A Fundamental Lower Bound of Actuating Energy for Broadband Photon Switching

We derive a universal lower bound of actuating energy $E_s$ for broadband photon switching by using an uncertainty relation between time and the negative energy density of quantum fields. We find that broadband photon switching between perfect reflection and perfect transmission over a time $t_s$ should satisfy $E_s\ge \frac{\mathrm{\hslash }}{6\pi t_s}$.