Dynamics of a two-level system in the superposition of two dephasing environments with Ohmic-like spectral density is studied when considering initial system-environment correlations. The quantum system and one environment are treated as whole thermal equilibrium state, while the other environment is at thermal equilibrium state alone. Which environment the system interacts with is determined by an ancillary two-level system. When the system interacts with mixture of two sub-Ohmic environments, initial correlations can make the mixed dynamics non-Markovian. For two identical sub-Ohmic environments, if performing the projective measurement on the ancillary two-level system at the special time points, whatever the initial state of the system is, the coherence can be enhanced. For two different environments with βħω0/2>>, we get the approximate expression about the coherence of the system when measuring the ancillary two-level system.
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.
The fundamental building blocks of quantum computers, called qubits, can be physically realized through any quantum system that is restricted to two possible states. The power of qubits arises from their ability to be in a superposition of these two states, allowing for the development of quantum algorithms that are impossible for classical computers. However, interactions with the surrounding environment destroy the superposition in a process called decoherence, which makes it important to find ways to model these interactions and mitigate them. In this thesis we derive a non-Markovian master equation for the spin-boson model, with a time-dependent two-level system, using the reaction coordinate representation. We show numerically that in the superconducting qubit regime this master equation maintains the positivity of the density operator for relevant parameter ranges, and is able to model non-Markovian effects between the system and the environment. We also compare the reaction coordinate master equation to a Markovian master equation with parameters taken from real superconducting qubits. We demonstrate that the Markovian master equation fails to capture the system–bath correlations for short times, and in many cases overestimates relaxation and coherence times. Finally, we test how a time-dependent bias affects the evolution of the two-level system. The bias is assumed to be constant with an additive term arising from an externally applied time-dependent plane wave control field. We show that an amplitude, angular frequency, and phase shift for the plane wave can be chosen such that the control field improves the coherence time of the two-level system.