Pulsed Dynamic Nuclear Polarization Research Articles

Observation of dynamic nuclear polarization echoes.

It is demonstrated that the time evolution of the electron-nuclear polarization transfer process during pulsed dynamic nuclear polarization (DNP) can be reversed on a microsecond timescale, leading to the observation of DNP echoes. The DNP echoes are induced by consecutive application of two pulse trains that produce effective Hamiltonians that differ only in the sign of the effective hyperfine coupling. The experiments have been performed on a frozen solution of trityl radicals in water/glycerol on a homebuilt X-band electron paramagnetic resonance/DNP spectrometer at 80 kelvins. We envisage that DNP echoes will play an important role in future development of pulsed DNP for sensitivity-enhanced nuclear magnetic resonance, hyperfine spectroscopy, and quantum sensing.

Large-enhancement nanoscale dynamic nuclear polarization near a silicon nanowire surface.

Dynamic nuclear polarization (DNP) has revolutionized the field of nuclear magnetic resonance spectroscopy, expanding its reach and capabilities to investigate diverse materials, biomolecules, and complex dynamic processes. Bringing high-efficiency DNP to the nanometer scale would open exciting avenues for studying nanoscale nuclear spin ensembles, such as single biomolecules, virus particles, and condensed matter systems. Combining pulsed DNP with nanoscale force-detected magnetic resonance measurements, we demonstrated a 100-fold enhancement in the Boltzmann polarization of proton spins in nanoscale sugar droplets at 6 kelvin and 0.33 tesla. Crucially, this enhancement corresponds to a factor of 200 reduction in the averaging time compared to measurements that rely on the detection of statistical fluctuations in nanoscale nuclear spin ensembles. These results substantially advance the capabilities of force-detected magnetic resonance detection as a practical tool for nanoscale imaging.

Investigation of the Alzofon weight reduction experiment using NMR spectroscopy

The origin of gravity is a fundamental question in physics that has yet to be conclusively answered. Frederick Alzofon came up with an alternative idea about the origin of the gravitational field, in which the gravitational force arises from the interaction of subatomic particles and that the gravitational force between the particles of a system decreases during a process of retrogression from an ordered system to a disordered system. To prove his hypothesis, Alzofon used pulsed dynamic nuclear polarization to create such an order of particles within a test object and claims to have measured distinct changes in weight. This work describes an experiment to investigate Alzofon’s assumptions using NMR spectroscopy for nuclear spin polarization. It was shown that with certain measurement parameters, an apparent change in weight was indeed measured, but was ultimately found to be a temperature effect.

Towards a unified picture of polarization transfer — pulsed DNP and chemically equivalent PHIP

Nuclear spin hyperpolarization techniques, such as dynamic nuclear polarization (DNP) and parahydrogen-induced polarization (PHIP), have revolutionized nuclear magnetic resonance and magnetic resonance imaging. In these methods, a readily available source of high spin order, either electron spins in DNP or singlet states in hydrogen for PHIP, is brought into close proximity with nuclear spin targets, enabling efficient transfer of spin order under external quantum control. Despite vast disparities in energy scales and interaction mechanisms between electron spins in DNP and nuclear singlet states in PHIP, a pseudo-spin formalism allows us to establish an intriguing equivalence. As a result, the important low-field polarization transfer regime of PHIP can be mapped onto an analogous system equivalent to pulsed-DNP. This establishes a correspondence between key polarization transfer sequences in PHIP and DNP, facilitating the transfer of sequence development concepts. This promises fresh insights and significant cross-pollination between DNP and PHIP polarization sequence developers.

Suppression of Pulsed Dynamic Nuclear Polarization by Many-Body Spin Dynamics.

We study a mechanism by which nuclear hyperpolarization due to the polarization transfer from a microwave-pulse-controlled electron spin is suppressed. From analytical and numerical calculations of the unitary dynamics of multiple nuclear spins, we uncover that, combined with the formation of the dark state within a cluster of nuclei, coherent higher-order nuclear spin dynamics impose limits on the efficiency of the polarization transfer even in the absence of mundane depolarization processes such as nuclear spin diffusion and relaxation. Furthermore, we show that the influence of the dark state can be partly mitigated by introducing a disentangling operation. Our analysis is applied to the nuclear polarizations observed in ^{13}C nuclei coupled with a single nitrogen-vacancy center in diamond [Randall etal., Science 374, 1474 (2021)SCIEAS0036-807510.1126/science.abk0603]. Our Letter sheds light on collective engineering of nuclear spins as well as future designs of pulsed dynamic nuclear polarization protocols.

Pulsed dynamic nuclear polarization: a comprehensive Floquet description.

Dynamic nuclear polarization (DNP) experiments using microwave (mw) pulse sequences are one approach to transfer the larger polarization on the electron spin to nuclear spins of interest. How the result of such experiments depends on the external magnetic field and the excitation power is part of an ongoing debate and of paramount importance for applications that require high chemical-shift resolution. To date numerical simulations using operator-based Floquet theory have been used to predict and explain experimental data. However, such numerical simulations provide only limited insight into parameters relevant for efficient polarization transfer, such as transition amplitudes or resonance offsets. Here we present an alternative method to describe pulsed DNP experiments by using matrix-based Floquet theory. This approach leads to analytical expressions for the transition amplitudes and resonance offsets. We validate the method by comparing computations by these analytical expressions to their numerical counterparts and to experimental results for the XiX, TOP and TPPM DNP sequences. Our results explain the experimental data and are in very good agreement with the numerical simulations. The analytical expressions allow for the discussion of the scaling behaviour of pulsed DNP experiments with respect to the external magnetic field. We find that the transition amplitudes scale inversely with the external magnetic field.

Dynamic nuclear polarization pulse sequence engineering using single-spin vector effective Hamiltonians.

Dynamic nuclear polarization (DNP) has proven to be a powerful technique to enhance nuclear spin polarization by transferring the much higher electron spin polarization to nuclear spins prior to detection. While major attention has been devoted to high-field applications with continuous microwave irradiation, the introduction of fast arbitrary waveform generators is gradually increasing opportunities for the realization of pulsed DNP. Here, we describe how static-powder DNP pulse sequences may systematically be designed using single-spin vector effective Hamiltonian theory. Particular attention is devoted to the intricate interplay between two important parts of the effective first-order Hamiltonian, namely, linear field (single-spin) terms and Fourier coefficients determining scaling of the bilinear coupling terms mediating polarization transfer. We address two cases. The first case operates in the regime, where the microwave field amplitude is lower than the nuclear Larmor frequency. Here, we illustrate the predictive strength of a single-spin vector model by comparing analytical calculations with experimental DNP results at 9.8 GHz/15 MHz on trityl radicals at 80 K. The second case operates in the high-power regime, where we combine the underlying single-spin vector design principles with numerical non-linear optimization to optimize the balance between the linear terms and the bilinear Fourier coefficients in a figure of merit function. We demonstrate, numerically and experimentally, a broadband DNP pulse sequence PLATO (PoLarizAtion Transfer via non-linear Optimization) with a bandwidth of 80 MHz and optimized for a microwave field with a maximum (peak) amplitude of 32 MHz.

Nitrogen Substitutions Aggregation and Clustering in Diamonds as Revealed by High-Field Electron Paramagnetic Resonance.

Diamonds have been shown to be an excellent platform for quantum computing and quantum sensing applications. These applications are enabled by the presence of defects in the lattice, which are also known as color centers. The most common nitrogen-based defect in synthetic diamonds is the paramagnetic nitrogen substitution (P1) center. While the majority of quantum applications rely on nitrogen-vacancy (NV) centers, the properties of the latter are heavily influenced by the presence and the spatial distribution of the P1 centers. Hence, understanding the spatial distribution and mutual interactions of P1 centers is crucial for the successful development of diamond-based quantum devices. Unlike NV centers, P1 centers do not have a spin-dependent optical signature, and their spin-related properties, therefore, have to be detected and characterized using magnetic resonance methods. We show that using high-field (6.9 and 13.8 T) pulsed electron paramagnetic resonance (EPR) and dynamic nuclear polarization (DNP) experiments, we can distinguish and quantify three distinct populations of P1 centers: isolated P1 centers, weakly interacting ones, and exchange-coupled ones that are clustered together. While such clustering was suggested before, these clusters were never detected directly and unambiguously. Moreover, by using electron-electron double resonance (ELDOR) pump-probe experiments, we demonstrate that the latter clustered population does not exist in isolation but coexists with the more weakly interacting P1 centers throughout the diamond lattice. Its presence thus strongly affects the quantum properties of the diamond. We also show that the existence of this population can explain recent hyperpolarization results in type Ib high-pressure, high-temperature (HPHT) diamonds. We propose a combination of high-field pulsed EPR, ELDOR, and DNP as a tool for probing the aggregation state and interactions among different populations of nitrogen substitution centers.

Designing broadband pulsed dynamic nuclear polarization sequences in static solids.

Dynamic nuclear polarization (DNP) is a nuclear magnetic resonance (NMR) hyperpolarization technique that mediates polarization transfer from unpaired electrons with large thermal polarization to NMR-active nuclei via microwave (mw) irradiation. The ability to generate arbitrarily shaped mw pulses using arbitrary waveform generators allows for remarkable improvement of the robustness and versatility of DNP. We present here novel design principles based on single-spin vector effective Hamiltonian theory to develop new broadband DNP pulse sequences, namely, an adiabatic version of XiX (X–inverse X)–DNP and a broadband excitation by amplitude modulation (BEAM)–DNP experiment. We demonstrate that the adiabatic BEAM-DNP pulse sequence may achieve a 1H enhancement factor of ∼360, which is better than ramped-amplitude NOVEL (nuclear spin orientation via electron spin locking) at ∼0.35 T and 80 K in static solids doped with trityl radicals. In addition, the bandwidth of the BEAM-DNP experiments (~50 MHz) is about three times the 1H Larmor frequency. The generality of our theoretical approach will be helpful in the development of new pulsed DNP sequences.

Efficient Pulsed Dynamic Nuclear Polarization with the X-Inverse-X Sequence.

Pulsed dynamic nuclear polarization (DNP) is a promising new approach to enhancing the sensitivity of high-resolution magic-angle spinning (MAS) NMR. In pulsed DNP, the transfer of polarization from unpaired electrons to nuclei (usually 1H) is induced by a sequence of microwave pulses. Enhancement factors of the thermal 1H polarization are expected to be independent of the magnetic field, and sample heating by absorption of microwave irradiation will be strongly reduced. The development of DNP pulse sequences is still in its infancy. Of the two basic sequences in existence, NOVEL and TOP DNP, the former is, due to an extremely high power requirement, incompatible with high-resolution MAS NMR, while the latter displays a relatively slow transfer of polarization from electrons to 1H. We introduce here a new pulse sequence for DNP of solids, termed X-inverse-X (XiX) DNP. In experiments at 1.2 T, XiX DNP produces, compared to TOP DNP, a 2-fold higher gain in sensitivity. Our data suggest that a faster transfer of polarization from electrons to 1H is behind the superior performance of XiX DNP. Numerical simulations and experiments indicate that microwave pulse lengths can be chosen across a broad range, without loss of efficiency. These findings are a substantial step toward the implementation of pulsed DNP at high magnetic fields.

DNPSOUP: A simulation software package for dynamic nuclear polarization

Dynamic Nuclear Polarization Simulation Optimized with a Unified Propagator (DNPSOUP) is an open-source numerical software program that models spin dynamics for dynamic nuclear polarization (DNP). The software package utilizes a direct numerical approach using the inhomogeneous master equation to treat the time evolution of the spin density operator under coherent Hamiltonians and stochastic relaxation effects. Here we present the details of the theory behind the software, starting from the master equation, and arriving at characteristic operators for any section of density operator time-evolution. We then provide an overview of the DNPSOUP software architecture. The efficacy of the program is demonstrated by simulating DNP field profiles on small spin systems exploiting both continuous wave and time-domain DNP mechanisms. Examples include Zeeman field profiles for the solid effect, Overhauser effect, and cross effect, and microwave field profiles for NOVEL, off-resonance NOVEL, the integrated solid effect, the stretched solid effect, and TOP-DNP. The software should facilitate a better understanding of the DNP process, aid in the design of optimized DNP polarizing agents, and allow us to examine new pulsed DNP methods at conditions that are not currently experimentally accessible, especially at high magnetic fields with high-power microwave pulses.

Adiabatic Solid Effect.

The solid effect (SE) is a two spin dynamic nuclear polarization (DNP) mechanism that enhances the sensitivity in NMR experiments by irradiation of the electron-nuclear spin transitions with continuous wave (CW) microwaves at ω0S ± ω0I, where ω0S and ω0I are electron and nuclear Larmor frequencies, respectively. Using trityl (OX063), dispersed in a 60/40 glycerol/water mixture at 80 K, as a polarizing agent, we show here that application of a chirped microwave pulse, with a bandwidth comparable to the EPR line width applied at the SE matching condition, improves the enhancement by a factor of 2.4 over the CW method. Furthermore, the chirped pulse yields an enhancement that is ∼20% larger than obtained with the ramped-amplitude NOVEL (RA-NOVEL), which to date has achieved the largest enhancements in time domain DNP experiments. Numerical simulations suggest that the spins follow an adiabatic trajectory during the polarization transfer; hence, we denote this sequence as an adiabatic solid effect (ASE). We foresee that ASE will be a practical pulsed DNP experiment to be implemented at higher static magnetic fields due to the moderate power requirement. In particular, the ASE uses only 13% of the maximum microwave power required for RA-NOVEL.

Theoretical Treatment of Pulsed DNP Experiments: Effects of Spectral Exchange

In the present work, we provide a theoretical treatment of pulsed Overhauser-type dynamic nuclear polarization (DNP) in the presence of spectral exchange, namely, Heisenberg exchange. The expression for the DNP enhancement of a nuclear magnetic resonance (NMR) signal is generalized by redefining the “deviation factor”, expressing the deviation of the electron spin polarization from its equilibrium value, averaged over the period of the pulse sequence. We can demonstrate that spectral exchange significantly increases the deviation factor and, thus, the NMR enhancement. The present treatment allows one to determine the optimal pumping frequency at different exchange rates.

Time-optimized pulsed dynamic nuclear polarization.

Pulsed dynamic nuclear polarization (DNP) techniques can accomplish electron-nuclear polarization transfer efficiently with an enhancement factor that is independent of the Zeeman field. However, they often require large Rabi frequencies and, therefore, high-power microwave irradiation. Here, we propose a new low-power DNP sequence for static samples that is composed of a train of microwave pulses of length τp spaced with delays d. A particularly robust DNP condition using a period τm = τp + d set to ~1.25 times the Larmor period τLarmor is investigated which is a time-optimized pulsed DNP sequence (TOP-DNP). At 0.35 T, we obtained an enhancement of ~200 using TOP-DNP compared to ~172 with nuclear spin orientation via electron spin locking (NOVEL), a commonly used pulsed DNP sequence, while using only ~7% microwave power required for NOVEL. Experimental data and simulations at higher fields suggest a field-independent enhancement factor, as predicted by the effective Hamiltonian.

Determination of the position of a single nuclear spin from free nuclear precessions detected by a solid-state quantum sensor

We report on a nanoscale quantum-sensing protocol which tracks a free precession of a single nuclear spin and is capable of estimating an azimuthal angle---a parameter which standard multipulse protocols cannot determine---of the target nucleus. Our protocol combines pulsed dynamic nuclear polarization, a phase-controlled radiofrequency pulse, and a multipulse AC sensing sequence with a modified readout pulse. Using a single nitrogen-vacancy center as a solid-state quantum sensor, we experimentally demonstrate this protocol on a single 13C nuclear spin in diamond and uniquely determine the lattice site of the target nucleus. Our result paves the way for magnetic resonance imaging at the single-molecular level.

Magic angle spinning NMR with metallized rotors as cylindrical microwave resonators.

We introduce a novel design for millimeter wave electromagnetic structures within magic angle spinning (MAS) rotors. In this demonstration, a copper coating is vacuum deposited onto the outside surface of a sapphire rotor at a thickness of 50nm. This thickness is sufficient to reflect 197-GHz microwaves, yet not too thick as to interfere with radiofrequency fields at 300MHz or prevent sample spinning due to eddy currents. Electromagnetic simulations of an idealized rotor geometry show a microwave quality factor of 148. MAS experiments with sample rotation frequencies of ωr /2π=5.4kHz demonstrate that the drag force due to eddy currents within the copper does not prevent sample spinning. Spectra of sodium acetate show resolved 13 C J-couplings of 60Hz and no appreciable broadening between coated and uncoated sapphire rotors, demonstrating that the copper coating does not prevent shimming and high-resolution nuclear magnetic resonance spectroscopy. Additionally, 13 C Rabi nutation curves of ω1 /2π=103kHz for both coated and uncoated rotors indicate no detrimental impact of the copper coating on radio frequency coupling of the nuclear spins to the sample coil. We present this metal coated rotor as a first step towards an MAS resonator. MAS resonators are expected to have a significant impact on developments in electron decoupling, pulsed dynamic nuclear polarization (DNP), room temperature DNP, DNP with low-power microwave sources, and electron paramagnetic resonance detection.

Frequency-agile gyrotron for electron decoupling and pulsed dynamic nuclear polarization

We describe a frequency-agile gyrotron which can generate frequency-chirped microwave pulses. An arbitrary waveform generator (AWG) within the NMR spectrometer controls the microwave frequency, enabling synchronized pulsed control of both electron and nuclear spins. We demonstrate that the acceleration of emitted electrons, and thus the microwave frequency, can be quickly changed by varying the anode voltage. This strategy results in much faster frequency response than can be achieved by changing the potential of the electron emitter, and does not require a custom triode electron gun. The gyrotron frequency can be swept with a rate of 20 MHz/μs over a 670 MHz bandwidth in a static magnetic field. We have already implemented time-domain electron decoupling with dynamic nuclear polarization (DNP) magic angle spinning (MAS) with this device. In this contribution, we show frequency-swept DNP enhancement profiles recorded without changing the NMR magnet or probe. The profile of endofullerenes exhibits a DNP profile with a <10 MHz linewidth, indicating that the device also has sufficient frequency stability, and therefore phase stability, to implement pulsed DNP mechanisms such as the frequency-swept solid effect. We describe schematics of the mechanical and vacuum construction of the device which includes a novel flanged sapphire window assembly. Finally, we discuss how commercially available continuous-wave gyrotrons can potentially be converted into similar frequency-agile high-power microwave sources.

Magic angle spinning NMR below 6 K with a computational fluid dynamics analysis of fluid flow and temperature gradients

We report magic angle spinning (MAS) up to 8.5 kHz with a sample temperature below 6 K using liquid helium as a variable temperature fluid. Cross polarization 13C NMR spectra exhibit exquisite sensitivity with a single transient. Remarkably, 1H saturation recovery experiments show a 1H T1 of 21 s with MAS below 6 K in the presence of trityl radicals in a glassy matrix. Leveraging the thermal spin polarization available at 4.2 K versus 298 K should result in 71 times higher signal intensity. Taking the 1H longitudinal relaxation into account, signal averaging times are therefore predicted to be expedited by a factor of >500. Computer assisted design (CAD) and finite element analysis were employed in both the design and diagnostic stages of this cryogenic MAS technology development. Computational fluid dynamics (CFD) models describing temperature gradients and fluid flow are presented. The CFD models bearing and drive gas maintained at 100 K, while a colder helium variable temperature fluid stream cools the center of a zirconia rotor. Results from the CFD were used to optimize the helium exhaust path and determine the sample temperature. This novel cryogenic experimental platform will be integrated with pulsed dynamic nuclear polarization and electron decoupling to interrogate biomolecular structure within intact human cells.

Off-resonance NOVEL.

Dynamic nuclear polarization (DNP) is theoretically able to enhance the signal in nuclear magnetic resonance (NMR) experiments by a factor γe/γn, where γ's are the gyromagnetic ratios of an electron and a nuclear spin. However, DNP enhancements currently achieved in high-field, high-resolution biomolecular magic-angle spinning NMR are well below this limit because the continuous-wave DNP mechanisms employed in these experiments scale as ω0-n where n ∼ 1-2. In pulsed DNP methods, such as nuclear orientation via electron spin-locking (NOVEL), the DNP efficiency is independent of the strength of the main magnetic field. Hence, these methods represent a viable alternative approach for enhancing nuclear signals. At 0.35 T, the NOVEL scheme was demonstrated to be efficient in samples doped with stable radicals, generating 1H NMR enhancements of ∼430. However, an impediment in the implementation of NOVEL at high fields is the requirement of sufficient microwave power to fulfill the on-resonance matching condition, ω0I = ω1S, where ω0I and ω1S are the nuclear Larmor and electron Rabi frequencies, respectively. Here, we exploit a generalized matching condition, which states that the effective Rabi frequency, ω1Seff, matches ω0I. By using this generalized off-resonance matching condition, we generate 1H NMR signal enhancement factors of 266 (∼70% of the on-resonance NOVEL enhancement) with ω1S/2π = 5 MHz. We investigate experimentally the conditions for optimal transfer of polarization from electrons to 1H both for the NOVEL mechanism and the solid-effect mechanism and provide a unified theoretical description for these two historically distinct forms of DNP.

Ramped-amplitude NOVEL.

We present a pulsed dynamic nuclear polarization (DNP) study using a ramped-amplitude nuclear orientation via electron spin locking (RA-NOVEL) sequence that utilizes a fast arbitrary waveform generator (AWG) to modulate the microwave pulses together with samples doped with narrow-line radicals such as 1,3-bisdiphenylene-2-phenylallyl (BDPA), sulfonated-BDPA (SA-BDPA), and trityl-OX063. Similar to ramped-amplitude cross polarization in solid-state nuclear magnetic resonance, RA-NOVEL improves the DNP efficiency by a factor of up to 1.6 compared to constant-amplitude NOVEL (CA-NOVEL) but requires a longer mixing time. For example, at τmix = 8 μs, the DNP efficiency reaches a plateau at a ramp amplitude of ∼20 MHz for both SA-BDPA and trityl-OX063, regardless of the ramp profile (linear vs. tangent). At shorter mixing times (τmix = 0.8 μs), we found that the tangent ramp is superior to its linear counterpart and in both cases there exists an optimum ramp size and therefore ramp rate. Our results suggest that RA-NOVEL should be used instead of CA-NOVEL as long as the electronic spin lattice relaxation T1e is sufficiently long and/or the duty cycle of the microwave amplifier is not exceeded. To the best of our knowledge, this is the first example of a time domain DNP experiment that utilizes modulated microwave pulses. Our results also suggest that a precise modulation of the microwave pulses can play an important role in optimizing the efficiency of pulsed DNP experiments and an AWG is an elegant instrumental solution for this purpose.