Quantum coherence can be preserved by exploiting topology, encoding information in global geometric properties that resist local perturbations. These properties depend on the trajectory of quantum operations and curvature in parameter space, offering a topology-based route to fault-tolerant quantum computation. While geometric phase interference (Berry phase) is widely studied to probe a system’s topology, its direct detection in 4f-based molecular magnets—promising qudit platforms—has remained elusive. We present a magneto-spectroscopic μSQUID-EPR approach to resolve tunnel splittings in the Gd-based molecular magnet [$^{160}$GdPc₂]⁻ (Pc = phthalocyanine). By irradiating single crystals with microwaves under transverse magnetic fields, we map the spin (S = 7/2) manifold and observe pronounced oscillations in tunnel splitting—a hallmark of quantum phase interference. These oscillations reveal topological quenching and higher-order anisotropy, underscoring the role of topology in 4f systems and opening pathways toward holonomic quantum computation.
Quantum coherence can be preserved by exploiting topology, encoding information in global geometric properties that resist local perturbations. These properties depend on the trajectory of quantum operations and curvature in parameter space, offering a topology-based route to fault-tolerant quantum computation. While geometric phase interference (Berry phase) is widely studied to probe a system’s topology, its direct detection in 4f-based molecular magnets—promising qudit platforms—has remained elusive. We present a magneto-spectroscopic μSQUID-EPR approach to resolve tunnel splittings in the Gd-based molecular magnet [160GdPc₂]⁻ (Pc = phthalocyanine). By irradiating single crystals with microwaves under transverse magnetic fields, we map the spin (S = 7/2) manifold and observe pronounced oscillations in tunnel splitting—a hallmark of quantum phase interference. These oscillations reveal topological quenching and higher-order anisotropy, underscoring the role of topology in 4f systems and opening pathways toward holonomic quantum computation.
Abstract Preservation of quantum coherence can be achieved by harnessing a system’s topology—encoding information in global geometric properties of quantum states insensitive to local perturbations. The robustness arises as certain geometric properties depend only on the trajectory of a quantum operation and the curvature in the controlled-parameter space, rather than on details of the system’s dynamics, thereby offering a topology-based framework for fault-tolerant quantum computation. To probe a system’s topology, geometric phase interference (Berry phase) has been studied in various optical systems and condensed matter physics, including molecular magnets (MMs). However, its direct detection in 4f-based MMs—prospective qudit (multi-level qubits) platforms—has remained elusive due to large tunnel gaps and environmental coupling. Here, we report a magneto-spectroscopic approach: the μSQUID-EPR technique, to directly resolve tunnel splittings in the 160 Gd-based MM [ 160 GdPc₂]⁻ (Pc = phthalocyanine). By irradiating single crystals with microwaves under transverse magnetic fields, we map the spin manifold and report the first direct observation of pronounced oscillations in the tunnel splitting—a signature of quantum phase interference. These oscillations reveal topological quenching of tunnelling and highlight the role of fourth-order transverse anisotropy in shaping the spin orientation space. Our findings uncover a nontrivial topological structure in 4f-MMs, opening possibilities towards holonomic quantum computation.
Topologically ordered phase has emerged as one of most exciting concepts that not only broadens our understanding of phases of matter, but also has been found to have potential application in fault-tolerant quantum computation. The direct measurement of topological properties, however, is still a challenge, especially in interacting quantum system. Here we realize two to four spin one-dimensional Heisenberg chains using nuclear magnetic resonance simulators and observe interaction-induced topological transitions, where Berry curvature in the parameter space of Hamiltonian is probed by means of dynamical response and then the first Chern number is extracted by integrating the curvature over the closed surface. The utilized experimental method provides a powerful means to explore topological phenomena in quantum systems with many-body interactions.
The Berry phase, a fundamental geometric phase in quantum systems, has become a crucial tool for probing the topological properties of materials. Quantum oscillations, such as Shubnikov-de Haas (SdH) oscillations, are widely used to extract this phase, but its unambiguous determination remains challenging. This work highlights the inherent ambiguities in interpreting the oscillation phase solely from SdH data, primarily due to the influence of the spin factor RS, which depends on the Landé g-factor and effective mass. While the Lifshitz-Kosevich (LK) theory provides a framework for analyzing oscillations, the unknown g-factor introduces significant uncertainty. For instance, a zero oscillation phase could arise either from a nontrivial Berry phase or a negative RS. We demonstrate that neglecting RS in modern studies, especially for topological materials with strong spin-orbit coupling, can lead to doubtful conclusions. Through theoretical analysis and numerical examples, we show how the interplay between the Berry phase and Zeeman effect complicates phase determination. Additionally, we also discuss another underappreciated mechanism - the magnetic field dependence of the Fermi level. Our discussion underscores the need for complementary experimental techniques to resolve these ambiguities and calls for further research to refine the interpretation of quantum oscillations in topological systems.
Molecular magnets are ideal systems to probe the realm that borders quantum and classical physics, as well as to study decoherence phenomena in nanoscale systems. The control of the quantum behavior of these materials and their structural characteristics requires synthesis of new complexes with desirable properties which will allow probing of the fundamental aspects of nanoscale physics and quantum information processing. Of particular interest among the magnetic molecular materials are single-molecule magnets (SMMs) and antiferromagnetic (AFM) molecular wheels in which the spin state of the molecule is known to behave quantum mechanically at low temperatures. In previous experiments the dynamics of the magnetic moment of the molecules is governed by incoherent quantum tunneling. Short decoherence times are mainly due to interactions between molecular magnets within the crystal and interactions of the electronic spin with the nuclear spin of neighboring ions within the molecule. This decoherence problem has imposed a limit to the understanding of the molecular spin dynamics and the sources of decoherence in condensed matter systems. Particularly, intermolecular dipolar interactions within the crystal, which shorten the coherence times in concentrated samples, have stymied progress in this direction. Several recent works have reported a direct measurement of the decoherence time in molecular magnets. This has been done by eliminating the dephasing created by dipolar interactions between neighboring molecules. This has been achieved by a) a dilution of the molecules in a liquid solution to decrease the dipolar interaction by separating the molecules, and b) by polarizing the spin bath by applying a high magnetic field at low temperatures. Unfortunately, both approaches restrict the experimental studies of quantum dynamics. For example, the dilution of molecular magnets in liquid solution causes a dispersion of the molecular spin orientation and anisotropy axes, while the large fields required to polarize the spin bath overcome the anisotropy of the molecular spin. In this thesis I have explored two methods to overcome dipolar interactions in molecular magnets: a) studying the dynamics of molecular magnets in single crystals where the separation between magnetic molecules is obtained by chemical doping or where the high crystalline quality allows observations intrinsic to the quantum mechanical nature of the tunneling of the spin, and b) studying the electronic transport through an individual magnetic molecule which has been carefully placed in a single-electron transistor device. I have used EPR microstrip resonators to measure Fe17Ga molecular wheels within single crystals of Fe18 AFM wheels, as well as demonstrating, for the first time in a Single Molecule Magnet, the complete suppression of a Quantum Tunneling of the Magnetization transition forbidden by molecular symmetry.
Quantum interference is studied for a charged particle on a multiply connected configuration space. The holes of the space are assumed to accommodate independent magnetic fluxes. As follows from an instanton calculation, tunneling of the particle is suppressed completely in such a geometry for appropriately chosen field strengths. This set of values defines an algebraic variety in parameter space, not a manifold. The quenching persists even if the geometric symmetry of the system is broken. Aharonov-Bohm–type experiments and mesoscopic tunneling devices are natural candidates to observe many-path interference.
We herein probe the fundamental factors that induce decoherence in ensembles of molecular magnetic materials. This is done by pulse Electron Paramagetic Resonance measurements at X-band (9.6 GHz) on single crystals of Gd@Y(trensal) at 0.5, 10^-1 , 10^-2 and 10^-3 % doping levels, using Hahn echo, partial refocusing and CPMG sequences. The phase memory time, Tm, obtained by the Hahn echo sequence at X-band is compared to the one previously determined at higher frequency/magnetic field (240 GHz). The combined information from these experiments allows to gain insight into the contributions to decoherence originating from various relaxation mechanisms such as spin-lattice relaxation, electron and nuclear spin diffusion and instantaneous diffusion. We show that while at high magnetic fields Tm is limited by spin-lattice relaxation seemingly attributed to a direct process, at lower fields the limiting factor is spectral diffusion. At X-band, for Gd@Y(trensal) we determine a Tm in the range 1 – 11 μs, at 5 K, depending on the magnetic field and concentration of Gd(trensal) in the isostructural diamagnetic host Y(trensal). Importantly, Gd@Y(trensal) displays measurable coherence at temperatures above liquid nitrogen ones, with 125 K being the upper limit. At the lowest dilution level of 10^-3 %, and under dynamic decoupling conditions, the ratio of Tm versus the time it takes t0 implement a quantum gate, TG, reaches the order of 104, in the example of a single qubit π-rotation, which corresponds to a gate fidelity of 99.99 %, reaching thus the lower limit for implementations in Quantum Information Technologies.