arXiv subjects

R. Fedaruk

Publications and source records attributed to R. Fedaruk.

18 recordsLinked to original sources

arXiv2026

Regular and chaotic dynamics of nonlinear optomechanical systems controlled by modulated light

The nonlinear dynamics of a mechanical resonator in an optomechanical system with linear, quadratic and cubic photon-vibration interactions (with respect to mechanical displacements) in a modulated driving field under conditions of adiabatic elimination of the optical field is studied. Based on the constructed bifurcation diagrams of the mechanical coordinate and the largest Lyapunov exponent as a function of the modulation amplitude, as well as power spectra, phase portraits and Poincare sections, regions of regular and chaotic dynamics of the optomechanical system are identified. It is also shown that for a certain modulation amplitude in the presence of all three types of interactions, chaotic dynamics of the mechanical resonator (oscillator) is realized, which is replaced by quasi-periodic oscillations in the absence of cubic interaction, and the system returns to chaotic behavior if only linear interaction remains. This non-monotonic dependence of chaotic dynamics on the order of nonlinearity originates from the interplay between parametric driving and effective potential reshaping and manifests that nonlinearity does not always enhance chaos. For an optomechanical system in a membrane-in-the-middle configuration, where only quadratic photon-vibration interaction is present, it is demonstrated that at small modulation amplitudes the mechanical oscillator exhibits quasi-periodic motion in each of the wells of a symmetric two-minimum potential, whereas large modulation amplitudes lead to chaotic motion, involving interwell transitions.

quant-ph↗

arXiv2025

Nonlinear optomechanical systems with quasi-periodic and chaotic dynamics

Model optomechanical systems with photon-vibration interactions linear, quadratic, and cubic in mechanical displacements are studied under conditions for adiabatic elimination of the photon field. The opportunity of transformation of effective potential describing the dynamics of the mechanical resonator from single-well to double-well is demonstrated. The dynamics of the mechanical resonator is considered in the presence of (i) only linear interaction, (ii) only quadratic interaction, (iii) both linear and quadratic interactions, and (iv) all three interactions, while other parameters of the optomechanical system, the modulation optical field, and the initial conditions remain fixed. Quasiperiodic oscillations of the mechanical resonator in the case (i) are replaced by chaotic ones when the cases (ii) or (iii) are realized. It is interesting that in the presence of all three interactions, the chaotic behavior of the mechanical oscillator becomes quasi-periodic. However, increasing the power of the modulation field again leads to chaos.

quant-ph↗

arXiv2024

Optomechanical systems with nonlinear interactions: photon blockade, collapse-revival effect and Fano-like resonance

Closed-form expressions for the average amplitude of the optical field in optomechanical systems are obtained, in which, in addition to the linear interaction, quadratic and cubic interactions of the vibrational mode of the mechanical resonator with the mode of the optical resonator are considered. In the framework of the non-secular perturbation theory, using the Bogoliubov averaging method, it is shown that the effects of photon blockade, collapse and revival of optical oscillations in such systems can be realized. The main contribution to the formation of revivals is provided by the Kerr self-action of the optical mode and the cross-Kerr interaction of the fourth degree in optical and mechanical amplitudes. The cross-Kerr interactions of the sixth- and eighth-order in amplitudes destroy the regular structure of revivals. The influence of these cross-Kerr nonlinearities disappears with an increase in the decay rate of the optical mode and is also completely suppressed at zero temperature. It is shown that the asymmetry of the spectral line of the optical field intensity in the cavity is most pronounced with an increase in the degree of nonlinearity and is explained by Fano interference.

quant-ph↗

arXiv2021

Kerr-like nonlinearities in an optomechanical system with an asymmetric anharmonic mechanical resonator

In the framework of the nonsecular perturbation theory based on the Bogoliubov averaging method, an optomechanical system with an asymmetric anharmonic mechanical resonator is studied. The cross-Kerr interaction and the Kerr-like self-interaction of photons and vibration quanta arise in the Hamiltonian. These interactions are induced by both cubic and quartic nonlinearities of oscillations of the mechanical resonator and the cavity-resonator interaction that is linear in mechanical displacements. We demonstrate a bistable behavior of the number of vibration quanta and find that this behavior is controlled by the cross-Kerr interaction. It is shown that, without driving and dissipation, the constructed superposition Yurke-Stoler-like states of the cavity (or the mechanical resonator) disentangle at certain times the entangled modes of the system. The obtained results offer new possibilities for control of optomechanical systems with asymmetric mechanical oscillations.

quant-ph↗

arXiv2020

Bloch-Siegert oscillations in the Rabi model with an amplitude-modulated driving field

We study the coherent dynamics of a qubit excited by an amplitude-modulated electromagnetic field under the Rabi resonance when the frequency of the low-frequency modulation field matches the Rabi frequency in the high-frequency field. Due to destructive interference of multiple photon processes at the ultrastrong coupling between the qubit and the low-frequency driving field, Rabi oscillations result exclusively from the Bloch-Siegert effect. It is directly observed in the time-resolved coherent dynamics as the Bloch-Siegert oscillation. In this case, triplets in Fourier spectra of the coherent response are transformed into doublets with the splitting between the lines equal to twice the Bloch-Siegert shift. These unusual properties are demonstrated in conditions of experiments with a nitrogen vacancy center in diamond.

cond-mat.mes-hall↗

arXiv2019

The possibility of direct observation of the Bloch-Siegert shift in coherent dynamics of multiphoton Raman transitions

We study Rabi oscillations of the second-order Raman transition realized on dressed states of a qubit excited by an amplitude-modulated microwave field. The co-rotating component of the ultrastrong low-frequency modulation field excites virtual multiple photon processes between the dressed states and forms the Rabi frequency in the so-called rotating wave approximation (RWA). The counter-rotating modulation component also gives a significant contribution to the Rabi frequency owing to the Bloch--Siegert effect. It is shown that for properly chosen parameters of the modulation field and qubit, the Rabi oscillations in the RWA vanish due to destructive interference of multiple photon processes. In this case the Rabi oscillation results exclusively from the Bloch--Siegert effect and is directly observed in the time-resolved coherent dynamics as the Bloch--Siegert oscillation. Correspondingly, in Fourier spectra of the coherent response, triplets are transformed into doublets with the splitting between the lines equal to twice the Bloch--Siegert shift. We demonstrate these features by calculations of the qubit's evolution in the conditions of experiments with a NV center in diamond, where Raman transitions were observed. The direct observation of the Bloch--Siegert oscillation offers new possibilities for studying driven quantum systems in the ultastrong regime.

quant-ph↗

arXiv2018

Multiphoton Raman transitions and Rabi oscillations in driven spin systems

In the framework of the non-secular perturbation theory based on the Bogoliubov averaging method, the coherent dynamics of multiphoton Raman transitions in a two-level spin system driven by an amplitude-modulated microwave field is studied. Closed-form expressions for the Rabi frequencies of these transitions have been obtained beyond the rotating wave approximation for the low-frequency driving component. It is shown that spin states dressed by the high-frequency component of the driving field are shifted due to the Bloch-Siegert-like effect caused by antiresonant interactions with the strong low-frequency driving. We predict that with increasing the order of the Raman transition the Rabi frequency decreases and the contribution of the Bloch-Siegert shift to this frequency becomes dominant. It is found that the amplitude and phase of the Rabi oscillations strongly depend on the initial phase of the low-frequency field as well as on detuning from multiphoton resonance. The recent experimental data for the second- and third-order Raman transitions observed for nitrogen-vacancy center in diamond [Z. Shu, et al., arXiv:1804. 10492] are well described in the frame of our approach. Our results provide new possibilities for coherent control of quantum systems.

cond-mat.mes-hall↗

arXiv2018

Suppression of electron spin decoherence in Rabi oscillations induced by an inhomogeneous microwave field

The decay of Rabi oscillations provides direct information about coherence of electron spins. When observed in EPR experiments, it is often shortened by spatial inhomogeneity of the microwave field amplitude in a bulk sample. In order to suppress this undesired loss of coherence, we propose an additional dressing of spin states by a weak longitudinal continuous radiofrequency field. Our calculations of the Rabi oscillations between the doubly dressed spin states show that the maximum suppression of decoherence is achieved at the so-called Rabi resonance when the radio-field frequency is in resonance with the Rabi frequency of spins in the microwave field. This effect is feasible even in the absence of phase matching in the radiofrequency field and for different types of inhomogeneity of the microwave field. The manifestations of such suppression in the published EPR experiments with the bichromatic driving are discussed. The realization of the Rabi resonance using the radiofrequency field could open new possibilities for separating the contributions of relaxation mechanisms from those due to the inhomogeneous driving in spin decoherence.

cond-mat.mes-hall↗

arXiv2017

Emission spectrum of a qubit under its deep strong driving in the high-frequency dispersive regime

We study the emission spectrum of a qubit under deep strong driving in the high-frequency dispersive regime when the driving frequency and strength exceed significantly the qubit transition frequency. Closed-form expressions for the steady-state first-order field correlation function and the multiphoton emission spectrum are obtained. The spectrum comprises a series of narrow delta-like lines that stem from coherent processes and Lorenzian peaks that result from the incoherent scattering of photons. The oscillating dependence of the widths of the emission lines on the driving strength is predicted. We show how the features of this dependence are governed by the qubit dephasing and relaxation rates.

quant-ph↗

arXiv2017

Dissipative Rabi model for deep strong far-off-resonant driving

We study the dissipative Rabi model under deep strong far-off-resonant driving when the driving frequency and strength exceed significantly the qubit transition frequency. We find analytical expressions for the density matrix, the steady-state first-order field correlation function and the multiphoton emission spectrum. This spectrum consists of a series of narrow delta-like lines, caused by coherent processes and of Lorenzian peaks resulted from the incoherent scattering of photons. It is shown that the width of emission lines as well as the decay rate of the time oscillations in the population difference have oscillating dependence on the driving strength. We show how the features of this dependence are controlled by the relative rates of energetic relaxation and pure dephasing.

cond-mat.mes-hall↗

arXiv2016

Dissipative two-level systems under ultrastrong off-resonant driving

We study the dissipative dynamics of a two-level system under ultrastrong driving when the frequency and strength of the exciting field exceed significantly the transition frequency. We find three qualitatively different regimes of such dynamics: 1) the collapse and revival of oscillations in the population difference, 2) the simple exponential decay of the oscillations resulting in their steady state with the finite amplitude, and 3) the steady-state stabilization of the equally populated levels. The nonmonotonic Bessel-function-like dependence on the driving strength is also predicted for the decay rate of these oscillations. The features of this dependence are determined by the relative rates of energetic relaxation and pure dephasing.

cond-mat.mes-hall↗

arXiv2016

Multi-photon transitions and Rabi resonance in continuous wave EPR

The study of microwave and radiofrequency multi-photon transitions in continuous wave (CW) EPR spectroscopy is extended to a Rabi resonance condition, when the radio frequency of the magnetic-field modulation matches the Rabi frequency of a spin system in the microwave field. Using the non-secular perturbation theory based on the Bogoliubov averaging method, the analytical description of the response of the spin system is derived for all modulation frequency harmonics. When the modulation frequency exceeds the EPR linewidth, multi-photon transitions result in sidebands in absorption EPR spectra measured with phase-sensitive detection at any harmonic. The saturation of different-order multi-photon transitions is shown to be significantly different and to be sensitive to the Rabi resonance. The noticeable frequency shifts of sidebands are found to be the signatures of this resonance. The inversion of two-photon lines in some spectral intervals of the out-of-phase first-harmonic signal is predicted under passage through the Rabi resonance. The inversion indicates the transition from absorption to stimulated emission or vice versa, depending on the sideband. The manifestation of the primary and secondary Rabi resonance is also demonstrated in time-resolved steady-state EPR signals formed by all harmonics of the modulation frequency. Our results provide a theoretical framework for future developments in multi-photon CW EPR spectroscopy, which can be useful for samples with long spin relaxation times and extremely narrow EPR lines

cond-mat.mes-hall↗

arXiv2015

Microwave Photon Antibunching at the Modulation of the Resonance Frequency of a Qubit Emitter

The statistics photons in the resonance fluorescence of a qubit excited by microwave and radio-frequency (RF) fields have been studied. It has been established that the coherent dissipative dynamics of the qubit with allowance for multiphoton emission and absorption of RF photons in each act of emission and absorption of a microwave photon results in periodic alternation of photon bunching and antibunching. It has been shown that periodically varying statistics photons can be smoothly transformed to the purely sub-Poisson statistics by varying the parameters of the RF field. The conditions for the formation of the "collapse-revival" of oscillations in the second-order correlation function photons have been determined. The described effects can be implemented on spin and superconducting qubits, quantum dots, and qubit-mechanical hybrid systems.

cond-mat.mes-hall↗

arXiv2014

Relaxation, decoherence and steady-state population inversion in qubits doubly dressed by microwave and radiofrequency fields

The coherent dynamics of relaxing spin qubits driven by a classical bichromatic field comprising a strong resonant component and a weaker component with a frequency close to the strong-field Rabi frequency is studied. The double dressing by the bichromatic field modifies dephasing and dissipation processes. We demonstrate that detuning of the weaker-field frequency from the strong-field Rabi frequency prolongs the decay of Rabi oscillations between some doubly dressed states. The sensitivity of Rabi oscillations to the modified detuning-dependent relaxation is illustrated for nitrogen-vacancy qubits in diamond. We discuss a steady-state population inversion of the doubly dressed-state levels.

cond-mat.mes-hall↗

arXiv2013

Detuning-dependent narrowing of Mollow triplet lines of driven quantum dots

We study the two-time correlation function and the resonance fluorescence spectrum of a semiconductor quantum dot excited by a strong off-resonant laser pulse. The obtained analytical expressions exhibit a specific detuning-dependent damping of Rabi oscillations of the dressed quantum dot as well as a detuning-dependent width of Mollow-triplet lines. In the absence of pure dephasing, the central peak of the triplet is broadened, upon increasing detuning, but the blue and red side peaks are narrowed. We demonstrate that pure dephasing processes can invert these dependences. A crossover between the regimes of detuning-dependent narrowing and broadening of the side and central peaks is identified. The predicted effects are consistent with resent experimental results and numerical calculations.

cond-mat.mes-hall↗

arXiv2012

Dissipative dynamics of qubits driven by a bichromatic field in the dispersive regime

We study the coherent dynamics of relaxing qubits driven by a bichromatic radiation in the dispersive regime, when detuning of the frequency $ω_{rf}$ of a longitudinal radiofrequency field from the Rabi frequency $ω_{1}$ in a transverse microwave field is comparable in magnitude to $ω_{rf}$ and $ω_{1}$. We analytically describe this regime beyond the rotating wave approximation and find that the dominant feature of dynamics of qubits is the shift of the Rabi frequency caused by the dynamical Zeeman and Bloch-Siegert-like effects. These fundamental effects can be experimentally separated because, unlike the Bloch-Siegert effect, the dynamical Zeeman effect depends on the detuning sign. Our theoretical results are in a good agreement with the experimental data obtained in pulse EPR for the $E'_{1}$ centers in crystalline quartz.

cond-mat.mes-hall↗

arXiv2011

Two types of proton-electron atoms in a vacuum and an extremely strong magnetic field

The Rutherford planetary model of a proton-electron atom is modified. Besides the Coulomb interaction of the point electron with the proton, its strong Coulomb interaction with the physical vacuum as well as the magnetic interaction between moving charges are taken into account. The vacuum interaction leads to the motion of the electron with the velocity of light \textit{c} in the circle with the radius being equal to the so-called classical electron radius $r_e$. Therefore, the velocity of the electron consists of two components: the velocity $\vec{\upsilon}$ of the mechanical motion and the velocity $\vec{c}$ of the photon-like motion. We postulate that $\vec{\upsilon}\bot \vec{c}$, and $\upsilon < c $. Hence, the electron inside the atom moves with the resulting faster-than-light velocity. The existence of two types of proton-electron atoms, the hydrogen atom and the neutron, is interpreted by the different motion and interaction of particles at large ($ r >> r_e $) and short ($ r < r_e $) distances. In the first atom, the effect of photon-like motion is small, and the electron moves around the proton with the velocity $\upsilon << c$ in an orbit of the radius $ r>>r_{e}$. In the second atom, the photon-like motion is the determining factor, and the electron moves around the proton with the faster-than-light velocity in an orbit of the radius $r < r_{e}$. The calculated ground-state properties of the free hydrogen atom and the free neutron are in good agreement with the experimental data. The properties of these atoms in extremely strong magnetic fields ($B >> 10^8 T$) that are typical for neutron stars are discussed.

physics.gen-ph↗

arXiv2010

Multiplication of Qubits in a Doubly Resonant Bichromatic Field

Multiplication of spin qubits arises at double resonance in a bichromatic field when the frequency of the radio-frequency (rf) field is close to that of the Rabi oscillation in the microwave field, provided its frequency equals the Larmor frequency of the initial qubit. We show that the operational multiphoton transitions of dressed qubits can be selected by the choice of both the rotating frame and the rf phase. In order to enhance the precision of dressed qubit operations in the strong-field regime, the counter-rotating component of the rf field is taken into account.

cond-mat.mes-hall↗