Two objects are entangled when their quantum mechanical wavefunctions cannot be written in a separable product form. Singlet states of two particle-spins or photon-polarizations are among the simplest examples. 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. Here we develop an experimental scheme allowing us to quantify hybridized nuclear-electronic states in the model transverse field Ising system LiHoF$_4$. 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.
Two objects are entangled when their quantum mechanical wavefunctions cannot be written in a separable product form. Singlet states of two particle-spins or photon-polarizations are among the simplest examples. 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. Here we develop an experimental scheme allowing us to quantify hybridized nuclear-electronic states in the model transverse field Ising system LiHoF4. 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.
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 Ho ion is exceptionally large, promoting a strong hybridization or entanglement between the nuclear and electronic moments. The magnetic coupling between the Ho 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 quantum magnet, whose wavefunctions can be readily obtained by diagonalizing the Hamiltonian using the mean-field approximation. In this thesis we develop an experimental setup to probe the entangled nuclear-electronic states in a 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 on mean-field calculations which provides close agreement with the experimental observations. Having established experimentally that the mean-field wavefunctions are an excellent approximation of the actual wavefunction, we used them to calculate the ground-state entanglement entropy between the electronic and nuclear magnetic moments. We find that the entanglement entropy between the nuclear and electronic moments exhibits a peak at the quantum phase transition. This suggests that the electronic entanglement is encoded onto each nuclear-electronic state. Our results pave the way for new theoretical and experimental investigations of quantum entanglement.
Quantum phase transitions in spin systems are supposed to be accompanied by a soft collective mode, which has not been seen in experiments. Here, we directly measure the low energy excitation modes of a well-known realization of the Ising model in transverse field, LiHoF4, using microwave spectroscopy techniques to probe energies well below what is accessible via neutron scattering experiments. Instead of the single excitation expected for a simple quantum Ising system, we find and characterize a remarkable array of `electronuclear' modes, arising from coupling of the spin-1/2 Ising electronic spins to a bath of spin-7/2 Ho nuclear spins. The lowest-lying electronuclear mode softens at the approach to the quantum critical point from below and above, a softening that can be quenched with the application of a longitudinal magnetic field. The electronuclear mode structure has direct implications for the Ising systems that serve as the building blocks of adiabatic quantum computers and quantum annealers.
Background: Entanglement plays a central role in a diverse array of increasingly important research areas, including quantum computation, simulation, measurement, sensing, and communication. Extensive suites of investigations have been performed to better understand entanglement in atomic and molecular quantum many-body systems, while the exploration of entanglement in the structure of nuclei and their reactions is presently in its infancy.Purpose: The goal of this work is to begin investigating the entanglement properties of nuclei from first-principles nuclear many-body calculations. We attempt to identify common features and emergent structures of entanglement that could ultimately lead to new and natural many-body schemes. With an eye toward quantum accelerators in future hybrid-supercomputers, criteria for partitioning nuclear many-body calculations into quantum and classical components may provide advantages in future large-scale computations. Along the way we look for explanations of the relative success of phenomenological models such as the nuclear shell model, and for better ways to match to low-energy nuclear effective field theories and lattice QCD calculations to nuclear many-body techniques that are based upon entanglement.Method: We explore the entanglement between single-particle states in 4He and 6He. The patterns of entanglement emerging from different single-particle bases are compared, and possible links with the convergence of observables are explored, in particular, ground-state energies. The nuclear wave functions are obtained by performing active-space no-core configuration-interaction calculations using a two-body nucleon-nucleon interaction derived from chiral effective field theory. Entanglement measures within single-particle bases exhibiting different degrees of complexity are determined, in particular, harmonic oscillator (HO), Hartree-Fock (HF), natural (NAT) and variational natural (VNAT) bases. Specifically, single-orbital entanglement entropy, two-orbital mutual information, and negativity are studied.Results: The entanglement structures in 4He and 6He are found to be more localized within NAT and VNAT bases than within a HO basis for the optimal HO parameters we have worked with. In particular a core-valence structure clearly emerges from the full no-core calculation of 6He. The two-nucleon mutual information shows that the VNAT basis, which typically exhibits good convergence properties, effectively decouples the active and inactive spaces.Conclusions: Measures of one- and two-nucleon entanglement are found to be useful in analyzing the structure of nuclear wave functions, in particular the efficacy of basis states, and may provide useful metrics toward developing more efficient schemes for ab initio computations of the structure and reactions of nuclei, and quantum many-body systems more generally.
In this work, we have been working on the concept of quantum entanglement. At first, we studied the theory of entanglement in its characterization and measurement, introducing a new scheme for detection of entanglement. The new approach links molecular-spin entities involving nuclear spins to quantum computing as more appropriate physical systems of interest. Then, we continued with the realization of entanglement in experiments. NMR has been the first choice due to its well approved advantages for quantum computing. NMR, however, has not been an appropriate system for demonstrating entangled states. Through a mathematical proof, NMR with low spin polarization has been invalidated for true implementations of non-local quantum algorithms, particularly supserdense coding. The point is that high spin polarization is inevitably required to acquire entanglement while in the current NMR it has been a formidable task to get highly polarized nuclear spins. In order to acquire high spin polarization, introducing electron spins can be much effective because of its three-order-of-magnitude larger gyromagnetic ratio compared to nuclear spins. Electron Nuclear DOuble Resonance (ENDOR) is spin manipulation technology that enables us to deal with both electron and nuclear spins. Thus, in this context, it can be more appropriate device for quantum computing. We emphasize that (pseudo)entanglement and interconversion between the entangled states have been realized with ENDOR on extremely stable organic molecular-spin entities. The required experimental conditions to obtain true quantum entanglement are also discussed. The appropriate entanglement witness for the corresponding ensemble quantum computing is introduced and examined.
Quantum entanglement is commonly assumed to be a central resource for quantum computing and quantum simulation.Nonetheless, the capability to detect it in many-body systems is severely limited by the absence of sufficiently scalable and flexible certification tools.This issue is particularly critical in situations where the structure of entanglement is a priori unknown, and where one cannot rely on existing entanglement witnesses.Here, we implement a scheme in which the knowledge of the mean value of arbitrary observables can be used to probe multipartite entanglement in a scalable, certified, and systematic manner.Specifically, we rely on positive semidefinite conditions, independent of partial-transpositionbased criteria, necessarily obeyed if the data can be reproduced by a separable state.The violation of any of these conditions yields a specific entanglement witness, tailored to the data of interest, revealing the salient features of the data which are impossible to reproduce without entanglement.We validate this approach by probing theoretical many-body states of several hundreds of qubits relevant to existing experiments: a single-particle quench in a one-dimensional XX chain; a many-body quench in a two-dimensional XX model with 1/r 3 interactions; and thermal equilibrium states of Heisenberg and transverse-field Ising chains.In all cases, these investigations have led us to discover new entanglement witnesses, some of which could be characterized analytically, generalizing existing results in the literature.In summary, our paper introduces a flexible data-driven entanglement detection technique for uncharacterized quantum many-body states, of immediate relevance to experiments in a quantum advantage regime.
Quantifying multipartite entanglement in quantum many-body systems and hybrid quantum computing architectures is a fundamental yet challenging task. In recent years, thermodynamic quantities such as the maximum extractable work from an isolated system (the ergotropy) have allowed for entanglement measures that are operationally more accessible. However, these measures can be restrictive when applied to systems governed by Hamiltonians with strong collective or interparticle interactions. Motivated by advances in quantum simulators, we propose a framework that circumvents these restrictions by evaluating global and local ergotropy either through controlled quenching of interactions or by measuring suitable local observables only. We show that this formalism allows us to correctly estimate genuine multipartite entanglement in both stationary and time-evolved states of systems with strong interactions, including parametrized quantum states simulated on a quantum circuit with varying circuit depth and noise. We demonstrate its applicability to realistic physical models, namely, the Tavis-Cummings model, the three-level Dicke model, and the transverse-field Ising model, highlighting its potential as a versatile tool for characterizing entanglement in near-term quantum simulators.