Ultrafast and reversible control of the exchange interaction in Mott insulators

The strongest interaction between microscopic spins in magnetic materials is the exchange interaction $J_\text{ex}$. Therefore, ultrafast control of $J_\text{ex}$ keeps the promise to control spins on ultimately fast timescales. We demonstrate that time-periodic modulation of the electronic structure by sub-picosecond laser pulses can be used to reversibly control the exchange interaction on ultrafast timescales in extended Mott insulators. In the regime of weak-driving strength relevant for condensed matter systems, we find that the exchange interaction can be enhanced and reduced for frequencies below and above gap, respectively. For strong driving strength, which might be achieved in cold-atom systems, even the sign of the exchange interaction can be reversed. We show that this causes time reversal of the associated quantum spin dynamics, which opens up possibilities for fundamental studies concerning the reversibility of the quantum many-body dynamics.