Controlled Magnetic Fields Unlock Entangled States for Quantum Technologies

Scientists are developing novel techniques utilising magnetic resonance to advance both quantum computing and the precise measurement of atomic and molecular nuclear moments. Zhichen Liu, Sunghyun Kim, and Richard A. Klemm, working at the Department of Physics, University of Central Florida, and in collaboration with the U. S. Air Force Research Laboratory, Wright-Patterson Air Force Base, have derived exact nuclear- and electronic-spin wave functions for systems exposed to rotating magnetic fields. These solutions facilitate controlled transitions between entangled states, potentially enabling molecules to function as qubits, and simultaneously offer a pathway to highly accurate nuclear moment measurements. The research addresses inconsistencies in existing hyperfine measurements, specifically for 133Cs, and proposes experiments capable of determining all seven of its nuclear moments with unprecedented precision, representing a significant step forward in both fundamental physics and quantum technology.

Scientists have unlocked a new level of precision in controlling and measuring the fundamental properties of atomic nuclei, paving the way for advancements in both quantum computing and high-precision spectroscopy. This work details a method for generating magnetic fields with a specific rotating wave form, H(t) = H0 z + H1[x cos(ωt) + y sin(ωt)], allowing for controlled transitions between entangled states within atoms and molecules. By manipulating these states, researchers demonstrate a pathway to utilise atoms or molecules as functional quantum bits, the building blocks of quantum computers, and the ability to precisely control nuclear spins opens possibilities for designing more stable and efficient quantum systems. The research centres on deriving exact wave functions describing the behaviour of nuclear and electronic spins, providing a means to accurately measure nuclear moments, intrinsic properties of atomic nuclei that govern their interactions with magnetic fields. The team focused on developing a technique applicable to a range of atoms and molecules, providing examples using nitrogen-14, lithium-7, and caesium-133, and crucially addresses long-standing inconsistencies in measurements of the nuclear moments of caesium-133, an element with seven nuclear moments. Existing measurements of the three lowest moments have yielded conflicting results, and this new approach offers a route to determine all seven with unprecedented accuracy, stemming from a refined understanding of how nuclei with varying spin quantum numbers, a measure of their intrinsic angular momentum, interact with magnetic fields. Nuclei with higher spin values possess more complex magnetic properties, including magnetic dipole, electric quadrupole, and even higher-order moments, and the research demonstrates that by carefully designing experiments using nuclear magnetic resonance (NMR) or electron paramagnetic resonance (EPR) techniques, these moments can be measured with far greater precision than previously possible, offering insights into the fundamental structure of matter and opening doors to more sophisticated quantum technologies. A 72-qubit superconducting processor underpins the methodology, allowing for the derivation of exact nuclear- and electronic-spin wave functions crucial for controlling transitions between entangled states within molecules. The research establishes closed-form expressions for these wave functions, facilitating precise NMR and EPR measurements of nuclear moments in molecules, achieved by subjecting the initial Hamiltonian to a series of rotations, first around the z-axis using the operators Ix and Iy, then further manipulated through a process mirroring a simple harmonic oscillator. This transformation simplifies the Schrödinger equation, allowing for the isolation of a time-independent effective Hamiltonian, Heff,n, and deliberately avoids approximations common in hyperfine spectroscopy, instead focusing on obtaining exact solutions for the energies of the nuclear moment series. A key innovation lies in the diagonalisation of the effective Hamiltonian by rotating the nuclear spin about the y-axis by an angle βn, aligning it with the z-axis, achieved by strategically inserting identity matrices between exponential operators, enabling the expansion and subsequent summation of a power series. The resulting wave function, |ψ0 n(t)⟩, is expressed in a form that facilitates accurate calculations at and near resonance conditions, offering a route to measuring all seven nuclear moments of 133Cs with enhanced precision, given the inconsistencies present in existing hyperfine measurements of this isotope. Calculations reveal that the probability amplitudes, P1/2(τ) and P−1/2(τ), for I = 1/2 exhibit distinct behaviours over time, τ, ranging from 0 to 1, under varying frequencies, ω/ωn0. Specifically, for ω/ωn0 = 0.95, 0.99, and 1.0, the plots of these amplitudes demonstrate oscillatory patterns dependent on the initial conditions; when C1/2 = C−1/2 = 1/√2, the amplitudes oscillate with a clear phase relationship, while setting C1/2 = 1 and C−1/2 = 0 results in a different oscillatory profile. These results, which also apply to J = 1/2 by substituting ωe0 for ωn0 and Dm for Cm, provide detailed insight into the time evolution of the spin states. Further analysis extends to I = 1, where the probabilities P1(τ), P0(τ), and P−1(τ) are calculated under the same frequency conditions, and with initial conditions C0 = C−1 = e−iπ/4C1 = 1/√3, the probability distributions show a complex interplay of peaks and troughs, altered significantly by changing the initial conditions to C1 = 1 and C0 = C−1 = 0. These observations are consistent across both nuclear and electronic spin systems, with appropriate substitutions of parameters. For I = 3/2, the study presents plots of P3/2(τ), P1/2(τ), P−1/2(τ), and P−3/2(τ), again for τ ranging from 0 to 1 and the specified frequencies, with initial conditions of C−3/2 = C−1/2 = C1/2 = e−iπ/4C3/2 = 1/2 yielding a characteristic probability distribution, and C3/2 = 1 and Cm = 0 for m = 3/2 producing a markedly different pattern. The behaviour remains consistent when applied to J = 3/2, demonstrating the generality of the derived expressions. Finally, for I = 2, the probabilities P2(τ), P1(τ), P0(τ), P−1(τ), and P−2(τ) are plotted, revealing intricate probability distributions influenced by both time and frequency, with the specific shapes of these curves determined by the chosen initial conditions, further emphasizing the importance of precise state preparation in controlling the system’s evolution. Scientists have long sought increasingly precise methods for probing the interiors of atomic nuclei, and this work represents an advance in that endeavour. The challenge lies in the subtle interplay of forces within the nucleus, and the difficulty of isolating and measuring the tiny magnetic moments that reveal its structure. Existing techniques often struggle with inconsistencies, particularly when attempting to determine the full suite of nuclear moments for complex nuclei, and this research offers a pathway to circumvent those limitations by leveraging controlled transitions between entangled states within molecules. The beauty of this approach is its potential to transform standard spectroscopic techniques, NMR and EPR, into high-precision tools for nuclear metrology, integrating with established experimental frameworks rather than requiring exotic setups or painstaking atomic-level control. This accessibility could broaden the scope of nuclear moment measurements, extending beyond the few isotopes and states that are currently well-characterised, with implications for refining our understanding of nuclear structure and testing the limits of theoretical models. However, the practical realisation of these measurements will depend on overcoming several hurdles, including maintaining precise control over the applied magnetic fields and accurately disentangling the various contributions to the observed spectra, and the complexity of molecular systems introduces additional challenges in interpreting the results. Future work will likely focus on applying this technique to specific nuclei where existing data are contradictory, such as caesium-133, and on exploring its sensitivity to even more subtle nuclear properties like the magnetic octupole moment, potentially paving the way for a more complete and accurate map of the nuclear landscape.