TY - JOUR
T1 - A quantum fluctuation description of charge qubits
AU - Benatti, F.
AU - Carollo, F.
AU - Floreanini, R.
AU - Narnhofer, H.
AU - Valiera, F.
N1 - Publisher Copyright:
© 2024 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft
PY - 2024/1
Y1 - 2024/1
N2 - 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.
AB - 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.
KW - charge qubits
KW - Josephson effect
KW - mesoscopic dynamics
KW - quantum fluctuations
UR - http://www.scopus.com/inward/record.url?scp=85184027905&partnerID=8YFLogxK
U2 - 10.1088/1367-2630/ad19ac
DO - 10.1088/1367-2630/ad19ac
M3 - Article
AN - SCOPUS:85184027905
VL - 26
JO - New Journal of Physics
JF - New Journal of Physics
SN - 1367-2630
IS - 1
M1 - 013057
ER -