Solomon equations for qubit and two-level systems: Insights into non-Poissonian quantum jumps

Abstract

We measure and model the combined relaxation of a qubit coupled to a discrete two-level system~(TLS) environment, also known as the central spin model. If the TLSs are much longer-lived than the qubit, non-exponential relaxation and non-Poissonian quantum jumps can be observed. In the limit of large numbers of TLSs, the relaxation is likely to follow a power law, which we confirm with measurements on a superconducting fluxonium qubit. Moreover, the observed relaxation and quantum jump statistics are described by the Solomon equations, for which we present a derivation starting from the general Lindblad equation for an arbitrary number of TLSs. We also show how to reproduce the non-Poissonian quantum jump statistics using a diffusive stochastic Schrödinger equation. The fact that the measured quantum jump statistics can be reproduced by the Solomon equations, which ignore the quantum measurement backaction, hints at a quantum-to-classical transition.

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Cited by in corpus (4)

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• Spin Environment of a Superconducting Qubit in High Magnetic Fields
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• Mitigating state transition errors during readout with a synchronized flux pulse