Generalized transmon Hamiltonian for Andreev spin qubits
Abstract: We solve the problem of an interacting quantum dot embedded in a Josephson junction between two superconductors with finite charging energy described by the transmon (Cooper pair box) Hamiltonian. The approach is based on the flat-band approximation of the Richardson model, which reduces the Hilbert space to the point where exact diagonalisation is possible while retaining all states that are necessary to describe the low energy phenomena. The presented method accounts for the physics of the quantum dot, the Josephson effect and the Coulomb repulsion (charging energy) at the same level. In particular, it captures the quantum fluctuations of the superconducting phase as well as the coupling between the superconducting phase and the quantum dot (spin) degrees of freedom. The method can be directly applied for modelling Andreev spin qubits embedded in transmon circuits in all parameter regimes, for describing time-dependent processes, and for the calculation of transition matrix elements for microwave-driven transmon, spin-flip and mixed transitions that involve coupling to charge or current degree of freedom.
- M. H. Devoret, A. Wallraff, and J. M. Martinis, Superconducting qubits: A short review (2004).
- G. Wendin, Reports on Progress in Physics 80, 106001 (2017).
- N. M. Chtchelkatchev and Y. V. Nazarov, Phys. Rev. Lett. 90, 226806 (2003).
- K. G. Wilson, Reviews of Modern Physics 47, 773 (1975).
- R. Bulla, T. A. Costi, and T. Pruschke, Reviews of Modern Physics 80, 395 (2008).
- M. Tinkham, Introduction to superconductivity, 2nd ed. (Dover Publications, 2004).
- D. Gobert, U. Schollwöck, and J. von Delft, The European Physical Journal B - Condensed Matter and Complex Systems 38, 501 (2004).
- L. Glazman and G. Catelani, SciPost Physics Lecture Notes 10.21468/scipostphyslectnotes.31 (2021).
- Y. Nakamura, Y. A. Pashkin, and J. S. Tsai, Nature 398, 786 (1999).
- A. Cottet, Implementation of a quantum bit in a superconducting circuit, Ph.D. thesis, Ecole normale superieure de Paris (2002).
- L. Yu, Acta Phys. Sin. 21, 75 (1965).
- H. Shiba and T. Soda, Progress of Theoretical Physics 41, 25 (1969).
- A. I. Rusinov, JETP Lett. 9, 85 (1969), zh. Eksp. Teor. Fiz. Pisma Red. 9, 146 (1968).
- A. C. Hewson, The Kondo Problem to Heavy Fermions (Cambridge University Press, 1993).
- A. V. Rozhkov and D. P. Arovas, Physical Review Letters 82, 2788 (1999).
- A. A. Clerk and V. Ambegaokar, Physical Review B 61, 9109 (2000).
- E. Vecino, A. Martín-Rodero, and A. L. Yeyati, Physical Review B 68, 10.1103/physrevb.68.035105 (2003).
- A. Oguri, Y. Tanaka, and A. C. Hewson, Journal of the Physical Society of Japan 73, 2494 (2004).
- R. Žitko, Josephson potentials for single impurity Anderson impurity in a junction between two superconductors (2022).
- L. Bulaevskii, V. Kuzii, and A. Sobyanin, Solid State Communications 25, 1053 (1978).
- R. W. Richardson and N. Sherman, Nuclear Physics 52, 221 (1964).
- J. Dukelsky and G. Sierra, Physical Review B 61, 12302 (2000).
- L. Pavešić, D. Bauernfeind, and R. Žitko, Physical Review B 104, 10.1103/physrevb.104.l241409 (2021).
- J. Román, G. Sierra, and J. Dukelsky, Nuclear Physics B 634, 483–510 (2002).
- J. Dukelsky, S. Pittel, and G. Sierra, Reviews of Modern Physics 76, 643 (2004).
- J. von Delft and D. Ralph, Physics Reports 345, 61 (2001).
- R. Žitko and L. Pavešić, Physical Review B 106, 10.1103/physrevb.106.024513 (2022).
- L. Pavešić and R. Žitko, Physical Review B 105, 10.1103/physrevb.105.075129 (2022).
- For detailed derivations and expressions at general filling see Ref. \rev@citealpflatband.
- S. T. Belyaev, JETP Letters 12, 968 (1961).
- V. A. Khodel’ and V. R. Shaginyan, JETP Letters 51, 488 (1990).
- G. E. Volovik, JETP Letters 107, 516 (2018).
- F. J. Matute-Cañadas, L. Tosi, and A. L. Yeyati, Quantum circuits with multiterminal josephson-andreev junctions (2023), arXiv:2312.17305 [cond-mat.mes-hall] .
- L. Pavešič, Flat band two channel, https://github.com/PavesicL/flat_band_two_channel (2023).
- M. H. Devoret, Journal of Superconductivity and Novel Magnetism 34, 1633–1642 (2021).
- I. Affleck, J.-S. Caux, and A. M. Zagoskin, Physical Review B 62, 1433 (2000).
- F. S. Bergeret, A. L. Yeyati, and A. Martín-Rodero, Physical Review B 76, 10.1103/physrevb.76.174510 (2007).
- C. Hermansen, A. L. Yeyati, and J. Paaske, Physical Review B 105, 10.1103/physrevb.105.054503 (2022).
- L. Pavešič, R. Aguado, and R. Žitko, Strong-coupling theory of quantum dot josephson junctions: role of the residual quasiparticle (2023).
- A. F. Andreev, Zh. Eksperim. i Teor. Fiz. 46, (1964).
- V. N. Golovach, M. Borhani, and D. Loss, Physical Review B 74, https://doi.org/10.1103/PhysRevB.74.165319 (2006).
- B. Li, T. Calarco, and F. Motzoi, PRX Quantum 3, 10.1103/prxquantum.3.030313 (2022).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.