Quantum Optics Theory of Electronic Noise in Coherent Conductors

We consider the electromagnetic field generated by a coherent conductor in which electron transport is described quantum mechanically. We obtain an input-output relation linking the quantum current in the conductor to the measured electromagnetic field. This allows us to compute the outcome of measurements on the field in terms of the statistical properties of the current. We moreover show how under ac bias the conductor acts as a tunable medium for the field, allowing for the generation of single- and two-mode squeezing through fermionic reservoir engineering. These results explain the recently observed squeezing using normal tunnel junctions [G. Gasse et al., Phys. Rev. Lett. 111, 136601 (2013); J.-C. Forgues et al., Phys. Rev. Lett. 114, 130403 (2015)].