[Paper Review] Radio-Frequency Manipulation of State Populations in an Entangled Fluorine-Muon-Fluorine System

David P. Billington, Edward A. Riordan+8 more|arXiv (Cornell University)|Jan 1, 2022

Muon and positron interactions and applications24 references3 citations

TL;DR

This study demonstrates radio-frequency (RF) manipulation of state populations in entangled fluorine-muon-fluorine (F–µ–F) spin states within single-crystal LiY0.95Ho0.05F4. By applying continuous RF magnetic fields resonant with the energy splitting between entangled spin eigenstates, the researchers experimentally control muon spin polarization evolution, confirming coherent population transfer via a semiclassical model of dipole-coupled spins. The key contribution is the first experimental demonstration of spectroscopic control over entangled muon-spin states using RF excitation.

ABSTRACT

Entangled spin states are created by implanting muons into single crystal LiY0.95Ho0.05F4 to form a cluster of correlated, dipole-coupled local magnetic moments. The resulting states have well-defined energy levels allowing experimental manipulation of the state populations by electromagnetic excitation. Experimental control of the evolution of the muon spin polarization is demonstrated through application of continuous, radio-frequency magnetic excitation fields. A semiclassical model of quantum, dipole-coupled spins interacting with a classical, oscillating magnetic field accounts for the muon spin evolution. On application of the excitation field, this model shows how changes in the state populations lead to the experimentally observed effects, thus enabling a spectroscopic probe of entangled spin states with muons.

Motivation & Objective

• To experimentally demonstrate control over state populations in entangled F–µ–F spin systems using continuous RF excitation.
• To validate a semiclassical model of dipole-coupled spins under oscillating RF fields as a framework for understanding muon spin evolution.
• To show that the F–µ–F system remains effectively isolated from external environmental decoherence during RF manipulation.
• To establish a proof-of-principle method for spectroscopic probing of entangled quantum states using muon spin relaxation (µ+SR) with RF excitation.

Proposed method

• Implanted 100% spin-polarized muons into single-crystal LiY0.95Ho0.05F4 to form F–µ–F complexes with entangled spin states.
• Applied continuous radio-frequency magnetic fields at frequencies near the energy splitting between entangled eigenstates (550 kHz and 825 kHz).
• Measured time-dependent muon spin polarization via muon spin relaxation (µ+SR) to track population dynamics.
• Used a semiclassical model of three coupled spin-1/2 systems (µ+ and two F− nuclei) interacting with a classical oscillating RF field.
• Fitted experimental data using a differential evolution algorithm to extract coupling strength (grel), driving frequency (ωc), and detuning (frel) parameters.
• Diagonalized the magnetic dipole Hamiltonian to identify the eight doubly-degenerate eigenstates, including separable and entangled configurations.

Experimental results

Research questions

• RQ1 Can continuous RF excitation be used to coherently manipulate population distributions among entangled F–µ–F spin states?
• RQ2 To what extent does the F–µ–F system remain isolated from environmental decoherence during RF excitation?
• RQ3 How well does a semiclassical model of dipole-coupled spins under classical RF fields reproduce the observed muon spin polarization dynamics?
• RQ4 What is the role of the F1–F2 and local Li2F2 interactions in preserving the nonseparable (entangled) character of the eigenstates under RF excitation?
• RQ5 Can RF-µ+SR be used as a spectroscopic tool to probe the energy level structure of entangled spin systems?

Key findings

• Continuous RF excitation at 550 kHz induced measurable changes in muon spin polarization dynamics, confirming coherent population transfer between entangled F–µ–F states.
• The experimental data were well-fit by a semiclassical model with a reduced chi-squared value (χ²_red) evaluated up to 12.5 µs, indicating good agreement between theory and experiment.
• The model successfully reproduced the observed oscillatory behavior of µ+ spin polarization under RF excitation, validating the theoretical framework for dipole-coupled spin systems.
• Eigenstates |3⟩, |4⟩, |7⟩, and |8⟩ were confirmed as nonseparable (entangled), maintaining their entangled character even under weak perturbations from F1–F2 and Li2F2 interactions.
• The F–µ–F system exhibited robust isolation from external environmental dephasing, as evidenced by sustained coherence and reproducible RF-induced dynamics.
• The study demonstrated that RF-µ+SR can be used as a spectroscopic probe of entangled spin states, opening new avenues for quantum state engineering and characterization.