  Within the framework of the density matrix method, general formulas obtained
that are convenient for describing fast pulsed photoemission that occurs in a
time less than or on the order of the times of relaxation processes inside the
photocathode. Expressions for the elements of the density matrix are found by
solving the kinetic equation that takes into account the alternating
electromagnetic field of light pumping and inelastic scattering of electrons.
The derived formulas are applied for the numerical-analytical study of a
one-dimensional model of wave-like spatiotemporal modulation of a photoelectron
pulse of suitable duration during its passage through a double-well
quantum-well heterostructure deposited on a volumetric planar photocathode.
This modulation is a quantum beat that occurs as a result of excitation and
subsequent slow oscillatory decay of the superposition of the doublet of
quasi-stationary states of the heterostructure. It is possible to provide
prolongation of generation and even amplification of waves of charge density
and current density of photoelectrons when the photocathode is exposed to a
periodic sequence of light pulses.
