Strong back-action of a linear circuit on a single electronic quantum channel

What are the quantum laws of electricity in mesoscopic circuits? This very fundamental question has also direct implications for the quantum engineering of nanoelectronic devices. Indeed, when a quantum coherent conductor is inserted into a circuit, its transport properties are modified. In particular, its conductance is reduced because of the circuit back-action. This phenomenon, called environmental Coulomb blockade, results from the granularity of charge transfers across the coherent conductor. Although extensively studied for a tunnel junction in a linear circuit, it is only fully understood for arbitrary short coherent conductors in the limit of small circuit impedances and small conductance reduction. Here, we investigate experimentally the strong back-action regime, with a conductance reduction of up to 90%. This is achieved by embedding a single quantum channel of tunable transmission in an adjustable on-chip circuit of impedance comparable to the resistance quantum $R_K=h/e^2$ at microwave frequencies. The experiment reveals important deviations from calculations performed in the weak back-action framework, and matches with recent theoretical results. From these measurements, we propose a generalized expression for the conductance of an arbitrary quantum channel embedded in a linear circuit.