. Furthermore, we describe two new photon-mediated regimes: Floquet broadening, determined by the dressing of the QD states, and broadening determined by photon loss in the system. Our results provide a method to simulate the high-frequency behaviour of QDs in a wide range of limits, describe past experiments, and propose novel explorations of QD-photon interactions.

Semiconductor quantum dots operated dynamically are the basis of many quantum technologies such as quantum sensors and computers. Here we develop a fully quantum formalism for a Quantum Dot coupled to a Reservoir and driven by a Photon Oscillator, including the finite lifetime of a charge in the Dot and non-idealities of the drive. We find fully analytical solution for the equivalent circuit of the driven system, also in the large-signal regime, and predict two novel phenomena: Floquet broadening and Photon-Loss broadening.

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[1] Daniel Loss and David P. DiVincenzo. Quantum computation with quantum dots. Physical Review A, 57 (11): 120–126, January 1998. 10.1103/​PhysRevA.57.120.
https:/​/​doi.org/​10.1103/​PhysRevA.57.120

[2] Stephan G. J. Philips, Mateusz T. Madzik, Sergey V. Amitonov, Sander L. de Snoo, Maximilian Russ, Nima Kalhor, Christian Volk, William I. L. Lawrie, Delphine Brousse, Larysa Tryputen, Brian Paquelet Wuetz, Amir Sammak, Menno Veldhorst, Giordano Scappucci, and Lieven M. K. Vandersypen. Universal control of a six-qubit quantum processor in silicon. Nature, 609 (7929): 919–924, September 2022. ISSN 1476-4687. 10.1038/​s41586-022-05117-x.
https:/​/​doi.org/​10.1038/​s41586-022-05117-x

[3] Francesco Borsoi, Nico W. Hendrickx, Valentin John, Marcel Meyer, Sayr Motz, Floor van Riggelen, Amir Sammak, Sander L. de Snoo, Giordano Scappucci, and Menno Veldhorst. Shared control of a 16 semiconductor quantum dot crossbar array. Nature Nanotechnology, 19 (1): 21–27, January 2024. ISSN 1748-3395. 10.1038/​s41565-023-01491-3.
https:/​/​doi.org/​10.1038/​s41565-023-01491-3

[4] Xiao Xue, Maximilian Russ, Nodar Samkharadze, Brennan Undseth, Amir Sammak, Giordano Scappucci, and Lieven M. K. Vandersypen. Quantum logic with spin qubits crossing the surface code threshold. Nature, 601 (78937893): 343–347, January 2022. ISSN 0028-0836, 1476-4687. 10.1038/​s41586-021-04273-w.
https:/​/​doi.org/​10.1038/​s41586-021-04273-w

[5] Akito Noiri, Kenta Takeda, Takashi Nakajima, Takashi Kobayashi, Amir Sammak, Giordano Scappucci, and Seigo Tarucha. Fast universal quantum gate above the fault-tolerance threshold in silicon. Nature, 601 (7893): 338–342, January 2022. ISSN 1476-4687. 10.1038/​s41586-021-04182-y.
https:/​/​doi.org/​10.1038/​s41586-021-04182-y

[6] Adam R. Mills, Charles R. Guinn, Michael J. Gullans, Anthony J. Sigillito, Mayer M. Feldman, Erik Nielsen, and Jason R. Petta. Two-qubit silicon quantum processor with operation fidelity exceeding 99 Science Advances, 8 (14): eabn5130, April 2022. 10.1126/​sciadv.abn5130.
https:/​/​doi.org/​10.1126/​sciadv.abn5130

[7] R. Maurand, X. Jehl, D. Kotekar-Patil, A. Corna, H. Bohuslavskyi, R. Laviéville, L. Hutin, S. Barraud, M. Vinet, M. Sanquer, and S. De Franceschi. A cmos silicon spin qubit. Nature Communications, 7 (11): 13575, November 2016. ISSN 2041-1723. 10.1038/​ncomms13575.
https:/​/​doi.org/​10.1038/​ncomms13575

[8] A. M. J. Zwerver, T. Krähenmann, T. F. Watson, L. Lampert, H. C. George, R. Pillarisetty, S. A. Bojarski, P. Amin, S. V. Amitonov, J. M. Boter, R. Caudillo, D. Correas-Serrano, J. P. Dehollain, G. Droulers, E. M. Henry, R. Kotlyar, M. Lodari, F. Lüthi, D. J. Michalak, B. K. Mueller, S. Neyens, J. Roberts, N. Samkharadze, G. Zheng, O. K. Zietz, G. Scappucci, M. Veldhorst, L. M. K. Vandersypen, and J. S. Clarke. Qubits made by advanced semiconductor manufacturing. 5: 184–190, March 2022. ISSN 2520-1131. 10.1038/​s41928-022-00727-9.
https:/​/​doi.org/​10.1038/​s41928-022-00727-9

[9] Xiao Xue, Bishnu Patra, Jeroen P. G. van Dijk, Nodar Samkharadze, Sushil Subramanian, Andrea Corna, Brian Paquelet Wuetz, Charles Jeon, Farhana Sheikh, Esdras Juarez-Hernandez, Brando Perez Esparza, Huzaifa Rampurawala, Brent Carlton, Surej Ravikumar, Carlos Nieva, Sungwon Kim, Hyung-Jin Lee, Amir Sammak, Giordano Scappucci, Menno Veldhorst, Fabio Sebastiano, Masoud Babaie, Stefano Pellerano, Edoardo Charbon, and Lieven M. K. Vandersypen. Cmos-based cryogenic control of silicon quantum circuits. Nature, 593 (7858): 205–210, May 2021. ISSN 1476-4687. 10.1038/​s41586-021-03469-4.
https:/​/​doi.org/​10.1038/​s41586-021-03469-4

[10] Andrea Ruffino, Tsung-Yeh Yang, John Michniewicz, Yatao Peng, Edoardo Charbon, and Miguel Fernando Gonzalez-Zalba. A cryo-cmos chip that integrates silicon quantum dots and multiplexed dispersive readout electronics. Nature Electronics, 5 (1): 53–59, January 2022. ISSN 2520-1131. 10.1038/​s41928-021-00687-6.
https:/​/​doi.org/​10.1038/​s41928-021-00687-6

[11] K. D. Petersson, C. G. Smith, D. Anderson, P. Atkinson, G. A. C. Jones, and D. A. Ritchie. Charge and spin state readout of a double quantum dot coupled to a resonator. Nano Letters, 10 (8): 2789–2793, August 2010. ISSN 1530-6984. 10.1021/​nl100663w.
https:/​/​doi.org/​10.1021/​nl100663w

[12] Florian Vigneau, Federico Fedele, Anasua Chatterjee, David Reilly, Ferdinand Kuemmeth, M. Fernando Gonzalez-Zalba, Edward Laird, and Natalia Ares. Probing quantum devices with radio-frequency reflectometry. Applied Physics Reviews, 10 (2), feb 2023. 10.1063/​5.0088229.
https:/​/​doi.org/​10.1063/​5.0088229

[13] M. G. House, I. Bartlett, P. Pakkiam, M. Koch, E. Peretz, J. van der Heijden, T. Kobayashi, S. Rogge, and M. Y. Simmons. High-sensitivity charge detection with a single-lead quantum dot for scalable quantum computation. Physical Review Applied, 6: 044016, 2016. ISSN 23317019. 10.1103/​PhysRevApplied.6.044016.
https:/​/​doi.org/​10.1103/​PhysRevApplied.6.044016

[14] G. A. Oakes, V. N. Ciriano-Tejel, D. F. Wise, M. A. Fogarty, T. Lundberg, C. Lainé, S. Schaal, F. Martins, D. J. Ibberson, L. Hutin, B. Bertrand, N. Stelmashenko, J. W. A. Robinson, L. Ibberson, A. Hashim, I. Siddiqi, A. Lee, M. Vinet, C. G. Smith, J. J. L. Morton, and M. F. Gonzalez-Zalba. Fast high-fidelity single-shot readout of spins in silicon using a single-electron box. Phys. Rev. X, 13: 011023, Feb 2023a. 10.1103/​PhysRevX.13.011023.
https:/​/​doi.org/​10.1103/​PhysRevX.13.011023

[15] Joost van der Heijden, Takashi Kobayashi, Matthew G. House, Joe Salfi, Sylvain Barraud, Romain Laviéville, Michelle Y. Simmons, and Sven Rogge. Readout and control of the spin-orbit states of two coupled acceptor atoms in a silicon transistor. Science Advances, 4 (12): eaat9199, Dec 2018. 10.1126/​sciadv.aat9199.
https:/​/​doi.org/​10.1126/​sciadv.aat9199

[16] Imtiaz Ahmed, Anasua Chatterjee, Sylvain Barraud, John J. L. Morton, James A. Haigh, and M. Fernando Gonzalez-Zalba. Primary thermometry of a single reservoir using cyclic electron tunneling to a quantum dot. Communications Physics, 1 (11): 1–7, October 2018. ISSN 2399-3650. 10.1038/​s42005-018-0066-8.
https:/​/​doi.org/​10.1038/​s42005-018-0066-8

[17] J.M.A. Chawner, S. Barraud, M.F. Gonzalez-Zalba, S. Holt, E.A. Laird, Yu. A. Pashkin, and J.R. Prance. Nongalvanic calibration and operation of a quantum dot thermometer. Physical Review Applied, 15 (33): 034044, March 2021. ISSN 2331-7019. 10.1103/​PhysRevApplied.15.034044.
https:/​/​doi.org/​10.1103/​PhysRevApplied.15.034044

[18] G.A. Oakes, L. Peri, L. Cochrane, F. Martins, L. Hutin, B. Bertrand, M. Vinet, A. Gomez Saiz, C.J.B. Ford, C.G. Smith, and M.F. Gonzalez-Zalba. Quantum dot-based frequency multiplier. PRX Quantum, 4 (2): 020346, June 2023b. 10.1103/​PRXQuantum.4.020346.
https:/​/​doi.org/​10.1103/​PRXQuantum.4.020346

[19] Laurence Cochrane, Theodor Lundberg, David J. Ibberson, Lisa A. Ibberson, Louis Hutin, Benoit Bertrand, Nadia Stelmashenko, Jason W. A. Robinson, Maud Vinet, Ashwin A. Seshia, and M. Fernando Gonzalez-Zalba. Parametric Amplifiers Based on Quantum Dots. Phys. Rev. Lett., 128 (19): 197701, 2022a. 10.1103/​PhysRevLett.128.197701.
https:/​/​doi.org/​10.1103/​PhysRevLett.128.197701

[20] 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 (6321): 156–158, January 2017. 10.1126/​science.aal2469.
https:/​/​doi.org/​10.1126/​science.aal2469

[21] 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 (6380): 1123–1127, March 2018. ISSN 0036-8075, 1095-9203. 10.1126/​science.aar4054.
https:/​/​doi.org/​10.1126/​science.aar4054

[22] I. Hansen, A. E. Seedhouse, K. W. Chan, F. E. Hudson, K. M. Itoh, A. Laucht, A. Saraiva, C. H. Yang, and A. S. Dzurak. Implementation of an advanced dressing protocol for global qubit control in silicon. Applied Physics Reviews, 9 (3): 031409, Sep 2022. ISSN 1931-9401. 10.1063/​5.0096467.
https:/​/​doi.org/​10.1063/​5.0096467

[23] Amanda E. Seedhouse, Ingvild Hansen, Arne Laucht, Chih Hwan Yang, Andrew S. Dzurak, and Andre Saraiva. Quantum computation protocol for dressed spins in a global field. Physical Review B, 104 (23): 235411, Dec 2021. 10.1103/​PhysRevB.104.235411.
https:/​/​doi.org/​10.1103/​PhysRevB.104.235411

[24] R. Mizuta, R. M. Otxoa, A. C. Betz, and M. F. Gonzalez-Zalba. Quantum and tunneling capacitance in charge and spin qubits. Phys. Rev. B, 95: 045414, Jan 2017. 10.1103/​PhysRevB.95.045414.
https:/​/​doi.org/​10.1103/​PhysRevB.95.045414

[25] M. Esterli, R.M. Otxoa, and M.F. Gonzalez-Zalba. Small-signal equivalent circuit for double quantum dots at low-frequencies. Applied Physics Letters, 114, 2019. ISSN 00036951. 10.1063/​1.5098889.
https:/​/​doi.org/​10.1063/​1.5098889

[26] Audrey Cottet, Christophe Mora, and Takis Kontos. Mesoscopic admittance of a double quantum dot. Physical Review B, 83 (12): 121311, March 2011. 10.1103/​PhysRevB.83.121311.
https:/​/​doi.org/​10.1103/​PhysRevB.83.121311

[27] A. Crepieux and M. Lavagna. Dynamical charge susceptibility in nonequilibrium double quantum dots. Physical Review B, 106 (11): 115439, Sep 2022. 10.1103/​PhysRevB.106.115439.
https:/​/​doi.org/​10.1103/​PhysRevB.106.115439

[28] Jay Gambetta, Alexandre Blais, M. Boissonneault, A. A. Houck, D. I. Schuster, and S. M. Girvin. Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect. Physical Review A, 77 (11): 012112, Jan 2008. ISSN 1050-2947, 1094-1622. 10.1103/​PhysRevA.77.012112.
https:/​/​doi.org/​10.1103/​PhysRevA.77.012112

[29] Jay Gambetta, Alexandre 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. Physical Review A, 74 (4): 042318. ISSN 1050-2947, 1094-1622. 10.1103/​PhysRevA.74.042318. Number: 4.
https:/​/​doi.org/​10.1103/​PhysRevA.74.042318

[30] D. H. Slichter, R. Vijay, S. J. Weber, S. Boutin, M. Boissonneault, J. M. Gambetta, A. Blais, and I. Siddiqi. Measurement-induced qubit state mixing in circuit QED from up-converted dephasing noise. Physical Review Letters, 109 (1515): 153601, Oct 2012. ISSN 0031-9007, 1079-7114. 10.1103/​PhysRevLett.109.153601.
https:/​/​doi.org/​10.1103/​PhysRevLett.109.153601

[31] Vahid Derakhshan Maman, M. F. Gonzalez-Zalba, and Andras Palyi. Charge noise and overdrive errors in dispersive readout of charge, spin, and majorana qubits. Physical Review Applied, 14 (66): 064024, Dec 2020. 10.1103/​PhysRevApplied.14.064024.
https:/​/​doi.org/​10.1103/​PhysRevApplied.14.064024

[32] Makoto Yamaguchi, Tatsuro Yuge, and Tetsuo Ogawa. Markovian quantum master equation beyond adiabatic regime. Physical Review E, 95 (1): 012136, Jan 2017. ISSN 2470-0045, 2470-0053. 10.1103/​PhysRevE.95.012136.
https:/​/​doi.org/​10.1103/​PhysRevE.95.012136

[33] Daniel Manzano. A short introduction to the Lindblad master equation. AIP Advances, 10 (2): 025106, February 2020. 10.1063/​1.5115323. Publisher: American Institute of Physics.
https:/​/​doi.org/​10.1063/​1.5115323

[34] Takashi Mori. Floquet states in open quantum systems. Annual Review of Condensed Matter Physics, 14 (1): 35 –56, 2023. 10.1146/​annurev-conmatphys-040721-015537.
https:/​/​doi.org/​10.1146/​annurev-conmatphys-040721-015537

[35] C. W. Gardiner and P. Zoller. Quantum noise: a handbook of Markovian and non-Markovian quantum stochastic methods with applications to quantum optics. Springer series in synergetics. Springer, 3rd ed edition, 2004. ISBN 978-3-540-22301-6.

[36] Jakub K. Sowa, Jan A. Mol, G. Andrew D. Briggs, and Erik M. Gauger. Beyond Marcus theory and the Landauer-Büttiker approach in molecular junctions: A unified framework. The Journal of Chemical Physics, 149 (15): 154112, Oct 2018. ISSN 0021-9606, 1089-7690. 10.1063/​1.5049537.
https:/​/​doi.org/​10.1063/​1.5049537

[37] C. W. Gardiner and C. W. Gardiner. Stochastic methods: a handbook for the natural and social sciences. Springer series in synergetics. Springer, Berlin, 4th ed edition, 2009. ISBN 978-3-540-70712-7.

[38] Laurence Cochrane, Ashwin A. Seshia, and M. Fernando Gonzalez Zalba. Intrinsic noise of the single electron box. (arXiv:2209.15086), September 2022b. 10.48550/​arXiv.2209.15086.
https:/​/​doi.org/​10.48550/​arXiv.2209.15086
arXiv:2209.15086

[39] R. C. Ashoori, H. L. Stormer, J. S. Weiner, L. N. Pfeiffer, S. J. Pearton, K. W. Baldwin, and K. W. West. Single-electron capacitance spectroscopy of discrete quantum levels. Physical Review Letters, 68 (20): 3088–3091, May 1992. 10.1103/​PhysRevLett.68.3088.
https:/​/​doi.org/​10.1103/​PhysRevLett.68.3088

[40] R. C. Ashoori, H. L. Stormer, J. S. Weiner, L. N. Pfeiffer, K. W. Baldwin, and K. W. West. N-electron ground state energies of a quantum dot in magnetic field. Physical Review Letters, 71 (4): 613–616, July 1993. 10.1103/​PhysRevLett.71.613.
https:/​/​doi.org/​10.1103/​PhysRevLett.71.613

[41] L. Peri, M. Benito, C. J. B. Ford, and M. F. Gonzalez-Zalba. Unified linear response theory of quantum dot circuits. (arXiv:2310.17399), October 2023. 10.48550/​arXiv.2310.17399.
https:/​/​doi.org/​10.48550/​arXiv.2310.17399
arXiv:2310.17399

[42] F. Persson, C. M. Wilson, M. Sandberg, G. Johansson, and P. Delsing. Excess dissipation in a single-electron box: The Sisyphus resistance. Nano Letters, 10 (3): 953–957, March 2010. ISSN 1530-6984, 1530-6992. 10.1021/​nl903887x.
https:/​/​doi.org/​10.1021/​nl903887x

[43] C. Ciccarelli and A. J. Ferguson. Impedance of the single electron transistor at radio-frequencies. New Journal of Physics, 13 (99): 093015, September 2011. ISSN 1367-2630. 10.1088/​1367-2630/​13/​9/​093015.
https:/​/​doi.org/​10.1088/​1367-2630/​13/​9/​093015

[44] YiJing Yan. Quantum Fokker-Planck theory in a non-Gaussian-Markovian medium. Physical Review A, 58 (4): 2721 –2732, Oct 1998. ISSN 1050-2947, 1094-1622. 10.1103/​PhysRevA.58.2721.
https:/​/​doi.org/​10.1103/​PhysRevA.58.2721

[45] Jakub K. Sowa, Neill Lambert, Tamar Seideman, and Erik M. Gauger. Beyond Marcus theory and the Landauer-Buttiker approach in molecular junctions. ii. a self-consistent Born approach. The Journal of Chemical Physics, 152 (6): 064103, Feb 2020. ISSN 0021-9606, 1089-7690. 10.1063/​1.5143146.
https:/​/​doi.org/​10.1063/​1.5143146

[46] Carlos Alexandre Brasil, Felipe Fernandes Fanchini, and Reginaldo de Jesus Napolitano. A simple derivation of the Lindblad equation. Revista Brasileira de Ensino de Física, 35 (1): 01 –09, Mar 2013. ISSN 1806-9126, 1806-1117. 10.1590/​S1806-11172013000100003.
https:/​/​doi.org/​10.1590/​S1806-11172013000100003

[47] Roie Dann, Amikam Levy, and Ronnie Kosloff. Time dependent markovian quantum master equation. Physical Review A, 98 (5): 052129, Nov 2018. ISSN 2469-9926, 2469-9934. 10.1103/​PhysRevA.98.052129.
https:/​/​doi.org/​10.1103/​PhysRevA.98.052129

[48] Sigmund Kohler, Thomas Dittrich, and Peter Hänggi. Floquet-markovian description of the parametrically driven, dissipative harmonic quantum oscillator. Physical Review E, 55 (1): 300–313, 1997. 10.1103/​PhysRevE.55.300. Publisher: American Physical Society.
https:/​/​doi.org/​10.1103/​PhysRevE.55.300

[49] M. F. Gonzalez-Zalba, S. Barraud, A. J. Ferguson, and A. C. Betz. Probing the limits of gate-based charge sensing. Nature Communications, 6 (1): 6084, January 2015. ISSN 2041-1723. 10.1038/​ncomms7084.
https:/​/​doi.org/​10.1038/​ncomms7084

[50] Seogjoo J. Jang. Partially polaron-transformed quantum master equation for exciton and charge transport dynamics. The Journal of Chemical Physics, 157 (1010): 104107, Sep 2022. ISSN 0021-9606, 1089-7690. 10.1063/​5.0106546.
https:/​/​doi.org/​10.1063/​5.0106546

[51] Dazhi Xu and Jianshu Cao. Non-canonical distribution and non-equilibrium transport beyond weak system-bath coupling regime: A polaron transformation approach. Frontiers of Physics, 11 (44): 110308, Aug 2016. ISSN 2095-0462, 2095-0470. 10.1007/​s11467-016-0540-2.
https:/​/​doi.org/​10.1007/​s11467-016-0540-2

[52] Eli Y. Wilner, Haobin Wang, Michael Thoss, and Eran Rabani. Sub-ohmic to super-ohmic crossover behavior in nonequilibrium quantum systems with electron-phonon interactions. Physical Review B, 92 (1919): 195143, Nov 2015. ISSN 1098-0121, 1550-235X. 10.1103/​PhysRevB.92.195143.
https:/​/​doi.org/​10.1103/​PhysRevB.92.195143

[53] William Lee, Nicola Jean, and Stefano Sanvito. Exploring the limits of the self-consistent born approximation for inelastic electronic transport. Physical Review B, 79 (8): 085120, Feb 2009. 10.1103/​PhysRevB.79.085120.
https:/​/​doi.org/​10.1103/​PhysRevB.79.085120

[54] Sigmund Kohler. Dispersive readout of adiabatic phases. Physical Review Letters, 119 (19): 196802, 2017. 10.1103/​PhysRevLett.119.196802. Publisher: American Physical Society.
https:/​/​doi.org/​10.1103/​PhysRevLett.119.196802

[55] Sigmund Kohler. Dispersive readout: Universal theory beyond the rotating-wave approximation. Physical Review A, 98 (2): 023849, 2018. 10.1103/​PhysRevA.98.023849. Publisher: American Physical Society.
https:/​/​doi.org/​10.1103/​PhysRevA.98.023849

[56] M. Benito, X. Mi, J. M. Taylor, J. R. Petta, and Guido Burkard. Input-output theory for spin-photon coupling in Si double quantum dots. Physical Review B, 96 (23): 235434, Dec 2017. 10.1103/​PhysRevB.96.235434.
https:/​/​doi.org/​10.1103/​PhysRevB.96.235434

[57] Si-Si Gu, Sigmund Kohler, Yong-Qiang Xu, Rui Wu, Shun-Li Jiang, Shu-Kun Ye, Ting Lin, Bao-Chuan Wang, Hai-Ou Li, Gang Cao, and Guo-Ping Guo. Probing two driven double quantum dots strongly coupled to a cavity. Physical Review Letters, 130 (23): 233602, June 2023. 10.1103/​PhysRevLett.130.233602.
https:/​/​doi.org/​10.1103/​PhysRevLett.130.233602

[58] Beatriz Pérez-González, Álvaro Gómez-León, and Gloria Platero. Topology detection in cavity QED. Physical Chemistry Chemical Physics, 24 (26): 15860–15870, 2022. 10.1039/​D2CP01806C.
https:/​/​doi.org/​10.1039/​D2CP01806C

[59] J. V. Koski, A. J. Landig, A. Palyi, P. Scarlino, C. Reichl, W. Wegscheider, G. Burkard, A. Wallraff, K. Ensslin, and T. Ihn. Floquet spectroscopy of a strongly driven quantum dot charge qubit with a microwave resonator. Physical Review Letters, 121 (4): 043603, Jul 2018. ISSN 0031-9007, 1079-7114. 10.1103/​PhysRevLett.121.043603.
https:/​/​doi.org/​10.1103/​PhysRevLett.121.043603

[60] Tatsuhiko Ikeda, Koki Chinzei, and Masahiro Sato. Nonequilibrium steady states in the floquet-lindblad systems: van Vleck’s high-frequency expansion approach. SciPost Physics Core, 4 (4): 033, Dec 2021. ISSN 2666-9366. 10.21468/​SciPostPhysCore.4.4.033.
https:/​/​doi.org/​10.21468/​SciPostPhysCore.4.4.033

[61] P. K. Tien and J. P. Gordon. Multiphoton process observed in the interaction of microwave fields with the tunneling between superconductor films. Physical Review, 129 (22), Jan 1963. ISSN 0031-899X. 10.1103/​PhysRev.129.647.
https:/​/​doi.org/​10.1103/​PhysRev.129.647

[62] John R. Tucker and Marc J. Feldman. Quantum detection at millimeter wavelengths. Reviews of Modern Physics, 57 (4): 1055–1113, October 1985. ISSN 0034-6861. 10.1103/​RevModPhys.57.1055.
https:/​/​doi.org/​10.1103/​RevModPhys.57.1055

[63] Sigmund Kohler, Jörg Lehmann, and Peter Hänggi. Driven quantum transport on the nanoscale. Physics Reports, 406 (6): 379–443, February 2005. ISSN 03701573. 10.1016/​j.physrep.2004.11.002.
https:/​/​doi.org/​10.1016/​j.physrep.2004.11.002

[64] Gloria Platero and Ramón Aguado. Photon-assisted transport in semiconductor nanostructures. Physics Reports, 395 (1): 1 –157, May 2004. ISSN 0370-1573. 10.1016/​j.physrep.2004.01.004.
https:/​/​doi.org/​10.1016/​j.physrep.2004.01.004

[65] Mark S. Rudner and Netanel H. Lindner. The Floquet engineer’s handbook. (arXiv:2003.08252), Jun 2020. 10.48550/​arXiv.2003.08252.
https:/​/​doi.org/​10.48550/​arXiv.2003.08252
arXiv:2003.08252

[66] Victor V. Albert, Barry Bradlyn, Martin Fraas, and Liang Jiang. Geometry and response of lindbladians. Physical Review X, 6 (4): 041031, Nov 2016. ISSN 2160-3308. 10.1103/​PhysRevX.6.041031.
https:/​/​doi.org/​10.1103/​PhysRevX.6.041031

[67] M. G. House, T. Kobayashi, B. Weber, S. J. Hile, T. F. Watson, J. van der Heijden, S. Rogge, and M. Y. Simmons. Radio frequency measurements of tunnel couplings and singlet -triplet spin states in Si:P quantum dots. Nature Communications, 6 (11): 8848, Nov 2015. ISSN 2041-1723. 10.1038/​ncomms9848.
https:/​/​doi.org/​10.1038/​ncomms9848

[68] Ronald M. Foster. A reactance theorem. Bell System Technical Journal, 3 (2): 259–267, 1924. ISSN 1538-7305. 10.1002/​j.1538-7305.1924.tb01358.x.
https:/​/​doi.org/​10.1002/​j.1538-7305.1924.tb01358.x

[69] Simon E. Nigg, Hanhee Paik, Brian Vlastakis, Gerhard Kirchmair, S. Shankar, Luigi Frunzio, M. H. Devoret, R. J. Schoelkopf, and S. M. Girvin. Black-box superconducting circuit quantization. Physical Review Letters, 108 (24): 240502, Jun 2012. ISSN 0031-9007, 1079-7114. 10.1103/​PhysRevLett.108.240502.
https:/​/​doi.org/​10.1103/​PhysRevLett.108.240502

[70] Anasua Chatterjee, Sergey N. Shevchenko, Sylvain Barraud, Rubén M. Otxoa, Franco Nori, John J. L. Morton, and M. Fernando Gonzalez-Zalba. A silicon-based single-electron interferometer coupled to a fermionic sea. Physical Review B, 97 (4): 045405, Jan 2018. 10.1103/​PhysRevB.97.045405.
https:/​/​doi.org/​10.1103/​PhysRevB.97.045405

[71] Oleh V. Ivakhnenko, Sergey N. Shevchenko, and Franco Nori. Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference. Physics Reports, 995: 1 –89, Jan 2023. ISSN 0370-1573. 10.1016/​j.physrep.2022.10.002.
https:/​/​doi.org/​10.1016/​j.physrep.2022.10.002

[72] S.N. Shevchenko, S. Ashhab, and Franco Nori. Landau-Zener-Stückelberg interferometry. Phy Rep, 492 (1): 1–30, 2010. ISSN 0370-1573. https:/​/​doi.org/​10.1016/​j.physrep.2010.03.002.
https:/​/​doi.org/​10.1016/​j.physrep.2010.03.002

[73] Alexandre Blais, Ren-Shou Huang, Andreas 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, Jun 2004a. 10.1103/​PhysRevA.69.062320.
https:/​/​doi.org/​10.1103/​PhysRevA.69.062320

[74] Jonathan McTague and Jonathan J. Foley. Non-hermitian cavity quantum electrodynamics–configuration interaction singles approach for polaritonic structure with ab initio molecular hamiltonians. The Journal of Chemical Physics, 156 (15): 154103, 2022. 10.1063/​5.0091953.
https:/​/​doi.org/​10.1063/​5.0091953

[75] S M Dutra. Correspondence principle approach to cavity losses. European Journal of Physics, 18 (3): 194, may 1997. 10.1088/​0143-0807/​18/​3/​012.
https:/​/​doi.org/​10.1088/​0143-0807/​18/​3/​012

[76] Federico Roccati, Salvatore Lorenzo, Giuseppe Calajò , G. Massimo Palma, Angelo Carollo, and Francesco Ciccarello. Exotic interactions mediated by a non-hermitian photonic bath. Optica, 9 (5): 565, may 2022. 10.1364/​optica.443955.
https:/​/​doi.org/​10.1364/​optica.443955

[77] Fei Yan, Simon Gustavsson, Archana Kamal, Jeffrey Birenbaum, Adam P. Sears, David Hover, Ted J. Gudmundsen, Danna Rosenberg, Gabriel Samach, S. Weber, Jonilyn L. Yoder, Terry P. Orlando, John Clarke, Andrew J. Kerman, and William D. Oliver. The flux qubit revisited to enhance coherence and reproducibility. Nature Communications, 7 (11): 12964, Nov 2016. ISSN 2041-1723. 10.1038/​ncomms12964.
https:/​/​doi.org/​10.1038/​ncomms12964

[78] Alexandre Blais, Ren-Shou Huang, Andreas Wallraff, S. M. Girvin, and R. J. Schoelkopf. Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation. Physical Review A, 69 (6): 062320, Jun 2004b. ISSN 1050-2947, 1094-1622. 10.1103/​PhysRevA.69.062320.
https:/​/​doi.org/​10.1103/​PhysRevA.69.062320

[79] A. P. Sears, A. Petrenko, G. Catelani, L. Sun, Hanhee Paik, G. Kirchmair, L. Frunzio, L. I. Glazman, S. M. Girvin, and R. J. Schoelkopf. Photon shot noise dephasing in the strong-dispersive limit of circuit QED. Physical Review B, 86 (18): 180504(R), Nov 2012. 10.1103/​PhysRevB.86.180504.
https:/​/​doi.org/​10.1103/​PhysRevB.86.180504

[80] Moein Malekakhlagh, Easwar Magesan, and Luke C. G. Govia. Time-dependent schrieffer-wolff-lindblad perturbation theory: Measurement-induced dephasing and second-order stark shift in dispersive readout. Physical Review A, 106 (5): 052601, November 2022. 10.1103/​PhysRevA.106.052601.
https:/​/​doi.org/​10.1103/​PhysRevA.106.052601

[81] Felix-Ekkehard von Horstig, David J. Ibberson, Giovanni A. Oakes, Laurence Cochrane, Nadia Stelmashenko, Sylvain Barraud, Jason A. W. Robinson, Frederico Martins, and M. Fernando Gonzalez-Zalba. Multi-module microwave assembly for fast read-out and charge noise characterization of silicon quantum dots. (arXiv:2304.13442). 10.48550/​arXiv.2304.13442.
https:/​/​doi.org/​10.48550/​arXiv.2304.13442
arXiv:2304.13442

[82] Morag Am-Shallem, Amikam Levy, Ido Schaefer, and Ronnie Kosloff. Three approaches for representing lindblad dynamics by a matrix-vector notation. (arXiv:1510.08634), December 2015. 10.48550/​arXiv.1510.08634.
https:/​/​doi.org/​10.48550/​arXiv.1510.08634
arXiv:1510.08634

[83] Andrew M. Childs, Edward Farhi, and John Preskill. Robustness of adiabatic quantum computation. Physical Review A, 65 (1): 012322, Dec 2001. 10.1103/​PhysRevA.65.012322.
https:/​/​doi.org/​10.1103/​PhysRevA.65.012322

[84] Massimiliano Esposito and Michael Galperin. Self-consistent quantum master equation approach to molecular transport. The Journal of Physical Chemistry C, 114 (48): 20362 –20369, Dec 2010. ISSN 1932-7447. 10.1021/​jp103369s.
https:/​/​doi.org/​10.1021/​jp103369s

[85] Dong Hou, Shikuan Wang, Rulin Wang, LvZhou Ye, RuiXue Xu, Xiao Zheng, and YiJing Yan. Improving the efficiency of hierarchical equations of motion approach and application to coherent dynamics in Aharonov-Bohm interferometers. The Journal of Chemical Physics, 142 (10): 104112, Mar 2015. ISSN 0021-9606. 10.1063/​1.4914514.
https:/​/​doi.org/​10.1063/​1.4914514

[86] Tobias Hartung, Karl Jansen, and Chiara Sarti. Zeta-regularized lattice field theory with lorentzian background metrics. (arXiv:2208.08223), August 2022. 10.48550/​arXiv.2208.08223.
https:/​/​doi.org/​10.48550/​arXiv.2208.08223
arXiv:2208.08223

[87] P. Scarlino, J. H. Ungerer, D. J. van Woerkom, M. Mancini, P. Stano, C. Muller, A. J. Landig, J. V. Koski, C. Reichl, W. Wegscheider, T. Ihn, K. Ensslin, and A. Wallraff. In situ tuning of the electric-dipole strength of a double-dot charge qubit: Charge-noise protection and ultrastrong coupling. Physical Review X, 12 (3): 031004, Jul 2022. 10.1103/​PhysRevX.12.031004.
https:/​/​doi.org/​10.1103/​PhysRevX.12.031004

[88] E. T. Whittaker and G. N. Watson. A Course of Modern Analysis. Cambridge Mathematical Library. Cambridge University Press, 4 edition, 1996. 10.1017/​CBO9780511608759.
https:/​/​doi.org/​10.1017/​CBO9780511608759

[89] Kevin E. Cahill and Roy J. Glauber. Density operators for fermions. Physical Review A, 59 (2): 1538 –1555, Feb 1999. ISSN 1050-2947, 1094-1622. 10.1103/​PhysRevA.59.1538. arXiv:physics/​9808029.
https:/​/​doi.org/​10.1103/​PhysRevA.59.1538
arXiv:physics/9808029

Cited by

[1] Mathieu de Kruijf, Grayson M. Noah, Alberto Gomez-Saiz, John J.L. Morton, and M.Fernando Gonzalez-Zalba, "Measurement of cryoelectronics heating using a local quantum dot thermometer in silicon", Chip 100097 (2024).

[2] Mathieu de Kruijf, Grayson M. Noah, Alberto Gomez-Saiz, John J. L. Morton, and M. Fernando Gonzalez-Zalba, "Measurement of cryoelectronics heating using a local quantum dot thermometer in silicon", arXiv:2310.11383, (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2024-07-15 09:21:06) and SAO/NASA ADS (last updated successfully 2024-07-15 09:21:06). The list may be incomplete as not all publishers provide suitable and complete citation data.