Abstract
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.
- Received 29 October 2021
- Revised 7 March 2022
- Accepted 10 June 2022
DOI:https://doi.org/10.1103/PhysRevX.12.031014
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Quantum objects reveal their quantum properties if you cool them toward their energetic ground state. But even the best refrigerators—which cool a system by bringing it in contact with a cold reservoir—are not cold enough to reveal the quantum properties of some low-energy systems. An alternative is to actively engage with a complex quantum system via another simpler quantum system and direct the former toward a chosen quantum state with active stabilization. Here, we design and implement a new quantum algorithm to cool a spin system composed of about nuclei.
The nuclei live within a 10-nm-wide island of semiconductor—a quantum dot. To talk to the nuclei, we load the quantum dot with a single electron, which acts as a spin qubit over which we have a high degree of control. Our algorithm runs three operations on the electron qubit. First, the electron senses the nuclear state. Second, it corrects deviations from a target state by flipping one of the nuclei. Third, it is reset by connecting it to a cold optical bath, after which the algorithm is repeated to arrive at the target state. The state of the nuclei is then known to within one nuclear spin flip.
Taking this as the starting point, we show numerically that we can engineer exciting quantum states of the nuclei, such as a “Schrödinger kitten state,” in which the spins point up and down simultaneously. A future application is storing an electronic qubit state among the nuclei—a quantum memory.
