Wigner-Function Fingerprints of Collective Excitations in Mirror-Terminated Waveguide QED

Abstract

We investigate the emission profiles of singly excited collective states and propose a matched-mode witnessing protocol in a mirror-terminated waveguide quantum electrodynamics system. The amplitudes and relative phases of the initial collective excitation are encoded in the temporal mode of the emitted single-photon wavepacket, providing a route to state verification through the common waveguide output. We identify the emission mode associated with a chosen target state and employ an auxiliary virtual-cavity representation to evaluate the quantum state of this selected output mode. For a matched initial state, the selected mode contains the emitted single photon, whose Wigner function exhibits a pronounced non-classical negative dip, serving as a distinct fingerprint of the target many-body state. With the reference mode held fixed, different initial configurations yield different photon occupations and phase-space distributions, demonstrating the state selectivity of the protocol. These results connect collective-state verification with temporal-mode analysis of the emitted radiation, offering access to collective coherence with reduced reliance on qubit-resolved correlation measurements.