Margaret Gregory, Paul Hockett, Albert Stolow, Varun Makhija
arXiv:2012.04561, Dec. 2020
The application of a matrix-based reconstruction protocol for obtaining Molecular Frame (MF) photoelectron angular distributions (MFPADs) from laboratory frame (LF) measurements (LFPADs) is explored. Similarly to other recent works on the topic of MF reconstruction, this protocol makes use of time-resolved LF measurements, in which a rotational wavepacket is prepared and probed via photoionization, followed by a numerical reconstruction routine; however, in contrast to other methodologies, the protocol developed herein does not require determination of photoionization matrix elements, and consequently takes a relatively simple numerical form (matrix transform making use of the Moore-Penrose inverse). Significantly, the simplicity allows application of the method to the successful reconstruction of MFPADs for polyatomic molecules. The scheme is demonstrated numerically for two realistic cases, N2 and C2H4. The new technique is expected to be generally applicable for a range of MF reconstruction problems involving photoionization of polyatomic molecules.
Update Jan 2018 – a presentation covering this work was given at the PQE conference, video and slides are available online.
Update August 2017 – this article is now published in PRL, under the alternative title Molecular Frame Reconstruction Using Time-Domain Photoionization Interferometry.
Phys. Rev. Lett. 119, 083401 (2017), DOI: 10.1103/PhysRevLett.119.083401
(Feb 2017) New manuscript on the arxiv:
(Submitted on 29 Jan 2017)
Photoionization of molecular species is, essentially, a multi-path interferometer with both experimentally controllable and intrinsic molecular characteristics. In this work, XUV photoionization of impulsively aligned molecular targets (N2) is used to provide a time-domain route to “complete” photoionization experiments, in which the rotational wavepacket controls the geometric part of the photoionization interferometer. The data obtained is sufficient to determine the magnitudes and phases of the ionization matrix elements for all observed channels, and to reconstruct molecular frame interferograms from lab frame measurements. In principle this methodology provides a time-domain route to complete photoionization experiments, and the molecular frame, which is generally applicable to any molecule (no prerequisites), for all energies and ionization channels.
arxiv 1701.08432 (2017)
Supplementary material (theory, data and code) available at DOI: 10.6084/m9.figshare.4480349.
Slides for Paul’s DAMOP talk are now available on figshare (DOI: 10.6084/m9.figshare.5049142).
Photoionization is an interferometric process, in which multiple paths can contribute to the final continuum photoelectron state. At the simplest level, interferences between different final angular momentum states are manifest in the energy and angle resolved photoelectron spectra: metrology schemes making use of these interferograms are thus phase-sensitive, and provide a powerful route to detailed understanding of photoionization . At a more complex level, such measurements can also provide a powerful probe for other processes of interest, for example: (a) dynamical process in time-resolved measurements, such as rotational, vibrational and electronic wavepackets, and (b) in order to understand and develop control schemes . In this talk recent work in this vein will be discussed, touching on “complete” photoionization studies of atoms and molecules with shaped laser pulses [1,2] and XUV , metrology schemes using Angle-Resolved RABBIT, and molecular photoionization dynamics in the time-domain (Wigner delays) .
 Hockett, P. et. al. (2015). Phys. Rev. A, 92, 13412.  Hockett, P. et. al. (2014). Phys. Rev. Lett., 112, 223001.  Marceau, C. et. al. (2017). Submitted. DOI: 10.6084/m9.figshare.4480349.  Hockett, P. et. al. (2016). J. Phys B, 49, 95602.
Update 29th June 2017 – a video of the talk is now also available.
Phase-sensitive Photoelectron Metrology – Dr. P. Hockett, presentation at DAMOP 2017 from femtolab.ca on Vimeo.
The above image shows simulated velocity map images (left, middle) and angle and time-resolved measurements (right) for angle-resolved RABBIT measurements. In this type of measurement, XUV and IR pulses are combined, and create a set of 1 and 2-photon bands in the photoelectron spectrum. The presence of multiple interfering pathways to each final photoelectron band (energy) results in complex and information rich interferograms, with both angle and time-dependence.
A manuscript detailing this work is currently in preparation, and a recent presentation detailing some aspects of the work can be found on Figshare.
Update 24th March – new manuscript, Angle-resolved RABBIT: theory and numerics, pre-print available.
Quantum imaging with undetected photons
Gabriela Barreto Lemos, Victoria Borish, Garrett D. Cole, Sven Ramelow, Radek Lapkiewicz & Anton Zeilinger
Nature 512, 409–412 (2014)
Interferometric imaging based on photon pairs, from the intro:
Information is central to quantum mechanics. In particular, quantum interference occurs only if there exists no information to distinguish between the superposed states. The mere possibility of obtaining information that could distinguish between overlapping states inhibits quantum interference1, 2. Here we introduce and experimentally demonstrate a quantum imaging concept based on induced coherence without induced emission3, 4. Our experiment uses two separate down-conversion nonlinear crystals (numbered NL1 and NL2), each illuminated by the same pump laser, creating one pair of photons (denoted idler and signal). If the photon pair is created in NL1, one photon (the idler) passes through the object to be imaged and is overlapped with the idler amplitude created in NL2, its source thus being undefined. Interference of the signal amplitudes coming from the two crystals then reveals the image of the object. The photons that pass through the imaged object (idler photons from NL1) are never detected, while we obtain images exclusively with the signal photons (from NL1 and NL2), which do not interact with the object. Our experiment is fundamentally different from previous quantum imaging techniques, such as interaction-free imaging5 or ghost imaging6, 7, 8, 9, because now the photons used to illuminate the object do not have to be detected at all and no coincidence detection is necessary. This enables the probe wavelength to be chosen in a range for which suitable detectors are not available. To illustrate this, we show images of objects that are either opaque or invisible to the detected photons. Our experiment is a prototype in quantum information—knowledge can be extracted by, and about, a photon that is never detected.
Two new articles, on quantum metrology via polarization-shaped pulses (mostly theory) and maximum-information photoelectron metrology via tomographic measurements (mostly experiment), have just been published in PRA.
Complete photoionization experiments via ultrafast coherent control with polarization multiplexing. II. Numerics and analysis methodologies
P. Hockett, M. Wollenhaupt, C. Lux, and T. Baumert
Phys. Rev. A 92, 013411 – Published 13 July 2015
(also available at arXiv:1503.08247 (2015))
Maximum-information photoelectron metrology
P. Hockett, C. Lux, M. Wollenhaupt, and T. Baumert
Phys. Rev. A 92, 013412 – Published 13 July 2015
(also available at arXiv:1503.08308 (2015))
Playing around with visualization of the information content of polarization-shaped pulses, which represent a way to coherently sample (over the pulse duration) a range of points in polarization space. Here’s a plot showing the coherent paths followed for a range of different pulses, generated by putting a step function on the spectral phase of a broadband (~60fs) pulse, with the instantaneous pulse polarization expressed as Stokes vectors and projected onto a Poincare Sphere.
Update 4th May – the manuscript (a version of) this figure appears in is now on the arxiv.