Double-quantum Coherence Research Articles

Ultrafast four-wave-mixing spectroscopy with two vacuum fields and coincidence-double-heterodyne detection

In classical macroscopic ultrafast optical four-wave mixing signals, phase matching selects three classes of light–matter interaction pathways: double quantum coherence; non-rephasing; and photon-echo. Multiple pathways contribute to each of these signals. We show that a coincidence-double-heterodyne detection scheme that employs two classical and two vacuum fields can isolate a single pathway contribution to each of these signals. We further demonstrate the advantage of the proposed technique by comparing it with the classical photon-echo signal for a model Frenkel-exciton dimer.

An analysis of double-quantum coherence ESR in an N-spin system: Analytical expressions and predictions.

Electron spin resonance pulsed dipolar spectroscopy (PDS) has become popular in protein 3D structure analysis. PDS studies yield distance distributions between a pair or multiple pairs of spin probes attached to protein molecules, which can be used directly in structural studies or as constraints in theoretical predictions. Double-quantum coherence (DQC) is a highly sensitive and accurate PDS technique to study protein structures in the solid state and under physiologically relevant conditions. In this work, we have derived analytical expressions for the DQC signal for a system with N-dipolar coupled spin-1/2 particles in the solid state. The expressions are integrated over the relevant spatial parameters to obtain closed form DQC signal expressions. These expressions contain the concentration-dependent "instantaneous diffusion" and the background signal. For micromolar and lower concentrations, these effects are negligible. An approximate analysis is provided for cases of finite pulses. The expressions obtained in this work should improve the analysis of DQC experimental data significantly, and the analytical approach could be extended easily to a wide range of magnetic resonance phenomena.

Extracting double-quantum coherence in two-dimensional electronic spectroscopy under pump-probe geometry.

Two-dimensional electronic spectroscopy (2DES) can be implemented with different geometries, e.g., BOXCARS, collinear, and pump-probe geometries. The pump-probe geometry has the advantage of overlapping only two beams and reducing phase cycling steps. However, its applications are typically limited to observing the dynamics with single-quantum coherence and population, leaving the challenge to measure the dynamics of the double-quantum (2Q) coherence, which reflects the many-body interactions. We demonstrate an experimental technique in 2DES under pump-probe geometry with a designed pulse sequence and the signal processing method to extract 2Q coherence. In the designed pulse sequence, with the probe pulse arriving earlier than the pump pulses, our measured signal includes the 2Q signal as well as the zero-quantum signal. With phase cycling and data processing using causality enforcement, we extract the 2Q signal. The proposal is demonstrated with rubidium atoms. We observe the collective resonances of two-body dipole-dipole interactions in both the D1 and D2 lines.

Various facets of intermolecular transfer of phase coherence by nuclear dipolar fields.

It has long been recognized that dipolar fields can mediate intermolecular transfer of phase coherence from abundant solvent to sparse solute spins. Generally, the dipolar field has been considered while acting during prolonged free-precession delays. Recently, we have shown that transfer can also occur during suitable uninterrupted radio frequency pulse trains that are used for total correlation spectroscopy. Here, we will expand upon the latter work. First, analytical expressions for the evolution of the solvent magnetization under continuous irradiation and the influence of the dipolar field are derived. These expressions facilitate the simulations of the transfer process. Then, a pulse sequence for the retrieval of high-resolution spectra in inhomogeneous magnetic fields is described, along with another sequence to detect a transfer from an intermolecular double-quantum coherence. Finally, various schemes are discussed where the magnetization is modulated by a combination of multiple selective radio frequency pulses and pulsed field gradients in different directions. In these schemes, the magnetization is manipulated in such a way that the dipolar field, which originates from a single-spin species, can be decomposed into two components. Each component originates from a part of the magnetization that is modulated in a different direction. Both can independently, but simultaneously, mediate an intermolecular transfer of phase coherence.

Double Quantum Coherence ESR at Q-Band Enhances the Sensitivity of Distance Measurements at Submicromolar Concentrations.

Recently, there have been remarkable improvements in pulsed ESR sensitivity, paving the way for broader applicability of ESR in the measurement of biological distance constraints, for instance, at physiological concentrations and in more complex systems. Nevertheless, submicromolar distance measurements with the commonly used nitroxide spin label take multiple days. Therefore, there remains a need for rapid and reliable methods of measuring distances between spins at nanomolar concentrations. In this work, we demonstrate the power of double quantum coherence (DQC) experiments at Q-band frequencies. With the help of short and intense pulses, we showcase DQC signals on nitroxide-labeled proteins with modulation depths close to 100%. We show that the deep dipolar modulations aid in the resolution of bimodal distance distributions. Finally, we establish that distance measurements with protein concentrations as low as 25 nM are feasible. This limit is approximately 4-fold lower than previously possible. We anticipate that nanomolar concentration measurements will lead to further advancements in the use of ESR, especially in cellular contexts.

Time-Frequency Analysis of Two-Dimensional Electron Spin Resonance Signals.

Two-dimensional electron spin resonance (2D ESR) spectroscopy is a unique experimental technique for probing protein structure and dynamics, including processes that occur at the microsecond time scale. While it provides significant resolution enhancement over the one-dimensional experimental setup, spectral broadening and noise make extraction of spectral information highly challenging. Traditionally, two-dimensional Fourier transform (2D FT) is applied for the analysis of 2D ESR signals, although its efficiency is limited to stationary signals. In addition, it often fails to resolve overlapping peaks in 2D ESR. In this work, we propose a time-frequency analysis of 2D time-domain signals, which identifies all frequency peaks by decoupling a signal into its distinct constituent components via projection on the time-frequency plane. The method utilizes 2D undecimated discrete wavelet transform (2D UDWT) as an intermediate step in the analysis, followed by signal reconstruction and 2D FT. We have applied the method to a simulated 2D double quantum coherence (DQC) signal for validation and a set of experimental 2D ESR signals, demonstrating its efficiency in resolving overlapping peaks in the frequency domain, while displaying frequency evolution with time in case of non-stationary data.

Pulse overlap artifacts and double quantum coherence spectroscopy.

The double quantum coherence (DQC) signal in nonlinear spectroscopy gives information about the many-body correlation effects not easily available by other methods. The signal is short-lived, consequently, a significant part of it is generated during the pulse overlap. Since the signal is at two times the laser frequency, one may intuitively expect that the pulse overlap-related artifacts are filtered out by the Fourier transform. Here, we show that this is not the case. We perform explicit calculations of phase-modulated two-pulse experiments of a two-level system where the DQC is impossible. Still, we obtain a significant signal at the modulation frequency, which corresponds to the DQC, while the Fourier transform over the pulse delay shows a double frequency. We repeat the calculations with a three-level system where the true DQC signal occurs. We conclude that with realistic dephasing times, the pulse-overlap artifact can be significantly stronger than the DQC signal. Our results call for great care when analyzing such experiments. As a rule of thumb, we recommend that only delays larger than 1.5 times the pulse length should be used.

In situ enzymatic hydrolysis characterisation of phospholipid using 1H NMR in a heterogeneous environment

Enzymatic hydrolysis of phospholipids is an important biological event in organisms that is also widely applied in the food industry. In situ nuclear magnetic resonance (NMR) is a powerful non-invasive technique for studying the mechanism of enzymatic reactions. However, their application in phospholipid hydrolysis is limited. In this study, we demonstrated that in a phospholipase A1 (PLA1)-catalysed 1,2-diacyl-sn-glycero-3-phosphocholine (POPC) hydrolysis system in an aqueous emulsion, the accumulation of POPC hydrolysates caused severe heterogeneity, which significantly reduced the 1H NMR spectral intensity and resolution. To overcome the sample heterogeneity, we used the intermolecular dipolar-interaction enhanced all lines-II (IDEAL-II) sequence to obtain one-dimensional (1D) high-resolution 1H intermolecular double quantum coherence (iDQCs) NMR spectra through two-dimensional (2D) acquisition. These spectra enabled us to assign and trace the characteristic peaks of POPC and its hydrolysates in real time. In particular, we performed quantitative estimation of the reaction kinetics based on the g2 and g3 protons and provided direct evidence of the enzymatic hydrolysis process. This study not only fills the gap in 1D 1H spectrum data of phospholipids and their mixtures with hydrolysates, but also provides an effective method for a comprehensive and rapid analysis of fatty acids and even more complex heterogeneous systems.

Vibrational response functions for multidimensional electronic spectroscopy in nonadiabatic models.

The interplay of nuclear and electronic dynamics characterizes the multidimensional electronic spectra of various molecular and solid-state systems. Theoretically, the observable effect of such interplay can be accounted for by response functions. Here, we report analytical expressions for the response functions corresponding to a class of model systems. These are characterized by coupling between the diabatic electronic states and the vibrational degrees of freedom, resulting in linear displacements of the corresponding harmonic oscillators, and by nonadiabatic couplings between pairs of diabatic states. In order to derive the linear response functions, we first perform the Dyson expansion of the relevant propagators with respect to the nonadiabatic component of the Hamiltonian, then derive and expand with respect to the displacements the propagators at given interaction times, and finally provide analytical expressions for the time integrals that lead to the different contributions to the linear response function. The approach is then applied to the derivation of third-order response functions describing different physical processes: ground state bleaching, stimulated emission, excited state absorption, and double quantum coherence. Comparisons between the results obtained up to sixth order in the Dyson expansion and independent numerical calculation of the response functions provide evidence of the series convergence in a few representative cases.

Comparison of through-space homonuclear correlations between quadrupolar nuclei in solids

Various two-dimensional (2D) homonuclear correlation experiments have been proposed to observe proximities between identical half-integer spin quadrupolar nuclei in solids. These experiments select either the single- or double-quantum coherences during the indirect evolution period, t1. We compare here the efficiency and the robustness of the 2D double-quantum to single-quantum (DQ-SQ) and SQ-SQ homonuclear correlations for two half-integer spin quadrupolar isotopes subject to small chemical shift anisotropy (CSA): 11B with a nuclear spin I = 3/2 and 27Al with I = 5/2. Such a comparison is performed using experiments on two model samples: Li2B4O7 for 11B and AlPO4-14 for 27Al. For both isotopes, the DQ-SQ homonuclear correlations are recommended since they allow probing the proximities between nuclei with close or identical frequencies. In the case of small or moderate isotropic chemical shift differences (e.g. 11B) the [SR221] or [BR221] bracketed DQ-SQ recoupling schemes are recommended; whereas it is the BR221 un-bracketed one otherwise (e.g. 27Al).

Two-dimensional electronic spectroscopy of an ultracold gas.

Femtosecond coherent multidimensional spectroscopy is demonstrated for an ultracold gas. A setup for phase modulation spectroscopy is used to probe the 32S1/2-22P1/2,3/2 transition in an 800μK-cold sample of 7Li atoms confined in a magneto-optical trap. The observation of a double quantum coherence response, a signature of interparticle interactions, paves the way for detailed investigations of few- and many-body effects in ultracold gases using this technique. The experiment combines a frequency resolution of 3 GHz with a potential time resolution of 200 fs, which allows for high-resolution studies of ultracold atoms and molecules both in the frequency and in the time domain.

Origin and remedy for HSQC artifacts in proton-detected INADEQUATE spectra.

NMR pulse sequences visualizing 1JCC and nJCC bond connectivity via an intermediate state of 13C-13C double-quantum coherence and 1H detection are an indispensable tool to solve small-molecule structures at the natural abundance level of 13C. A longstanding issue with these experiments set up to display 2D spectra with single-quantum frequencies is that in addition to the 1H-13C-13C correlations of interest, appearance of HSQC-type artifacts can complicate analysis and obscure JCC connectivities. The origin of these artifacts is described and remedies for their suppression are introduced. They include refocusing of 1JCH couplings prior to creation of 13C-13C double-quantum coherence, which is known to enhance sensitivity by reducing loss into zero-quantum coherence for pairs of two protonated 13C.

A new 13C trityl-based spin label enables the use of DEER for distance measurements

Triarylmethyl (TAM)-based labels, while still underutilized, are a powerful class of labels for pulsed-Electron Spin Resonance (ESR) distance measurements. They feature slow relaxation rates for long-lasting signals, high stability for cellular experiments, and narrow spectral features for efficient excitation of the spins. However, the typical narrow line shape limits the available distance measurements to only single-frequency experiments, such as Double Quantum Coherence (DQC) and Relaxation Induced Dipolar Modulation Enhancement (RIDME), which can be complicated to perform or hard to process. Therefore, widespread usage of TAM labels can be enhanced by the use of Double Electron-Electron Resonance (DEER) distance measurements. In this work, we developed a new spin label, 13C1-mOX063-d24, with a 13C isotope as the radical center. Due to the resolved hyperfine splitting, the spectrum is sufficiently broadened to permit DEER-based experiments at Q-band spectrometers. Additionally, this new label can be incorporated orthogonally with Cu(II)-based protein label. The orthogonal labeling scheme enables DEER distance measurement at X-band frequencies. Overall, the new trityl label allows for DEER-based distance measurements that complement existing TAM-label DQC and RIDME experiments.

In-phase simultaneous spectral editing of lactate and alanine with suppression of J-coupled lipids by the modified selective multiple quantum coherence sequences

1H magnetic resonance spectroscopy (MRS) with the multiple quantum coherence (MQC) technique allows for the detection of lactate, an end product of glycolysis, in the environment of lipids. The method can also be used to detect alanine, a byproduct of glutaminolysis. An issue is that when both lactate and alanine are detected together by the MQC technique, a phase mismatch arises between lactate and alanine signals due to off-resonance rotations and the difference in double quantum coherence frequencies between the two molecules. Such phase mismatch can cause errors in spectral fitting and metabolite quantification. In this study, we designed two pulse sequences that eliminate such phase differences of lactate and alanine while suppressing lipid signals by modifications of the Selective Multiple Quantum Coherence (Sel-MQC) sequence, a well-known MQC technique. Using the product operator formalism and the off-resonance rotation matrices, the phase evolutions of lactate and alanine during the spectrally selective pulses and the free precession times of the sequence at the single quantum, double quantum and zero quantum coherence states of these molecules were calculated. The multiple quantum (MQ) evolution time t1 that can remove the phase difference of lactate and alanine at the echo was calculated and fine-tuned with experiments. The lactate and alanine signal intensities and the editing efficiencies from the two modified Sel-MQC sequences were theoretically predicted by using the product operator evolutions and compared with the experimental data. The J-coupled lipid signals were successfully suppressed by both sequences. One of the two developed sequences was applied to a human body with a phantom of lactate and alanine, which resulted in successful in-phase editing of lactate and alanine and suppression of the lipid signals from the body. The study sets an important foundation for the noninvasive detection of lactate and alanine from tumors of cancer patients.

Ramsey envelope modulation in NV diamond magnetometry

Nitrogen-vacancy (NV) spin ensembles in diamond provide an advanced magnetic sensing platform, with applications in both the physical and life sciences. The development of isotopically engineered $^{15}$NV diamond offers advantages over naturally occurring $^{14}$NV for magnetometry, due to its simpler hyperfine structure. However, for sensing modalities requiring a bias magnetic field not aligned with the sensing NV axis, the absence of a quadrupole moment in the $^{15}$N nuclear spin leads to pronounced envelope modulation effects in time-dependent measurements of $^{15}$NV spin evolution. While such behavior in spin echo experiments are well studied, analogous effects in Ramsey measurements and the implications for magnetometry remain under-explored. Here, we derive the modulated $^{15}$NV Ramsey response to a misaligned bias field, using a simple vector description of the effective magnetic field on the nuclear spin. The predicted modulation properties are then compared to experimental results, revealing significant magnetic sensitivity loss if unaddressed. We demonstrate that double-quantum coherences of the NV $S=1$ electronic spin states dramatically suppress these envelope modulations, while additionally proving resilient to other parasitic effects such as strain heterogeneity and temperature shifts.

Entangled Biphoton Enhanced Double Quantum Coherence Signal as a Probe for Cavity Polariton Correlations in Presence of Phonon Induced Dephasing

We theoretically propose a biphoton entanglement-enhanced multidimensional spectroscopic technique as a probe for the dissipative polariton dynamics in the ultrafast regime. It is applied to the cavity-confined monomeric photosynthetic complex that represents a prototypical multi-site excitonic quantum aggregate. The proposed technique is shown to be particularly sensitive to inter-manifold polariton coherence between the two and one-excitation subspaces. It is demonstrated to be able to monitor the dynamical role of cavity-mediated excitonic correlations, and dephasing in the presence of phonon-induced dissipation. The non-classicality of the entangled biphoton sources is shown to enhance the ultra-fast and broadband correlation features of the signal, giving an indication about the underlying state correlations responsible for long-range cavity-assisted exciton migration.

Cover Image

The cover image is based on the Research Article Evaluation of brown adipose tissue with intermolecular double-quantum coherence magnetic resonance spectroscopy at 3.0 T by Liangjie Lin et al., https://doi.org/10.1002/nbm.4676.

Concerning the stability of biexcitons in hybrid HJ aggregates of π-conjugated polymers.

Frenkel excitons are the primary photoexcitations in organic semiconductors and are ultimately responsible for the optical properties of such materials. They are also predicted to form bound exciton pairs, termed biexcitons, which are consequential intermediates in a wide range of photophysical processes. Generally, we think of bound states as arising from an attractive interaction. However, here, we report on our recent theoretical analysis, predicting the formation of stable biexciton states in a conjugated polymer material arising from both attractive and repulsive interactions. We show that in J-aggregate systems, 2J-biexcitons can arise from repulsive dipolar interactions with energies E2J > 2EJ, while in H-aggregates, 2H-biexciton states with energies E2H < 2EH can arise corresponding to attractive dipole exciton/exciton interactions. These predictions are corroborated by using ultrafast double-quantum coherence spectroscopy on a [poly(2,5-bis(3-hexadecylthiophene-2-yl)thieno[3,2-b]thiophene)] material that exhibits both J- and H-like excitonic behavior.

Some aspects of transition selective NMR involving rare spins

Satellite transition selective excitation/inversion of abundant spins across chemical shifts offers a robust opportunity for sensitivity enhancement of rare spins that are coupled to them. It is also well established that reconversion of rare spin double quantum coherence (DQC) to single quantum-single transitions (SQ-ST's) over a wide range of chemical shifts offers sensitivity enhancement in INADEQUATE-style experiments. The present contribution gives an overview of the latter category of experiments, including a brief summary of the literature, and the contributions from our Lab. In particular, the transition selective “composite refocusing” approach of Sørensen and his group is discussed for reconversion of DQC to SQ-ST's. A shorter transition selective DQC reconversion module introduced from our Lab is also described. A 2D rare spin correlation experiment introduced by us is then reviewed, in which we replace rare spin DQ evolution with immediate reconversion of DQC to SQ-ST's, followed by evolution of SQ-ST's, that is then terminated by a mixing period to deliver a diagonal-free COSY-like correlation map. Finally, our ‘indirect’, 1H detected version of this experiment is reviewed. Transition selective reconversion in ADEQUATE-style experiments was also introduced by us and is briefly mentioned. Interestingly, partial 1H transition selectivity is shown to result as a consequence of reconversion of rare spin DQC to SQ-ST's, followed by coherence order selective heteronuclear reverse transfer. The performance of these experiments when applied to small molecules is illustrated.

Obtention of biocompatible hydrogels containing PEGs/silicon fatty blocks with potential use as A controlled release system

Novel crosslinked polyesters were designed to obtain hydrogels friendly with the environment and able to display potential biologic applications. Through polycondensation reactions, the synthesis used polyethylene glycols (PEGs) of different molecular weights and a silylated fatty methyl ester obtained from methyl 10-undecenoate, a derivative of castor oil. Depending on the PEGs molecular weights, a series of crosslinked polyesters were obtained and characterized by spectroscopic methods. Thanks to double quantum coherence (DQ) proton experiments, the synthesis was optimized by determining the highest crosslink density achieved from the parameter “Constant residual dipole coupling” (Dres), which is proportional to the crosslink density. These amphiphilic polyesters showed biocompatible properties according to ISO 10993-5. Besides, they could form hydrogels structurally confirmed by scanning electron microscopy. The swelling capacity was remarkable, depending on the PEGs molecular weights. The studies of encapsulation and release using rhodamine as host molecules revealed very conclusive and promising results, demonstrating that it was possible to control the releasing time by modifying the molar mass of the PEGs used in the synthesis. This critical outcome could be considered an essential parameter for tailoring materials for different drug or fertilizer release applications.