By laws of physics, time and space forms the fundamental multidimensional continuum through the universe that is interwoven and was suggested first by Einstein. We humans occupy a small part of this large space-time continuum and inhabit within it with limited range in our naked perception. Considering space as a dimension, humans have so far been able to measure the distance across our observable universe (46.508 billion light years) using advanced telescopes and radio detectors, and the smallest measured distance in the quantum scale which is the planck length (1.616255*10-35m). In the time domain with the use of advanced attosecond (10^-18 s) laser technologies, scientists have found the way to track ultra fast events that were only previously predicted by their initial and final outcomes such as of a chemical reaction. They have recently been able to measure the shortest time interval or the time taken by light photons to travel across a molecule of hydrogen. The time interval is 247 zeptoseconds (zs) where 1 zs is 10-21 of a second.

Atomic physicists in Reinhard Dorner’s team published their article in Science journal in 16th October, 2020 (and that forms the basis of PhD dissertation work of Sven Grundmann of Goethe University, Frankfurt) where they successfully were able to exploit the ultrafast photo-ionization process to measure the birth time delay in the subsequent emission of the two photoelectrons in a hydrogen molecule upon bombardment of X-ray photon pulses. Photo-ionization is a fundamental process of investigating the atomic and molecular structure of elements where electrons in their orbital are knocked out by photon particles (photon-matter interaction), generating anions in the process and transforming a part of the photon energy into kinetic energy of the emitted electrons. These emissions manifest itself in the form of electron waves which interact with the other emitted electron waves (if any) to generate a diffraction pattern in the detector.

Source: cosmosmagazine.com

In Grundmann et al.’s work, the element that is taken for investigation is a H2 molecule consisting of two protons and two electrons. A high energy photon particle (enough to knock out both the electrons) from an x-ray laser source named PETRA III setup at the accelerator facility in Hamburg was used to irradiate the H2 molecule. Irradiation generates two electron waves from two ends of the molecule which interferes into constructive and destructive diffraction pattern and is detected. The waves generally tend to propagate at a direction perpendicular to the molecular axis. The phase differences in their diffraction pattern can yield birth time delay (tb) also termed the Wigner delay (delay in the emission of both the electron waves) by the equation below:

\[{t_b} = \frac{{Rcos\left( {{\alpha _0}} \right)}}{{{v_{ph}}}}--->(1)\]

Where, ‘R’ is the inter-nuclear distance, α_0 is the angle between the zeroth order maximum in the diffraction pattern and the molecular axis orientation. The phase velocity, vph is given from the photoelectron energy (E) and momentum (p) by the equation below:

\[{v_{ph}} = \frac{E}{p}--->(2)\]

A momentum space imaging technique named Cold target recoil ion momentum spectroscopy (COLTRIMS) (see description of the instrument in the below section) was used to measure the dynamics of the remaining two protons (with the remaining energy) in terms of momentum, which also gives the measurement of the photoelectron’s momentum (p). By determining relative momentum of the left out electron deficit protons caused due to Coulomb repulsive force, the Kinetic energy release (KER) and the molecular axis orientation can also be measured. Once the KER is determined and along with the known ionization energies of the photoelectrons, the remaining energy is shared equally between both the electrons (E). In order to avoid coulomb attraction between the moving photoelectrons, only fast moving electrons possessing 96% of the excess energy have been considered which also satisfies the single particle assumption of a double slit interference effect. The inter-nuclear distance (R) of the H2 molecule is then measured which is inversely related to the value of the KER. Finally, with the determination of all the parameters using COLTRIMS, the birth time delay can be evaluated from equation 1.

The birth time delay can also now be obtained considering phase shift in the electron wave diffraction upon irradiating the H2 molecule with x-ray pulses at an angle ‘B’ with the obtained orientation of the molecular axis.

\[{t_b} = \frac{{R\cos \left( B \right)}}{c}\] where ‘c’ is now the velocity of light.

From this equation, it is clear that the time delay is maximum when the light is incident parallel to the orientation of the molecular axis (or the light wave reaches the two electrons at different time) which also shifts the diffraction pattern to the right. The delay is again zero when the light is incident perpendicular to the molecular axis (or the light reaches the two electrons simultaneously) with no diffraction pattern shift. Considering the average value of the inter-nuclear distance of R=0.740A and B=00, the time delay obtained is 247 zs.

Being able to determine the birth time delay has an important contribution in understanding the molecular nature and structure of different substances which basically quantifies the extent to which the delocalized molecular orbitals behave as a single electron system upon interacting with the photon.

COLTRIMS reaction microscope

The entire process of high energy photon collision with H2 molecule (that is in a gas phase) occurs in a specialized instrument called COLTRIMS for multidimensional momentum determination of particles. The sources for impacting the molecule (or ionizing) can be in the form of electrons, ions, antiprotons, positrons and photons. Photon impact on a molecule to release electrons is basically the phenomenon of photo electric effect discovered by Einstein which forms the basis of the study. The setup comprises of a main chamber with a region of interaction into which a narrow, supersonic and cooled molecular beam is injected using a small aperture nozzle and skimmers. The chamber is maintained at an ultra high vacuum using turbo-pumps when the high energy pulse of x-ray beam is allowed to pass through the molecular beam at the interaction area. A spectrometer is placed in the main chamber consisting of Helmholtz coils to trap the released fast photoelectrons by generating a 3D magnetic field and copper plates on both sides of the interaction region to separate protons from electrons by generating an electric field. Thus the entire region in the spectrometer can be mainly divided into two: acceleration (where the electric field is constant) and drift region (where the electric field is zero). Electric and magnetic fields are tuned based on the velocity of the ejected particles in this acceleration region while the drift region helps in magnifying the differences in readings by spreading the particles onto the detectors. The time of flight of the particles can be recorded considering the distance of the detectors from the molecular centre. With all the required readings of time of flight and position of particles on the detector, a 3D momentum vector can easily be computed.

References:

• Sven Grundmann, Daniel Trabert, Kilian Fehre, Nico Strenger, Andreas Pier, Leon Kaiser, Max Kircher, Miriam Weller, Sebastian Eckart, Lothar Ph. H. Schmidt, Florian Trinter, Till Jahnke, Markus S. Schöffler and Reinhard Dörner, (2020) Zeptosecond birth time delay in molecular photoionization. Science 370 (6514), 339-341