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Physical Review Letters

Spin Polarization in Strong-Field Ionization as Sensor of Trapped Electron Orbits

Linxuan Zhang, Stefanos Carlström, Olga V. Smirnova, Misha Ivanov, Difa Ye

Published Nov 6, 2025• 4 citations
Publisher

Abstract

We show how spin polarization of photoelectrons produced in strong-field ionization of noble-gas atoms can be used to detect highly unexpected electron orbits created in strong, circularly polarized near-infrared fields. In such fields, ionization is expected to generate photoelectrons rapidly moving away from the ionic core, freezing their initial spin due to the short-range nature of the spin-orbit interaction between the photoelectron and the core. However, we find clear evidence of spin flips in the photoelectron spectra at low photoelectron energies and confirm that they happen because a photoelectron has been trapped near the core. The presence of such highly unexpected orbits explains the marked deviations between the recent experimental measurements of spin polarization [Nat. Photonics 10, 526 (2016)NPAHBY1749-488510.1038/nphoton.2016.109] and simulations with frozen spin.

DOI
10.1103/9f8y-td77

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We show how spin polarization of photoelectrons produced in strong-field ionization of noble-gas atoms can be used to detect highly unexpected electron orbits created in strong, circularly polarized near-infrared fields. In such fields, ionization is expected to generate photoelectrons rapidly moving away from the ionic core, freezing their initial spin due to the short-range nature of the spin-orbit interaction between the photoelectron and the core. However, we find clear evidence of spin flips in the photoelectron spectra at low photoelectron energies and confirm that they happen because a photoelectron has been trapped near the core. The presence of such highly unexpected orbits explains the marked deviations between the recent experimental measurements of spin polarization [Nat. Photonics 10, 526 (2016)NPAHBY1749-488510.1038/nphoton.2016.109] and simulations with frozen spin.
We show that ionization of noble gas atoms by a strong infrared circularly polarized laser field under standard experimental conditions can yield electrons with up to 100% spin polarization in energy-resolved measurements. Spin polarization arises due to the interplay of the electron-core entanglement and the sensitivity of ionization in circularly polarized fields to the sense of electron rotation in the initial state.
The ionization of the prealigned nitric oxide molecule by strong circularly polarized laser fields is studied via theoretical simulations of the spin-resolved photoelectron momentum distributions by solving numerically the three-dimensional time-dependent Schr\"odinger equation. Due to the spin-orbit entanglement in the ground state of nitric oxide and the sensitivity of the tunnel ionization of its doubly degenerate valence $2{\ensuremath{\pi}}_{\ifmmode\pm\else\textpm\fi{}}$ orbitals carrying opposite electron ring currents to the sense of the laser-field rotation, the momentum-resolved spin-polarized photoelectrons are produced. We show that the spin polarization exhibits strong dependence on the kinetic energy as well as the emitting angle of the photoelectron. In addition to the laser control, the momentum gate in strong-field experiments would enable full control of the spin polarization.
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Summary form only given. Spin plays a fundamental role in the electronic structure of matter, from single atoms and molecules through to condensed matter. However, spin dynamics and the spin response of electrons to ultra-short, strong laser pulses has remained largely unexplored until today. In 2011 and 2013, pioneering theoretical work [1, 2] extended the fundamental PPT theory [3] to treat ionization of p+ and p” electrons by circular fields. This work predicted the sensitivity of ionization probabilities in strong field ionization using circular fields to the magnetic quantum number, showing that counter rotating electrons can tunnel ionize easier. It also predicted the possibility to obtain spin polarized electrons from strong, circularly polarized fields with a high degree of efficiency. The preference of ionization was later confirmed experimentally by [4], however, the experiment in [4] did not provide a confirmation of the spin polarization predictions.
Attosecond chronoscopy represents a major breakthrough in the study of ultrafast phenomena and has the potential to revolutionize our understanding of the fundamental physics of matter. We theoretically investigate the spin-orientation-resolved attosecond chronoscopy for the first time by the circular RABBIT technique for Kr atoms. Due to the spin-orbit interaction and the sensitivity of ionization in circularly polarized fields to the sense of electron rotation in the initial state, the spin-resolved ionization rates of photoelectrons emitted from 2P1/2^2P_{1/2}2P1/2​ and 2P3/2^2P_{3/2}2P3/2​ channels can be expressed via mmm-resolved ionization rates of initial state, where mmm is the orbital magnetic quantum number. We demonstrate that the yields difference between spin-up and spin-down photoelectrons from each channel are closely associated with the different behaviors of corresponding Wigner time delay. We find that the Wigner time delay between spin-up and spin-down photoelectrons in the polarization plane can reach several tens of attoseconds in the co-rotating geometry, but a few attoseconds in the counter-rotating geometry. Our approach opens up a new avenue for probing the spin-dependent behavior of Wigner time delay, and lays the foundation for spin-orientation-resolved attosecond chronoscopy, which can be verified by the current experimental techniques.
We demonstrate that strong-field ionization of atoms in circularly polarized laser fields generates a photoelectron spin texture with toroidal topology in momentum space. Using time-dependent Schrödinger equation simulations, spin-resolved classical-trajectory Monte Carlo calculations, and an extended spin-resolved strong-field approximation including intermediate excitation pathways, we show that the rotation angle of this spin torus provides access to attosecond relative time delays associated with photoelectron wave packets released by tunneling from the counter-rotating and co-rotating ppp-orbital channels. When intermediate-state dynamics become significant, the torus develops a clear splitting. These results establish photoelectron spin textures as a complementary source of dynamical information beyond conventional momentum spectroscopy, and identify spin polarization as a robust internal degree of freedom for self-referenced attosecond metrology.