Resonating valence bonds and spinon pairing in the Dicke model

Abstract

Resonating valence bond (RVB) states are a class of entangled quantum many body wavefunctions with great significance in condensed matter physics. We propose a scheme to synthesize a family of RVB states using a cavity QED setup with two-level atoms coupled to a common photon mode. In the lossy cavity limit, starting with an initial state with MM atoms excited and NN atoms in the ground state, we show that this setup can be configured as a Stern Gerlach experiment. A measurement of photon emission collapses the wavefunction of atoms onto an RVB state composed of resonating long-ranged singlets. Each emitted photon reduces the number of singlets by unity, replacing it with a pair of lone spins or ‘spinons’. As spinons are formed coherently in pairs, they are analogous to Cooper pairs in a superconductor. To simulate pair fluctuations, we propose a protocol in which photons are allowed to escape the cavity undetected. This leads to an inchoate superconductor – mixed quantum state with a fluctuating number of spinon pairs. Remarkably, in the limit of large system sizes, this protocol reveals an underlying quantum phase transition. Upon tuning the initial spin polarization, the emission exhibits a continuous transition from a dark state to a bright state. This opens an exciting route to simulate RVB states and superconductivity.