Two-level system hyperpolarization with a quantum Szilard engine

In the last decades, superconducting circuits have made important contributions to the study of quantum mechanical phenomena. Their performance approaches the threshold allowing for fault tolerant quantum computation. However, the innate complexity of solid-state physics exposes superconducting quantum circuits to interactions with uncontrolled degrees of freedom degrading their coherence. Although tremendous progress has been made to improve the coherence of superconducting circuits, they still have to cope with various loss and decoherence mechanisms, and with further improvements, it becomes increasingly challenging to track down individual decoherence mechanisms.

By implementing a quantum Szilard engine with an active feedback control loop, we show that a superconducting granular aluminum fluxonium qubit is coupled weakly to a two-level system (TLS) environment of unknown physical origin, with a relatively long intrinsic energy relaxation time exceeding 50ms. As part of the hyperpolarization with the quantum Szilard engine, the TLSs can be cooled down, resulting in a four times lower qubit population, or they can be heated up to manifest themselves as a negative-temperature environment. ... mehrWe show that the TLSs and the qubit are each other's dominant loss mechanism and that the qubit relaxation is independent of the TLS populations. Since the TLSs are much longer lived than the qubit, non-exponential relaxation and non-Poissonian quantum jumps can be observed. The incoherent relaxation dynamics of the system is described by the Solomon equations, for which a rigorous derivation is presented starting from a general Lindblad equation for the qubit and an arbitrary number of TLSs. In the limit of large numbers of TLSs, the relaxation is likely to follow a power law, which is deduced from the Solomon equations and confirmed experimentally. Moreover, the measured non-Poissonian quantum jump statistics can be reproduced by a diffusive stochastic Schrödinger equation. With increasing number of TLSs, entanglement and measurement back action can be ignored, and the quantum jump statistics can also be reproduced by the Solomon equations. The transition from a stochastic Schrödinger equation model to the Solomon equations hints at a quantum-to-classical transition.