Quantum state tomography of molecules by ultrafast diffraction

Abstract

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 capture only the probability density of the nuclear wavepackets to determine the time-dependent molecular structures, while the full quantum state has not been accessed. 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, which encodes the amplitude and phase of the wavepacket, for molecules of arbitrary degrees of freedom, will enable the reconstruction of a quantum molecular movie from experimental x-ray or electron diffraction data.

Label-free quantum super-resolution imaging using entangled multi-mode squeezed light

“…which produces the estimated maximum Q = 5. We found that adding a higher-order prolate spheroidal functions made the estimate φ(s ′ ) quickly diverging due to the denominator λ j in equation (17), which decreases fast by multiple order-of-magnitudes with a slightly increased index j. Figure 6 shows the reconstructed object plane's optical phase distribution φ(s ′ ) for both MEMSL imaging and coherent light imaging.…”

“…There are many cases where the number of photons impinging on the imaging sample must be limited: quantum state tomography of molecules requires only a small number of probing photons in order not to disturb the quantum state to be measured [17][18][19]. Bioimaging, in general, requires only a small number of photons in order not to disturb the bioprocesses or overheat the fragile biomolecules [20].…”

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

“…For example, the S 1 ( nπ *) state population evolution of pyridine is reflected by an inelastic signal related to the two-electron correlation effect due to Coulomb repulsion between electrons . Starting from the probability densities of a molecular rotational wavepacket determined by ultrafast diffraction, the density matrix of the quantum wave packet can be obtained by quantum tomography …”

“…However, the underlying nature of QT is to retrieve the phase information lost in measurement . Analogous to crystallographic phase retrieval, the dimension problem can be solved by an iterative projection algorithm using the additional physical constraints of the density matrix . The generalized QT algorithm resolves the dimension problem and can be applied to make a quantum version of the “molecular movie” for rotational and vibrational motions.…”

“…44 Starting from the probability densities of a molecular rotational wavepacket determined by ultrafast diffraction, 46 the density matrix of the quantum wave packet can be obtained by quantum tomography. 47 In this Perspective, we emphasize the ultrafast imaging methods illustrated in Figure 1, which make use of table-top laser, XFEL, and electron sources.…”