The sensitivity of the Rabi oscillations of a resonantly driven spin-1 2 system to a weak and slow modulation of the static longitudinal magnetic field, B0, is studied theoretically. We establish the mapping of a weakly driven two-level system with modulation onto a strongly driven system without modulation. The mapping suggests that different regimes of spin dynamics, known for a strongly driven system, can be realized under common experimental conditions of weak driving (driving field B1 B0) upon proper choice of the domains of modulation frequency, ωm, and amplitude, B2. Fast modulation ωm ΩR, where ΩR is the Rabi frequency, emulates the regime of driving frequency much bigger than the resonant frequency. Strong modulation, B2 B1, emulates the regime B1 B0. Resonant modulation, ωm ≈ ΩR, gives rise to an envelope of the Rabi oscillations. The shape of this envelope is highly sensitive to the detuning of the driving frequency from the resonance. Theoretical predictions for different domains of B2 and ωm were tested experimentally using NMR of protons in water, where, without modulation, the pattern of Rabi oscillations could be observed over many periods. We present experimental results which reproduce the three predicted modulation regimes, and agree with theory quantitatively.

We study the correspondence between boundary excitation distribution spectrum of non-chiral topological orders on an open surface M with gapped boundaries and the entanglement spectrum in the bulk of gapped topological orders on a closed surface. The closed surface is bipartitioned into two subsystems, one of which has the same topology as M. Specifically, we focus on the case of generalized string-net models and discuss the cases where M is a disk or a cylinder. When M has the topology of a cylinder, different combinations of boundary conditions of the cylinder will correspond to different entanglement cuts on the torus. When both boundaries are charge (smooth) boundaries, the entanglement spectrum can be identified with the boundary excitation distribution spectrum at infinite temperature and constant fugacities. Examples of toric code, ZN theories, and the simple non-abelian case of doubled Fibonacci are demonstrated. arXiv:1806.07794v3 [cond-mat.str-el] 12 May 2019where the decomposition matrix M is 4 × 2-dimensional, with the first subscript taking values from {1, m, e, }, i.e. the output category, and the second subscript from {0, 1}, the input category. 59 Specifically,