Magnetic excitation and readout of methyl group tunnel coherence

Light-induced electron spin qubit coherences in the purple bacteria reaction center protein

Photosynthetic reaction center proteins (RCs) provide ideal model systems for studying quantum entanglement between multiple spins, a quantum mechanical phenomenon wherein the properties of the entangled particles become inherently correlated. Following light-generated sequential electron transfer, RCs generate spin-correlated radical pairs (SCRPs), also referred to as entangled spin qubit (radical) pairs (SQPs). Understanding and controlling coherence mechanisms in SCRP/SQPs is important for realizing practical uses of electron spin qubits in quantum sensing applications. The bacterial RC (bRC) provides an experimental system for exploring quantum effects in the SCRP P865+ QA-, where P865, a special pair of bacteriochlorophylls, is the primary donor, and QA is the primary quinone acceptor. In this study, we focus on understanding how local molecular environments and isotopic substitution, particularly deuteration, influence spin coherence times (TM). Using high-frequency electron paramagnetic resonance (EPR) spectroscopy, we observed that the local environment surrounding P865 and QA plays a significant role in determining TM. Our findings show that while deuteration led to a modest increase in TM, particularly at low temperatures, but the effect was substantially smaller than predicted by classical nuclear spin diffusion alone. This result is in contrast to our previous study of the photosystem I (PSI) RC, where no increase in TM was observed upon deuteration. Theoretical modeling identified several methyl groups at key distances from the spin centers of both bRC and PSI, and methyl group tunneling at low temperatures has been previously suggested as a mechanism for enhanced spin decoherence. Additionally, our study revealed a strong dependence of spin coherence on the orientation of the external magnetic field, highlighting the influence of the protein microenvironment on spin dynamics. These results offer new insights for optimizing coherence times in quantum system design for quantum information science and sensing applications.

The contribution of methyl groups to electron spin decoherence of nitroxides in glassy matrices

Long electron spin coherence lifetimes are crucial for high sensitivity and resolution in many pulse electron paramagnetic resonance (EPR) experiments aimed at measuring hyperfine and dipolar couplings, as well as in potential quantum sensing applications of molecular spin qubits. In immobilized systems, methyl groups contribute significantly to electron spin decoherence as a result of methyl torsional quantum tunneling. We examine the electron spin decoherence dynamics of the nitroxide radical 2,2,6,6-tetramethylpiperidin-1-oxyl (TEMPO) in both a methyl-free solvent and a methyl-containing solvent at cryogenic temperature. We model nitroxide and solvent methyl effects on decoherence using cluster correlation expansion (CCE) simulations extended to include methyl tunneling and compare the calculations to experimental data. We show that by using the methyl tunneling frequency as a fit parameter, experimental Hahn echo decays can be reproduced fairly well, allowing structural properties to be investigated in silico. In addition, we examine the Hahn echo of a hypothetical system with an unpaired electron and a single methyl to determine the effect of geometric configuration on methyl-driven electron spin decoherence. The simulations show that a methyl group contributes the most to electron spin decoherence if it is located between 2.5 and 6-7 Å from the electron spin, with its orientation being of secondary importance.

Exploring tunneling ESEEM beyond methyl groups in nitroxides at low temperatures

Tunneling of methyl rotors coupled to an electron spin causes magnetic field independent electron spin echo envelope modulation (ESEEM) at low temperatures. For nitroxides containing alkyl substituents, we observe this effect as a contribution at the beginning of the Hahn echo decay signal occurring on a faster time scale than the matrix-induced decoherence. The tunneling ESEEM contribution includes information on the local environment of the methyl rotors, which manifests as a distribution of rotation barriers P(V3) when measuring the paramagnetic species in a glassy matrix. Here, we investigate the differences in tunneling behaviour of geminal methyl and ethyl group rotors in nitroxides while exploring different levels of theory in our previously introduced methyl quantum rotor (MQR) model. Moreover, we extend the MQR model to analyze the tunneling ESEEM originating from two different rotor types coupled to the same electron spin. We find that ethyl groups in nitroxides give rise to stronger tunneling ESEEM contributions than methyl groups because the difference between hyperfine couplings of their methyl protons better matches the tunneling frequency. The methyl rotors of both ethyl and propyl groups exhibit distributions at lower rotation barriers compared to geminal methyl groups. This is in good agreement with density functional theory (DFT) calculations of their rotation barriers and showcases that conformational flexibility impacts the hindrance of rotation. Using Monte-Carlo based fitting in combination with an identifiability analysis of the MQR model parameter space, we extract rotation barrier distributions for the individual rotor types in mixed-rotor nitroxides as well as identify which rotors dominate the observed tunneling contribution in the Hahn echo decay signal.

Probing structural and dynamic properties of MAPbCl3 hybrid perovskite using Mn2+ EPR

Hybrid methylammonium (MA) lead halide perovskites have emerged as materials exhibiting excellent photovoltaic performance related to their rich structural and dynamic properties. Here, we use multifrequency (X-, Q-, and W-band) electron paramagnetic resonance (EPR) spectroscopy of Mn2+ impurities in MAPbCl3 to probe the structural and dynamic properties of both the organic and inorganic sublattices of this compound. The temperature dependent continuous-wave (CW) EPR experiments reveal a sudden change of the Mn2+ spin Hamiltonian parameters at the phase transition to the ordered orthorhombic phase indicating its first-order character and significant slowing down of the MA cation reorientation. Pulsed EPR experiments are employed to measure the temperature dependences of the spin-lattice relaxation T1 and decoherence T2 times of the Mn2+ ions in the orthorhombic phase of MAPbCl3 revealing a coupling between the spin center and vibrations of the inorganic framework. Low-temperature electron spin echo envelope modulation (ESEEM) experiments of the protonated and deuterated MAPbCl3 analogues show the presence of quantum rotational tunneling of the ammonium groups, allowing to accurately probe their rotational energy landscape.

Spin qubits of Cu(II) doped in Zn(II) metal-organic frameworks above microsecond phase memory time

With the aim of creating Cu(II) spin qubits in a rigid metal-organic framework (MOF), this work demonstrates a doping of 5 %, 2 %, 1 %, and 0.1 % mol of Cu(II) ions into a perovskite-type MOF [CH6 N3 ][ZnII (HCOO)3 ]. The presence of dopant Cu(II) sites are confirmed with anisotropic g-factors (gx =2.07, gy =2.12, and gz =2.44) in the S=1/2 system by experimentally and theoretically. Magnetic dynamics indicate the occurrence of a slow magnetic relaxation via the direct and Raman processes under an applied field, with a relaxation time (τ) of 3.5 ms (5 % Cu), 9.2 ms (2 % Cu), and 15 ms (1 % Cu) at 1.8 K. Furthermore, pulse-ESR spectroscopy reveals spin qubit properties with a spin-spin relaxation (phase memory) time (T2 ) of 0.21 μs (2 %Cu), 0.39 μs (1 %Cu), and 3.0 μs (0.1 %Cu) at 10 K as well as Rabi oscillation between MS =±1/2 spin sublevels. T2 above microsecond is achieved for the first time in the Cu(II)-doped MOFs. It can be observed at submicrosecond around 50 K. These spin relaxations are very sensitive to the magnetic dipole interactions relating with cross-relaxation between the Cu(II) sites and can be tuned by adjusting the dopant concentration.

Coherences of Photoinduced Electron Spin Qubit Pair States in Photosystem I

This publication presents the first comprehensive experimental study of electron spin coherences in photosynthetic reaction center proteins, specifically focusing on photosystem I (PSI). The ultrafast electron transfer in PSI generates spin-correlated radical pairs (SCRPs), which are entangled spin pairs formed in well-defined spin states (Bell states). Since their discovery in our group in the 1980s, SCRPs have been extensively used to enhance our understanding of structure-function relationships in photosynthetic proteins. More recently, SCRPs have been utilized as tools for quantum sensing. Electron spin decoherence poses a significant challenge in realizing practical applications of electron spin qubits, particularly the creation of quantum entanglement between multiple electron spins. This work is focused on the systematic characterization of decoherence in SCRPs of PSI. These decoherence times were measured as electron spin echo decay times, termed phase memory times (TM), at various temperatures. Decoherence was recorded on both transient SCRP states P700+A1- and thermalized states. Our study reveals that TM exhibits minimal dependence on the biological species, biochemical treatment, and paramagnetic species. The analysis indicates that nuclear spin diffusion and instantaneous diffusion mechanisms alone cannot explain the observed decoherence. As a plausible explanation we discuss the assumption that the low-temperature dynamics of methyl groups in the protein surrounding the unpaired electron spin centers is the main factor governing the loss of the spin coherence in PSI.

Exact tunneling splittings from symmetrized path integrals

We develop a new simulation technique based on path-integral molecular dynamics for calculating ground-state tunneling splitting patterns from ratios of symmetrized partition functions. In particular, molecular systems are rigorously projected onto their J = 0 rotational state by an "Eckart spring" that connects two adjacent beads in a ring polymer. Using this procedure, the tunneling splitting can be obtained from thermodynamic integration at just one (sufficiently low) temperature. Converged results are formally identical to the values that would have been obtained by solving the full rovibrational Schrödinger equation on a given Born-Oppenheimer potential energy surface. The new approach is showcased with simulations of hydronium and methanol, which are in good agreement with wavefunction-based calculations and experimental measurements. The method will be of particular use for the study of low-barrier methyl rotations and other floppy modes, where instanton theory is not valid.

Mechanistic origins of methyl-driven Overhauser DNP

The Overhauser effect in the dynamic nuclear polarization (DNP) of non-conducting solids has drawn much attention due to the potential for efficient high-field DNP as well as a general interest in the underlying principles that enable the Overhauser effect in small molecules. We recently reported the observation of 1H and 2H Overhauser effects in H3C- or D3C-functionalized Blatter radical analogs, which we presumed to be caused by methyl rotation. In this work, we look at the mechanism for methyl-driven Overhauser DNP in greater detail, considering methyl librations and tunneling in addition to classical rotation. We predict the temperature dependence of these mechanisms using density functional theory and spin dynamics simulations. Comparisons with results from ultralow-temperature magic angle spinning-DNP experiments revealed that cross-relaxation at temperatures above 60 K originates from both libration and rotation, while librations dominate at lower temperatures. Due to the zero-point vibrational nature of these motions, they are not quenched by very low temperatures, and methyl-driven Overhauser DNP is expected to increase in efficiency down to 0 K, predominantly due to increases in nuclear relaxation times.

Probing Methyl Group Tunneling in [(CH3)2NH2][Zn(HCOO)3] Hybrid Perovskite Using Co2+ EPR

At low temperature, methyl groups act as hindered quantum rotors exhibiting rotational quantum tunneling, which is highly sensitive to a local methyl group environment. Recently, we observed this effect using pulsed electron paramagnetic resonance (EPR) in two dimethylammonium-containing hybrid perovskites doped with paramagnetic Mn²⁺ ions. Here, we investigate the feasibility of using an alternative fast-relaxing Co²⁺ paramagnetic center to study the methyl group tunneling, and, as a model compound, we use dimethylammonium zinc formate [(CH₃)₂NH₂][Zn(HCOO)₃] hybrid perovskite. Our multifrequency (X-, Q- and W-band) EPR experiments reveal a high-spin state of the incorporated Co²⁺ center, which exhibits fast spin-lattice relaxation and electron spin decoherence. Our pulsed EPR experiments reveal magnetic field independent electron spin echo envelope modulation (ESEEM) signals, which are assigned to the methyl group tunneling. We use density operator simulations to extract the tunnel frequency of 1.84 MHz from the experimental data, which is then used to calculate the rotational barrier of the methyl groups. We compare our results with the previously reported Mn²⁺ case showing that our approach can detect very small changes in the local methyl group environment in hybrid perovskites and related materials.

Regularized dynamical decoupling noise spectroscopy - a decoherence descriptor for radicals in glassy matrices

Decoherence arises from a fluctuating spin environment, captured by its noise spectrum S(ω). Dynamical decoupling (DD) with n π pulses extends the dephasing time if the associated filter function attenuates S(ω). Inversely, DD noise spectroscopy (DDNS) reconstructs S(ω) from DD data by approximating the filters pass band by a δ-function. This restricts application to qubit-like spin systems with inherently long dephasing times and/or many applicable pulses. We introduce regularized DDNS to lift this limitation and thereby infer S(ω) from DD traces of paramagnetic centers in glassy o-terphenyl and water-glycerol matrices recorded with n ≤ 5. For nitroxide radicals at low temperatures, we utilize deuteration to identify distinct matrix- and spin center-induced spectral features. The former extends up to a matrix-specific cut-off frequency and characterizes nuclear spin diffusion. We demonstrate that rotational tunneling of intramolecular methyl groups drives the latter process, whereas at elevated temperatures S(ω) reflects the classical methyl group reorientation. Ultimately, S(ω) visualizes and quantifies variations in the electron spins couplings and thus reports on the underlying spin dynamics as a powerful decoherence descriptor.

Rotational Coupling in Methyl-Tunneling Electron Spin Echo Envelope Modulation

Coherence between tunnel-split states of a methyl quantum rotor can be generated and observed in stimulated and spin-locked echo experiments, if hyperfine coupling of a nearby electron spin to the methyl protons breaks C 3 symmetry and is of the same order of magnitude as the tunnel splitting. Here, we consider the case of two methyl groups bound to the same sp 3 -hybridized atom, which is important in the context of common nitroxide spin labels. For a simple form of the rotor-rotor coupling Hamiltonian, we provide an approach that allows for density operator computations of this system with 1152 quantum states with moderate computational effort. We find that, in the regime where the ratio between rotor-rotor coupling and rotational barrier is much smaller than unity, three-pulse ESEEM and hyperfine-decoupled ESEEM depend only on the tunnel splitting, but not on this ratio. This finding may simplify the treatment of tunnel-induced electron decoherence in systems where the methyl groups are bound to sp 3 -hybridized atoms.

Quantum dynamics of Mn2+ in dimethylammonium magnesium formate

Dimethylammonium magnesium formate, [(CH₃)₂NH₂][Mg(HCOO)₃] or DMAMgF, is a model used to study high temperature hybrid perovskite-like dielectrics. This compound displays an order-disorder phase transition at about 260 K. Using multifrequency electron spin resonance in continuous wave and pulsed modes, we herein present the quantum dynamics of the Mn²⁺ ion probe in DMAMgF. In the high temperature paraelectric phase, we observe a large distribution of the zero field splitting that is attributed to the high local disorder and further supported by density functional theory computations. In the low temperature ferroelastic phase, a single structure phase is detected and shown to contain two magnetic structures. The complex electron paramagnetic resonance signals were identified by means of the Rabi oscillation method combined with the crystal field kernel density estimation.

Electron paramagnetic resonance study of ferroelectric phase transition and dynamic effects in a Mn2+ doped [NH4][Zn(HCOO)3] hybrid formate framework

We present an X- and Q-band continuous wave (CW) and pulse electron paramagnetic resonance (EPR) study of a manganese doped [NH4][Zn(HCOO)3] hybrid framework, which exhibits a ferroelectric structural phase transition at 190 K. The CW EPR spectra obtained at different temperatures exhibit clear changes at the phase transition temperature. This suggests a successful substitution of the Zn2+ ions by the paramagnetic Mn2+ centers, which is further confirmed by the pulse EPR and 1H ENDOR experiments. Spectral simulations of the CW EPR spectra are used to obtain the temperature dependence of the Mn2+ zero-field splitting, which indicates a gradual deformation of the MnO6 octahedra indicating a continuous character of the transition. The determined data allow us to extract the critical exponent of the order parameter (β = 0.12), which suggests a quasi two-dimensional ordering in [NH4][Zn(HCOO)3]. The experimental EPR results are supported by the density functional theory calculations of the zero-field splitting parameters. Relaxation time measurements of the Mn2+ centers indicate that the longitudinal relaxation is mainly driven by the optical phonons, which correspond to the vibrations of the metal-oxygen octahedra. The temperature behavior of the transverse relaxation indicates a dynamic process in the ordered ferroelectric phase.