During the last ten years, the studies on non-Markovian open system dynamics has become increasingly popular and having contributions from diverse set of research communities. This interest has arisen due to fundamental problematics how to define and quantify memory effects in the quantum domain, how to exploit and develop applications based on them, and also due to the question what are the ultimate limits for controlling open system dynamics. We give here a simple theoretical introduction to the basic approaches to define and quantify quantum non-Markovianity -also highlighting their connections and differences. In addition to the importance of the development for open quantum systems studies, we also discuss the implications of the progress for other fields including, e.g., formal studies of stochastic processes and quantum information science, and conclude with possible future directions the recent developments open.

Optically addressable spin defects in wide-band-gap semiconductors as promising systems for quantum information and sensing applications have recently attracted increased attention. Spin defects in two-dimensional materials are expected to show superiority in quantum sensing due to their atomic thickness. Here, we demonstrate that an ensemble of negatively charged boron vacancies (VB –) with good spin properties in hexagonal boron nitride (hBN) can be generated by ion implantation. We carry out optically detected magnetic resonance measurements at room temperature to characterize the spin properties of ensembles of VB – defects, showing a zero-field splitting frequency of ∼3.47 GHz. We compare the photoluminescence intensity and spin properties of VB – defects generated using different implantation parameters, such as fluence, energy, and ion species. With the use of the proper parameters, we can successfully create VB – defects with a high probability. Our results provide a simple and practicable method to create spin defects in hBN, which is of great significance for realizing integrated hBN-based devices.

The modeling and analysis of the dynamics of complex systems often requires to employ non-Markovian stochastic processes. While there is a clear and well-established mathematical definition for non-Markovianity in the case of classical systems, the extension to the quantum regime recently caused a vivid debate, leading to many different proposals for the characterization and quantification of memory effects in the dynamics of open quantum systems. Here, we derive a mathematical representation for the non-Markovianity measure based on the exchange of information between the open system and its environment, which reveals the locality and universality of non-Markovianity in the quantum state space and substantially simplifies its numerical and experimental determination. We further illustrate the application of this representation by means of an all-optical experiment which allows the measurement of the degree of memory effects in a photonic quantum process with high accuracy.

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