Quadrupolar Systems Research Articles

Non-equilibrium thermodynamics in NMR: understanding quadrupolar spin-1 systems.

In this study, we explore the non-equilibrium thermodynamics of a quantum system,
specifically focusing on spin-1 quadrupole nuclei. By employing fundamental principles
from quantum mechanics and statistical mechanics, we aim to understand the behavior
of the quadrupole spin-1 nuclei when subjected to external perturbations. Our analysis
involves the investigation of the system's dynamic response to non-equilibrium conditions through the manipulation of a work parameter. By treating work as a random
variable, we gather data from multiple cycles of finite duration, enabling us to compute
the complete distribution of the work generated during this process. Through these
finite-time non-equilibrium process data, we are able to determine equilibrium values
for important quantities such as the difference in free energy between the initial and
final states of the system. Additionally, we explore various properties of the system's
work distribution.

Discovery of orbital ordering in Bi2Sr2CaCu2O8+x.

The primordial ingredient of cuprate superconductivity is the CuO2 unit cell. Theories usually concentrate on the intra-atom Coulombic interactions dominating the 3d9 and 3d10 configurations of each copper ion. However, if Coulombic interactions also occur between electrons of the 2p6 orbitals of each planar oxygen atom, spontaneous orbital ordering may split their energy levels. This long-predicted intra-unit-cell symmetry breaking should generate an orbitally ordered phase, for which the charge transfer energy ε separating the 2p6 and 3d10 orbitals is distinct for the two oxygen atoms. Here we introduce sublattice-resolved ε(r) imaging to CuO2 studies and discover intra-unit-cell rotational symmetry breaking of ε(r). Spatially, this state is arranged in disordered Ising domains of orthogonally oriented orbital order bounded by dopant ions, and within whose domain walls low-energy electronic quadrupolar two-level systems occur. Overall, these data reveal a Q = 0 orbitally ordered state that splits the oxygen energy levels by ~50 meV, in underdoped CuO2.

Two-Photon Absorption Activity of BOPHY Derivatives: Insights from Theory

We present a theoretical study of a two-photon absorption (2PA) process in dipolar and quadrupolar systems containing two BF2 units. For this purpose, we considered 13 systems studied by Ponce-Vargas et al. [J. Phys. Chem. B2017, 121, 10850−1085829136383] and performed linear and quadratic response theory calculations based on the RI-CC2 method to obtain the 2PA parameters. Furthermore, using the recently developed generalized few-state model, we provided an in-depth view of the changes in 2PA properties in the molecules considered. Our results clearly indicate that suitable electron-donating group substitution to the core BF2 units results in a large red-shift of the two-photon absorption wavelength, thereby entering into the desired biological window. Furthermore, the corresponding 2PA strength also increases significantly (up to 30-fold). This makes the substituted systems a potential candidate for biological imaging.

Long-range order in quadrupolar systems on spherical surfaces.

The interplay between curvature, confinement and ordering on curved manifolds, with anisotropic interactions between building blocks, takes a central role in many fields of physics. In this paper, we investigate the effects of lattice symmetry and local positional order on orientational ordering in systems of long-range interacting point quadrupoles on a sphere in the zero temperature limit. Locally triangular spherical lattices show long-range ordered quadrupolar configurations only for specific symmetric lattices as strong geometric frustration prevents general global ordering. Conversely, the ground states on Caspar-Klug lattices are more diverse, with many different symmetries depending on the position of quadrupoles within the fundamental domain. We also show that by constraining the quadrupole tilts with respect to the surface normal, which models interactions with the substrate, and by considering general quadrupole tensors, we can manipulate the ground state configuration symmetry.

Satellite nutation of half integer quadrupolar nuclei: Theory and practice.

For quadrupolar spin systems, interpretation of solid state NMR spectra can be hampered by the presence of resonances from both satellite and central transitions. This is particularly true for disordered systems, where many different quadrupolar sites exist, which can have strongly different quadrupolar coupling constants. If second order effects are too strong for obtaining meaningful MAS, MQMAS or STMAS spectra, an approach is needed to successfully separate central and satellite transitions. In this work, we provide a rigorous treatment of 2D quadrupolar nutation NMR for the study of central and satellite transitions in quadrupolar systems. Using this SATURN experiment (SAtellite Transition nUtation of quadRupolar Nuclei) spectral intensity can be assigned to contributions from either central or satellite transitions. We show that the experiment can be applied to any half-integer spin (3/2, 5/2, 7/2 and 9/2), and that spectra can be obtained that closely match simulations. We furthermore show that distributions in quadrupolar parameters do not hamper the assignment of central and satellite transitions from a SATURN experiment.

Wavelength-optimized Two-Photon Polymerization Using Initiators Based on Multipolar Aminostyryl-1,3,5-triazines

Two-photon induced polymerization (2PP) based 3D printing is a powerful microfabrication tool. Specialized two-photon initiators (2PIs) are critical components of the employed photosensitive polymerizable formulations. This work investigates the cooperative enhancement of two-photon absorption cross sections (σ2PA) in a series of 1,3,5-triazine-derivatives bearing 1-3 aminostyryl-donor arms, creating dipolar, quadrupolar and octupolar push-pull systems. The multipolar 2PIs were successfully prepared and characterized, σ2PA were determined using z-scan at 800 nm as well as spectrally resolved two-photon excited fluorescence measurements, and the results were compared to high-level ab initio computations. Modern tunable femtosecond lasers allow 2PP-processing at optimum wavelengths tailored to the absorption behavior of the 2PI. 2PP structuring tests revealed that while performance at 800 nm is similar, at their respective σ2PA-maxima the octupolar triazine-derivative outperforms a well-established ketone-based quadrupolar reference 2PI, with significantly lower fabrication threshold at exceedingly high writing speeds up to 200 mm/s and a broader window for ideal processing parameters.

Dicationic and monocationic benzobisthiazolium salts as potential NLO chromophores

Dicationic salts derived from linear and angular benzobisthiazole skeleton were prepared by methylation under microwave conditions. The following condensation with aromatic aldehydes afforded two-armed conjugated molecules, which represent quadrupolar systems. Monocationic angular derivatives were also prepared to study the differences in properties between the quadrupolar and dipolar structures. Absorption and fluorescence characteristics were determined, in the case of dipolar derivatives solvatochromism was studied as well. Quantum chemical calculation of absorption spectra and nonlinear optical properties (first and second hyperpolarizability) were performed. The predicted values correlate well with the experimental ones and helped to explain the split character of the main band in absorption spectra of quadrupolar angular derivatives. Although high values of second hyperpolarizability are predicted for the linear compounds, their very low solubility in common solvents is a strongly limiting factor when practical use is considered. On the contrary, the applicability of one dicationic and one monocationic angular dye, with better solubility, was successfully verified in confocal laser scanning microscopy with nonlinear excitation.

(Invited) Trans-Substituted Benzodiazaporphyrin, a Hybrid Dye Between Porphyrins and Phthalocyanines, Opens Promising Performances in Dye-Sensitized Solar Cells

Porphyrinoid derivatives such as porphyrin and phthalocyanine have been thoroughly investigated as light collectors for photovoltaic applications, namely in dye-sensitized and organic solar cells. Benzo diazaporphyrins can be considered as hybrid dyes between porphyrins and phthalocyanines. The two interesting and valuable features of benzodiazaporphyrins is first, the presence of an intense and long wavelength absorption band like phthalocyanines, and the possibility to envision the preparation of push-pull or quadrupolar systems by trans functionalization of the two adjacent carbon meso positions. In this communication we present the synthesis and the promising photovoltaic properties of trans-substituted benzodiazaporphyrin in dye sensitized solar cells.

Efficient Excited-State Symmetry Breaking in a Cationic Quadrupolar System Bearing Diphenylamino Donors.

We report a joint experimental and theoretical investigation of a quadrupolar D-π-A(+) -π-D system, the electron donors being diphenylamino groups and the electron acceptor being a methylpyridinium, in comparison with the dipolar D-π-A(+) system. The emission spectra of the two compounds overlap in all the investigated solvents. This finding could be rationalized by TD-DFT calculations: the LUMO-HOMO molecular orbitals involved in the emission transition are localized on the same branch of the quadrupolar structure that becomes the fluorescent portion, corresponding to that of the single-arm compound. Excited-state symmetry breaking has been rarely observed for quadrupolar systems showing negative solvatochromism and is here surprisingly revealed, even in low polarity solvents. Femtosecond transient absorption measurements revealed that an efficient photoinduced intramolecular charge transfer takes place in the quadrupolar chromophore, more efficient than in its dipolar analogue. This result is promising in view of the application of these compounds as novel two-photon absorbing materials.

Optical gyrotropy in quadrupolar Kondo systems

Recent experiments point to a variety of intermetallic systems which exhibit exotic quadrupolar orders driven by the Kondo coupling between conduction electrons and localized quadrupolar degrees of freedom. Using a Luttinger $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ Hamiltonian for the conduction electrons, we study the impact of such quadrupolar order on their energies and wave functions. We discover that such quadrupolar orders can induce a nontrivial Berry curvature for the conduction electron bands, leading to a nonvanishing optical gyrotropic effect. We estimate the magnitude of the gyrotropic response in a candidate quadrupolar material, ${\mathrm{PrPb}}_{3}$, and discuss the resulting Faraday rotation in thin films.

AFNMR/NQR signal enhancement via population transfer

Antiferromagnetic nuclear magnetic resonance (AFNMR) and nuclear quadrupole resonance (NQR) are useful techniques to characterize materials in bulk volumes without applying external static magnetic fields. For industrial materials characterization applications, it is crucial to maximize signal‐to‐noise ratio in the available time. We simulate the AFNMR and NQR signal enhancement via population transfer in single crystals and powders and predict the enhancement factors for half‐integer quadrupolar nuclei spin systems. Differences to conventional high‐field NMR population transfer experiments are emphasized. We restrict our discussion to electric field gradients with axial symmetry = 0. Triple resonance tuned crossed coil experiments on CuFeS2 and In2O3 powders support the numerical results. © 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part A 43A: 147–156, 2015.

Berry-phase-induced dimerization in one-dimensional quadrupolar systems.

We investigate the effect of the Berry phase on quadrupoles that occur, for example, in the low-energy description of spin models. Specifically, we study here the one-dimensional bilinear-biquadratic spin-one model. An open question for many years about this model is whether it has a nondimerized fluctuating nematic phase. The dimerization has recently been proposed to be related to Berry phases of the quantum fluctuations. We use an effective low-energy description to calculate the scaling of the dimerization according to this theory and then verify the predictions using large scale density-matrix renormalization group simulations, giving good evidence that the state is dimerized all the way up to its transition into the ferromagnetic phase. We furthermore discuss the multiplet structure found in the entanglement spectrum of the ground state wave functions.

ChemInform Abstract: Quantum Phase Transitions in Heavy Fermion Metals and Kondo Insulators

AbstractReview: 129 refs.

Non-classical donor–acceptor–donor chromophores. A strategy for high two-photon brightness

Rod-like π-expanded bis-imidazo[1,2-a]pyridines were designed and synthesized. Strategic placement of a central electron-poor unit at position C3 of the imidazo[1,2-a]pyridine core resulted in donor–acceptor–donor quadrupolar systems. We further demonstrated the applicability of the Ortoleva–King–Chichibabin tandem process in the preparation of complex imidazo[1,2-a]pyridines. The monomer model heterocycles, differing by substitution at C2 and C3, displayed luminescence properties marginally dependent on the substitution pattern and conjugation extension. The highest luminescence quantum yield (ϕflca. 0.2) is shown by the model compounds without a substitution at C3, whereas lower values are measured for the others. Quantum yields in toluene for the quadrupolar systems varied from ϕfl = 0.7 to ϕfl > 0.9. Apart from bis-imidazo[1,2-a]pyridine possessing two methyl groups, with ϕfl = 0.69 in toluene and 0.35 in dichloromethane, the luminescence properties were only slightly affected by the change in the solvent. Most of the fluorescence lifetimes ranged from 1–2 ns and the radiative rate constants reached values of ca. 6 × 108 s−1. Intense phosphorescence spectra at 77 K with lifetimes in the second range (τ = 0.6–1.3 s) are recorded for the monomers, whereas for the bis-imidazo[1,2-a]pyridines, phosphorescence spectra are detected only after enhancing intersystem crossing by heavy atoms. Non-linear optical properties of bis-imidazo[1,2-a]pyridines revealed two-photon absorption cross-sections (σ2) typically of the order of 500–800 GM. The remarkable fluorescence quantum yield, in combination with high a two-photon absorption cross-section, generated a two-photon brightness of ∼500 to 750 GM units within the biological window (700–800 nm).

Spin coherent states in NMR quadrupolar system: experimental and theoretical applications

Working with nuclear magnetic resonance (NMR) in quadrupolar spin systems, in this paper we transfer the concept of atomic coherent state to the nuclear spin context, where it is referred to as pseudo-nuclear spin coherent state (pseudo-NSCS). Experimentally, we discuss the initialization of the pseudo-NSCSs and also their quantum control, implemented by polar and azimuthal rotations. Theoretically, we compute the geometric phases acquired by an initial pseudo-NSCS on undergoing three distinct cyclic evolutions: (i) the free evolution of the NMR quadrupolar system and, by analogy with the evolution of the NMR quadrupolar system, that of (ii) single-mode and (iii) two-mode Bose-Einstein Condensate like system. By means of these analogies, we derive, through spin angular momentum operators, results equivalent to those presented in the literature for orbital angular momentum operators. The pseudo-NSCS description is a starting point to introduce the spin squeezed state and quantum metrology into nuclear spin systems of liquid crystal or solid matter.

Nuances of multi-quantum excitation in solid state NMR of quadrupolar nuclei

In this article, a simple heuristic approach that is in agreement with the density operator formalism is presented for understanding the mechanism of multi-quantum (MQ) excitation in half-integral quadrupolar systems. Employing the population level diagram of the nuclear spin states, the effect of radio-frequency (RF) pulses on multi-level systems is described. Based on this approach, alternate schemes that involve non-equilibrium spin states are proposed for improving the sensitivity of MQ experiments in spin 3/2 and 5/2 systems. Additionally, the utility of frequency sweep techniques in the excitation of MQ transitions is discussed. The results obtained from the analytic theory are substantiated through numerical simulations.

Preparing Pseudo-Pure States in a Quadrupolar Spin System Using Optimal Control

Pseudo-pure state (PPS) preparation is crucial in nuclear magnetic resonance quantum computation. There have been some methods in spin-1/2 systems and a few attempts in quadrupolar spin systems. As optimal control via gradient ascent pulses engineering (GRAPE) has been widely used in quantum information science, we apply this technique to PPS preparation in quadrupolar spin systems. This approach shows an effective and fast quantum control method for both the state preparation and the realization of quantum gates in quadrupolar systems.

Quantum information processing by nuclear magnetic resonance on quadrupolar nuclei

Nuclear magnetic resonance is viewed as an important technique for the implementation of many quantum information algorithms and protocols. Although the most straightforward approach is to use the two-level system composed of spin 1/2 nuclei as qubits, quadrupolar nuclei, which possess a spin greater than 1/2, are being used as an alternative. In this study, we show some unique features of quadrupolar systems for quantum information processing, with an emphasis on the ability to execute efficient quantum state tomography (QST) using only global rotations of the spin system, whose performance is shown in detail. By preparing suitable states and implementing logical operations by numerically optimized pulses together with the QST method, we follow the stepwise execution of Grover's algorithm. We also review some work in the literature concerning the relaxation of pseudo-pure states in spin 3/2 systems as well as its modelling in both the Redfield and Kraus formalisms. These data are used to discuss differences in the behaviour of the quantum correlations observed for two-qubit systems implemented by spin 1/2 and quadrupolar spin 3/2 systems, also presented in the literature. The possibilities and advantages of using nuclear quadrupole resonance experiments for quantum information processing are also discussed.

Direct simulation of magnetic resonance relaxation rates and line shapes from molecular trajectories.

We simulate spin relaxation processes, which may be measured by either continuous wave or pulsed magnetic resonance techniques, using trajectory-based simulation methodologies. The spin-lattice relaxation rates are extracted numerically from the relaxation simulations. The rates obtained from the numerical fitting of the relaxation curves are compared to those obtained by direct simulation from the relaxation Bloch-Wangsness-Abragam-Redfield theory (BWART). We have restricted our study to anisotropic rigid-body rotational processes, and to the chemical shift anisotropy (CSA) and a single spin-spin dipolar (END) coupling mechanisms. Examples using electron paramagnetic resonance (EPR) nitroxide and nuclear magnetic resonance (NMR) deuterium quadrupolar systems are provided. The objective is to compare those rates obtained by numerical simulations with the rates obtained by BWART. There is excellent agreement between the simulated and BWART rates for a Hamiltonian describing a single spin (an electron) interacting with the bath through the chemical shift anisotropy (CSA) mechanism undergoing anisotropic rotational diffusion. In contrast, when the Hamiltonian contains both the chemical shift anisotropy (CSA) and the spin-spin dipolar (END) mechanisms, the decay rate of a single exponential fit of the simulated spin-lattice relaxation rate is up to a factor of 0.2 smaller than that predicted by BWART. When the relaxation curves are fit to a double exponential, the slow and fast rates extracted from the decay curves bound the BWART prediction. An extended BWART theory, in the literature, includes the need for multiple relaxation rates and indicates that the multiexponential decay is due to the combined effects of direct and cross-relaxation mechanisms.

QUANTUM STATE TOMOGRAPHY AND QUANTUM LOGICAL OPERATIONS IN A THREE QUBITS NMR QUADRUPOLAR SYSTEM

In this work, we present an implementation of quantum logic gates and algorithms in a three effective qubits system, represented by a (I = 7/2) NMR quadrupolar nuclei. To implement these protocols we have used the strong modulating pulses (SMP) and the various stages of each implementation were verified by quantum state tomography (QST). The results for the computational base states, Toffolli logic gates, and Deutsch–Jozsa and Grover algorithms are presented here. Also, we discuss the difficulties and advantages of implementing such protocols using the SMP technique in quadrupolar systems.