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We calculate the persistent spin current inside a quantum ring as a functionof the strength of the Rashba or Dresselhaus spin-orbit interaction. We provideanalytical results for the spin current of a one-dimensional (1D) ring ofnon-interacting electrons for comparison. Furthermore, we calculate the timeevolution in the transient regime of a two-dimensional (2D) quantum ringconnected to electrically biased semi-infinite leads using atime-convolutionless non-Markovian generalized master equation. In the lattercase, the electrons are correlated via the Coulomb interaction and the ring canbe embedded in a photon cavity with a single mode of linearly polarized photonfield. The electron-electron and electron-photon interactions are described byexact numerical diagonalization. The photon field can be polarizedperpendicular or parallel to the charge transport. We find a pronounced chargecurrent dip associated with many-electron level crossings at theAharonov-Casher phase $\Delta\Phi=\pi$, which can be disguised by linearlypolarized light. Qualitative agreement is found for the spin currents of the 1Dand 2D ring. Quantatively, however, the spin currents are weaker in the morerealistic 2D ring, especially for weak spin-orbit interaction, but can beconsiderably enhanced with the aid of a linearly polarized electromagneticfield. Specific spin current symmetries relating the Dresselhaus spin-orbitinteraction case to the Rashba one are found to hold for the 2D ring in thephoton cavity.

Geometry and linearly polarized cavity photon effects on the charge and spin currents of spin-orbit interacting electrons in a quantum ring