Quantum state tomography of molecules by ultrafast diffraction

Quantum tomography of molecules using ultrafast electron diffraction

We propose a quantum tomography (QT) approach to retrieve the temporally evolving reduced density matrix in electronic state basis, where the populations and coherence between the ground state and excited state are reconstructed from the ultrafast electron diffraction signal. In order to showcase the capability of the proposed QT approach, we simulate the nuclear wavepacket dynamics and ultrafast electron diffraction of photoexcited pyrrole molecules using the ab initio quantum chemical CASSCF method. From the simulated time-resolved diffraction data, we retrieve the evolving density matrix in a crude diabatic representation basis and reveal the symmetry of the excited pyrrole wavepacket. Our QT approach opens the route to make a quantum version of "molecular movie" that covers the electronic degree of freedom and equips ultrafast electron diffraction with the power to reveal the coherence between electronic states, relaxation, and dynamics of population transfer.

Extracting the electronic structure signal from X-ray and electron scattering in the gas phase

X-ray and electron scattering from free gas-phase molecules is examined using the independent atom model (IAM) and ab initio electronic structure calculations. The IAM describes the effect of the molecular geometry on the scattering, but does not account for the redistribution of valence electrons due to, for instance, chemical bonding. By examining the total, i.e. energy-integrated, scattering from three molecules, fluoroform (CHF3), 1,3-cyclohexadiene (C6H8) and naphthalene (C10H8), the effect of electron redistribution is found to predominantly reside at small-to-medium values of the momentum transfer (q ≤ 8 Å-1) in the scattering signal, with a maximum percent difference contribution at 2 ≤ q ≤ 3 Å-1. A procedure to determine the molecular geometry from the large-q scattering is demonstrated, making it possible to more clearly identify the deviation of the scattering from the IAM approximation at small and intermediate q and to provide a measure of the effect of valence electronic structure on the scattering signal.

Ultrafast Molecular Frame Quantum Tomography

We develop and experimentally demonstrate a methodology for a full molecular frame quantum tomography (MFQT) of dynamical polyatomic systems. We exemplify this approach through the complete characterization of an electronically nonadiabatic wave packet in ammonia (NH_{3}). The method exploits both energy and time-domain spectroscopic data, and yields the lab frame density matrix (LFDM) for the system, the elements of which are populations and coherences. The LFDM fully characterizes electronic and nuclear dynamics in the molecular frame, yielding the time- and orientation-angle dependent expectation values of any relevant operator. For example, the time-dependent molecular frame electronic probability density may be constructed, yielding information on electronic dynamics in the molecular frame. In NH_{3}, we observe that electronic coherences are induced by nuclear dynamics which nonadiabatically drive electronic motions (charge migration) in the molecular frame. Here, the nuclear dynamics are rotational and it is nonadiabatic Coriolis coupling which drives the coherences. Interestingly, the nuclear-driven electronic coherence is preserved over longer timescales. In general, MFQT can help quantify entanglement between electronic and nuclear degrees of freedom, and provide new routes to the study of ultrafast molecular dynamics, charge migration, quantum information processing, and optimal control schemes.

Visualizing ultrafast weak-field-induced rotational revivals of air molecules at room temperature

The ability to observe quantum coherence and interference is crucial for understanding quantum effects in nonlinear optical spectroscopy and is of fundamental interest in quantum mechanics. Here, we present an experimental study combined with theoretical analysis and numerical simulations to identify the underlying process behind the rotational revivals induced by a pair of time-delayed ultrafast femtosecond laser pulses for air molecules under ambient conditions. Our time-resolved two-dimensional alignment measurements confirm that one-step non-resonant Raman transitions from initial states of mixed molecules play a dominant role, showing a signature of weak-field-induced rotational revivals. Furthermore, we demonstrate that such rotational revival spectra can simultaneously measure the entire pure rotational Raman spectra and observe the quantum interference between two transition pathways from a given initial state. This work provides a powerful tool to observe, control, and identify the rotational dynamics of mixed molecular samples under weak-field excitations.

Ultrafast Imaging of Molecular Dynamics Using Ultrafast Low-Frequency Lasers, X-ray Free Electron Lasers, and Electron Pulses

The requirement of high space-time resolution and brightness is a great challenge for imaging atomic motion and making molecular movies. Important breakthroughs in ultrabright tabletop laser, X-ray, and electron sources have enabled the direct imaging of evolving molecular structures in chemical processes, and recent experimental advances in preparing ultrafast laser and electron pulses resulted in molecular imaging with femtosecond time resolution. This Perspective presents an overview of the versatile imaging methods of molecular dynamics. High-order harmonic generation imaging and photoelectron diffraction imaging are based on laser-induced ionization and rescattering processes. Coulomb explosion imaging retrieves molecular structural information by detecting the momentum vectors of fragmented ions. Diffraction imaging encodes molecular structural and electronic information in reciprocal space. We also present various applications of these ultrafast imaging methods in resolving laser-induced nuclear and electronic dynamics.