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Oscillator-strength sum rule in light-induced transitions is one general formof quantum-mechanical identities. Although this sum rule is well established inequilibrium photo-physics, an experimental corroboration for the validation ofthe sum rule in a nonequilibrium regime has been a long-standing unexploredquestion. The simple band structure of graphene is an ideal system forinvestigating this question due to the linear Dirac-like energy dispersion.Here, we employed both ultrafast terahertz and optical spectroscopy to directlymonitor the transient oscillator-strength balancing between quasi-freelow-energy oscillators and high-energy Fermi-edge ones. Upon photo-excitationof hot Dirac fermions, we observed that the ultrafast depletion of high-energyoscillators precisely complements the increased terahertz absorptionoscillators. Our results may provide an experimental priori to understand, forexample, the intrinsic free-carrier dynamics to the high-energyphoto-excitation, responsible for optoelectronic operation such asgraphene-based phototransistor or solar-energy harvesting devices.

Ultrafast zero balance of the oscillator-strength sum rule in graphene