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Quantum Information and Measurement (QIM)

Optimal quantum feedback algorithm for spin ensemble purification

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

Published Jan 1, 2021• 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. Moreover our feedback can engineer classically correlated states extending over multiple modes.
DOI
10.1364/qim.2021.th2b.5

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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.
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.
Cold atomic ensembles and spinor Bose-Einstein condensates are potential candidates for quantum memories as they have long coherence times and can be coherently controlled. Unlike most candidates for quantum memories, which are genuine or effective single-particle systems, in atomic ensembles the quantum information is stored as a spin coherent state involving a very large number of atoms. A typical task with such ensembles is to drive the state towards a particular quantum state. While such quantum control methods are well developed for qubit systems, it is a nontrivial task to extend quantum control methods to the many-particle case. The objective of this work is to deterministically steer an arbitrary state of the atomic ensemble into a desired spin coherent state. To this end, we design our control law using stochastic stability theory, the quantum filtering theorem, and phase contrast imaging. We apply our control laws to different axes and show that it is possible to manipulate the atoms into different target states.
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.