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Within the framework of the density matrix method, general formulas obtainedthat are convenient for describing fast pulsed photoemission that occurs in atime less than or on the order of the times of relaxation processes inside thephotocathode. Expressions for the elements of the density matrix are found bysolving the kinetic equation that takes into account the alternatingelectromagnetic field of light pumping and inelastic scattering of electrons.The derived formulas are applied for the numerical-analytical study of aone-dimensional model of wave-like spatiotemporal modulation of a photoelectronpulse of suitable duration during its passage through a double-wellquantum-well heterostructure deposited on a volumetric planar photocathode.This modulation is a quantum beat that occurs as a result of excitation andsubsequent slow oscillatory decay of the superposition of the doublet ofquasi-stationary states of the heterostructure. It is possible to provideprolongation of generation and even amplification of waves of charge densityand current density of photoelectrons when the photocathode is exposed to aperiodic sequence of light pulses.

Density matrix and space-time distributions of the electronic density and current at fast pulsed photoemission through a double quantum well