Vector polarizability of atomic state induced by a linearly polarized vortex beam: External control of magic, tune-out wavelengths, and heteronuclear spin oscillations

TL;DR

This paper develops a theory for the vector polarizability of atomic states induced by focused linearly polarized vortex beams, enabling external control of magic and tune-out wavelengths, and influencing heteronuclear spin oscillations.

Contribution

The authors introduce a novel theoretical framework for atomic polarizability under linearly polarized vortex beams, including calculations for specific ions and implications for quantum control.

Findings

Calculated magic wavelengths for $^{87}$Sr$^{+}$ ion transitions.

Demonstrated control of fictitious magnetic fields via beam focusing and OAM.

Showed enhanced heteronuclear spin oscillation flexibility.

Abstract

Experiments with vortex beams have shown a surge of interest in controlling cold atoms. Most of the controlling protocols are dominated by circularly polarized light due to its ability to induce vector polarization at atoms, which is impossible for paraxial linearly polarized light. Here we develop a theory for frequency dependent polarizability of an atomic state interacting with a focused linearly polarized vortex beam. The naturally induced spin-orbit coupling in this type of linearly polarized beam produces vector component of the valence polarizability to an atomic state, obeying the total angular momentum conservation of the beam. The theory is employed on $^{87}$Sr$^{+}$ ion to accurately calculate the magic wavelengths for the clock transitions and tune-out wavelengths for the clock states using relativistic coupled-cluster method. The induced vector component in the dynamic polarizability due to the linearly polarized focused vortex beam promotes fictitious magnetic field to the atomic state. We demonstrate that this fictitious magnetic field, depending on the focusing angle and OAM of the beam, improves the flexibility of the coherent heteronuclear spin oscillations in a spin-1 mixture of $^{87}$Rb and $^{23}$Na atoms.