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Conference on Lasers and Electro-Optics

Optimal purification of a spin ensemble by quantum-algorithmic feedback

Urs Haeusler, Daniel M. Jackson, Leon Zaporski, Jonathan H. Bodey, Noah Shofer, Edmund Clarke, Maxime Hugues, Mete Atatüre, Claire Le Gall, Dorian A. Gangloff

Published Jan 1, 2022• 0 citations
Publisher

Abstract

We present a coherent quantum feedback algorithm to purify a mesoscopic spin ensemble at the ultimate level of a single spin. Applying it to a quantum dot narrowed nuclear-spin fluctuations by two orders of magnitude.
DOI
10.1364/cleo_qels.2022.fm4d.6

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Purifying a high-temperature ensemble of quantum particles toward a known state is a key requirement to exploit quantum many-body effects.An alternative to passive cooling, which brings a system to its ground state, is active feedback, which stabilizes the system at a chosen target state.This alternative, if realized, offers additional control capabilities for the design of quantum states.Here we present a feedback algorithm applied to a quantum system, which is capable of stabilizing the collective state of an ensemble from its maximum entropy state to the limit of single quantum fluctuations.Our algorithmic approach maximizes the rate of state purification given the system's physical constants; thus it remains the optimal feedback approach even in the presence of dissipation and disorder.We test experimentally the robustness of this feedback on the highly inhomogeneous nuclear-spin ensemble of a semiconductor quantum dot, reducing nuclear-spin fluctuations 83-fold, down to 5.7(2) spin macrostates.Simulations demonstrate that without system-specific inhomogeneities, our algorithm can purify the system down to single-spin fluctuations.Further, we exploit our algorithmic approach to tailor nontrivial nuclear-spin distributions that go beyond simple polarization, including weighted bimodality and latticed multistability.This control is a precursor toward quantum-correlated macrostates, which an extended version of our algorithm could generate in homogeneous systems.
Purifying a high-temperature ensemble of quantum particles towards a known state is a key requirement to exploit quantum many-body effects. An alternative to passive cooling, which brings a system to its ground state, is based on feedback to stabilise the system actively around a target state. This alternative, if realised, offers additional control capabilities for the design of quantum states. Here we present a quantum feedback algorithm capable of stabilising the collective state of an ensemble from an infinite-temperature state to the limit of single quanta. We implement this on ~50,000 nuclei in a semiconductor quantum dot, and show that the nuclear-spin fluctuations are reduced 83-fold down to 10 spin macrostates. While our algorithm can purify a single macrostate, system-specific inhomogeneities prevent reaching this limit. Our feedback algorithm further engineers classically correlated ensemble states via macrostate tuning, weighted bimodality, and latticed multistability, constituting a pre-cursor towards quantum-correlated macrostates.
We describe a method for precise estimation of the polarization of a mesoscopic spin ensemble by using its coupling to a single two-level system. Our approach requires a minimal number of measurements on the two-level system for a given measurement precision. We consider the application of this method to the case of nuclear-spin ensemble defined by a single electron-charged quantum dot: we show that decreasing the electron spin dephasing due to nuclei and increasing the fidelity of nuclear-spin-based quantum memory could be within the reach of present day experiments.
A controlled quantum system can alter its environment by feedback, leading to reduced-entropy states of the environment and to improved system coherence. Here, using a quantum-dot electron spin as a control and probe, we prepare the quantum-dot nuclei under the feedback of coherent population trapping and observe their evolution from a thermal to a reduced-entropy state, with the immediate consequence of extended qubit coherence. Via Ramsey interferometry on the electron spin, we directly access the nuclear distribution following its preparation and measure the emergence and decay of correlations within the nuclear ensemble. Under optimal feedback, the inhomogeneous dephasing time of the electron, T_{2}^{*}, is extended by an order of magnitude to 39 ns. Our results can be readily exploited in quantum information protocols utilizing spin-photon entanglement and represent a step towards creating quantum many-body states in a mesoscopic nuclear-spin ensemble.