Optical precursors in waveguide quantum electrodynamics

When a broadband signal propagates through dispersive medium, some frequency components move faster than the center of pulse. This leads to appearance precursors, transient signals that emerge from medium earlier main part pulse and seem propagate superluminally. Here, we investigate microscopic origin precursors in minimal setup: an array qubits coupled waveguide. The linear transmission function only converges continuous for large qubit numbers. Nevertheless, dispersion produced by two is enough produce oscillatory transients. Precursors are best observed under conditions electromagnetically-induced transparency, as significantly delayed. Under these conditions, just single qutrit generate precursor. Our results pave way towards engineering light with few qubits, can be realized superconducting lines or atoms optical waveguides.