A quantum fluctuation description of charge qubits

F. Benatti, F. Carollo, R. Floreanini, H. Narnhofer, F. Valiera

Publications: Contribution to journalArticlePeer Reviewed

Abstract

We consider a specific instance of a superconducting circuit, the so-called charge-qubit, consisting of a capacitor and a Josephson junction that we describe by means of the BCS microscopic model in terms of two tunnelling superconducting systems in the strong-coupling quasi-spin formulation. Then, by means of collective observables we derive the Hamiltonian governing the quantum behaviour of the circuit in the limit of a large number N of quasi-spins. Our approach relies on suitable quantum fluctuations, i.e. on collective quasi-spin operators, different from mean-field observables, that retain a quantum character in the large-N limit. These collective operators generate the Heisenberg algebra on the circle and we show that their dynamics reproduces the phenomenological one generated by the charge qubit Hamiltonian obtained by quantizing the macroscopic classical Hamiltonian of the circuit. The microscopic derivation of the emergent, large-N behaviour provides a rigorous setting to investigate more in detail both general quantum circuits and quantum macroscopic scenarios; in particular, in the specific case of charge-qubits, it allows to explicitly obtain the temperature dependence of the critical Josephson current in the strong coupling regime, a result not accessible using standard approximation techniques.
Original languageEnglish
Article number013057
Number of pages27
JournalNew Journal of Physics
Volume26
Issue number1
DOIs
Publication statusPublished - Jan 2024

Austrian Fields of Science 2012

  • 103025 Quantum mechanics
  • 103019 Mathematical physics

Keywords

  • charge qubits
  • Josephson effect
  • mesoscopic dynamics
  • quantum fluctuations

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