Molecular Frame Photoelectron Angular Distributions in Polyatomic Molecules from Lab Frame Coherent Rotational Wavepacket Evolution

Molecular Frame Photoelectron Angular Distributions in Polyatomic Molecules from Lab Frame Coherent Rotational Wavepacket Evolution

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.


 

Photoelectron angular distributions from resonant two-photon ionisation of adiabatically aligned naphthalene and aniline molecules

Photoelectron angular distributions from resonant two-photon ionisation of adiabatically aligned naphthalene and aniline molecules

Molecular Physics, Article: e1836411 | Received 03 Aug 2020, Accepted 06 Oct 2020, Published online: 22 Oct 2020,
https://doi.org/10.1080/00268976.2020.1836411

Photoelectron images have been measured following the ionisation of aligned distributions of gas phase naphthalene and aniline molecules. Alignment in the adiabatic regime was achieved by interaction with a 100 ps infrared laser pulse, with ionisation achieved in a two-photon resonant scheme using a low intensity UV pulse of ∼6 ps duration. The resulting images are found to exhibit anisotropy that increases when the alignment pulse is present, with the aniline PADs peaking along the polarisation vector of the ionising light and the naphthalene PADs developing a characteristic four-lobed structure. Photoelectron angular distributions (PADs) that result from the ionisation of unaligned and fully aligned distributions of molecules are calculated using the ePolyScat ab initio suite and converted into two-dimensional photoelectron images. In the case of naphthalene excellent agreement is observed between experiment and the simulation for the fully aligned distribution, showing that the alignment step allows us to probe the molecular frame, but in the case of aniline it is clear that additional processes occur following the one-photon resonant step.

Quantum Metrology with Photoelectrons (book)

Quantum Metrology with Photoelectrons (book)

Update April 2018 – the books are now available via IOP, see details at end of post.

Book for IOP Concise Physics series, due early 2018

Dr. Paul Hockett

National Research Council of Canada

Online resources

OSF project (ID: q2v3g) with interactive content and additional resources, DOI: 10.17605/OSF.IO/Q2V3G

femtolab.ca website, posts tagged “metrology-book”

femtolab.ca website, posts tagged “video”

Abstract

Photoionization is an interferometric process, in which multiple paths can contribute to the final continuum photoelectron wavefunction. 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. In these cases, the continuum wavefunction (and underlying scattering dynamics) can be characterised. At a more complex level, such measurements can also provide a powerful probe for other processes of interest, leading to a more general class of quantum metrology built on phase-sensitive photoelectron imaging.  Since the turn of the century, the increasing availability of photoelectron imaging experiments, along with the increasing sophistication of experimental techniques, and the availability of computational resources for analysis and numerics, has allowed for significant developments in such photoelectron metrology.

Volume I covers the core physics of photoionization, including a range of computational examples. The material is presented as both reference and tutorial, and should appeal to readers of all levels.  Volume II explores applications, and the development of quantum metrology schemes based on photoelectron measurements. The material is more technical, and will appeal more to the specialist reader.

Full text

Quantum Metrology with Photoelectrons

Volume 1
ISBN 978-1-6817-4684-5
http://iopscience.iop.org/book/978-1-6817-4684-5
Volume 2
ISBN 978-1-6817-4688-3
http://iopscience.iop.org/book/978-1-6817-4688-3

 

Photoionization Interferometry & Metrology

Photoionization Interferometry & Metrology

Photoionization is a complex quantum mechanical process, with a range of interfering channels playing a role in even the simplest case. For problems in quantum metrology and sensing, a detailed understanding of the process is desirable for accurate measurements; quantum control is also a possible outcome of such understanding. New research in this area will build on recent cutting-edge work at NRC (see below), which probed the fundamental quantum physics of photoionization in atoms and molecules, and metrology work which demonstrated the retrieval of electron wavefunctions via interferometric time-domain measurements.

Four areas of photoionization interferometry are the target of current research:

  1. Metrology and control with rotational wavepackets.
  2. Metrology and control with shaped laser pulses.
  3. Quantum dynamics probed via photoionization interferometry.
  4. Fundamental properties of photoion and photoelectron coherence.

Depending on interests and experience, project work will be in one (or more) of these areas.

An introduction to this topic, and recent work, can be found in Paul’s DAMOP 2017 talk Phase-sensitive Photoelectron Metrology (below), and via our blog.

Phase-sensitive Photoelectron Metrology – Dr. P. Hockett, presentation at DAMOP 2017 from femtolab.ca on Vimeo.

Phase-sensitive Photoelectron Metrology (presentation at DAMOP 2017)

Phase-sensitive Photoelectron Metrology (presentation at DAMOP 2017)

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 [1]. 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 [1]. 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 [3], metrology schemes using Angle-Resolved RABBIT, and molecular photoionization dynamics in the time-domain (Wigner delays) [4].

[1] Hockett, P. et. al. (2015). Phys. Rev. A, 92, 13412. [2] Hockett, P. et. al. (2014). Phys. Rev. Lett., 112, 223001. [3] Marceau, C. et. al. (2017). Submitted. DOI: 10.6084/m9.figshare.4480349. [4] 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.

Time-dependent Wavepackets and Photoionization – CS2

Time-dependent Wavepackets and Photoionization – CS2

Our ongoing work on the calculation of time-dependent wavepackets and observables in photoionization is now collected in an OSF project (DOI: 10.17605/OSF.IO/RJMPD). Aspects of this work have previously been published, but much of the detail and methodology underlying the calculations has remained sitting on our computers. As part of our Open Science Initiative, we’re letting this data go free! Head over to the OSF project “Time-dependent Wavepackets and Photoionization – CS2” for more.

Figure shows TRPADs results (a) Calculated TRPADs (0.7eV) (b), (c) Comparison with expt. TRPADs (discrete times).

Press Release: The Inner Lives of Molecules

Press Release: The Inner Lives of Molecules

Our latest work with the PImMS camera, femtosecond VUV pulses, and velocity-map imaging, has been picked up for a press release by AIP.

The Inner Lives of Molecules

New method takes 3-D images of molecules in action

WASHINGTON, D.C., April 4, 2017 — Quantum mechanics rules. It dictates how particles and forces interact, and thus how atoms and molecules work — for example, what happens when a molecule goes from a higher-energy state to a lower-energy one. But beyond the simplest molecules, the details become very complex.

“Quantum mechanics describes how all this stuff works,” said Paul Hockett of the National Research Council of Canada. “But as soon as you go beyond the two-body problem, you can’t solve the equations.” So, physicists must rely on computer simulations and experiments.

Now, he and an international team of researchers from Canada, the U.K. and Germany have developed a new experimental technique to take 3-D images of molecules in action. This tool, he said, can help scientists better understand the quantum mechanics underlying bigger and more complex molecules.

The new method, described in The Journal of Chemical Physics, from AIP Publishing, combines two technologies. The first is a camera developed at Oxford University, called the Pixel-Imaging Mass Spectrometry (PImMS) camera. The second is a femtosecond vacuum ultraviolet light source built at the NRC femtolabs in Ottawa.

Mass spectrometry is a method used to identify unknown compounds and to probe the structure of molecules. In most types of mass spectrometry, a molecule is fragmented into atoms and smaller molecules that are then separated by molecular weight. In time-of-flight mass spectrometry, for example, an electric field accelerates the fragmented molecule. The speed of those fragments depends on their mass and charge, so to weigh them, you measure how long it takes for them to hit the detector.

Most conventional imaging detectors, however, can’t discern exactly when one particular particle hits. To measure timing, researchers must use methods that effectively act as shutters, which let particles through over a short time period. Knowing when the shutter is open gives the time-of-flight information. But this method can only measure particles of the same mass, corresponding to the short time the shutter is open.

The PImMS camera, on the other hand, can measure particles of multiple masses all at once. Each pixel of the camera’s detector can time when a particle strikes it. That timing information produces a three-dimensional map of the particles’ velocities, providing a detailed 3-D image of the fragmentation pattern of the molecule.

To probe molecules, the researchers used this camera with a femtosecond vacuum ultraviolet laser. A laser pulse excites the molecule into a higher-energy state, and just as the molecule starts its quantum mechanical evolution — after a few dozen femtoseconds –another pulse is fired. The molecule absorbs a single photon, a process that causes it to fall apart. The PImMS camera then snaps a 3-D picture of the molecular debris.

By firing a laser pulse at later and later times at excited molecules, the researchers can use the PImMS camera to take snapshots of molecules at various stages while they fall into lower energy states. The result is a series of 3-D blow-by-blow images of a molecule changing states.

The researchers tested their approach on a molecule called C2F3I. Although a relatively small molecule, it fragmented into five different products in their experiments. The data and analysis software is available online as part of an open science initiative, and although the results are preliminary, Hockett said, the experiments demonstrate the power of this technique.

“It’s effectively an enabling technology to actually do these types of experiments at all,” Hockett said. It only takes a few hours to collect the kind of data that would take a few days using conventional methods, allowing for experiments with larger molecules that were previously impossible.

Then researchers can better answer questions like: How does quantum mechanics work in larger, more complex systems? How do excited molecules behave and how do they evolve?

“People have been trying to understand these things since the 1920s,” Hockett said. “It’s still a very open field of investigation, research, and debate because molecules are really complicated. We have to keep trying to understand them.”

Text reproduced from AIP.

The article, Time-resolved multi-mass ion imaging: femtosecond UV-VUV pump-probe spectroscopy with the PImMS camera, is now published in the Journal of Chemical Physics, and also available via the arXiv 1702.00744 and Authorea (original text), DOI: 10.22541/au.149030711.19068540.

The full dataset and analysis scripts are available via OSF, DOI: 10.17605/OSF.IO/RRFK3.

Angle-resolved RABBIT: theory and numerics

Angle-resolved RABBIT: theory and numerics

Update 28/06/17 – Now published in J. Phys. B, special issue on Correlations in Light-Matter Interactions.

New manuscript:

Angle-resolved RABBIT: theory and numerics

P. Hockett

Angle-resolved (AR) RABBIT measurements offer a high information content measurement scheme, due to the presence of multiple, interfering, ionization channels combined with a phase-sensitive observable in the form of angle and time-resolved photoelectron interferograms. In order to explore the characteristics and potentials of AR-RABBIT, a perturbative 2-photon model is developed; based on this model, example AR-RABBIT results are computed for model and real systems, for a range of RABBIT schemes. These results indicate some of the phenomena to be expected in AR-RABBIT measurements, and suggest various applications of the technique in photoionization metrology.

Paul Hockett 2017 J. Phys. B: At. Mol. Opt. Phys. 50 154002

Pre-print available via Authorea, DOI: 10.22541/au.149037518.89916908.

arXiv 1703.08586 (2017) 

See also the recent AR-RABBIT presentation for a brief intro to this topic.