Measurement time in billionths of a billionth of a second

How fast do electrons inside a molecule move? Well, it’s so fast that it only takes them a few attoseconds (a billionth of a billionth of a second) to jump from one atom to another. Blink and you’ve missed it – millions of billions of times. Measuring such ultrafast processes is therefore a difficult task.

Scientists from the Australian Attosecond Science Facility and the Center for Quantum Dynamics at Griffith University in Brisbane, Australia, led by Professor Robert Sang and Professor Igor Litvinyuk, have developed a new interferometric technique capable of measuring delays zeptosecond (one trillionth of a billionth of a second) resolution.

They used this technique to measure the delay between pulses of extreme ultraviolet light emitted by two different isotopes of hydrogen molecules – H₂ and D₂—interacting with intense infrared laser pulses.

This delay was found to be less than three attoseconds (a quintillionth of a second long) and is caused by slightly different motions of the lighter and heavier nuclei.

This study was published in Ultra-fast science.

First author Dr. Mumta Hena Mustary explains, “Such unprecedented temporal resolution is achieved via interferometric measurement – riding the delayed light waves and measuring their combined luminosity.”

The light waves themselves were generated by molecules exposed to intense laser pulses in the process called high harmonic generation (HHG).

HHG occurs when an electron is removed from a molecule by a strong laser field, is accelerated by the same field, and then recombines with the ion yielding energy in the form of extreme ultraviolet (XUV) radiation. The intensity and phase of this XUV HHG radiation is sensitive to the exact dynamics of the electronic wave functions involved in this process – all different atoms and molecules emit HHG radiation differently.

Although it is relatively simple to measure the spectral intensity of HHG – a simple grating spectrometer can do this – measuring the HHG phase is a much more difficult task. And the phase contains the most relevant information about the timing of the different stages of the issuance process.

To measure this phase, it is customary to carry out a so-called interferometric measurement when two replicas of the wave with a finely controlled delay are overlapped (or interfered with). They can interfere constructively or destructively depending on the delay and the relative phase difference between them.

This measurement is performed by a device called an interferometer. It is very difficult to build an interferometer for XUV light, especially to produce and maintain a stable, known and finely tunable delay between two XUV pulses.

The Griffith researchers solved this problem by taking advantage of the phenomenon known as Gouy’s phase, when the phase of a light wave is shifted in a certain way as it passes through a focus.

For their experiments, the researchers used two different isotopes of molecular hydrogen, the simplest molecule in nature. Isotopes—light (H₂) and heavy (D₂) hydrogen – differ only in the mass of nuclei – protons in H₂ and deuterons in D₂. Everything else, including the electronic structure and the energies, are identical.

Due to their larger mass, the nuclei of D₂ move slightly slower than those in H₂. Because nuclear and electronic motions in molecules are coupled, nuclear motion affects the dynamics of electronic wave functions during the HHG process, resulting in a small ΔφH phase shift₂-D₂ between the two isotopes.

This phase shift is equivalent to a time delay Δt = ΔφH₂-D₂ /ω where ω is the frequency of the XUV wave. Griffith scientists measured this emission delay for all observed harmonics in the HHG spectrum – it was nearly constant and just under 3 attoseconds.

To understand their result, the Griffith researchers were supported by theorists from Shanghai Jiao Tong University in Shanghai, China, led by Professor Feng He.

SJTU scientists used the most advanced theoretical methods to comprehensively model the HHG process in both isotopes of molecular hydrogen, including all degrees of freedom for nuclear and electronic motion at different levels of approximation. .

Their simulation reproduced the experimental results well, and this agreement between theory and experiment gave the team confidence that the model captured the most essential features of the underlying physical process. Thus, the adjustment of model parameters and levels of approximation can determine the relative importance of various effects.

Although the actual dynamics are quite complex, it has been found that two-center interference during the electronic recombination step is the dominant effect.

“Because hydrogen is the simplest molecule in nature and can be modeled theoretically with great accuracy, it was used in these proof-of-principle experiments for comparative analysis and method validation. “, Professor Litvinyuk said.

“In the future, this technique may be used to measure the ultrafast dynamics of various light-induced processes in atoms and molecules with unprecedented time resolution.”

The study, “Attosecond Delays of High-Harmonic Emissions from Hydrogen Isotopes Measured by XUV Interferometer,” was published in Ultra-fast science.