Abstract Nanomechanical oscillators offer numerous advantages for quantum technologies. Their integration with superconducting qubits shows promise for hardware-efficient quantum error-correction protocols involving superpositions of mechanical coherent states. Limitations of this approach include mechanical decoherence processes, particularly two-level system (TLS) defects, which have been widely studied using classical fields and detectors. In this manuscript, we use a superconducting qubit as a quantum sensor to perform phonon number-resolved measurements on a piezoelectrically coupled phononic crystal cavity. This enables a high-resolution study of mechanical dissipation and dephasing in coherent states of variable size (
nˉ≃1−10 n ¯ ≃ 1 − 10 phonons). We observe nonexponential relaxation and state size-dependent reduction of the dephasing rate, which we attribute to TLS. Using a numerical model, we reproduce the dissipation signatures (and to a lesser extent, the dephasing signatures) via emission into a small ensemble ( N = 5) of rapidly dephasing TLS. Our findings comprise a detailed examination of TLS-induced phonon decoherence in the quantum regime.
Spin-phonon interactions are known to drive magnetic relaxation in solid-state systems but are generally overlooked as a contribution to spin decoherence through dephasing. Here, we extend quantum master equations to account for coherence terms and describe the full effect of up to two-phonon processes on spin dynamics. We implement this method fully ab initio for a molecule with large magnetization blocking temperature and show that, although strong axial magnetic anisotropy ensures slow magnetic relaxation approaching seconds at 77 kelvins, the superposition of Kramers doublets is coherent for less than 10 nanoseconds due to a two-phonon pure dephasing mechanism. This process, in principle, applies to any quantum system interacting with a thermal bath of phonons, advancing our understanding of quantum decoherence in solid-state systems.
We present a detailed theory for the Andreev level qubit, a 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 a path integral method. We also derive a kinetic equation describing qubit decoherence due to interaction of the Andreev levels with acoustic phonons. The collision terms are nonlinear due to the fermionic nature of the Andreev states, leading to slow nonexponential relaxation and dephasing of the qubit at temperatures smaller than the qubit level spacing.