Abstract We 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.
Abstract We 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.
We consider an external feedback control loop implementing the action of a Maxwell demon. Applying control actions that are conditioned on measurement outcomes, the demon may transport electrons against a bias voltage and thereby effectively converts information into electric power. While the underlying model---a feedback-controlled quantum dot that is coupled to two electronic leads---is well explored in the limit of small tunnel couplings, we can address the strong-coupling regime with a fermionic reaction-coordinate mapping. This exact mapping transforms the setup into a serial triple quantum dot coupled to two leads. We find that a continuous projective measurement of the central dot occupation would lead to a complete suppression of electronic transport due to the quantum Zeno effect. In contrast, by using a microscopic detector model we can implement a weak measurement, which allows for closure of the control loop without transport blockade. Then, in the weak-coupling regime, the energy flows associated with the feedback loop are negligible, and dominantly the information gained in the measurement induces a bound for the generated electric power. In the strong coupling limit, the protocol may require more energy for operating the control loop than electric power produced, such that the whole device is no longer information dominated and can thus not be interpreted as a Maxwell demon.
Abstract In a closed‐loop controlled single‐electron transistor (SET) the optimal feedback response is investigated, leading to a maximum suppression of shot‐noise. Using a coupled quantum point contact (QPC) charge detector, the tunneling process is monitored in real‐time and the fluctuations are fed back periodically to the tunneling barriers of the SET. The feedback response is applied proportional to the deviation from the target number of average transferred electrons. This leads to a strong suppression and temporal saturation of the cumulants of the full counting statistics. For the optimal feedback response, the saturation value of second cumulant is found to be given by target number. Astonishingly, the feedback works robust even for target numbers much smaller than one.
The long-standing paradigm of Maxwell’s demon is till nowadays a frequently investigated issue, which still provides interesting insights into basic physical questions. Considering a single-electron transistor, where we implement a Maxwell demon by a piecewise-constant feedback protocol, we investigate quantum implications of the Maxwell demon. To this end, we harness a dynamical coarse-graining method, which provides a convenient and accurate description of the system dynamics even for high measurement rates. In doing so, we are able to investigate the Maxwell demon in a quantum-Zeno regime leading to transport blockade. We argue that there is a measurement rate providing an optimal performance. Moreover, we find that besides building up a chemical gradient, there can be also a regime where the feedback loop additionally extracts energy, which results from the energy non-conserving character of the projective measurement.
A metallic double-dot is measured with radio frequency reflectometry. Changes in the total electron number of the double-dot are determined via single electron tunnelling contributions to the complex electrical impedance. Electron counting experiments are performed by moni-toring the impedance, demonstrating operation of a single electron ammeter without the need for external charge detection. Single electron ammeters count each individual electron that passes. They enable the detec-tion of tiny (I < aA) currents;1 show the real-time dynamics of single electron tunnelling;2,3 and may be of use in metrology for the definition of the Ampere.4–8 These devices are made possible by high sensitivity, high bandwidth charge detection which can register the passage of an elec-tron through multiple island single electron devices.9 Typically the charge detector employed is the single electron transistor10 or quantum point contact,11–13 which may be operated in a radio-frequency impedance matching circuit to increase both bandwidth and sensitivity.14–16 In this Let-ter we show that use of external electrometry is unnecessary, simplifying the fabrication of a single electron ammeter. Rather, the internal tunnelling processes within a metallic double dot can be used to herald the passage of single electrons through the system, so the double dot acts as its own ∗To whom correspondence should be addressed 1 ar
One of the essential limitations for a physical realisation of topological-qubit based quantum computing is the problem of uncontrolled quasiparticle poisoning of the superconducting charge island. These quasiparticles have been previously reported as a known limiting factor in most of the superconducting architectures. To this end, we consider the importance of equilibrium quasiparticle poisoning in hybrid semiconducting-superconducting systems believed to be able to host Majoranas. We employed gate-based dispersive sensing by investigating a reflected radiofrequency (RF) signal from a resonator, which is capacitively coupled to one of the gate electrodes of the hybrid double dot realised in an InAs nanowire. This way, the quantum capacitance of the system can be probed, which in turn reveals charge tunnelling processes, and can be used as an indicator of single-electron tunnelling events. By operating the device in a so-called floating regime, where a double dot system is entirely decoupled from the leads, external non-equilibrium quasiparticle poisoning events can be exponentially suppressed. By appropriately tuning the chemical potentials on the quantum dot and the superconducting island, we attempt to scrutinise the dynamics of the quasiparticles innate to the superconductor. We investigated the dependence of quasiparticle tunnelling rates on the temperature of the system, as well as the applied RF power, as both are predicted to increase the average number of quasiparticles on the island. In both cases, we could find no observational proof of quasiparticle tunnelling events through the use of our measurement technique. We report an observation of a two-level resonator response, which we explain using a two-level fluctuator. Analysing telegraph measurements, we demonstrate the viability of the analysis tool, which allows us to determine the average occupation times of each state. In principle, for processes occurring at rates slower than the measurement frequency, this technique can be used to convert a\nrelatively faint difference between the “poisoned and unpoisoned state”, to the signal of the gate being on coulomb resonance versus on Coulomb blockade, which is a much clearer signal to distinguish. Both, the technique, as well as the expected rates of the physical processes within the island, are evaluated in the context of the experiment.
We consider the transport properties of a single-electron transistor consisting of a diffusive normal-metal island and superconducting electrodes. We show that the interplay of a dissipative impedance of the gate electrode, a weak magnetic field, and a charging energy of the island causes a suppression of the critical supercurrent of the transistor. When the device is voltage biased, pumping of single electrons can be achieved by a periodic modulation of the gate voltage. We derive the analytic expressions for the error rates and show that they are suppressed by the applied magnetic field.