Nuclear Spin States Research Articles

Spin-bearing molecules as optically addressable platforms for quantum technologies

Abstract Efforts to harness quantum hardware relying on quantum mechanical principles have been steadily progressing. The search for novel material platforms that could spur the progress by providing new functionalities for solving the outstanding technological problems is however still active. Any physical property presenting two distinct energy states that can be found in a long-lived superposition state can serve as a quantum bit (qubit), the basic information processing unit in quantum technologies. Molecular systems that can feature electron and/or nuclear spin states together with optical transitions are one of the material platforms that can serve as optically addressable qubits. The attractiveness of molecular systems for quantum technologies relies on the fact that molecular structures of atomically defined nature can be obtained in endless diversity of chemical compositions. Crucially, by harnessing the molecular design protocols, the optical and spin (electronic and nuclear) properties of molecules can be tailored, aiding the design of optically addressable spin qubits and quantum sensors. In this contribution, we present a concise and collective discussion of optically addressable spin-bearing molecules – namely, organic molecules, transition metal (TM) and rare-earth ion (REI) complexes – and highlight recent results such as chemical tuning of optical and electron spin quantum coherence, optical spin initialization and readout, intramolecular quantum teleportation, optical coherent storage, and photonic-enhanced optical addressing. We envision that optically addressable spin-carrying molecules could become a scalable building block of quantum hardware for applications in the fields of quantum sensing, quantum communication and quantum computing.

Effective light-induced Hamiltonian for atoms with large nuclear spin

Ultracold fermionic atoms, having two valence electrons, exhibit a distinctive internal state structure, wherein the nuclear spin becomes decoupled from the electronic degrees of freedom in the ground electronic state. Consequently, the nuclear spin states are well isolated from the environment, rendering these atomic systems an opportune platform for quantum computation and quantum simulations. Coupling with off-resonance light is an essential tool to selectively and coherently manipulate the nuclear spin states. In this paper, we present a systematic derivation of the effective Hamiltonian for the nuclear spin states of ultracold fermionic atoms due to such an off-resonance light. We obtain compact expressions for the scalar, vector, and tensor light shifts taking into account both linear and quadratic contributions to the hyperfine splitting. The analysis has been carried out using the Green operator approach and solving the corresponding Dyson equation. Finally, we analyze different scenarios of light configurations which lead to the vector- and tensor-light shifts, as well as the pure spin-orbit coupling for the nuclear spin. Published by the American Physical Society 2024

Preserving the symmetry of cis-1,2-difluoroethylene in the gas-phase heterodimer with hydrogen chloride: A microwave rotational study revealing a novel structure.

The microwave spectra of three isotopologues of the gas-phase heterodimer formed between cis-1,2-difluoroethylene and hydrogen chloride are obtained in the 5-21GHz region using Fourier transform microwave spectroscopy. The molecular structure, determined from the analysis of the spectra and supported by quantum chemistry calculations, has the hydrogen atom of the hydrogen chloride molecule interacting with both fluorine atoms of the fluoroethylene and no interaction between the chlorine atom and the olefin. Although the equilibrium structure has two inequivalent H⋯F interactions, zero-point motion averages over the two equivalent choices for these interactions, rendering the pairs of like atoms (C, H, and F) of the fluoroethylene equivalent, retaining the C2v symmetry of the olefin. This results in only one unique singly substituted 13C isotopologue and in the observed effects on transition intensities due to nuclear spin statistics. The heterodimer structure allows for a strong, linear hydrogen bond between the HCl donor and the fluoroethylene acceptor that is more important here than in the analogous acetylene containing complex, where the interaction between the π electrons of acetylene and an electrophilic hydrogen atom on the olefin compensates for the loss of linearity required for binding to a geminal F/H pair.

Hyperpolarized 13C NMR Reveals Pathway Regulation in Lactococcus lactis and Metabolic Similarities and Differences Across the Tree of Life.

The control of metabolic networks is incompletely understood, even for glycolysis in highly studied model organisms. Direct real-time observations of metabolic pathways can be achieved in cellular systems with 13C NMR using dissolution Dynamic Nuclear Polarization (dDNP NMR). The method relies on a short-lived boost of NMR sensitivity using a redistribution of nuclear spin states to increase the alignment of the magnetic moments by more than four orders of magnitude. This temporary boost in sensitivity allows detection of metabolism with sub-second time resolution. Here, we hypothesized that dDNP NMR would be able to investigate molecular phenotypes that are not easily accessible with more conventional methods. The use of dDNP NMR allows real-time insight into carbohydrate metabolism in a Gram-positive bacterium (Lactoccocus lactis), and comparison to other bacterial, yeast and mammalian cells shows differences in the kinetic barriers of glycolysis across the kingdoms of life. Nevertheless, the accumulation of non-toxic precursors for biomass at kinetic barriers is found to be shared across the kingdoms of life. We further find that the visualization of glycolysis using dDNP NMR reveals kinetic characteristics in transgenic strains that are not evident when monitoring the overall glycolytic rate only. Finally, dDNP NMR reveals that resting Lactococcus lactis cells use the influx of carbohydrate substrate to produce acetoin rather than lactate during the start of glycolysis. This metabolic regime can be emulated using suitably designed substrate mixtures to enhance the formation of the C4 product acetoin more than 400-fold. Overall, we find that dDNP NMR provides analytical capabilities that may help to clarify the intertwined mechanistic determinants of metabolism and the optimal usage of biotechnologically important bacteria.

On accurate calculations of equilibrium H/D fractionations at super-cold conditions (≤200 K) I: Full Partition Function Ratio (FPFR) vs. Path Integral Monte Carlo (PIMC)

Accurate estimations of Hydrogen/Deuterium (H/D) isotope effects have been a long-standing problem since the beginning of stable isotope geochemistry, primarily due to their strong nuclear quantum effects (NQEs). Currently, the D/H ratio plays a key role in deciphering the origin and evolution of water ice and organics in the solar system. Additionally, the Big-bang origin of Deuterium necessitates that the observed D/H variations be linked to isotope exchange reactions, such as HD + H2O ↔ H2 + HDO. Therefore, an accurate benchmark dataset describing the equilibrium H/D isotope fractionations at low temperatures (≤ 200 K) is essential for interpreting rapidly accumulating astrochemical observation data. In this study, we implemented and compared two methods developed for evaluating the NQEs of H/D isotopes: 1) the Full Partition Function Ratio (FPFR) method and 2) the Path Integral Monte Carlo (PIMC) method. Both were assessed for their accuracy and efficiency in estimating equilibrium isotope effects (EIEs) using 10 common interstellar small molecules (H2, HF, HCl, HCN, HNC, H2O, H2S, NH3, HCHO, and CH4) as examples. Most of them are calculated at high precision for the first time. For the FPFR method, several higher-order corrections to the Urey-Bigeleisen-Mayer model were considered, including anharmonicity, quantum mechanical rotation with nuclear-spin statistics, and corrections to the Born-Oppenheimer approximation. For the PIMC method, four different actions related to the thermal density matrix are used. These include the primitive and three fourth-order actions (Takahashi and Imada, Suzuki-Chin and Chin approximations), based on the direct scaled-coordinates transformation. Three main conclusions are obtained: 1) Under the framework of Born-Oppenheimer approximation, the PIMC method holds the same and even slightly better accuracy (more comprehensive descriptions of quantum anharmonicities) in estimating EIEs for H/D isotopes as the FPFR method. However, both methods suffer from the neglection of the DBOC when using the Born-Oppenheimer potential energy surfaces. For the PIMC method, additional corrections for particle distinguishability must be considered when nuclear spin statistics exhibit its effects at low temperatures (e.g., < 160 K for H2). 2) Among the four actions, three fourth-order actions show better convergence and efficiency (2.2 to 26.5 times speedups at 50 K) than the primitive action, making them superior candidates for PIMC simulations at super-cold (≤ 200 K) conditions. 3) A combination of accurate potential energy surface with the PIMC method serves as an alternative way for theoretical estimations of H/D isotope effects.

Overhauser enhanced liquid state nuclear magnetic resonance spectroscopy in one and two dimensions

Nuclear magnetic resonance (NMR) is fundamental in the natural sciences, from chemical analysis and structural biology, to medicine and physics. Despite its enormous achievements, one of its most severe limitations is the low sensitivity, which arises from the small population difference of nuclear spin states. Methods such as dissolution dynamic nuclear polarization and parahydrogen induced hyperpolarization can enhance the NMR signal by several orders of magnitude, however, their intrinsic limitations render multidimensional hyperpolarized liquid-state NMR a challenge. Here, we report an instrumental design for 9.4 Tesla liquid-state dynamic nuclear polarization that enabled enhanced high-resolution NMR spectra in one and two-dimensions for small molecules, including drugs and metabolites. Achieved enhancements of up to two orders of magnitude translate to signal acquisition gains up to a factor of 10,000. We show that hyperpolarization can be transferred between nuclei, allowing DNP-enhanced two-dimensional 13C–13C correlation experiments at 13C natural abundance. The enhanced sensitivity opens up perspectives for structural determination of natural products or characterization of drugs, available in small quantities. The results provide a starting point for a broader implementation of DNP in liquid-state NMR.

Impact of Zeeman and hyperfine interactions on the magnetic properties of paramagnetic metal ions: II. Super-hyperfine interactions with surrounding nuclei

The anisotropic Zeeman and strong hyperfine interactions of a Kramers ion can significantly affect its magnetic properties as well as the interactions with the nearby nuclei. The interactions with the local environment are described in the preceding article. In the current work, the change of the spin states of distant nuclei is studied. Analytical expressions describing the depth of the electron spin echo envelope modulation (ESEEM) are obtained for the ions with anisotropic Zeeman and strong hyperfine interactions. Due to the g-tensor anisotropy, the electron Zeeman interaction axis is tilted in respect to the direction of the external magnetic field which makes non-collinear with the Zeeman interaction axes of the ion and the nearby nuclei and significantly modifies the nuclear spin states. Thus, the isotropic hyperfine interaction, and particularly the Fermi contact interaction can directly contribute to the ESEEM. An additional factor, that can significantly modify the ESEEM signal is the mixing of the multiple oscillations arising when several nuclei occur in optimal conditions for the generation of the nuclear coherence. This situation arises when several EPR transitions of the ion covering a wide range of magnetic fields are examined.

Cross-correlated relaxation in the NMR of near-equivalent spin pairs: Longitudinal relaxation and long-lived singlet order.

The evolution of nuclear spin state populations is investigated for the case of a 13C2-labeled triyne in solution, for which the near-equivalent coupled pairs of 13C nuclei experience cross-correlated relaxation mechanisms. Inversion-recovery experiments reveal different recovery curves for the main peak amplitudes, especially when the conversion of population imbalances to observable coherences is induced by a radio frequency pulse with a small flip angle. Measurements are performed over a range of magnetic fields by using a sample shuttle apparatus. In some cases, the time constant TS for decay of nuclear singlet order is more than 100 times larger than the time constant T1 for the equilibration of longitudinal magnetization. The results are interpreted by a theoretical model incorporating cross-correlated relaxation mechanisms, anisotropic rotational diffusion, and an external random magnetic field. A Lindbladian formalism is used to describe the dissipative dynamics of the spin system in an environment of finite temperature. Good agreement is achieved between theory and experiment.

Parallel Gate Fidelity of Flip‐Flop Qubits in Small 1D‐ and 2D‐Arrays in a Noisy Environment

AbstractThe long coherence time of donor atom nuclear spin states and of its bounded electron in can be exploited to define a qubit. This work is focused on a type of donor‐ and quantum dot‐based qubit, the flip‐flop (FF) qubit, that leverages antiparallel electron‐nuclear spin states of a donor atom controlled by an electric field. It can provide long‐range inter‐qubit interactions in the order of some hundreds of nanometers, thus relaxing the common constraints and tolerances on inter‐qubit distances in donor‐based qubits. Simulation results of linear array (LA) and square array (SA) of four FF qubits are presented to study the effect of noise, idle qubits, and simultaneous gating (parallel gating) on gate fidelity. The impact of noise and qubit mutual coupling for both considered types of array are presented and the obtained fidelity results are compared.

Spectroscopic observation and ab initio calculations of a new isomer of the CS2 trimer

We report spectroscopic observation and theoretical calculations of a new isomer of (CS2)3 as observed in the regions of the ν3 fundamental band of CS2 (6.5 μm) and the ν1 + ν3 combination band (4.5 μm), using tunable laser sources and a pulsed supersonic slit-jet. The previously observed CS2 trimer has a barrel-shaped structure with three equivalent monomers and D3 symmetry. The new isomer consists of a staggered parallel “dimer pair” of equivalent CS2 monomers with a third CS2 monomer sitting “on top”, similar to the known non-cyclic CO2 trimer. This structure has C2 rotational symmetry corresponding to the b inertial axis of the trimer, as proven by observed nuclear spin statistics. Ab initio calculations correctly give the two observed isomer structures and indicate that they lie very close in binding energy.

Spin Light Emitting Diode Based on Exciton Fine Structure Tuning in Quantum Dots.

We propose a concept of quantum dot based light emitting diode that produces circularly polarized light without magnetic contacts due to the hyperfine interaction at the crossing of the exciton levels in a weak magnetic field. The electroluminescence circular polarization degree can reach 100%. The concept is compatible with the micropillar cavities, which allows for the generation of single circularly polarized photons. Second order photon correlation function includes information about the nuclear spin dynamics in the quantum dot, and the nuclear spin state can be purified by the quantum measurement backaction.

Approaching a fully-polarized state of nuclear spins in a solid

Magnetic noise of atomic nuclear spins is a major source of decoherence in solid-state spin qubits. In theory, near-unity nuclear spin polarization can eliminate decoherence of the electron spin qubit, while turning the nuclei into a useful quantum information resource. However, achieving sufficiently high nuclear polarizations has remained an evasive goal. Here we implement a nuclear spin polarization protocol which combines strong optical pumping and fast electron tunneling. Nuclear polarizations well above 95% are generated in GaAs semiconductor quantum dots on a timescale of 1 minute. The technique is compatible with standard quantum dot device designs, where highly-polarized nuclear spins can simplify implementations of qubits and quantum memories, as well as offer a testbed for studies of many-body quantum dynamics and magnetism.

Nuclear spin ratios of deuterated ammonia in prestellar cores

Context. Molecules containing two or more hydrogen or deuterium atoms have different nuclear spin states which behave as separate chemical species. The relative abundances of these species can give clues to their origin. Formation on grains is believed to yield statistical spin ratios whereas gas-phase reactions are predicted to result in clear deviations from them. This is also true for ammonia and its deuterated forms NH2D, NHD2, and ND3. Aims. Here we aim to determine the ortho/para ratios of NH2D and NHD2 in dense, starless cores, where their formation is supposed to be dominated by gas-phase reactions. Methods. The Large APEX sub-Millimeter Array (LAsMA) multibeam receiver of the Atacama Pathfinder EXperiment (APEX) telescope was used to observe the prestellar cores H-MM1 and Oph D in Ophiuchus in the ground-state lines of ortho and para NH2D and NHD2. The fractional abundances of these molecules were derived employing three-dimensional radiative transfer modelling, using different assumptions about the abundance profiles as functions of density. We also ran gas-grain chemistry models with different scenarios concerning proton or deuteron exchanges and chemical desorption from grains to find out if one of these models can reproduce the observed spin ratios. Results. The observationally deduced ortho/para ratios of NH2D and NHD2 are in both cores within 10% of their statistical values 3 and 2, respectively, and taking 3 σ limits, deviations from these of about 20% are allowed. Of the chemistry models tested here, the model that assumes proton hop (as opposed to full scrambling) in reactions contributing to ammonia formation, and a constant efficiency of chemical desorption, comes nearest to the observed abundances and spin ratios. Conclusions. The nuclear spin ratios derived here are in contrast with spin-state chemistry models that assume full scrambling in proton donation and hydrogen abstraction reactions leading to deuterated ammonia. The efficiency of chemical desorption strongly influences the predicted abundances of NH3, NH2D, and NHD2, but has a lesser effect on their ortho/para ratios. For these the proton exchange scenario in the gas is decisive. We suggest that this is because of rapid re-processing of ammonia and related cations by gas-phase ion-molecule reactions.

Rotational conformers and nuclear spin isomers of carbonyl diisothiocyanate.

Nuclear spin isomers of molecules play a pivotal role in our understanding of quantum mechanics and can have significant implications for various fields. In this work, we report the isolation and characterization of stable nuclear spin isomers as well as conformational isomers of a reactive compound, namely carbonyl diisothiocyanate. It can exist as three rotational conformers, two of which, the syn-syn and syn-anti, were observed in a pulsed supersonic jet by chirped pulse Fourier transform microwave spectroscopy in the 2-12 GHz frequency region. The rotational spectra of two distinct nuclear spin isomers of syn-syn-carbonyl diisothiocyanate, ortho and para, were recorded and analyzed. Experimental molecular rotational parameters for the identified rotational and nuclear spin isomers were determined, including rotational constants, centrifugal distortion constants, and nuclear quadrupole coupling constants. The two nuclear spin isomers are distinguished by unique hyperfine splitting signatures in their rotational spectra as an outcome of their different nuclear spin states. The relative abundances of the two observed conformers in the gas phase were estimated from the intensity of their rotational transitions. Following detection of singly substituted rare isotopologues of the syn-syn conformer, a partial substitution (rs) structure was determined.

High-resolution infrared spectroscopy of jet cooled cyclobutyl in the α-CH stretch region: large-amplitude puckering dynamics in a 4-membered ring radical.

Gas-phase cyclobutyl radical (c-C4H7) is generated at a rotational temperature of Trot = 26(1) K in a slit-jet discharge mixture of 70% Ne/30% He and 0.5-0.6% cyclobromobutane (c-C4H7Br). A fully rovibrationally resolved absorption spectrum of the α-CH stretch fundamental band between 3062.9 cm-1 to 3075.7 cm-1 is obtained and analyzed, yielding first precision structural and dynamical information for this novel radical species. The α-CH stretch band origin is determined to be 3068.7887(4) cm-1, which implies only a modest (≈0.8 cm-1) blue shift from rotationally unresolved infrared spectroscopic studies of cyclobutyl radicals in liquid He droplets [A. R. Brown, P. R. Franke and G. E. Douberly, J. Phys. Chem. A, 2017, 121, 7576-7587]. Of particular dynamical interest, a one-dimensional potential energy surface with respect to the ring puckering coordinate is computed at CCSD(T)/ANO2 level of theory and reveals a double minimum Cs puckered geometry, separated by an exceedingly shallow planar C2v transition state barrier (Ebarr ≈ 1 cm-1). Numerical solutions on this double minimum potential yield a zero-point energy for the ground state (Ezero-point ≈ 27 cm-1) greatly in excess of the interconversion barrier. This is indicative of highly delocalized, large amplitude motion of the four-membered ring structure, for which proper vibrationally averaging of the moment of inertia tensor reproduces the experimentally determined inertial defect remarkably well. Finally, intensity alternation in the experimental spectrum due to nuclear spin statistics upon exchange of three indistinguishable H atom pairs (IH = ½) matches Ka + Kc = even : odd = 36 : 28 predictions, implying that the unpaired electron in the radical center lies in an out-of-plane pπ orbital. Thus, high-resolution infrared spectroscopy provides first experimental confirmation of a shallow double minimum ring puckering potential with a highly delocalized ground state wave function peaked at a planar C2v transition state geometry consistent with a cyclobutyl π radical.

The squeezed dark nuclear spin state in lead halide perovskites

Coherent many-body states are highly promising for robust quantum information processing. While far-reaching theoretical predictions have been made for various implementations, direct experimental evidence of their appealing properties can be challenging. Here, we demonstrate optical manipulation of the nuclear spin ensemble in the lead halide perovskite semiconductor FAPbBr3 (FA = formamidinium), targeting a long-postulated collective dark state that is insensitive to optical pumping after its build-up. Via optical orientation of localized hole spins we drive the nuclear many-body system into this entangled state, requiring a weak magnetic field of only a few milli-Tesla strength at cryogenic temperatures. During its fast establishment, the nuclear polarization along the optical axis remains small, while the transverse nuclear spin fluctuations are strongly reduced, corresponding to spin squeezing as evidenced by a strong violation of the generalized nuclear squeezing-inequality with ξs < 0.5. The dark state corresponds to an ~35-body entanglement between the nuclei. Dark nuclear spin states can be exploited to store quantum information benefiting from their long-lived many-body coherence and to perform quantum measurements with a precision beyond the standard limit.

Nonequilibrium Nuclear Spin States of Ethylene during Acetylene Hydrogenation with Parahydrogen over Immobilized Iridium Complexes

Nonequilibrium Nuclear Spin States of Ethylene during Acetylene Hydrogenation with Parahydrogen over Immobilized Iridium Complexes

Development of Hyperpolarized NMR Molecular Probes for Biological Applications

Abstract Our bodies are composed of molecules. The dynamic activity of molecules is the essence of living phenomena. Toward the analysis of this, the establishment of in vivo molecular imaging techniques has been sought. Hyperpolarized nuclear magnetic resonance (NMR) is a promising technique that enables in vivo molecular imaging using highly sensitive hyperpolarized NMR molecular probes and is expected to be a next-generation molecular imaging technology. However, a major challenge lies in the rapid relaxation of the hyperpolarized nuclear spin state of the molecule, i.e., a short lifetime of high sensitivity. We have made our efforts to address this critical issue. This award account mainly describes our research to develop hyperpolarized molecular probes with long hyperpolarization lifetime. Based on the understanding of the relaxation mechanism of hyperpolarized spin states, we successfully developed various hyperpolarized 13C molecular probes, some of which were applied for in vivo studies. In addition, we demonstrated the development of hyperpolarized 15N molecular probes with remarkably long hyperpolarization lifetimes. These results pave the way for the rational design of hyperpolarized molecular probes, which has been difficult to achieve so far.

Anisotropic and Coherent Control of Radical Pairs by Optimized RF Fields.

Radical pair kinetics is determined by the coherent and incoherent spin dynamics of spin pair and spin-selective chemical reactions. In a previous paper, reaction control and nuclear spin state selection by designed radiofrequency (RF) magnetic resonance was proposed. Here, we present two novel types of reaction control calculated by the local optimization method. One is anisotropic reaction control and the other is coherent path control. In both cases, the weighting parameters for the target states play an important role in the optimizing of the RF field. In the anisotropic control of radical pairs, the weighting parameters play an important role in the selection of the sub-ensemble. In coherent control, one can set the parameters for the intermediate states, and it is possible to specify the path to reach a final state by adjusting the weighting parameters. The global optimization of the weighting parameters for coherent control has been studied. These manifest calculations show the possibility of controlling the chemical reactions of radical pair intermediates in different ways.

Thermalization of Nuclear Spins in Lanthanide Molecular Magnets.

Single-molecule magnets (SMMs) distinguish themselves in the field of quantum magnetism through the ability to combine fundamental research with promising applications. The evolution of quantum spintronics in the last decade exemplifies the potential held by molecular-based quantum devices. Notably, the readout and manipulation of the nuclear spin states embedded in a lanthanide-based SMM hybrid device were employed in proof of principle studies of quantum computation at the single-molecule level. In the quest for further understanding of the relaxation behavior in SMMs for their integration in novel applications, herein, we study the relaxation dynamics of the 159Tb nuclear spins in a diluted molecular crystal employing the recently acquired understanding of the nonadiabatic dynamics of TbPc2 molecules. Through numerical simulation, we find that phonon-modulated hyperfine interaction opens a direct relaxation channel between the nuclear spins and the phonon bath. The mechanism is of potential importance for the theory of spin bath and the relaxation dynamics of the molecular spins.