arXiv subjects

Viktor Novičenko

Publications and source records attributed to Viktor Novičenko.

15 recordsLinked to original sources

arXiv2026

Floquet framework for driven polar quantum systems

We present an analytical and numerical Floquet treatment of a driven polar two-level quantum system characterized by both longitudinal and transverse coupling to a periodic field. Analytically, we derive a dressed-frame effective Hamiltonian up to first order in the inverse driving frequency, incorporating the longitudinal coupling nonperturbatively. This yields closed expressions for the effective transverse coupling strength and the effective detuning, both of which are modified by the presence of the longitudinal interaction. In the nonpolar limit, these expressions recover the usual near-resonant Rabi coupling and the Bloch-Siegert shift. As a second main result, we develop a numerical flow-equation framework that yields a time-independent effective Hamiltonian across a broad range of transverse and longitudinal coupling strengths. This dual framework is relevant for a variety of platforms, including driven polar quantum systems, optical lattices, superconducting circuits, and solids subject to surface acoustic waves.

quant-ph↗

arXiv2025

Controller for rejection of the first harmonic in a periodic signal with uncertain delay

The plant (the system to be controlled) is disturbed by a periodic external force with a broad spectrum of Fourier harmonics. The first Fourier harmonic (sine-type signal) is assumed to be undesirable and should be removed by a control force, whereas the other harmonics should be preserved without distortion. Because the measured plant data have an unknown amount of time delay (dead time) and the sensitivity of the plant to external force is unknown, therefore the amplitude and phase of a sine-type control force are also unknown. Based on the internal model principle, we developed a feedback controller described as a linear time-invariant system that can remove the first harmonic from the plant's output by constantly adjusting its control force parameters. Using this controller, we aimed to further extend the capabilities of a newly developed high-speed, large-area rotational scanning atomic force microscopy. In such a scanning technique, the sample is rotated, and the tilt angle between the normal of the sample surface and the axis of rotation produces a parasitic first Fourier harmonic, which significantly limits the scanning area.

nlin.AO↗

arXiv2024

Magnetically generated spin-orbit coupling for ultracold atoms with slowly varying periodic driving

The spin-orbit coupling (SOC) affecting the center of mass of ultracold atoms can be simulated using a properly chosen periodic sequence of magnetic pulses. Yet such a method is generally accompanied by micro-motion which hinders a precise control of atomic dynamics and thus complicating practical applications. Here we show how to by-pass the micro-motion emerging in the magnetically induced SOC by switching on and off properly the oscillating magnetic fields at the initial and final times. We consider the exact dynamics of the system and demonstrate that the overall dynamics can be immune to the micro-motion. The exact dynamics is shown to agree well with the evolution of the system described by slowly changing effective Floquet Hamiltonian including the SOC term. The agreement is shown to be the best when the phase of the periodic driving takes a specific value for which the effect of the spin-orbit coupling is maximum.

cond-mat.quant-gas↗

arXiv2021

Flow-equation approach to quantum systems driven by an amplitude-modulated time-periodic force

We apply the method of flow equations to describe quantum systems subject to a time-periodic drive with a time-dependent envelope. The driven Hamiltonian is expressed in terms of its constituent Fourier harmonics with amplitudes that may vary as a function of time. The time evolution of the system is described in terms of the phase-independent effective Hamiltonian and the complementary micromotion operator that are generated by deriving and solving the flow equations. These equations implement the evolution with respect to an auxiliary flow variable and facilitate a gradual transformation of the quasienergy matrix (the Kamiltonian) into a block diagonal form in the extended space. We construct a flow generator that prevents the appearance of additional Fourier harmonics during the flow, thus enabling implementation of the flow in a computer algebra system. Automated generation of otherwise cumbersome high-frequency expansions (for both the effective Hamiltonian and the micromotion) to an arbitrary order thus becomes straightforward for driven Hamiltonians expressible in terms of a finite algebra of Hermitian operators. We give several specific examples and discuss the possibility to extend the treatment to cover rapid modulation of the envelope.

quant-ph↗

arXiv2021

Floquet chiral hinge modes and their interplay with Weyl physics in a three-dimensional lattice

We demonstrate that a three dimensional time-periodically driven (Floquet) lattice can exhibit chiral hinge states and describe their interplay with Weyl physics. A peculiar type of the hinge states are enforced by the repeated boundary reflections with lateral Goos-Hänchen like shifts occurring at the second-order boundaries of our system. Such chiral hinge modes coexist in a wide range of parameters regimes with Fermi arc surface states connecting a pair of Weyl points in a two-band model. We find numerically that these modes still preserve their locality along the hinge and their chiral nature in the presence of local defects and other parameter changes. We trace the robustness of such chiral hinge modes to special band structure unique in a Floquet system allowing all the eigenstates to be localized in quasi-one-dimensional regions parallel to each other when open hinge boundaries are introduced. The implementation of a model featuring both the second-order Floquet skin effect and the Weyl physics is straightforward with ultracold atoms in optical superlattices.

cond-mat.mes-hall↗

arXiv2021

Unstable delayed feedback control to change sign of coupling strength for weakly coupled limit cycle oscillators

Weakly coupled limit cycle oscillators can be reduced into a system of weakly coupled phase models. These phase models are helpful to analyze the synchronization phenomena. For example, a phase model of two oscillators has a one-dimensional differential equation for the evolution of the phase difference. The existence of fixed points determines frequency-locking solutions. By treating each oscillator as a black-box possessing a single input and a single output, one can investigate various control algorithms to change the synchronization of the oscillators. In particular, we are interested in a delayed feedback control algorithm. Application of this algorithm to the oscillators after a subsequent phase reduction should give the same phase model as in the control-free case, but with a rescaled coupling strength. The conventional delayed feedback control is limited to the change of magnitude but does not allow the change of sign of the coupling strength. In this work, we present a modification of the delayed feedback algorithm supplemented by an additional unstable degree of freedom, which is able to change the sign of the coupling strength. Various numerical calculations performed with Landau-Stuart and FitzHugh-Nagumo oscillators show successful switching between an in-phase and anti-phase synchronization using the provided control algorithm. Additionally, we show that the control force becomes non-invasive if our objective is stabilization of an unstable phase difference for two coupled oscillators.

nlin.AO↗

arXiv2020

Comment on "Adaptive modification of the delayed feedback control algorithm with a continuously varying time delay" https://doi.org/10.1016/j.physleta.2011.08.072

In the paper https://doi.org/10.1016/j.physleta.2011.08.072 authors propose a modification of the conventional delayed feedback control algorithm, where time-delay is varied continuously to minimize the power of control force. Minimization is realized via gradient-descent method. However, the derivation of the gradient with respect to time-delay is not accurate. In particular, a scalar factor is omitted. The absolute value of the scalar factor is not crucial, as it only changes the speed of the gradient method. On the other hand, the factor's sign changes the gradient direction, therefore for negative value of the multiplier the gradient-decent becomes gradient-ascent method and fail power minimization. Here the accurate derivation of the gradient is presented. We obtain an analytical expression for the missing factor and show an example of the Lorenz system where the negative factor occurs. We also discuss a relation between the negativeness of the factor and the odd number limitation theorem.

nlin.AO↗

arXiv2019

Non-Abelian geometric potentials and spin-orbit coupling for periodically driven systems

We demonstrate the emergence of the non-Abelian geometric potentials and thus the three-dimensional (3D) spin-orbit coupling (SOC) for ultracold atoms without using the laser beams. This is achieved by subjecting an atom to a periodic perturbation which is the product of a position-dependent Hermitian operator $\hat{V}\left(\mathbf{r}\right)$ and a fast oscillating periodic function $f\left(ωt\right)$ with a zero average. To have a significant spin-orbit coupling (SOC), we analyze a situation where the characteristic energy of the periodic driving is not necessarily small compared to the driving energy $\hbarω$. Applying a unitary transformation to eliminate the original periodic perturbation, we arrive at a non-Abelian (non-commuting) vector potential term describing the 3D SOC. The general formalism is illustrated by analyzing the motion of an atom in a spatially inhomogeneous magnetic field oscillating in time. A cylindrically symmetric magnetic field provides the SOC involving the coupling between the spin $\mathbf{F}$ and all three components of the orbital angular momentum (OAM) $\mathbf{L}$. In particular, the spherically symmetric monopole-type synthetic magnetic field $\mathbf{B}\propto\mathbf{r}$ generates the 3D SOC of the $\mathbf{L}\cdot \mathbf{F}$ form, which resembles the fine-structure interaction of hydrodgen atom. However, the strength of the SOC here goes as $1/r^{2}$ for larger distances, instead of $1/r^3$ as in atomic fine structure. Such a longer-ranged SOC significantly affects not only the lower states of the trapped atom, but also the higher ones. Furthermore, by properly tailoring the external trapping potential, the ground state of the system can occur at finite OAM, while the ground state of hydrogen atom has zero OAM.

cond-mat.quant-gas↗

arXiv2019

In-phase synchronization in complex oscillator networks by adaptive delayed feedback control

In-phase synchronization is a special case of synchronous behavior when coupled oscillators have the same phases for any time moments. Such behavior appears naturally for nearly identical coupled limit-cycle oscillators when the coupling strength is greatly above the synchronization threshold. We investigate the general class of nearly identical complex oscillators connected into network in a context of a phase reduction approach. By treating each oscillator as a black-box possessing a single-input single-output, we provide a practical and simply realizable control algorithm to attain the in-phase synchrony of the network. For a general diffusive-type coupling law and any value of a coupling strength (even greatly below the synchronization threshold) the delayed feedback control with a specially adjusted time-delays can provide in-phase synchronization. Such adjustment of the delay times performed in an automatic fashion by the use of an adaptive version of the delayed feedback algorithm when time-delays become time-dependent slowly varying control parameters. Analytical results show that there are many arrangements of the time-delays for the in-phase synchronization, therefore we supplement the algorithm by an additional requirement to choose appropriate set of the time-delays, which minimize power of a control force. Performed numerical validations of the predictions highlights the usefulness of our approach.

nlin.AO↗

arXiv2019

Non-Abelian geometric phases in periodically driven systems

We consider a periodically driven quantum system described by a Hamiltonian which is the product of a slowly varying Hermitian operator $V\left(\boldsymbolλ\left(t\right)\right)$ and a dimensionless periodic function with zero average. We demonstrate that the adiabatic evolution of the system within a fully degenerate Floquet band is accompanied by non-Abelian (non-commuting) geometric phases appearing when the slowly varying parameter $\boldsymbolλ=\boldsymbolλ\left(t\right)$ completes a closed loop. The geometric phases can have significant values even after completing a single cycle of the slow variable. Furthermore, there are no dynamical phases masking the non-Abelian Floquet geometric phases, as the former average to zero over an oscillation period. This can be used to precisely control the evolution of quantum systems, in particular for performing qubit operations. The general formalism is illustrated by analyzing a spin in an oscillating magnetic field with arbitrary strength and a slowly changing direction.

quant-ph↗

arXiv2019

Quantum dynamics in potentials with fast spatial oscillations

We consider quantum dynamics of systems with fast spatial modulation of the Hamiltonian. Employing the formalism of supersymmetric quantum mechanics and decoupling fast and slow spatial oscillations we demonstrate that the effective dynamics is governed by a Schrödinger-like equation of motion and obtain the expression of the resulting effective Hamiltonian. In particular, we show that there exists an attractive effective potential even in the case when the oscillating potential averages to zero.

quant-ph↗

arXiv2017

Floquet analysis of a quantum system with modulated periodic driving

We consider a quantum system periodically driven with a strength which varies slowly on the scale of the driving period. The analysis is based on a general formulation of the Floquet theory relying on the extended Hilbert space. It is shown that the dynamics of the system can be described in terms of a slowly varying effective Floquet Hamiltonian that captures the long-term evolution, as well as rapidly oscillating micromotion operators. We obtain a systematic high-frequency expansion of all these operators. Generalizing the previous studies, the expanded effective Hamiltonian is now time-dependent and contains extra terms appearing due to changes in the periodic driving. The same applies to the micromotion operators which exhibit a slow temporal dependence in addition to the rapid oscillations. As an illustration, we consider a quantum-mechanical spin in an oscillating magnetic field with a slowly changing direction. The effective evolution of the spin is then associated with non-Abelian geometric phases reflecting the geometry of the extended Floquet space. The developed formalism is general and also applies to other periodically driven systems, such as shaken optical lattices with a time-dependent shaking strength, a situation relevant to the cold atom experiments.

cond-mat.quant-gas↗

arXiv2016

Optimal waveform for the entrainment of oscillators perturbed by an amplitude-modulated high-frequency force

We analyze limit cycle oscillators under perturbation constructed as a product of two signals, namely, an envelope with a period close to natural period of an oscillator and a high-frequency carrier signal. A theory for obtaining an envelope waveform that achieves the maximal frequency interval of entrained oscillators is presented. The optimization problem for fixed power and maximal allowed amplitude is solved by employing the phase reduction method and the Pontryagin's maximum principle. We have shown that the optimal envelope waveform is a bang-bang-type solution. Also, we have found "inversion" symmetry that relates two signals with different powers, but the same interval of entrained frequencies. The theoretical results are confirmed numerically on FitzHugh-Nagumo oscillators.

nlin.AO↗

arXiv2015

Delayed feedback control of synchronization in weakly coupled oscillator networks

We study control of synchronization in weakly coupled oscillator networks by using a phase reduction approach. Starting from a general class of limit cycle oscillators we derive a phase model, which shows that delayed feedback control changes effective coupling strengths and effective frequencies. We derive the analytical condition for critical control gain, where the phase dynamics of the oscillator becomes extremely sensitive to any perturbations. As a result the network can attain phase synchronization even if the natural interoscillatory couplings are small. In addition, we demonstrate that delayed feedback control can disrupt the coherent phase dynamic in synchronized networks. The validity of our results is illustrated on networks of diffusively coupled Stuart--Landau and FitzHugh--Nagumo models.

nlin.PS↗

arXiv2015

Phase reduction of a limit cycle oscillator perturbed by a strong amplitude-modulated high-frequency force

The phase reduction method for a limit cycle oscillator subjected to a strong amplitude-modulated high-frequency force is developed. An equation for the phase dynamics is derived by introducing a new, effective phase response curve. We show that if the effective phase response curve is everywhere positive (negative), then an entrainment of the oscillator to an envelope frequency is possible only when this frequency is higher (lower) than the natural frequency of the oscillator. Also, by using the Pontryagin maximum principle, we have derived an optimal waveform of the perturbation that ensures an entrainment of the oscillator with minimal power. The theoretical results are demonstrated with the Stuart-Landau oscillator and model neurons.

nlin.CD↗