A quantum fluctuation description of charge qubits

• URL: http://arxiv.org/abs/2304.13351v1
• Date: Wed, 26 Apr 2023 07:43:43 GMT
• Title: A quantum fluctuation description of charge qubits
• Authors: F. Benatti, F. Carollo, R. Floreanini, H. Narnhofer, F. Valiera
• Abstract summary: We consider a specific instance of a superconducting circuit, the so-called charge-qubit, consisting of a capacitor and a Josephson junction. We derive the Hamiltonian governing the quantum behavior of the circuit in the limit of a large number $N$ of quasi-spins.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider a specific instance of a superconducting circuit, the so-called charge-qubit, consisting of a capacitor and a Josephson junction. Starting from the microscopic description of the latter in terms of two tunneling BCS models in the strong-coupling quasi-spin formulation, we derive the Hamiltonian governing the quantum behavior of the circuit in the limit of a large number $N$ of quasi-spins. Our approach relies on the identification of suitable quantum fluctuations, i.e. of collective quasi-spin operators, which account for the presence of fluctuation operators in the superconducting phase that retain a quantum character in spite of the large-$N$ limit. We show indeed that these collective quantum fluctuations generate the Heisenberg algebra on the circle and that their dynamics reproduces the one of the quantized charge-qubit, without the need of a phenomenological ``third quantization'' of a semiclassically inspired model. As a byproduct of our derivation, we explicitly obtain the temperature dependence of the junction critical Josephson current in the strong coupling regime, a result which is not directly accessible using standard approximation techniques.

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