Tomography of the molecular quantum state by time-resolved electron diffraction

Abstract

A procedure is described that can be used to reconstruct the quantum state of a molecular ensemble from time-averaged position probability density functions determined by time- resolved electron diffraction (TRED). The procedure makes use of established techniques for evaluating the density matrix and the phase space joint probability density; i.e., the Wigner function. A novel expression for describing electron diffraction intensities in terms of the Wigner function is presented. An approximate variant of the method, neglecting the off-diagonal elements of the density matrix, was tested by analyzing gas electron diffraction data for N<SUB>2</SUB> in a Boltzmann distribution, and TRED data obtained from the 193 nm photodissociation of CS<SUB>2</SUB> to carbon monosulfide, CS, at 20, 40, and 120 ns after irradiation. Although the diagonal density matrix elements do not define completely the quantum state of a system, nonetheless, the approximate Wigner functions derived from them display the expected features of a Gaussian-like function in the case of N<SUB>2</SUB>; and, in the case of CS, they are in agreement with other investigations, indicating collision-less vibrational energy transfer mechanisms for nascent CS during the first 20 ns, and collision-induced electronic S(<SUP>1</SUP>D<SUB>J</SUB>) to vibrational CS(X<SUP>1</SUP>(Sigma) <SUB>g</SUB><SUP>+</SUP>) energy transfer.