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Register a new userQuantum state tomography of molecules by ultrafast diffraction
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Ultrafast electron diffraction and time-resolved serial crystallography are the basis of the ongoing revolution in capturing at the atomic level of detail the structural dynamics of molecules. However, most experiments employ the classical ball-and-stick depictions, and the information of molecular quantum states, such as the density matrix, is missing. Here, we introduce a framework for the preparation and ultrafast coherent diffraction from rotational wave packets of molecules, and we establish a new variant of quantum state tomography for ultrafast electron diffraction to characterize the molecular quantum states. The ability to reconstruct the density matrix of molecules of arbitrary degrees of freedom will provide us with an unprecedentedly clear view of the quantum states of molecules, and enable the visualization of effects dictated by the quantum dynamics of molecules.
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Knowledge of molecular structure is paramount in understanding, and ultimately influencing, chemical reactivity. For nearly a century, diffractive imaging has been used to identify the structures of many biologically-relevant gas-phase molecules with atomic (i.e. Angstrom, A; 1 A = 10$^{-10}$ m) spatial resolution. Unravelling the mechanisms of chemical reactions requires the capability to record multiple well-resolved snapshots of the molecular structure as it is evolving on the nuclear (i.e. femtosecond, fs; 1 fs = 10$^{-15}$ s) timescale. We present the latest, state-of-the-art ultrafast electron diffraction methods used to retrieve the molecular structure of gas-phase molecules with Angstrom and femtosecond spatio-temporal resolution. We first provide a historical and theoretical background to elastic electron scattering in its application to structural retrieval, followed by details of field-free and field-dressed ultrafast electron diffraction techniques. We discuss the application of these ultrafast methods to time-resolving chemical reactions in real-time, before providing a future outlook of the field and the challenges that exist today and in the future.
We propose a strategy for enabling photodissociation of a normally photostable molecule through coupling to a nanoparticle plasmon. The large possible coupling on the single-molecule level combined with the highly lossy nature of plasmonic modes, with lifetimes on the order of femtoseconds, opens an ultrafast decay channel for the molecule. For plasmon mode frequencies below the vertical photoexcitation energy of the molecule, the difference between excitation and emission energy is converted into vibrational energy on the molecular ground state in a Raman-like process. Under the correct conditions, this energy can be high enough to enable efficient photodissociation on the electronic ground state. We demonstrate the concept using numerical simulations of the Lindblad master equation for the hydrogen molecule in the vicinity of an aluminum nanoparticle, and explore the photodissociation efficiency as a function of various system parameters.
The need to perform quantum state tomography on ever larger systems has spurred a search for methods that yield good estimates from incomplete data. We study the performance of compressed sensing (CS) and least squares (LS) estimators in a fast protocol based on continuous measurement on an ensemble of cesium atomic spins. Both efficiently reconstruct nearly pure states in the 16-dimensional ground manifold, reaching average fidelities FCS = 0.92 and FLS = 0.88 using similar amounts of incomplete data. Surprisingly, the main advantage of CS in our protocol is an increased robustness to experimental imperfections.
We address the feasibility of imaging geometric and orbital structure of a polyatomic molecule on an attosecond time-scale using the laser induced electron diffraction (LIED) technique. We present numerical results for the highest molecular orbitals of the CO2 molecule excited by a near infrared few-cycle laser pulse. The molecular geometry (bond-lengths) is determined within 3% of accuracy from a diffraction pattern which also reflects the nodal properties of the initial molecular orbital. Robustness of the structure determination is discussed with respect to vibrational and rotational motions with a complete interpretation of the laser-induced mechanisms.
Bayesian estimation of a mixed quantum state can be approximated via maximum likelihood (MaxLike) estimation when the likelihood function is sharp around its maximum. Such approximations rely on asymptotic expansions of multi-dimensional Laplace integrals. When this maximum is on the boundary of the integration domain, as it is the case when the MaxLike quantum state is not full rank, such expansions are not standard. We provide here such expansions, even when this maximum does not belong to the smooth part of the boundary, as it is the case when the rank deficiency exceeds two. These expansions provide, aside the MaxLike estimate of the quantum state, confidence intervals for any observable. They confirm the formula proposed and used without precise mathematical justifications by the authors in an article recently published in Physical Review A.
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