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arXiv:1209.1226 · New Journal of Physics

Reverse quantum state engineering using electronic feedback loops

Gerold Kießlich, Clive Emary, Gernot Schaller, Tobias Brandes

Published Dec 31, 2012• 16 citations
arXivHTMLPDF

Abstract

We propose an all-electronic technique to manipulate and control interacting quantum systems by unitary single-jump feedback conditioned on the outcome of a capacitively coupled electrometer and, in particular, a single-electron transistor. We provide a general scheme for stabilizing pure states in the quantum system and use an effective Hamiltonian method for the quantum master equation to elaborate on the nature of stabilizable states and the conditions under which state purification can be achieved. The state engineering within the quantum feedback scheme is shown to be linked with the solution of an inverse eigenvalue problem. Two applications of the feedback scheme are presented in detail: (i) stabilization of delocalized pure states in a single charge qubit and (ii) entanglement stabilization in two coupled charge qubits. In the latter example, we demonstrate the stabilization of a maximally entangled Bell state for certain detector positions and local feedback operations.

DOI
10.1088/1367-2630/14/12/123036

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We propose an all-electronic technique to manipulate and control interacting quantum systems by unitary single-jump feedback conditioned on the outcome of a capacitively coupled electrometer and, in particular, a single-electron transistor. We provide a general scheme for stabilizing pure states in the quantum system and use an effective Hamiltonian method for the quantum master equation to elaborate on the nature of stabilizable states and the conditions under which state purification can be achieved. The state engineering within the quantum feedback scheme is shown to be linked with the solution of an inverse eigenvalue problem. Two applications of the feedback scheme are presented in detail: (i) stabilization of delocalized pure states in a single charge qubit and (ii) entanglement stabilization in two coupled charge qubits. In the latter example, we demonstrate the stabilization of a maximally entangled Bell state for certain detector positions and local feedback operations.
We propose the manipulation of an isolated qubit by a simple instantaneous closed-loop feedback scheme in which a time-dependent electronic detector current is directly back-coupled into qubit parameters. As a specific detector model, we employ a capacitively coupled single-electron transistor. We demonstrate the stabilization of pure delocalized qubit states above a critical detector-qubit coupling. This electronic purification is independent of the initial qubit state and is accomplished after few electron jumps through the detector. Our simple scheme can be used for the efficient and robust initialization of solid-state qubits in quantum computational algorithms at arbitrary temperatures.
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.
In the context of a charge qubit under continuous monitoring by a single electron transistor, we propose an unraveling of the generalized quantum Markovian master equation into an ensemble of individual quantum trajectories for stochastic point process. A suboptimal feedback algorism is implemented into individual quantum trajectories to protect a desired pure state. Coherent oscillations of the charge qubit could be maintained in principle for an arbitrarily long time in case of sufficient feedback strength. The effectiveness of the feedback control is also reflected in the detector's noise spectrum. The signal-to-noise ratio rises significantly with increasing feedback strength such that it could even exceed the Korotkov-Averin bound in quantum measurement, manifesting almost ideal quantum coherent oscillations of the qubit. The proposed unraveling and feedback protocol may open up the prospect to sustain ideal coherent oscillations of a charge qubit in quantum computation algorithms.
Feedback control in open quantum dynamics is crucial for the advancement of various coherent platforms. However, currently only a handful of feedback master equations exist in the literature, which are restricted to specific types of feedback. In this letter we first introduce a unifying framework, based on a single general equation, that describes all possible feedback schemes in sequentially (and continuously) measured systems, and from which all previous results follow. Next, we specialize it to the case of quantum jumps and introduce a new type of feedback based on the channel of the last detected jump, as well as the time elapsed since it occurred. Our description is experimentally grounded, and naturally allows for the introduction of realistic effects, such as time-delays in the feedback loop. We illustrate our results with two time-dependent feedback protocols conditioned on quantum-jump detections: one achieving population inversion of a two-level system against a thermal bath, and another enabling real-time reversal of quantum transitions, both admitting steady-state solutions.
As a specific trait of quantum mechanics, quantum superposition is exploited in many applications such as quantum computation. This paper proposes a feedback scheme to stabilize the desired quantum superposition states. To this aim, a new factorization is derived for the stochastic master equation of a quantum system which is driven by the field in the superposition of coherent states. Then, a feedback scheme is proposed, which consists of a quantum system driven by the field in the superposition of coherent states and a classical feedback channel proportional to the observations of a Homodyne detector. Afterward, the quantum filter of the closed loop system is attained using the SLH framework. Finally, the factorization of the closed loop quantum filter is obtained and the control law is calculated such that the proposed factorization satisfies the stabilization condition. Finally, as an example, the control method is simulated for a two-level atom and the stabilization of the superposition states is achieved.
Feedback control is expected to considerably protect quantum states against decoherence caused by interaction between the system and environment. Especially, Markovian feedback scheme developed by Wiseman can modify the properties of decoherence and eventually recover the purity of the steady state of the corresponding master equation. This paper provides a condition for which the modified master equation has a pure steady state. By applying this condition to a two-qubit system, we obtain a complete parametrization of the feedback Hamiltonian such that the steady state becomes a maximally entangled state.