The loss of coherence is one of the main obstacles for the implementation of quantum information processing. The efficiency of dynamical decoupling schemes, which have been introduced to address this problem, is limited itself by the fluctuations in the driving fields which will themselves introduce noise. We address this challenge by introducing the concept of concatenated continuous dynamical decoupling, which can overcome not only external magnetic noise but also noise due to fluctuations in driving fields. We show theoretically that this approach can achieve relaxation limited coherence times, and demonstrate experimentally that already the most basic implementation of this concept yields an order of magnitude improvement to the decoherence time for the electron spin of nitrogen vacancy centers in diamond. The proposed scheme can be applied to a wide variety of other physical systems, including trapped atoms and ions and quantum dots, and may be combined with other quantum technologies challenges such as quantum sensing and quantum information processing.

It is shown that the theory of stochastic diffusion processes on graphs is a natural tool for the analysis of noise in hysteretic systems. In particular, by using this theory, analytical expressions for stationary characteristics of random outputs of some hysteretic systems are derived.

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A unified semi-classical theory applicable to ion-polar molecule reaction kinetics and electron-dipole spectroscopy is presented within a planar ion/ point-dipole model. The forms of the trapped periodic orbits that constitute dividing surfaces between internal and external regions of phase space are determined and their properties are shown to be well represented by a semianalytical adiabatic theory. Subsequent applications of the adiabatic theory to electron-dipole dynamics (a) yield a good approximation to the critical dipole for electron capture and (b) predict an exponential gap law for the excited states of electron/fixed dipole states, in good agreement with recent ab initio calculations. Extension of the theory to include dipoles of finite length, d, provides a correlation of the critical strength with d/I 1/2 where I is the molecular moment of inertia.