Nuclear Spin Transitions Research Articles

Optimising control over nuclear spin transitions

Optimising control over nuclear spin transitions

Temperature Sensitivity of 14N-V and 15N-V Ground-State Manifolds.

We measure electron- and nuclear-spin transition frequencies in the ground state of nitrogen-vacancy (N-V) centers in diamond for two nitrogen isotopes (14N-V and 15N-V) over temperatures ranging from 77 to 400 K. Measurements are performed using Ramsey interferometry and direct optical readout of the nuclear and electron spins. We extract coupling parameters Q (for 14N-V), D, A‖, A⊥, and , and their temperature dependences for both isotopes. The temperature dependences of the nuclear-spin transitions within the spin manifold near room temperature are found to be 0.52(1) ppm/K for 14N-V(|mI = -1⟩ ↔ |mI = +1⟩) and -1.1(1) ppm/K for 15N-V(|mI = -1/2⟩ ↔ |mI = +1/2⟩). An isotopic shift in the zero-field splitting parameter D between 14N-V and 15N-V is measured to be ~ 120 kHz. Residual transverse magnetic fields are observed to shift the nuclear-spin transition frequencies, especially for 15N-V. We have precisely determined the set of parameters relevant for the development of nuclear-spin-based diamond quantum sensors with greatly reduced sensitivity to environmental factors.

Calorimetric measurement of nuclear spin-lattice relaxation rate in metals

The quasiparticle density of states in correlated and quantum-critical metals directly probes the effect of electronic correlations on the Fermi surface. Measurements of the nuclear spin-lattice relaxation rate provide one such experimental probe of quasiparticle mass through the electronic density of states. By far the most common way of accessing the spin-lattice relaxation rate is via nuclear magnetic resonance and nuclear quadrupole resonance experiments, which require resonant excitation of nuclear spin transitions. Here we report non-resonant access to spin-lattice relaxation dynamics in AC-calorimetric measurements. The nuclear spin-lattice relaxation rate is inferred in our measurements from its effect on the frequency dispersion of the thermal response of the calorimeter-sample assembly. We use fast, lithographically-defined nanocalorimeters to access the nuclear spin-lattice relaxation times in metallic indium from 0.3~K to 7~K and in magnetic fields up to 35~T.

High cooperativity coupling to nuclear spins on a circuit quantum electrodynamics architecture

Nuclear spins are candidates to encode qubits or qudits due to their isolation from magnetic noise and potentially long coherence times. However, their weak coupling to external stimuli makes them hard to integrate into circuit quantum electrodynamics architectures, the leading technology for solid-state quantum processors. Here, we study the coupling of 173Yb(III) nuclear spin states in an [Yb(trensal)] molecule to superconducting cavities. Experiments have been performed on magnetically dilute single crystals placed on the inductors of lumped-element LC superconducting resonators with characteristic frequencies spanning the range of nuclear and electronic spin transitions. We achieve a high cooperative coupling to all electronic and most nuclear [173Yb(trensal)] spin transitions, a necessary ingredient for the implementation of qudit protocols with molecular spins using a hybrid architecture.

Seconds-Scale Coherence on Nuclear Spin Transitions of Ultracold Polar Molecules in 3D Optical Lattices.

Ultracold polar molecules (UPMs) are emerging as a novel and powerful platform for fundamental applications in quantum science. Here, we report characterization of the coherence between nuclear spin levels of ultracold ground-state sodium-rubidium molecules loaded into a 3D optical lattice with a nearly photon scattering limited trapping lifetime of 9(1)seconds. After identifying and compensating the main sources of decoherence, we achieve a maximum nuclear spin coherence time of T_{2}^{*}=3.3(6) s with two-photon Ramsey spectroscopy. Furthermore, based on the understanding of the main factor limiting the coherence of the two-photon Rabi transition, we obtain a Rabi line shape with linewidth below 0.8Hz. The simultaneous realization of long lifetime and coherence time, and ultrahigh spectroscopic resolution in our system unveils the great potentials of Ultracold polar molecules in quantum simulation, computation, and metrology.

Robust optical readout and characterization of nuclear spin transitions in nitrogen-vacancy ensembles in diamond

Nuclear spin ensembles in diamond are promising candidates for quantum sensing applications, including rotation sensing. Here we perform a characterization of the optically detected nuclear-spin transitions associated with the 14N nuclear spin within diamond nitrogen vacancy (NV) centers. We observe nuclear-spin-dependent fluorescence with the contrast of optically detected 14N nuclear Rabi oscillations comparable to that of the NV electron spin. Using Ramsey spectroscopy, we investigate the temperature and magnetic-field dependence of the nuclear spin transitions in the 77.5-420 K and 350-675 G range, respectively. The nuclear quadrupole coupling constant Q was found to vary with temperature T yielding d|Q|/dT=-35.0(2) Hz/K at T=297 K. The temperature and magnetic field dependencies reported here are important for quantum sensing applications such as rotation sensing and potentially for applications in quantum information processing.

Coherent electrical control of a single high-spin nucleus in silicon.

Nuclear spins are highly coherent quantum objects. In large ensembles, their control and detection via magnetic resonance is widely exploited, for example, in chemistry, medicine, materials science and mining. Nuclear spins also featured in early proposals for solid-state quantum computers1 and demonstrations of quantum search2 and factoring3 algorithms. Scaling up such concepts requires controlling individual nuclei, which can be detected when coupled to an electron4-6. However, the need to address the nuclei via oscillating magnetic fields complicates their integration in multi-spin nanoscale devices, because the field cannot be localized or screened. Control via electric fields would resolve this problem, but previous methods7-9 relied on transducing electric signals into magnetic fields via the electron-nuclear hyperfine interaction, which severely affects nuclear coherence. Here we demonstrate the coherent quantum control of a single 123Sb (spin-7/2) nucleus using localized electric fields produced within a silicon nanoelectronic device. The method exploits an idea proposed in 196110 but not previously realized experimentally with a single nucleus. Our results are quantitatively supported by a microscopic theoretical model that reveals how the purely electrical modulation of the nuclear electric quadrupole interaction results in coherent nuclear spin transitions that are uniquely addressable owing to lattice strain. The spin dephasing time, 0.1 seconds, is orders of magnitude longer than those obtained by methods that require a coupled electron spin to achieve electrical driving. These results show that high-spin quadrupolar nuclei could be deployed as chaotic models, strain sensors and hybrid spin-mechanical quantum systems using all-electrical controls. Integrating electrically controllable nuclei with quantum dots11,12 could pave the way to scalable, nuclear- and electron-spin-based quantum computers in silicon that operate without the need for oscillating magnetic fields.

Dual-frequency spin-resonance spectroscopy of diamond nitrogen-vacancy centers in zero magnetic field

The methods for controlling spin states of negatively charged nitrogen-vacancy (NV) centers using microwave (MW) or radiofrequency (RF) excitation fields for electron spin and nuclear spin transitions are effective in strong magnetic fields where a level anti-crossing (LAC) occurs. A LAC can also occur at zero field in the presence of transverse strain or electric fields in the diamond crystal, leading to mixing of the spin states. In this paper, we investigate zero-field LAC of NV centers using dual-frequency excitation spectroscopy. Under RF modulation of the spin states, we observe sideband transitions and Autler-Townes splitting in the optically detected magnetic resonance (ODMR) spectra. Numerical simulations show that the splitting originates from Landau-Zener transition between electron spin |$\pm$1> states, which potentially provides a new way of manipulating NV center spin states in zero or weak magnetic field.

Multi-frequency ODMR of Nitrogen-Vacancy Color Centers in Diamond Crystals in zero magnetic fields

Techniques of optical detection of magnetic resonance, as applied tothe nitrogen-vacancy center in diamond, provide a tool for controlling both electron and nuclear spins. These techniques generally use a combination of microwave (MW) drive field for electronic spin transitions and radiofrequency (RF) drive field for nuclear spin transitions. They are most effective in strong magnetic fields where levels anticrossing (LAC) occurs; therefore NV spin system dynamics is mostly studied under these conditions. Nevertheless, zero-field LAC can probably also be used for controlling electron and nuclear spin states as well for exciting narrow resonances for metrological application, and these perspectives are not yet properly investigated. Here we present two-quantum resonances appearing in ODMR spectra of NV centers in bulk diamond under multi-frequency (MW+RF) resonance excitation in zero and ultra-low magnetic fields, and discuss their specifics.

Nuclear spin coherence properties of 151Eu3+ and 153Eu3+ in a Y2O3 transparent ceramic

We have measured inhomogeneous linewidths and coherence times (T2) of nuclear spin transitions in a Eu3+ :Y2O3 transparent ceramic by an all-optical spin echo technique. The nuclear spin echo decay curves showed a strong modulation which was attributed to interaction with Y nuclei in the host. The coherence time of the 29 MHz spin transition in 151Eu3+ was 16 ms in a small applied magnetic field. Temperature dependent measurements showed that the coherence time was constant up to 18 K and was limited by spin-lattice relaxation for higher temperatures. Nuclear spin echoes in 153Eu3+ gave much weaker signals than for the case of 151Eu3+ . The spin coherence time for the 73 MHz spin transition in 153Eu3+ was estimated to 14 ms in a small magnetic field. The study shows that the spin transitions of ceramic Eu3+ :Y2O3 have coherence properties comparable to the best rare-earth-doped materials available.

Proposal for Quantum Sensing Based on Two-Dimensional Dynamical Decoupling: NMR Correlation Spectroscopy of Single Molecules

Nuclear magnetic resonance (NMR) has enormous applications. Two-dimensional NMR is an essential technique to characterize correlations between nuclei and, hence, molecule structures. Towards the ultimate goal of single-molecule NMR, dynamical-decoupling- (DD) enhanced diamond quantum sensing enables the detection of single nuclear spins and nanoscale NMR. However, there is still the lack of a standard method in DD-based quantum sensing to characterize correlations between nuclear spins in single molecules. Here we present a scheme of two-dimensional DD-based quantum sensing, as a universal method for correlation spectroscopy of single molecules. We design two-dimensional DD sequences composed of two sets of periodic DD sequences with different periods, which can be independently set to match two different transition frequencies for resonant DD. We find that under the resonant DD condition the sensor coherence patterns, as functions of the two independent pulse numbers of DD subsequences, can fully determine different types of correlations between nuclear spin transitions. This work offers a systematic approach to correlation spectroscopy for single-molecule NMR.

Wide-band nanoscale magnetic resonance spectroscopy using quantum relaxation of a single spin in diamond

We demonstrate a wide-band all-optical method of nanoscale magnetic resonance (MR) spectroscopy under ambient conditions. Our method relies on cross-relaxation between a probe spin, the electronic spin of a nitrogen-vacancy centre in diamond, and target spins as the two systems are tuned into resonance. By optically monitoring the spin relaxation time ($T_1$) of the probe spin while varying the amplitude of an applied static magnetic field, a frequency spectrum of the target spin resonances, a $T_1$-MR spectrum, is obtained. As a proof of concept, we measure $T_1$-MR spectra of a small ensemble of $^{14}$N impurities surrounding the probe spin within the diamond, with each impurity comprising an electron spin 1/2 and a nuclear spin 1. The intrinsically large bandwidth of the technique and probe properties allows us to detect both electron spin transitions -- in the GHz range -- and nuclear spin transitions -- in the MHz range -- of the $^{14}$N spin targets. The measured frequencies are found to be in excellent agreement with theoretical expectations, and allow us to infer the hyperfine, quadrupole and gyromagnetic constants of the target spins. Analysis of the strength of the resonances obtained in the $T_1$-MR spectrum reveals that the electron spin transitions are probed via dipole interactions, while the nuclear spin resonances are dramatically enhanced by hyperfine coupling and an electron-mediated process. Finally, we investigate theoretically the possibility of performing $T_1$-MR spectroscopy on nuclear spins without hyperfine interaction and predict single-proton sensitivity using current technology. This work establishes $T_1$-MR as a simple yet powerful technique for nanoscale MR spectroscopy, with broadband capability and a projected sensitivity down to the single nuclear spin level.

Transition-Selective Pulses in Zero-Field Nuclear Magnetic Resonance.

We use low-amplitude, ultralow frequency pulses to drive nuclear spin transitions in zero and ultralow magnetic fields. In analogy to high-field NMR, a range of sophisticated experiments becomes available as these allow narrow-band excitation. As a first demonstration, pulses with excitation bandwidths 0.5-5 Hz are used for population redistribution, selective excitation, and coherence filtration. These methods are helpful when interpreting zero- and ultralow-field NMR spectra that contain a large number of transitions.

Spatially encoded multiple-quantum excitation

In this work, we present a simple method to spatially encode the transition frequencies of nuclear spin transitions and to read out these frequencies within a single scan. The experiment works by combining pulsed field gradients with an excitation sequence that selectively excites spin transitions within certain sample regions. After the initial excitation, imaging the resulting ẑ-magnetization is used to determine the locations where the excitations occurred, from which the corresponding transition frequencies are determined. Simple experimental demonstrations of this technique on one- and two-spin systems are presented.

Solid-State NMR Spectroscopy for the Physical Chemistry Laboratory

Solid-state nuclear magnetic resonance (NMR) spectroscopy finds growing application to inorganic and organic materials, biological samples, polymers, proteins, and cellular membranes. However, this technique is often neither included in laboratory curricula nor typically covered in undergraduate courses. On the other hand, spectroscopy and molecular structure taught in second-semester undergraduate physical chemistry courses meet the minimal background prerequisites for interpreting data obtained in many solid-state NMR experiments. A solid-state 2H NMR experiment is described in which the student obtains and interprets the spectrum of a powder sample of hexamethylbenzene-d18 using a solution NMR spectrometer as found in many undergraduate institutions. A quadrupolar-echo pulse sequence is applied to the sample to obtain the 2H NMR spectrum. The spectrum of a randomly oriented powder sample consists of two spectral branches with broad shoulders. The quadrupolar frequencies corresponding to the nuclear spin transitions are interpreted in terms of molecular mobility in the solid state, that is, 3-fold rotation of the methyl groups and 6-fold rotation of the hexamethylbenzene ring. In this way, students discover that solid substances may have significant molecular motions. This undergraduate investigation employing solid-state 2H NMR provides an informative exposure to state-of-the-art research techniques by using facilities that are already in place at many undergraduate institutions. Furthermore, it demonstrates a real-life manifestation of quantum mechanics as explained in physical chemistry courses, as well as fundamentals of molecular motions such as rotation of aromatic ring compounds and methyl groups in the solid state.

Resonant nuclear spin pumping in (In,Ga)As quantum dots

We report on the observation of resonant optical pumping of nuclear spin polarization in an ensemble of singly charged (In,Ga)As/GaAs quantum dots subject to a transverse magnetic field. Electron spin orientation by circularly polarized light with the polarization modulated at the nuclear spin transition frequency is found to create a significant nuclear spin polarization, precessing about the magnetic field. Synchronous rf field application along the optical excitation axis considerably enhances the effect. Nuclear spin resonances for all isotopes in the quantum dots are found in that way. In particular, transitions between states split off from the $|\ifmmode\pm\else\textpm\fi{}1/2\ensuremath{\rangle}$ doublets by the nuclear quadrupole interaction are identified.

Electrical Detection of Coherent Nuclear Spin Oscillations in Phosphorus-Doped Silicon using Pulsed ENDOR

We demonstrate the electrical detection of pulsed X-band electron nuclear double resonance (ENDOR) in phosphorus-doped silicon at 5 K. A pulse sequence analogous to Davies ENDOR in conventional electron spin resonance is used to measure the nuclear spin transition frequencies of the (31)P nuclear spins, where the (31)P electron spins are detected electrically via spin-dependent transitions through Si/SiO(2) interface states, thus not relying on a polarization of the electron spin system. In addition, the electrical detection of coherent nuclear spin oscillations is shown, demonstrating the feasibility to electrically read out the spin states of possible nuclear spin qubits.

IMSG09: A 57Fe-119Sn Mössbauer spectra computer fitting program with novel interactive user interface

A recently developed computer based 57Fe-119Sn Mössbauer spectra fitting program is described. The program uses full Hamiltonian matrices to generate theoretical Mössbauer spectral contributions with which fits the experimental data based on a least-squares minimization procedure. The user of the program can exploit its interactive user interface to built and modify on-the-fly a starting theoretical model of proposed contributions without the need to write or alter the initial Mössbauer parameter values to or from any file. Changes in the Mössbauer parameters values for the proposed model can be made on the screen and the theoretical contributions can be displayed during those changes in real time together with the experimental spectrum in order to give the user the ability to approximate with the best and fast way the desired solution before launching the minimization procedure. Single as well as multiple sub-component contributions with Gaussian-type spreading of quadrupole splitting/shift or hyperfine magnetic field values can be realized to fit transmission, conversion electron or X-ray Mössbauer spectra of randomly or non-randomly oriented powder or single crystal samples. The program is currently written for 3/2→1/2 nuclear spin transitions but can be modified to include higher spins, as well as distributions of other types and of other Mössbauer parameters values.

Optical polarization ofC13nuclei in diamond through nitrogen vacancy centers

We determine the polarization of the bulk $^{13}$C nuclear spin system in diamond produced by interaction with optically oriented nitrogen-vacancy (NV-) defect centers. $^{13}$C nuclei are polarized into the higher energy Zeeman state with a bulk-average polarization up to 5.2%, although local polarization may be higher. The kinetics of polarization are temperature independent, and occur within 5 minutes. Fluctuations in the dipolar field of the NV- center spin bath are identified as the mechanism by which nuclear spin transitions are induced near defect centers. Polarization is then transported to the bulk material via spin diffusion, which accounts for the observed kinetics of polarization. These results indicate control over the nuclear spin bath, a methodology to study dynamics of an NV- center ensemble, and application to sensitivity-enhanced NMR.

The quadrupole enhanced 1H spin–lattice relaxation of the amide proton in slow tumbling proteins

An analysis, based on the stochastic Liouville approach, is presented of the R(1)-NMRD or field dependent spin-lattice relaxation rate of amide protons. The proton relaxivity, displayed as R(1)-NMRD profiles, is calculated for a reorienting (1)H-(14)N spin group, where the inter spin coupling is due to spin dipole-dipole coupling or the scalar coupling. The quadrupole nucleus (14)N has an asymmetry parameter eta = 0.4 and a quadrupole interaction which is modulated by the overall reorientational motion of the protein. In the very slow reorientational regime, omega(Q)tau(R) >> 1 and tau(R) > or = 2.0 micros, both the dipole-dipole coupling and the scalar coupling yield a T(1)-NMRD profile with three marked peaks of proton spin relaxation enhancement. These peaks appear when the proton Larmor frequency, omega(I), matches the nuclear quadrupole spin transition frequencies: omega(1) = omega(Q)2eta/3, omega(2) = omega(Q)(1-eta/3) and omega(3) = omega(Q)(1 + eta/3), and the quadrupole spin system thus acts as a relaxation sink. The relative relaxation enhancements of the peaks are different for the dipole-dipole and the scalar coupling. Considering the dipole-dipole coupling, the low frequency peak, omega(1), is small compared to the high field peaks whereas for the scalar coupling the situation is changed. For slow tumbling proteins with a correlation time of tau(R) = 400 ns, omega(2) and omega(3) are not resolved but become one relatively broad peak. At even faster reorientation, tau(R) < 60 ns, the marked peaks disappear. In this motional regime, the main effect of the cross relaxation phenomenon is a subtle perturbation of the main amide proton T(1) NMRD dispersion. The low field part of it can be approximately described by a Lorentzian function: R(DD,SC)(0.01)/(1 + (omega(I)tau(R)3/2)(2)) whereas the high field part coincides with R(DD,SC)(0.01)/(1 + (omega(I)tau(R))(2)).