Fluctuation-Regularized Quantum Master Equations for Open Quantum Systems

Abstract

In the last decade, we have witnessed remarkable progress in quantum computing aided by an ever increasing number of qubits, enhanced error correction methods, and advances in hardware. One of the major obstacles that quantum computing must deal with is environmental effects on quantum dynamics. The obstacle originates from quantum systems being – unavoidably – a part of nature and, thereby, not isolated and noise-free. Thoroughly understanding the dynamics of quantum systems connected to the environment, or open quantum systems remains one of the critical research areas.

The primary focus of our research at Spin Lab is the dynamics of open quantum systems. The research relies on home-grown theoretical tools and experimental work using Nuclear Magnetic Resonance spectroscopy. The theoretical part involves the formulation and applications of a novel form of quantum master equation that takes into account the fluctuations in the local environment. To completely incorporate their effects, a propagator is designed to include finite evolution due to the fluctuations and infinitesimal evolution due to system Hamiltonians. The resulting quantum master equation (named, fluctuation-regularized quantum master equation or FRQME) is characterized by the presence of an exponential kernel in the dissipator and – most importantly – by the inclusion of dissipators from external drives and coupling. The later dissipators have been shown to play a major role in explaining many of the hitherto enigmatic features of spin dynamics, such as the emergence of prethermal plateau in spin-locking experiments, the emergence of superradiance in dipolar systems. The new master equation was used to show optimal behavior in various quantum control experiments. FRQME had been used in quantum optics to show the nonlinear behavior of light shifts and in quantum sensing. FRQME has also been used to explore foundational aspects of quantum mechanics.
In the presentation, the FRQME and some of its applications in wide-ranging areas will be highlighted.