arXiv subjects

Kirill F. Sheberstov

Publications and source records attributed to Kirill F. Sheberstov.

11 recordsLinked to original sources

arXiv2026

Interpretable Activation-Selection Neural Networks for Symbolic Regression of Parameter-Dependent Hamiltonian Eigenvalues

Analytical approximations to eigenvalues of parameter-dependent Hamiltonians can provide physical insight that is not readily apparent from numerical diagonalization alone. Here, we introduce an activation-selection network (ASN), a differentiable symbolic-regression architecture in which each input node learns a sparse combination of predefined analytical functions, and the trained network can be converted directly into an explicit expression. Before regression, the Hamiltonian parameters and eigenvalues are expressed as dimensionless ratios. This normalization enforces dimensional homogeneity, reduces the number of independent variables, and ensures that the extracted expressions do not depend on the choice of energy units. Using the library {0, x, x^2}, compositions across successive hidden layers generate polynomial expansions of progressively higher degree; polynomial expansions of arbitrary finite degree can therefore be obtained in principle by increasing the network depth. We apply the ASN to effective three- and four-site spin-chain Hamiltonians relevant to zero-quantum nuclear magnetic resonance. Comparisons with degenerate perturbation theory show that the extracted expressions capture the expected constant, linear, and quadratic structure. Fixed-basis least-squares models match or slightly outperform the ASN when an appropriate quadratic basis is specified in advance, while inclusion of a radial feature improves the local approximation near the degeneracy. These results establish the ASN as a differentiable framework for selecting compact symbolic representations when several functional forms are plausible, while showing that adaptive activation selection does not provide an intrinsic accuracy advantage over a suitable predefined basis.

quant-ph↗

arXiv2026

Origin of Long-Lived Nuclear Spin States and Coherences in Aliphatic Chains Revealed by Relaxation Theory

Delocalized long-lived states (LLSs) and collective zero-quantum long-lived coherences (LLCs) in aliphatic chains provide a promising route for preserving nuclear spin order with lifetimes that exceed the conventional $T_1$ and $T_2$ relaxation times, respectively. Their extended lifetimes make them attractive for applications including hyperpolarization storage, ligand-observed drug screening based on the loss of longevity upon binding to a target protein, and quantum information processing exploiting the collective properties of many-body spin systems. Although LLSs and LLCs have been observed experimentally in methylene networks, their origin and general structure in chains of arbitrary length have remained unclear. Here we show that these relaxation-protected modes follow directly from Redfield relaxation theory. Specifically, we construct the long-lived subspace, i.e., the zero-eigenvalue subspace of the relaxation superoperator associated with the dominant intra-pair dipole--dipole relaxation mechanism. The long-lived subspace contains $2^N-1$ independent non-trivial operators, which excludes the identity operator, where $N>1$ is the number of $-\mathrm{CH}_2-$ groups in the chain. In achiral molecules, conservation of the global intra-pair permutation parity restricts experimental access to at most $2^N-2$ of these operators, whereas in chiral molecules this parity is not conserved, making up to $2^N-1$ long-lived operators accessible. We further develop a general framework for constructing both LLSs and LLCs in aliphatic chains containing an arbitrary number of $-\mathrm{CH}_2-$ groups in achiral molecules, and illustrate the approach explicitly for chains with $N=2$, 3, and 4 methylene groups.

quant-ph↗

arXiv2026

Wavelength-Resolved Photoinduced Spin Polarization in a Broad Optical Range for a Porphyrin-Quinone System

Photochemically induced dynamic nuclear polarization (photo-CIDNP) in liquid-state donor-acceptor systems is typically studied at a limited number of excitation wavelengths, leaving its spectral dependence incompletely characterized. Understanding the wavelength dependence of photo-CIDNP is important both for elucidating the underlying spin-chemical mechanisms and for optimizing hyperpolarization strategies in chemically and biologically relevant molecular systems. Here, we investigate wavelength-resolved photo-CIDNP in a tetraphenylporphyrin-1,4-benzoquinone donor-acceptor system over the 350-800 nm spectral range. Photon-flux-normalized CIDNP amplitudes were measured using both a tunable laser system and a broadband xenon lamp equipped with interchangeable 10 nm interference filters. The CIDNP response exhibits a non-monotonic dependence on excitation wavelength. Pronounced hyperpolarization is observed near 350 nm and in the 500-550 nm region, whereas excitation within the strongly absorbing 400-450 nm range results in a substantially reduced CIDNP response. Comparison with the UV-Vis absorption spectrum demonstrates that photo-CIDNP efficiency is not governed solely by optical absorption and reflects wavelength-dependent photophysical processes. After normalization to the excitation photon flux, lamp- and laser-based measurements yield consistent CIDNP results, validating broadband filtered excitation as a reliable and experimentally accessible approach for wavelength-resolved photo-CIDNP studies. These results establish excitation wavelength as an independent control parameter for liquid-state photo-CIDNP and provide a framework for systematic investigations of wavelength-dependent spin hyperpolarization.

physics.chem-ph↗

arXiv2025

Aliphatic Chains as One-Dimensional XY Spin Chains

Spin waves are propagating disturbances of spin order in lattices with nearest-neighbor interactions. They are traditionally observed in magnetically ordered solids using inelastic neutron, light, or electron scattering, and ferromagnetic resonance. Here, we show that analogous spin dynamics can arise in liquid-state nuclear magnetic resonance (NMR) of molecules containing aliphatic chains. In such molecules, each CH_2 group must have a distinct chemical shift and be magnetically inequivalent via out-of-pair couplings. Under these conditions, singlet state populations of geminal protons propagate along (CH_2)_n segments forming magnetically silent spin waves. For a chain with translational symmetry, the spin Hamiltonian factorizes into subspaces formally equivalent to the one-dimensional XY model. This correspondence yields analytic expressions for eigenstates and eigenenergies in a spectroscopy we term spin-chain zero-quantum NMR. We identify molecular systems in which these conditions are met. Their collective dynamics rapidly exceed classical computational tractability, making them targets for quantum-computer simulations of spin transport and many-body dynamics.

quant-ph↗

arXiv2025

Zero- to Ultralow-field Nuclear Magnetic Resonance

Zero and ultralow-field nuclear magnetic resonance (ZULF NMR) is an NMR modality where experiments are performed in fields at which spin-spin interactions within molecules and materials are stronger than Zeeman interactions. This typically occurs at external fields of microtesla strength or below, considerably smaller than Earth's field. In ZULF NMR, the measurement of spin-spin couplings and spin relaxation rates provides a nondestructive means for identifying chemicals and chemical fragments, and for conducting sample or process analyses. The absence of the symmetry imposed by a strong external magnetic field enables experiments that exploit terms in the nuclear spin Hamiltonian that are suppressed in high-field NMR, which in turn opens up new capabilities in a broad range of fields, from the search for dark matter to the preparation of hyperpolarized contrast agents for clinical imaging. Furthermore, as in ZULF NMR the Larmor frequencies are typically in the audio band, the nuclear spins can be manipulated with d.c. magnetic field pulses, and highly sensitive magnetometers are used for detection. In contrast to high-field NMR, the low-frequency signals readily pass through conductive materials such as metals, and heterogeneous samples do not lead to resonance line broadening, meaning that high-resolution spectroscopy is possible. Notable practical advantages of ZULF NMR spectroscopy are the low cost and relative simplicity and portability of the spectrometer system. In recent years ZULF NMR has become more accessible, thanks to improvements in magnetometer sensitivity and their commercial availability, and the development of hyperpolarization methods that provide a simple means to boost signal strengths by several orders of magnitude. These topics are reviewed and a perspective on potential future avenues of ZULF-NMR research is presented.

physics.chem-ph↗

arXiv2024

Zero-Field J-spectroscopy of Quadrupolar Nuclei

Zero- to ultralow-field nuclear magnetic resonance (ZULF NMR) is a powerful version of NMR that allows studying molecules and their transformations in the regime dominated by intrinsic spin-spin interactions. While spin dynamics at zero magnetic field can be probed indirectly - via shuttling a sample that underwent evolution at zero field to a high-field NMR spectrometer for detection - J-spectra can also be measured directly at zero field by using non-inductive sensors, for example, atomic magnetometers. To date, no zero-field J-spectra of molecules featuring the coupling to quadrupolar nuclei were reported. Here we show that zero-field J-spectra can be collected from molecules containing quadrupolar nuclei with I = 1 and demonstrate this for solutions containing various isotopologues of ammonium cations, namely, 14NH4+ and 15NDxH(4-x)+ (where x = 0, 1, 2, or 3). Lower ZULF NMR signals are observed for molecules containing larger numbers of deuterons compared to protons; this is attributed to less overall magnetization and not to the scalar relaxation of the second kind. Values for the 15N-1H and 14N-1H J-couplings of -73.416(3) Hz, 52.395(2) Hz, respectively, are extracted from the ZULF NMR spectra. Precision measurement of the J(15NH)/J(14NH) ratio resulted in the value within a range of 1.4009-1.4013; this is statistically different from {γ_{15N}}/{γ_{14N}}=1.4027 reported in the literature indicating the presence of the primary isotope effect. We analyze the energy structure for the studied molecular cations in detail and demonstrate that spectral line positions depend dramatically both on the sign of each J-coupling and on the magnetic pulse length.

physics.chem-ph↗

arXiv2022

Constant-adiabaticity ultralow magnetic field manipulations of parahydrogen-induced polarization: application to an AA'X spin system

The field of magnetic resonance imaging with hyperpolarized contrast agents is rapidly expanding, and parahydrogen-induced polarization (PHIP) is emerging as an inexpensive and easy-to-implement method for generating the required hyperpolarized biomolecules. Hydrogenative PHIP delivers hyperpolarized proton spin order to a substrate via chemical addition of H2 in the spin-singlet state, but prior to imaging it is typically necessary to transfer the proton polarization to a heteronucleus (usually 13C) in the molecule. Adiabatic ultralow magnetic field manipulations can be used to induce the polarization transfer, but this is necessarily a slow process, which is undesirable since the spins continually relax back to thermal equilibrium. Here we demonstrate constant-adiabaticity field cycling and field sweeping for optimal polarization transfer on a model AA$'$X spin system, [1-13C]fumarate. We introduce a method for calculating constant-adiabaticity magnetic field ramps and demonstrate that they enable much faster spin-order conversion as compared to linear ramps used before. The present method can thus be utilized to manipulate nonthermal order in heteronuclear spin systems.

physics.chem-ph↗

arXiv2021

Hyperpolarization of cis-15N,15N'-azobenzene by parahydrogen at ultralow magnetic fields

Development of the methods to exploit nuclear hyperpolarization and search for molecules whose nuclear spins can be efficiently hyperpolarized is an active area in nuclear magnetic resonance. Of particular interest are those molecules that have long nuclear relaxation times, making them to be suitable candidates as contrast agents in magnetic resonance imaging. In this work, we present a detailed study of SABRE SHEATH (Signal Amplification By Reversible Exchange in Shield Enabled Alignment Transfer to Heteronuclei) experiments of 15N,15N' azobenzene. In SABRE SHEATH experiments nuclear spins of the target are hyperpolarized by transfer of spin polarization from parahydrogen at ultralow fields during a reversible chemical process. The studied system is complicated, and we are concerned only about a subset of the data, presenting details for the molecules that experience fast chemical exchange at the catalytic complex and thus are involved in polarizing the free azobenzene. Azobenzene exists in two isomers trans- and cis-. We show that all nuclear spins in cis-azobenzene can be efficiently hyperpolarized by SABRE at suitable magnetic fields. Enhancement factors (relative to 9.4 T) reach several thousands of times for 15N spins and a few tens of times for the 1H spins. There are two approaches to observe either hyperpolarized magnetization of 15N/1H spins or hyperpolarized singlet order of the 15N spin pair. We compare these approaches and present the field dependencies of SABRE experiments for them. No hyperpolarization of trans 15N,15N' azobenzene was observed. The results presented here will be useful for further experiments where hyperpolarized cis-15N,15N' azobenzene is switched by light to trans 15N,15N' azobenzene for storing the produced hyperpolarization in the long-lived spin state of the 15N pair of trans-15N,15N' azobenzene.

physics.chem-ph↗

arXiv2021

Photochemically induced dynamic nuclear polarization of heteronuclear singlet order

Photochemically induced dynamic nuclear polarization (photo-CIDNP) is a method to hyperpolarize nuclear spins using light. In most cases, CIDNP experiments are performed at a high magnetic field and the sample is irradiated by the light inside a nuclear magnetic resonance (NMR) spectrometer. Here we demonstrate photo-CIDNP hyperpolarization generated in the Earth magnetic field and under zero- to ultralow field (ZULF) conditions. Irradiating a sample for several seconds with inexpensive light-emitting diodes produces a strong hyperpolarization of 1H and 13C nuclear spins enhancing the NMR signals several hundred times. The hyperpolarized spin states at the Earth field and in ZULF are different. In the latter case, the state corresponds to the singlet order between scalar-coupled 1H-13C nuclear spins. This state has a longer lifetime than the state hyperpolarized at Earth field. The method is simple and cost-efficient and should be applicable to many molecular systems known to exhibit photo-CIDNP, including amino acids and nucleotides.

physics.chem-ph↗

arXiv2019

Algorithmic Cooling of Nuclear Spin Pairs using a Long-Lived Singlet State

Algorithmic cooling methods manipulate an open quantum system in order to lower its temperature below that of the environment. We show that significant cooling is achieved on an ensemble of spin-pair systems by exploiting the long-lived nuclear singlet state, which is an antisymmetric quantum superposition of the "up" and "down" qubit states. The effect is demonstrated by nuclear magnetic resonance (NMR) experiments on a molecular system containing a coupled pair of near-equivalent 13C nuclei. The populations of the system are subjected to a repeating sequence of cyclic permutations separated by relaxation intervals. The long-lived nuclear singlet order is pumped well beyond the unitary limit, and the nuclear magnetization is enhanced by 21% relative to its thermal equilibrium value. To our knowledge this is the first demonstration of algorithmic cooling using a quantum superposition state and without making a distinction between rapidly and slowly relaxing qubits.

quant-ph↗

arXiv2018

Constant-adiabaticity RF-pulses for generating long-lived singlet spin states in NMR

A method is implemented to perform "fast" adiabatic variation of the spin Hamiltonian by imposing the constant adiabaticity condition. The method is applied to improve the performance of singlet-state Nuclear Magnetic Resonance (NMR) experiments, specifically, for efficient generation and readout of the singlet spin order in coupled spin pairs by applying adiabatically ramped RF-fields. Test experiments have been performed on a specially designed molecule having two strongly coupled C-13 spins and on selectively isotopically labelled glycerol having two pairs of coupled protons. Optimized RF-ramps show improved performance in comparison, for example, to linear ramps. We expect that the methods described here are useful, not only for singlet-state NMR experiments, but also for other experiments in magnetic resonance, which utilize adiabatic variation of the spin Hamiltonian.

physics.chem-ph↗