Fermionic State Engineering through Weak Measurement

Weak measurement enables the extraction of targeted information from a quantum system while minimizing decoherence due to measurement backaction. However, in many-body quantum systems, backaction from weak measurements can have novel effects on wavefunction collapse. We theoretically study continuously measured one-dimensional non-interacting fermions, starting in a ground-state Fermi sea. Repeated measurement of on-site occupation number drives the system from the completely delocalized Fermi sea toward a Fock state. We find that the spatial measurement resolution---in relation to the Fermi length---strongly affects both the collapse dynamics and the final state. We compare small-system exact numerical results to an analytical model and find that the quantum state undergoing measurement is described by a modified diffusion equation. These results indicate that weak measurement may be a powerful tool for state engineering in fermionic quantum systems.