Non-invasive measurement of currents in analog quantum simulators

Despite the pristine abilities of analog quantum simulators to study quantum dynamics, possibilities to detect currents are sparse. Here, we propose a flexible non-invasive technique to measure currents in quantum many-body systems by weakly coupling the system to an ancilla, followed by a measurement of the ancilla population. We numerically benchmark the scheme at the example of interacting bosons in a Harper- Hofstadter optical-lattice ladder, and discuss potential experimental error sources. The highly flexible protocol can be used with both hard-core and soft-core bosons as well as fermions, is easily extendable to more general observables like current-current correlations, and applies to other setups beyond cold atoms as we exemplify for the trapped-ion platform.