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

TL;DR

This paper investigates non-Poissonian quantum jumps in a qubit coupled to multiple two-level systems, deriving Solomon equations from Lindblad dynamics, and demonstrating power-law relaxation and quantum-to-classical transition insights.

Contribution

It derives Solomon equations from Lindblad dynamics for multiple TLSs and links non-Poissonian jumps to classical-like behavior in qubit relaxation.

Findings

Observation of non-exponential, power-law relaxation in superconducting fluxonium qubits.

Derivation of Solomon equations from Lindblad for multiple TLSs.

Reproduction of quantum jump statistics via diffusive stochastic Schrödinger equation.

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 Schr\"odinger 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.