The state of a quantum mechanical system, pure or mixed, is described by a density operator. Surprisal – the logarithm of the density matrix – follows the same unitary evolution as the density operator. The maximal entropy formalism provides an explicit form of the density as an exponential function of a set of operators, observables, whose mean values are given. It allows a description of the state of the system explicitly via our knowledge about its observables. A well-known example of such a function is the Boltzmann distribution, ρ = Z-1exp(-βH), where the state of the system is defined by only one observable – its energy. In general, there can be more than one operator that contributes to the density and these operators do not necessarily commute. Hence, the representation of the surprisal, logarithm of the exponential function, enables a simpler description of the quantum state. We examine a compact representation of the density and its surprisal as a function of a few observables for the coupled electron-nuclear dynamics unfolding on three electronic states. The time-evolution of the density matrix is compressed as a vector of nine time-dependent Lagrange multipliers, coefficients of a set of nine dominant observables. The representation of the surprisal as a linear sum of operators fully retains the quantum character of the dynamics. We use a specific example of the isotope effect in an atto-pumped N2 to illustrate that both classical and quantal effects of mass are well reproduced by this compact description. In particular, we show that the isotope effect in the non-adiabatic transfer between the two excited states is determined by the Lagrange multipliers of the coherence operators. Simple analytical results for the surprisal are given, which allows a factorization of these two effects.

Electronic coherence in the density of an atto-pumped quantum state

ACS Fall 2021

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