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arXiv:1005.0018 · Physical Review Letters

Feedback Control of Quantum Transport

Tobias Brandes

Published Aug 5, 2010• 52 citations
arXivHTMLPDF

Abstract

The current through nanostructures like quantum dots can be stabilized by a classical feedback loop that continuously adjusts system parameters as a function of the number of tunnelled particles n. At large times, the feedback loop freezes the fluctuations of n, which leads to highly accurate, continuous single particle transfers. For the simplest case of feedback acting simultaneously on all system parameters, we show how to reconstruct the original full counting statistics from the frozen distribution.

DOI
10.1103/physrevlett.105.060602

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The current through nanostructures like quantum dots can be stabilized by a classical feedback loop that continuously adjusts system parameters as a function of the number of tunnelled particles n. At large times, the feedback loop freezes the fluctuations of n, which leads to highly accurate, continuous single particle transfers. For the simplest case of feedback acting simultaneously on all system parameters, we show how to reconstruct the original full counting statistics from the frozen distribution.
We propose a feedback control scheme for generating and stabilizing pure states of transport devices, such as charge qubits, under nonequilibrium conditions. The purification of the device state is conditioned on single electron jumps and leaves a clear signal in the full counting statistics which can be used to optimize control parameters. As an example of our control scheme, we are presenting the stabilization of pure transport states in a double-quantum-dot setup with the inclusion of phonon dephasing.
A controllable low noise current lies at the heart of high-precision measurements in quantum transport and metrology. While the previous research dealt with the suppression of noise in transport through a tunneling junction or a single quantum dot (QD) device, the present work investigates noise inhibition of a double quantum dot (DQD) transport system based on closed-loop feedback control. The unique advantage of a DQD device is that bidirectional transport at low bias can be measured by a nearby quantum point contact. However, the continuous monitoring of the DQD states inevitably leads to a measurement-induced dephasing. To appropriately characterize its transport properties in the presence of feedback action, we here develop a numerical method dubbed auxiliary density matrix approach, motivated by the hierarchical expansion of the moment-generating function in the hierarchy equations of motion [J. Cerrillo et al., Phys. Rev. B 94, 214308 (2016)]. This generic method has no restriction on the system structure and parameters and is able to evaluate the feedback current cumulants to an arbitrary order. It is revealed that the feedback control of the tunnel coupling between the two dots is the most effective to suppress the noise under various tunnel coupling configurations. The influence of interdot Coulomb interaction, measurement-induced dephasing, and finite time delay on feedback is also analyzed in detail.
Quantum Feedback Loop for Dynamical System Stability addresses the inherent challenges of stabilizing dynamic systems through traditional methods. This paper introduces a novel quantum-based feedback loop designed to continuously adapt to the system's internal state, thereby achieving a state of equilibrium. We propose a mechanism utilizing quantum measurement and entanglement to identify deviations from a target state and dynamically adjust system parameters. This approach offers a fundamentally new pathway to achieve robustness and adaptability in dynamical systems, potentially surpassing the limitations of classical stability analysis.
It is notoriously known that in contrast to the measure of classical macro systems, the quantum measurement will in general cause quantum state collapse. In this note, we will present some further results on stabilizing control of quantum systems with measurement being involved. To be precise, we will study the effects of the open-loop control and the feedback control in preparing an arbitrarily desired eigenstate of an effective Hamiltonian, respectively. For the open-loop control case, it is shown that no matter how to select the measurement channel, control channel and the control law, one cannot prepare all the eigenstates of the effective Hamiltonian with arbitrary high fidelity for all sufficient large time. While for the feedback case, we not only demonstrate how to select the measurement channel properly to achieve the control target, but also show if not, what cannot be done by the measurement-based feedback control.
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.