arXiv subjects

Ilya Kuprov

Publications and source records attributed to Ilya Kuprov.

At least 19 recordsLinked to original sources

arXiv2026

Quantum optimal control of steady orbits

Periodically driven dissipative systems can settle into steady orbits - fixed loops on their dynamical manifolds. In quantum mechanics, steady orbits occur in cooling engines (used to initialise quantum devices), coherent oscillators (such as lasers and masers), precision metrology devices (atomic clocks, optical and spin magnetometers), and magnetic resonance (steady state free precession, dynamic nuclear polarisation). Steady orbits and stroboscopic steady states are a promising target for quantum optimal control, but the numerical complexity is prohibitive: the infinite loop defeats gradient ascent pulse engineering (GRAPE) which relies on explicit numerical propagation in the time domain. Here we propose an efficient quantum control strategy for stroboscopic steady states and limit cycles that are approached asymptotically when a control sequence is repeated infinitely many times. The formalism is different from Floquet-Lindblad state engineering and effective Hamiltonian theories: it finds control sequences that drive a dissipative quantum system towards a steady orbit passing through user-specified waypoints. The software implementation (same numerical complexity scaling as GRAPE) is done for the Spinach library.

quant-ph↗

arXiv2025

Simulation of pulsed dynamic nuclear polarization in the steady state

In pulsed dynamic nuclear polarization (DNP), enhancement of the polarization of bulk nuclei requires the repeated application of a microwave pulse sequence. So far, analysis of a one-time transfer of electron spin polarization to a dipolar-coupled nuclear spin has guided the design of DNP pulse sequences. This has obvious shortcomings, such as an inability to predict the optimal repetition time. In an actual pulsed DNP experiment, a balance is reached between the polarization arriving from the unpaired electrons and nuclear relaxation. In this article, we explore three algorithms to compute this stroboscopic steady state: (1) explicit time evolution by propagator squaring, (2) generation of an effective propagator using the matrix logarithm, and (3) direct calculation of the steady state with the Newton-Raphson method. Algorithm (2) is numerically unstable for this purpose. Algorithm (1) and (3) are both stable; algorithm (3) is the most efficient. We compare the steady-state simulations to existing experimental results at 0.34 T and 1.2 T and to the first experimental observation of X-inverse-X (XiX) DNP at 3.4 T: agreement is good, and improves further when electron-proton distance and electron Rabi frequency distributions are accounted for. We demonstrate that the trajectory of the spin system during one-time application of a microwave pulse sequence differs from the steady orbit. This has implications for DNP pulse sequence design.

physics.chem-ph↗

arXiv2025

Chemical hydrodynamics of nuclear spin states

Quantum mechanical equations of motion are strictly linear in state descriptors, such as wavefunctions and density matrices, but equations describing chemical kinetics and hydrodynamics may be non-linear in concentrations. This incompatibility is fundamental, but special cases can be handled - for example, in magnetic resonance where nuclear spin interactions may be too weak influence concentration dynamics. For processes involving single spins and first-order chemical reactions, this is a well-researched topic, but time evolution of complex nuclear spin systems in the presence of second-order kinetics, diffusion, and flow has so far remained intractable. This creates obstacles in microfluidics, homogeneous catalysis, and magnetic resonance imaging of metabolic processes. In this communication we report a numerically stable formalism for time-domain quantum mechanical description of nuclear spin dynamics and decoherence in the simultaneous presence of diffusion, flow, and second-order chemical reactions. The formalism is implemented in versions 2.11 and later of the open-source Spinach library. As an illustration, we use Diels-Alder cycloaddition of acrylonitrile to cyclopentadiene, yielding endo- and exo-norbornene carbonitrile, in the presence of diffusion and flow in the detection chamber of a microfluidic NMR probe (a finite element model with thousands of Voronoi cells) with a spatially localised stripline radiofrequency coil.

physics.chem-ph↗

arXiv2025

Instrumental distortions in quantum optimal control

Quantum optimal control methods, such as gradient ascent pulse engineering (GRAPE), are used for precise manipulation of quantum states. Many of those methods were pioneered in magnetic resonance spectroscopy where instrumental distortions are often negligible. However, that is not the case elsewhere: the usual jumble of cables, resonators, modulators, splitters, amplifiers, and filters can and would distort control signals. Those distortions may be non-linear, their inverse functions may be ill-defined and unstable; they may even vary from one day to the next, and across the sample. Here we introduce the response-aware gradient ascent pulse engineering (RAW-GRAPE) framework, which accounts for any cascade of differentiable distortions within the GRAPE optimisation loop, does not require filter function inversion, and produces control sequences that are resilient to user-specified distortion cascades with user-specified parameter ensembles. The framework is implemented into the optimal control module supplied with versions 2.10 and later of the open-source Spinach library; the user needs to provide function handles returning the actions by the distortions and, optionally, parameter ensembles for those actions.

quant-ph↗

arXiv2023

Optimizing beam-splitter pulses for atom interferometry: a geometric approach

We present a methodology for the design of optimal Raman beam-splitter pulses suitable for cold atom inertial sensors. The methodology, based on time-dependent perturbation theory, links optimal control and the sensitivity function formalism in the Bloch sphere picture, thus providing a geometric interpretation of the optimization problem. Optimized pulse waveforms are found to be more resilient than conventional beam-splitter pulses and ensure a near-flat superposition phase for a range of detunings approaching the Rabi frequency. As a practical application, we have simulated the performance of an optimized Mach-Zehnder interferometer in terms of scale-factor error and bias induced by inter-pulse laser intensity variations. Our findings reveal enhancements compared to conventional interferometers operating with constant-power beam-splitter pulses.

physics.atom-ph↗

arXiv2023

Simulation and design of shaped pulses beyond the piecewise-constant approximation

Response functions of resonant circuits create ringing artefacts if their input changes rapidly. When physical limits of electromagnetic spectroscopies are explored, this creates two types of problems. Firstly, simulation: the system must be propagated accurately through every response transient, this may be computationally expensive. Secondly, optimal control: circuit response must be taken into account; it may be advantageous to design pulses that are resilient to such distortions. At the root of both problems is the popular piecewise-constant approximation for control sequences in the rotating frame; in magnetic resonance it has persisted since the earliest days and has become entrenched in the commercially available hardware. In this paper, we report an implementation and benchmarks of recent Lie-group methods that can efficiently simulate and optimise smooth control sequences.

eess.SY↗

arXiv2022

Toroidal optical transitions in hydrogen-like atoms

It is commonly believed that electromagnetic spectra of atoms and molecules can be fully described by interactions of electric and magnetic multipoles. However, it has recently become clear that interactions between light and matter also involve toroidal multipoles - toroidal absorption lines have been observed in electromagnetic metamaterials. Here we show that a new type of spectroscopy of the hitherto largely neglected toroidal dipolar interaction becomes feasible if, apart from the classical r{\times}r{\times}p toroidal dipole density term responsible for the toroidal transitions in metamaterials, the spin-dependent r{\times}σ term (that only occurs in relativistic quantum mechanics) is taken into account. We show that toroidal transitions are odd under parity and time-reversal symmetries; they can therefore be observed and distinguished from electric multipole and magnetic dipole transitions.

physics.atom-ph↗

arXiv2022

Neural networks in pulsed dipolar spectroscopy: a practical guide

This is a methodological guide to the use of deep neural networks in the processing of pulsed dipolar spectroscopy (PDS) data encountered in structural biology, organic photovoltaics, photosynthesis research, and other domains featuring long-lived radical pairs and paramagnetic metal ions. PDS uses distance dependence of magnetic dipolar interactions; measuring a single well-defined distance is straightforward, but extracting distance distributions is a hard and mathematically ill-posed problem requiring careful regularisation and background fitting. Neural networks do this exceptionally well, but their "robust black box" reputation hides the complexity of their design and training - particularly when the training dataset is effectively infinite. The objective of this paper is to give insight into training against simulated databases, to discuss network architecture choices, to describe options for handling DEER (double electron-electron resonance) and RIDME (relaxation-induced dipolar modulation enhancement) experiments, and to provide a practical data processing flowchart.

physics.chem-ph↗

arXiv2021

J-driven Dynamic Nuclear Polarization for sensitizing high field solution state NMR

Dynamic nuclear polarization is widely used to enhance the sensitivity of nuclear magnetic resonance. It is presently the method of choice for enhancing the sensitivity of high-field solid state NMR experiments performed under cryogenic conditions. In liquids, however, its efficiency decays rapidly with magnetic field Bo and with the rotational correlation time, leading to negligible enhancements in mid- and high-field solution-state NMR experiments for all but exceptional cases. This study discusses a potential solution to this fundamental sensitivity problem, that relies on biradical species possessing inter-electron exchange couplings, that are on the order of the electron Larmor frequency.

physics.chem-ph↗

arXiv2021

Heteronuclear transfers from labile protons in biomolecular NMR: Cross Polarization, revisited

INEPT- and HMQC-based pulse sequences are widely used to transfer polarization between heteronuclei, particularly in biomolecular spectroscopy: they are easy to setup and involve low power deposition. Still, these short-pulse polarization transfers schemes are challenged by fast solvent chemical exchange. An alternative to improve these heteronuclear transfers is J-driven cross polarization (J-CP), which transfers polarization by spin-locking the coupled spins under Hartmann-Hahn conditions. J-CP provides certain immunity against chemical exchange and other T2-like relaxation effects, a behavior that is here examined in depth by both Liouville-space numerical and analytical derivations describing the transfer efficiency. While superior to INEPT-based transfers, fast exchange may also slow down these J-CP transfers, hurting their efficiency. This study therefore explores the potential of repeated projective operations to improve 1H->15N and 1H->15N->13C J-CP transfers in the presence of fast solvent chemical exchanges. It is found that while repeating J-CP provides little 1H->15N transfer advantages over a prolonged CP, multiple contacts that keep both the water and the labile protons effectively spin-locked can improve 1H->15N->13C transfers in the presence of chemical exchange. The ensuing Looped, Concatenated Cross Polarization (L-CCP) compensates for single J-CP losses by relying on the 13C longer lifetimes, leading to a kind of algorithmic cooling that can provide high polarization for the 15N as well as carbonyl and alpha 13Cs. This can facilitate certain experiments, as demonstrated with triple resonance experiments on intrinsically disordered proteins involving labile, chemically exchanging protons.

physics.chem-ph↗

arXiv2021

Optimal control gradient precision trade-offs: application to fast generation of DeepControl libraries for MRI

We have recently demonstrated supervised deep learning methods for rapid generation of radiofrequency pulses in magnetic resonance imaging (https://doi.org/10.1002/mrm.27740, https://doi.org/10.1002/mrm.28667). Unlike the previous iterative optimization approaches, deep learning methods generate a pulse using a fixed number of floating-point operations - this is important in MRI, where patient-specific pulses preferably must be produced in real time. However, deep learning requires vast training libraries, which must be generated using the traditional methods, e.g. iterative quantum optimal control methods. Those methods are usually variations of gradient descent, and the calculation of the fidelity gradient of the performance metric with respect to the pulse waveform can be the most numerically intensive step. In this communication, we explore various ways in which the calculation of fidelity gradients in quantum optimal control theory may be accelerated. Four optimization avenues are explored: truncated commutator series expansions at zeroth and first order, a novel midpoint truncation scheme at first order, and the exact complex-step method. For the spin systems relevant to MRI, the first-order truncation is found to be sufficiently accurate, but also up to five times faster than the machine precision gradient. This makes the generation of training databases for the machine learning methods considerably more realistic.

physics.med-ph↗

arXiv2020

High-field solution state DNP using cross-correlations

At the magnetic fields of common NMR instruments, electron Zeeman frequencies are too high for efficient electron-nuclear dipolar cross-relaxation to occur in solution. The rate of that process fades with the electron Zeeman frequency as omega^{-2} - in the absence of isotropic hyperfine couplings, liquid state dynamic nuclear polarisation (DNP) in high-field magnets is therefore impractical. However, contact coupling and dipolar cross-relaxation are not the only mechanisms that can move electron magnetisation to nuclei in liquids: multiple cross-correlated (CC) relaxation processes also exist, involving various combinations of interaction tensor anisotropies. The rates of some of those processes have more favourable high-field behaviour than dipolar cross-relaxation, but due to the difficulty of their numerical - and particularly analytical - treatment, they remain largely uncharted. In this communication, we report analytical evaluation of every rotationally driven relaxation process in liquid state for 1e1n and 2e1n spin systems, as well as numerical optimisations of the steady-state DNP with respect to spin Hamiltonian parameters. A previously unreported cross-correlation DNP (CCDNP) mechanism was identified for the 2e1n system, involving multiple relaxation interference effects and inter-electron exchange coupling. Using simulations, we found realistic spin Hamiltonian parameters that yield stronger nuclear polarisation at high magnetic fields than dipolar cross-relaxation.

quant-ph↗

arXiv2020

Neural network interpretation using descrambler groups

The lack of interpretability and trust is a much-criticised feature of deep neural networks. In fully connected nets, the signalling between inner layers is scrambled because backpropagation training does not require perceptrons to be arranged in any particular order. The result is a black box; this problem is particularly severe in scientific computing and digital signal processing (DSP), where neutral nets perform abstract mathematical transformations that do not reduce to features or concepts. We present here a group-theoretical procedure that attempts to bring inner layer signalling into a human-readable form, the assumption being that this form exists and has identifiable and quantifiable features - for example, smoothness or locality. We applied the proposed method to DEERNet (a DSP network used in electron spin resonance) and managed to descramble it. We found considerable internal sophistication: the network spontaneously invents a bandpass filter, a notch filter, a frequency axis rectifier, frequency division multiplexing, group embedding, spectral filtering regularisation, and a Fourier-like transform that maps harmonic functions into Chebyshev polynomials - in ten minutes of unattended training from a random initial guess.

eess.SP↗

arXiv2020

Bi-selective pulses for large-area atom interferometry

We present designs for the augmentation 'mirror' pulses of large-momentum-transfer atom interferometers that maintain their fidelity as the wavepacket momentum difference is increased. These bi-selective pulses, tailored using optimal control methods to the evolving bi-modal momentum distribution, should allow greater interferometer areas and hence increased inertial measurement sensitivity, without requiring elevated Rabi frequencies or extended frequency chirps. Using an experimentally validated model, we have simulated the application of our pulse designs to large-momentum-transfer atom interferometry using stimulated Raman transitions in a laser-cooled atomic sample of $^{85}$Rb at 1 $μ$K. After the wavepackets have separated by 42 photon recoil momenta, our pulses maintain a fringe contrast of 90% whereas, for adiabatic rapid passage and conventional $π$ pulses, the contrast is less than 10%. Furthermore, we show how these pulses may be adapted to suppress the detrimental off-resonant excitation that limits other broadband pulse schemes.

physics.atom-ph↗

arXiv2019

Optimized Raman pulses for atom interferometry

We present mirror and beamsplitter pulse designs that improve the fidelity of atom interferometry and increase its tolerance of systematic inhomogeneities. These designs are demonstrated experimentally with a cold thermal sample of $^{85}$Rb atoms. We first show a stimulated Raman inversion pulse design that achieves a ground hyperfine state transfer efficiency of 99.8(3)%, compared with a conventional $π$ pulse efficiency of 75(3)%. This inversion pulse is robust to variations in laser intensity and detuning, maintaining a transfer efficiency of 90% at detunings for which the $π$ pulse fidelity is below 20%, and is thus suitable for large momentum transfer interferometers using thermal atoms or operating in non-ideal environments. We then extend our optimization to all components of a Mach-Zehnder atom interferometer sequence and show that with a highly inhomogeneous atomic sample the fringe visibility is increased threefold over that using conventional $π$ and $π/2$ pulses.

quant-ph↗

arXiv2018

Feedback control optimisation of ESR experiments

Numerically optimised microwave pulses are used to increase excitation efficiency and modulation depth in electron spin resonance experiments performed on a spectrometer equipped with an arbitrary waveform generator. The optimisation procedure is sample-specific and reminiscent of the magnet shimming process used in the early days of nuclear magnetic resonance -- an objective function (for example, echo integral in a spin echo experiment) is defined and optimised numerically as a function of the pulse waveform vector using noise-resilient gradient-free methods. We found that the resulting shaped microwave pulses achieve higher excitation bandwidth and better echo modulation depth than the pulse shapes used as the initial guess. Although the method is theoretically less sophisticated than simulation based quantum optimal control techniques, it has the advantage of being free of the linear response approximation; rapid electron spin relaxation also means that the optimisation takes only a few seconds. This makes the procedure fast, convenient, and easy to use. An important application of this method is at the final stage of the implementation of theoretically designed pulse shapes: compensation of pulse distortions introduced by the instrument. The performance is illustrated using spin echo and out-of-phase electron spin echo envelope modulation experiments. Interface code between Bruker SpinJet arbitrary waveform generator and Matlab is included in versions 2.2 and later of the Spinach library.

physics.chem-ph↗

arXiv2018

Optimal control of mirror pulses for atom interferometry

Atom matterwave interferometry requires mirror and beamsplitter pulses that are robust to inhomogeneities in field intensity, magnetic environment, atom velocity and Zeeman sub-state. Pulse shapes determined using quantum control methods offer significantly improved interferometer performance by allowing broader atom distributions, larger interferometer areas and higher contrast. We have applied gradient ascent pulse engineering (GRAPE) to optimise the design of phase-modulated mirror pulses for a Mach-Zehnder light-pulse atom interferometer, with the aim of increasing fringe contrast when averaged over atoms with an experimentally relevant range of velocities, beam intensities, and Zeeman states. Pulses were found to be highly robust to variations in detuning and coupling strength, and offer a clear improvement in robustness over the best established composite pulses. The peak mirror fidelity in a cloud of $\sim 80\ μ$K ${}^{85}$Rb atoms is predicted to be improved by a factor of 2 compared with standard rectangular $π$ pulses.

quant-ph↗

arXiv2016

Pseudocontact shifts from mobile spin labels

This paper presents a detailed analysis of the pseudocontact shift (PCS) field induced by a mobile spin label that is viewed as a probability density distribution with an associated effective magnetic susceptibility anisotropy. It is demonstrated that non-spherically-symmetric density can lead to significant deviations from the commonly used point dipole approximation for PCS. Analytical and numerical solutions are presented for the general partial differential equation that describes the non-point case. It is also demonstrated that it is possible, with some reasonable approximations, to reconstruct paramagnetic centre probability distributions from the experimental PCS data.

physics.chem-ph↗