Universal Noise in Continuous Transport Measurements of Interacting Fermions

We propose and analyze continuous measurements of atom number and atomic currents using dispersive probing in an optical cavity. For an atom-number measurement in a closed system, we relate both the detection noise and the heating rate due to measurement back-action to Tan's contact, and identify an emergent universal quantum non-demolition (QND) regime in the good-cavity limit. We then show that such a continuous QND measurement of atom number serves as a quantum-limited current transducer in a two-terminal setup. We derive a universal bound on the precision of current measurement, which results from a tradeoff between detection noise and back-action of the atomic current measurement. Our results apply regardless of the strength of interaction or the state of matter and set fundamental bounds on future precision measurements of transport properties in cold-atom quantum simulators.