Probing Entangled States of the Nuclear-Electronic Quantum Magnet LiHoF4

Two objects are entangled when their quantum mechanical wavefunctions cannot be written in a separable product form. Entangling dissimilar quantum objects, or hybridization, has been suggested as a promising route to efficient quantum information processors, but mostly realized on a limited scale. Hybrid nuclear-electronic many-body systems remain a largely unexplored challenge to both experiments and theories. The prototypical transverse-field Ising ferromagnet LiHoF4 is an ideal platform to address this issue. The Ising model is considered as an archetype both for the investigation of quantum criticality and for the evaluation of quantum simulators. The hyperfine coupling strength of a Ho3+ ion is exceptionally large, promoting a strong hybridization or entanglement between the nuclear and electronic moments. The magnetic coupling between the Ho3+ ions that leads to ferromagnetic ordering is predominantly through long-range dipole interactions, while nearest-neighbor exchange interaction is negligibly weak. Applying a transverse field induces a zero temperature quantum phase transition driven by quantum fluctuations. Altogether LiHoF4 represents a unique nuclear-electronic quantummagnet, whose wavefunctions can be readily obtained by diagonalizing the Hamiltonian using the mean-field approximation. In this thesis we develop an experimental scheme allowing us to quantify hybridized nuclear-electronic states in the model transverse field Ising system LiHoF4. Using magnetic resonance the field and temperature evolution of the nuclear-electronic states are successfully traced across the whole phase diagram. We develop a theoretical framework based onmean-field calculations and linear response theory. Our experimental observation of the hybridization is remarkably well reproduced by the calculations based on parameters obtained from experiments probing three orders of magnitude higher energies. Thus armed, we find that the calculated entanglement entropy shows a peak at the quantum phase transition. This raises the tantalizing possibility that electronic entanglement is encoded onto the nuclear-electronic states, which presents an interesting avenue towards experimental probes of many-body entanglement.