Generating resonating-valence-bond states through Dicke subradiance
R. Ganesh, L. Theerthagiri, G. Baskaran · Physical Review A · 2017
Dicke's original thought experiment with two spins (two-level atoms) coupled to a photon mode has recently been experimentally realized. We propose extending this experiment to many spins as a way to synthesize highly entangled states. We suggest a protocol in which we start with a direct product state of $M$ atoms in the excited state and $N$ atoms in the ground state, placed within a lossy cavity. A null observation for photon emission collapses the system onto a dark state which, remarkably, has resonating-valence-bond (RVB) character. We demonstrate this by taking advantage of the symmetry of the initial state under permutations of the $M$ excited atoms and of the $N$ unexcited atoms. Using angular momentum analysis, we reexpress the wave function of the dark state to illustrate its RVB character. We discuss two limiting cases in detail, with $M=1$ (one excited atom) and $M=N$ (equal number of excited and unexcited atoms). In the latter case, we show that the probability for null emission scales as ${N}^{\ensuremath{-}1}$, making it possible to generate highly entangled RVB states of 20 spins or more.