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

Abstract

The question of which laws govern electricity in mesoscopic circuits is a fundamental matter that also has direct implications for the quantum engineering of nanoelectronic devices. 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, known as environmental Coulomb blockade, results from the granularity of charge transfers across the coherent conductor 1 . Although extensively studied for a tunnel junction in a linear circuit 2-5 , it is only fully understood for arbitrary short coherent conductors in the limit of small circuit impedances and small conductance reduction 6-8 . 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 significant deviations from calculations performed in the weak back-action framework 6,7 , and is in agreement with recent theoretical results 9,10 . Based on these measurements, we propose a generalized expression for the conductance of an arbitrary quantum channel embedded in a linear circuit.The transport properties of a coherent conductor depend on the surrounding circuit. First, electronic quantum interferences blend the conductor with its vicinity, resulting in a different coherent conductor (see for example ref. 11). Furthermore, the circuit backaction modifies the full counting statistics of charge transfers across coherent conductors 9,10,12 . This mechanism, which is our concern here, results in violations of the classical impedance composition laws even for distinct circuit elements, separated by more than the electronic phase coherence length. The present experimental work investigates the strong circuit back-action on the conductance of an arbitrary electronic quantum channel.The circuit back-action originates from the granularity in the transfer of charges across a coherent conductor. As a result of Coulomb interactions, an excitation by these current pulses of the circuit electromagnetic modes is possible, which impedes the charge transfers and therefore reduces the conductance of the coherent conductor. This environmental Coulomb blockade is best understood in the limit of a tunnel junction embedded in a circuit of very high series impedance, which is of particular importance for single-electron devices 13 . In this limit, each time an electron tunnels across the junction, its charge stays a very long time on the capacitor C inherent to the junction's geometry. Consequently, a charging energy e 2 /2C has to be paid. As this energy is not available at low The bottom-left metal split gate (yellow) is used to tune the studied QPC. The outer-edge channel, shown as a red line, is partially transmitted at the QPC. A small ohmic contact labelled (red) is used to co...

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