We demonstrate a new method to directly manipulate the state of individual two-level systems (TLSs) in phase qubits. It allows one to characterize the coherence properties of TLSs using standard microwave pulse sequences, while the qubit is used only for state readout. We apply this method to measure the temperature dependence of TLS coherence for the first time. The energy relaxation time T1 is found to decrease quadratically with temperature for the two TLSs studied in this work, while their dephasing time measured in Ramsey and spin-echo experiments is found to be T1 limited at all temperatures.
Two-level systems (TLS) are widely recognized as a dominant source of energy relaxation in superconducting qubits, limiting coherence times and device performance. While TLS-induced dissipation is often modeled as independent channels, interacting TLS can form finite many-body environments whose dynamical role in qubit relaxation remains insufficiently understood. Building on the information-erasure-based framework for irreversible thermalization developed in our previous work, we present a microscopic model and numerical simulations of a superconducting qubit coupled to a finite interacting many-body TLS environment as a concrete physical realization of this mechanism. We show that effective irreversible energy relaxation can emerge from intrinsic many-body dynamics without invoking external baths or phenomenological dissipation. The introduction of information erasure drives a transition from coherent oscillatory energy exchange to nonoscillatory exponential relaxation of the qubit. The relaxation times exhibit the scaling
T1,T2∝Jq,τ−2 with respect to the qubit-TLS coupling strength, consistent with Fermi's golden rule and Lindblad-type descriptions. Importantly, both exponential decay and its scaling behavior arise directly from microscopic many-body dynamics. These results provide quantitative insight into TLS-induced decoherence mechanisms and establish a microscopic link between information erasure, many-body thermalization, and irreversible relaxation in superconducting quantum systems.
Relaxation of a two-level system (TLS) into a resonant infinite-temperature reservoir with a Lorentzian spectrum is studied. The reservoir is described by a complex Gaussian-Markovian field coupled to the nondiagonal elements of the TLS Hamiltonian. The theory can be relevant for electromagnetic interactions in microwave high-Q cavities and muon spin depolarization. Analytical results are obtained for the strong-coupling regime, ${\ensuremath{\Omega}}_{0}\ensuremath{\gg}\ensuremath{\nu},$ where ${\ensuremath{\Omega}}_{0}$ is the rms coupling amplitude (Rabi frequency) and $\ensuremath{\nu}$ is the width of the reservoir spectrum. In this regime, the population difference and half of the initial coherence decay with two characteristic rates: most of the decay occurs at $t\ensuremath{\sim}{\ensuremath{\Omega}}_{0}^{\ensuremath{-}1},$ the relaxation being reversible for $t\ensuremath{\ll}({\ensuremath{\Omega}}_{0}^{2}\ensuremath{\nu}{)}^{\ensuremath{-}1/3},$ whereas for $t\ensuremath{\gg}({\ensuremath{\Omega}}_{0}^{2}\ensuremath{\nu}{)}^{\ensuremath{-}1/3}$ the relaxation becomes irreversible and is practically over. The other half of the coherence decays with a rate on the order of $\ensuremath{\nu},$ which may be slower by orders of magnitude than the time scale of the population relaxation. The above features are explained by the fact that at $t\ensuremath{\ll}{\ensuremath{\nu}}^{\ensuremath{-}1},$ the reservoir temporal fluctuations are effectively one-dimensional (adiabatic). Moreover, we identify the pointer basis, in which the reduction of the state vector occurs. The pointer states depend on the initial phase of the reservoir.