Real-Time Observation of Instantaneous ac Stark Shift of a Vacuum Using a Zeptosecond Laser Pulse

Based on the numerical solution of the time-dependent Dirac equation, we propose a method to observe in real time the ac Stark shift of a vacuum driven by an ultra-intense laser field. By overlapping the ultra-intense pump pulse with another zeptosecond probe pulse whose photon energy is smaller than 2mc², electron–positron pair creation can be controlled by tuning the time delay between the pump and probe pulses. Since the pair creation rate depends sensitively on the instantaneous vacuum potential, one can reconstruct the ac Stark shift of the vacuum potential according to the time-delay-dependent pair creation rate.