Feedback‐charging a metallic island

Abstract

AbstractWe consider electronic transport through a single‐electron quantum dot that is tunnel‐coupled to an electronic lead and a metallic island. A background reservoir keeps the metallic island at a thermal state with the ambient temperature, while the charge accumulated on the island is reflected in a time‐dependent chemical potential. Without feedback, a current would flow through the system until the chemical potentials of island and lead are equilibrated. A feedback loop can be implemented by a quantum point contact detecting the dot state, classical processing of the result, and appropriate feedback actions on the electronic tunneling rates taken, with the objective to direct the current in a preferred direction. Since we directly take the detector counting statistics into account, this automatically includes measurement errors in the description. When mainly the rates are modified but hardly any energy is exchanged with the system, this feedback loop effectively implements a Maxwell demon, capable of transporting electrons against an electric bias and thereby charging the metallic island. Once the feedback protocol is stopped, the metallic island simply discharges. We find that a quantitative detector model may be useful for a realistic statistical description of feedback loops.Sketch of the model. The system (S) consists of a single‐electron transistor (SET) dot that can be occupied with at most a single electron. It is tunnel‐coupled to a lead (R) held at a fixed thermal equilibrium state and to a metallic island (L). The metallic island is held at a fixed temperature by an additional background reservoir (bg), with which it can exchange energy but no particles (shaded contact region). Its chemical potential would normally evolve until . A simple feedback loop can be implemented by measuring the state of the system with a quantum point contact (dt), classical signal processing (SP), and using the gate controls (GC) to obtain occupation‐dependent tunneling rates. With feedback active, it is possible to charge the island (). Expressions in brackets (green) denote abbreviations used in the paper.