Time resolved quantum tomography in molecular spectroscopy by the Maximal Entropy Approach

TL;DR

This paper applies MaxEnt-based quantum tomography to photoexcited ammonia, enabling detailed analysis of electronic coherences and entanglement entropy, thus advancing ultrafast molecular spectroscopy and quantum information science.

Contribution

It introduces two methods for constructing measurement operators in MaxEnt quantum tomography and links Lagrange multipliers to molecular distribution moments, enabling new insights into molecular electron-nuclear coupling.

Findings

Successfully reconstructed electronic density matrix from partial data

Linked Lagrange multipliers to molecular angular distribution moments

First construction of entanglement entropy in molecular quantum states

Abstract

Attosecond science offers unprecedented precision in probing the initial moments of chemical reactions, revealing the dynamics of molecular electrons that shape reaction pathways. A fundamental question emerges: what role, if any, do quantum coherences between molecular electron states play in photochemical reactions? Answering this question necessitates quantum tomography: the determination of the electronic density matrix from experimental data, where the off-diagonal elements represent these coherences. The Maximal Entropy (MaxEnt) based Quantum State Tomography (QST) approach offers unique advantages in studying molecular dynamics, particularly with partial tomographic data. Here, we explore the application of MaxEnt-based QST on photoexcited ammonia, necessitating the operator form of observables specific to the performed measurements. We present two methodologies for constructing these operators: one leveraging Molecular Angular Distribution Moments (MADMs) which accurately capture the orientation-dependent vibronic dynamics of molecules; and another utilizing Angular Momentum Coherence Operators to construct measurement operators for the full rovibronic density matrix in the symmetric top basis. A key revelation of our study is the direct link between Lagrange multipliers in the MaxEnt formalism and the unique set of MADMs. Furthermore, we achieve a groundbreaking milestone by constructing, for the first time, the entanglement entropy of the electronic subsystem: a metric that was previously inaccessible. The entropy vividly reveals and quantifies the effects of coupling between the excited electron and nuclear degrees of freedom. Consequently, our findings open new avenues for research in ultrafast molecular spectroscopy within the broader domain of quantum information science.