Activated and non-activated dephasing in a spin bath

We analyze different decoherence processes in a system coupled to a bath. Apart from the well known standard dephasing mechanism which is temperature dependent an alternative mechanism is presented, the spin-swap dephasing which does not need initial bath activation and is temperature independent. We show that for dipole interaction in the weak coupling regime the separation of time scales between system and bath can not produce pure dephasing, the process being accompanied by dissipation. Activated and non-activated dephasing processes are analyzed in a diamond nitrogen-vacancy center.We thank D Gelman, A Levy, and C P Koch for fruitful discussions. We acknowledge funding by the Israel Science Foundation, the Basque Government (Grant No. IT472-10), Ministerio de Economía y Competitividad (FIS2015-67161-P), the program UFI 11/55 of UPV/EHU, and COST Action MP1209 'Thermodynamics in the quantum regime'. ET is supported by the Basque Government postdoctoral program