Correlated emission of electron-current waves

Correlated emission of light offer a potential avenue for entanglement generation between atomic spins, with potential application for sensing and quantum memory. In this work, we investigate the conditions for the correlated emission by color centers into an electronic bath of conduction electrons. Unlike emission into bosonic modes, electrons can absorb energy via two-particle processes across a large range of length scales. We find that two length scales are particularly relevant: one set by the Fermi velocity and the frequency of the color centers $v_F/\Delta$, and the other set by the Fermi wavelength $\lambda_F \ll v_F/\Delta$. Subradiance requires emitters to be spaced at a distance closer than the Fermi wavelength, while superradiance requires spacing less than $\sqrt{\lambda_F v_F/\Delta}$, so long as the emitters are initialized with coherence. We show that the emitted current burst has a spiral form, and we discuss the experimental possibility to observe correlated dissipation by color-center qubits coupled to electronic environments.