Many-body entanglement via 'which-path' information

We propose a multi-particle 'which-path' gedanken experiment with a quantum detector. Contrary to conventional 'which-path' experiments, the detector maintains its quantum state during interactions with the particles. We show how such interactions can create an interference pattern that vanishes on average, as in conventional 'which-path' schemes, but contains hidden many-body quantum correlations. Measuring the state of the quantum detector projects the joint-particle wavefunction into highly entangled states, such as GHZ's. Conversely, measuring the particles projects the detector wavefunction into desired states, such as Schrodinger-cat or GKP states for a harmonic-oscillator detector, e.g., a photonic cavity. Our work thus opens a new path to the creation and exploration of many-body quantum correlations in systems not often associated with these phenomena, such as atoms in waveguide QED and free electrons in transmission electron microscopy.