Quantum Brownian motion for periodic coupling to an Ohmic bath

We show theoretically how the periodic coupling between an engineered reservoir and a quantum Brownian particle leads to the formation of a dynamical steady state which is characterized by an effective temperature above the temperature of the environment. The average steady state energy of the system has a higher value than expected from the environmental properties. The system experiences repeatedly a non-Markovian behavior -- as a consequence the corresponding effective decay for long evolution times is always on average stronger than the Markovian one. We also highlight the consequences of the scheme to the Zeno--anti-Zeno crossover which depends, in addition to the periodicity $\tau$, also on the total evolution time of the system.