circular state

Named after the torus-like shape of the valence electron orbital in these states, which resembles a classical circular orbit.^[1]

circular state (plural circular states)

1. (physics) Any of those quantum states of an atom, which has a high principal quantum number ${\displaystyle n}$, and a magnetic quantum number ${\displaystyle m_{l}}$ with the maximum possible magnitude, ${\displaystyle |m_{l}|=n-1}$.
   • 1962 December, J.R. Rook, “The decay of K⁻ mesic atoms”, in Nuclear Physics, volume 39, →DOI, page 479:

     […] he selection rules on the Auger and X-ray transition probabilities tend to populate preferentially the circular states, that is those for which the orbital angular momentum ${\displaystyle l}$ is given by ${\displaystyle l=n-1}$.

   • 1983 October 17, Randall G. Hulet and Daniel Kleppner, “Rydberg Atoms in "Circular" States”, in Physical Review Letters, volume 51, →DOI, page 1430:

     We report the production of a population of atoms in a Rydberg state with ${\displaystyle |m|=n-1}$, where ${\displaystyle m}$ and ${\displaystyle n}$ are the magnetic and principal quantum numbers, respectively. We designate these states as "circular" because in the classical limit they describe an electron in a circular orbit. Among all the states with a given principal quantum number, the circular states have the largest magnetic moment, smallest Stark effect, and longest radiative lifetime.

   • 2021 August 6, Sam R. Cohen and Jeff D. Thompson, “Quantum Computing with Circular Rydberg Atoms”, in PRX Quantum, volume 2, →DOI, page 030322:

     So-called circular states with the maximal angular momentum ${\displaystyle L=n-1}$ can have lifetimes exceeding 100 s, ${\displaystyle 10^{6}}$ times longer than those of low-${\displaystyle L}$ states, in appropriately engineered environments.