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
  • Access by Xinjiang University

Balanced coupling in electromagnetic circuits

Daniel Sank*, Mostafa Khezri, Sergei Isakov, and Juan Atalaya

  • *Contact author: sank.daniel@gmail.com

Phys. Rev. Applied 23, 024012 – Published 5 February, 2025

DOI: https://doi.org/10.1103/PhysRevApplied.23.024012

Abstract

The rotating-wave approximation (RWA) is ubiquitous in the analysis of driven and coupled resonators. However, the limitations of the RWA seem to be poorly understood and in some cases the RWA disposes of essential physics. We investigate the RWA in the context of electrical circuits. Using a classical Hamiltonian approach, we find that by balancing electrical and magnetic components of the resonator drive or resonator-resonator coupling, the RWA can be made exact. This type of balance, in which the RWA is exact, has applications in superconducting qubits, where it suppresses nutation normally associated with strong Rabi driving. In the context of dispersive readout, balancing the qubit-resonator coupling changes the qubit leakage induced by the resonator drive but does not remove it in the case of the transmon qubit.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (38)

  1. P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, A quantum engineer’s guide to superconducting qubits, Appl. Phys. Rev. 6, 021318 (2019).
  2. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  3. F. Lecocq, L. Ranzani, G. Peterson, K. Cicak, R. Simmonds, J. Teufel, and J. Aumentado, Nonreciprocal microwave signal processing with a field-programmable Josephson amplifier, Phys. Rev. Appl. 7, 024028 (2017).
  4. G. A. Peterson, F. Lecocq, K. Cicak, R. W. Simmonds, J. Aumentado, and J. D. Teufel, Demonstration of efficient nonreciprocity in a microwave optomechanical circuit, Phys. Rev. X 7, 031001 (2017).
  5. L. Ranzani and J. Aumentado, Graph-based analysis of nonreciprocity in coupled-mode systems, New J. Phys. 17, 023024 (2015).
  6. W. H. Louisell, Parametric and Coupled Mode Electronics (John Wiley & Sons, Inc., London, 1960).
  7. D. Sank et al., Measurement-induced state transitions in a superconducting qubit: Beyond the rotating wave approximation, Phys. Rev. Lett. 117, 190503 (2016).
  8. D. I. Schuster, A. Wallraff, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. M. Girvin, and R. J. Schoelkopf, ac Stark shift and dephasing of a superconducting qubit strongly coupled to a cavity field, Phys. Rev. Lett. 94, 123602 (2005).
  9. 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 431, 162 (2004).
  10. A. Blais, R.-S. Huang, A. Wallraff, S. Girvin, and R. J. Schoelkopf, Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation, Phys. Rev. A 69, 062320 (2004).
  11. M. Khezri, E. Mlinar, J. Dressel, and A. N. Korotkov, Measuring a transmon qubit in circuit QED: Dressed squeezed states, Phys. Rev. A 94, 012347 (2016).
  12. D. Zeuch, F. Hassler, J. J. Slim, and D. P. DiVincenzo, Exact rotating wave approximation, Ann. Phys. 423, 168327 (2020).
  13. U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl. 45, 897 (2017).
  14. S. M. Girvin, in Quantum Machines: Measurement and Control of Engineered Quantum Systems: Lecture Notes of the Les Houches Summer School: Volume 96, July 2011 (Oxford University Press, Oxford, 2014).
  15. A. Ciani, D. P. DiVincenzo, and T. B. M., Lecture notes on quantum electrical circuits, (TU Delft OPEN Publishing, Delft, 2024).
  16. Φzpf and Qzpf are the flux and charge zero-point fluctuations in the ground state of the quantum LC resonator.
  17. H. Zhang, S. Chakram, T. Roy, N. Earnest, Y. Lu, Z. Huang, D. Weiss, J. Koch, and D. I. Schuster, Universal fast-flux control of a coherent, low-frequency qubit, Phys. Rev. X 11, 011010 (2021).
  18. B.-L. Najera-Santos, R. Rousseau, K. Gerashchenko, H. Patange, A. Riva, M. Villiers, T. Briant, P.-F. Cohadon, A. Heidmann, and J. Palomo et al., High-sensitivity ac-charge detection with a mHz-frequency fluxonium qubit, Phys. Rev. X 14, 011007 (2024).
  19. P. D. Kurilovich, T. Connolly, C. G. L. Bøttcher, D. K.Weiss, S. Hazra, V. R. Joshi, A. Z. Ding, H. Nho, S. Diamond, V. D. Kurilovich, W. Dai, V. Fatemi, L. Frun-zio, L. I. Glazman, and M. H. Devoret, High-frequency readout free from transmon multi-excitation resonances, arXiv:2501.09161.
  20. D. L. Campbell, Y.-P. Shim, B. Kannan, R. Winik, D. K. Kim, A. Melville, B. M. Niedzielski, J. L. Yoder, C. Tahan, S. Gustavsson, and W. D. Oliver, Universal nonadiabatic control of small-gap superconducting qubits, Phys. Rev. X 10, 041051 (2020).
  21. D. A. Rower, L. Ding, H. Zhang, M. Hays, J. An, P. M. Harrington, I. Rosen, J. M. Gertler, T. M. Hazard, B. M. Niedzielski, M. E. Schwartz, S. Gustavsson, K. Serniak, J. A. Grover, and W. D. Oliver, Suppressing counter-rotating errors for fast single-qubit gates with fluxonium, PRX Quantum 5, 040342 (2024).
  22. Private communication. Note that we do not know the power used for the capacitive and inductive drives in Ref. [21].
  23. Y. Chen et al., Qubit architecture with high coherence and fast tunable coupling, Phys. Rev. Lett. 113, 220502 (2014).
  24. A. Wallraff, D. Schuster, A. Blais, L. Frunzio, J. Majer, M. Devoret, S. Girvin, and R. Schoelkopf, Approaching unit visibility for control of a superconducting qubit with dispersive readout, Phys. Rev. Lett. 95, 060501 (2005).
  25. E. Jeffrey, D. Sank, J. Y. Mutus, T. C. White, J. Kelly, R. Barends, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. Megrant, P. J. J. O’Malley, C. Neill, P. Roushan, A. Vainsencher, J. Wenner, A. N. Cleland, and J. M. Martinis, Fast accurate state measurement with superconducting qubits, Phys. Rev. Lett. 112, 190504 (2014).
  26. J. Heinsoo, C. K. Andersen, A. Remm, S. Krinner, T. Walter, Y. Salathé, S. Gasparinetti, J.-C. Besse, A. Potočnik, A. Wallraff, and C. Eichler, Rapid high-fidelity multiplexed readout of superconducting qubits, Phys. Rev. Appl. 10, 034040 (2018).
  27. K. C. Miao, M. McEwen, J. Atalaya, D. Kafri, L. P. Pryadko, A. Bengtsson, A. Opremcak, K. J. Satzinger, Z. Chen, and P. V. Klimov et al., Overcoming leakage in quantum error correction, Nat. Phys. 19, 1780 (2023).
  28. M. Malekakhlagh, W. Shanks, and H. Paik, Optimization of the resonator-induced phase gate for superconducting qubits, Phys. Rev. A 105, 022607 (2022).
  29. M. Khezri, A. Opremcak, Z. Chen, K. C. Miao, M. McEwen, A. Bengtsson, T. White, O. Naaman, D. Sank, A. N. Korotkov, Y. Chen, and V. Smelyanskiy, Measurement-induced state transitions in a superconducting qubit: Within the rotating-wave approximation, Phys. Rev. Appl. 20, 054008 (2023).
  30. M. F. Dumas, B. Groleau-Paré, A. McDonald, M. H. Muñoz-Arias, C. Lledó, B. D’Anjou, and A. Blais, Measurement-induced transmon ionization, Phys. Rev. X 14, 041023 (2024).
  31. M. H. Muñoz-Arias, C. Lledó, and A. Blais, Qubit readout enabled by qubit cloaking, Phys. Rev. Appl. 20, 054013 (2023).
  32. C. Lledó, R. Dassonneville, A. Moulinas, J. Cohen, R. Shillito, A. Bienfait, B. Huard, and A. Blais, Cloaking a qubit in a cavity, Nat. Commun. 14, 6313 (2023).
  33. M. Kounalakis, C. Dickel, A. Bruno, N. Langford, and G. Steele, Tuneable hopping and nonlinear cross-Kerr interactions in a high-coherence superconducting circuit, npj Quantum Inf. 4, 38 (2018).
  34. Ω=γB where γ is the gyromagnetic ratio, so Ω has dimensions of frequency.
  35. This approximation leaves out terms proportional to σz, which can usually be ignored under assumptions similar to the RWA.
  36. Because matrix transposition and inversion commute, and because the matrix TC is symmetric, we can bring TC1 from the bra onto the ket for free.
  37. The choice of sign in iω makes positive values of the wave vector correspond to right-moving waves.
  38. M. Khezri, Ph.D. thesis, University of California, Riverside, 2018.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation