Dynamics and phonon-induced decoherence of Andreev level qubit

TL;DR

This paper develops a detailed theoretical model of an Andreev level qubit, analyzing its dynamics and phonon-induced decoherence, revealing slow non-exponential relaxation at low temperatures.

Contribution

It introduces a novel Hamiltonian and kinetic equation for Andreev level qubits, accounting for phase fluctuations and phonon interactions, advancing understanding of decoherence mechanisms.

Findings

Derived the two-level Hamiltonian for Andreev levels with phase fluctuations.

Formulated a kinetic equation describing phonon-induced decoherence.

Identified slow, non-exponential relaxation and dephasing at low temperatures.

Abstract

We present detailed theory for Andreev level qubit, the system consisting of a highly transmissive quantum point contact embedded in a superconducting loop. The two-level Hamiltonian for Andreev levels interacting with quantum phase fluctuations is derived by using the path integral method. We also derive kinetic equation describing qubit decoherence due to interaction of the Andreev levels with acoustic phonons. The collision terms are non-linear due to fermionic nature of the Andreev states, leading to slow non-exponential relaxation and dephasing of the qubit at temperature smaller than the qubit level spacing.