arXiv subjects

M. I. Dykman

Publications and source records attributed to M. I. Dykman.

At least 19 recordsLinked to original sources

arXiv2026

Multibranched parametric resonance and swallowtail catastrophe in electromechanical oscillators with nonlinear friction

Parametric resonance underpins the operation of a wide range of physical systems, from nanomechanical resonators to quantum-information systems and Ising machines. As an archetypal class of driven-dissipative systems, parametric oscillators are generally expected to exhibit a single pair of stable period-two states with opposite phases. This bistable behavior enables both the simulation of spin Hamiltonians and the preparation of superconducting cat states. Whether multiple pairs of such states can coexist in a single oscillator, however, remains an open question. Here, we show experimentally and theoretically that conventional controlled nonlinear friction can induce the coexistence of two distinct pairs of period-two states in a micromechanical oscillator. The friction is implemented via a canonical approach, utilizing a drive-induced resonant coupling that transfers two vibrational quanta from the oscillatory mode to a faster decaying mode. We demonstrate that the onset of multistability is governed by a swallowtail catastrophe and quantitatively map the associated bifurcation structure. Our results broaden the understanding of parametric resonance and establish micro- and nano-mechanical oscillators as a versatile platform for studying catastrophe theory and multistable nonequilibrium dynamics.

physics.class-ph↗

arXiv2026

Anomalous parametric resonance in a spin-1/2 chain: dynamical effects of nontrivial topology

Resonant parametric modulation is a major tool of studying magnetic systems. For a spin-1/2 chain in a strong magnetic field, the resulting excitations can be mapped on fermionic excitations in the Kitaev chain. We show that the response to turning on the modulation reveals dynamical bulk aspects of the nontrivial topology of the closed chain. In the topological regime, depending on the turn-on rate, the system displays an absence of frequency dispersion of the time-averaged magnetization and an absence or a suppression of its spatial correlations near resonance. The transition between the topological and trivial regimes is controlled by the modulation frequency.

cond-mat.mes-hall↗

arXiv2025

Non-Exponential Relaxation in the Rotating Frame of a Driven Nanomechanical Mode

We present direct observation of the ring-down dynamics in the rotating frame of a resonantly driven single-mode nonlinear nanomechanical resonator. An additional close to resonance harmonic force excites nonlinear oscillations about the fixed point in the rotating frame. When the secondary drive is removed, we measure decay of the in-phase and quadrature components toward this fixed point. We show that the decay of the in-phase signal is non-exponential, even though the vibration amplitude decays exponentially if both forces are switched off. A minimalistic model captures these dynamics as well as the spectrum of the vibrations excited by the additional force, relating them to the dissipation-induced symmetry breaking of the dynamics in the rotating frame.

cond-mat.mes-hall↗

arXiv2025

Electrons in quantum dots on helium: from charge qubits to synthetic color centers

Electrons trapped above the surface of helium provide a means to study many-body physics free from the randomness that comes from defects in other condensed-matter systems. Localizing an electron in an electrostatic quantum dot makes its energy spectrum discrete, with controlled level spacing. The lowest two states can act as charge qubit states. In this paper, we study how the coupling to the quantum field of capillary waves on helium -- ripplons -- affects electron dynamics. As we show, the coupling can be strong. This bounds the parameter range where electron-based charge qubits can be implemented. The constraint is different from the conventional relaxation time constraint. The electron-ripplon system in a dot is similar to a color center formed by an electron defect coupled to phonons in a solid. In contrast to solids, the coupling in the electron on helium system can be varied from strong to weak. This enables a qualitatively new approach to studying color center physics. We analyze the spectroscopy of the pertinent synthetic color centers in a broad range of the coupling strength

cond-mat.mes-hall↗

arXiv2025

Hidden vibrational bistability revealed by intrinsic fluctuations of a carbon nanotube

We demonstrate that a quiet state and large-amplitude self-sustained oscillations can co-exist in a carbon nanotube subject to time-independent drive. A feature of the bistability is that it would be hysteresis-free in the absence of noise and the oscillatory state would not be seen. It is revealed by random switching between the stable states, which we observe in the time domain. We attribute the switching to fluctuations in the system and show that it displays Poisson statistics. We propose a minimalistic model that relates the emergence of the bistability to a non-monotonic variation of nonlinear friction with the vibration amplitude. This new type of dynamical regime and the means to reveal it are generic and are of interest for various mesoscopic vibrational systems.

cond-mat.mes-hall↗

arXiv2025

Intrinsic Phononic Dressed States in a Nanomechanical System

Nanoelectromechanical systems (NEMS) provide a platform for probing the quantum nature of mechanical motion in mesoscopic systems. This nature manifests most profoundly when the device vibrations are nonlinear and, currently, achieving vibrational nonlinearity at the single-phonon level is an active area of pursuit in quantum information science. Despite much effort, however, this has remained elusive. Here, we report the first observation of intrinsic mesoscopic vibrational dressed states. The requisite nonlinearity results from strong resonant coupling between an eigenmode of our NEMS resonator and a single, two-level system (TLS) that is intrinsic to the device material. We control the TLS in situ by varying mechanical strain, tuning it in and out of resonance with the NEMS mode. Varying the resonant drive and/or temperature allows controlled ascent of the nonequidistant energy ladder and reveals the energy multiplets of the hybridized system. Fluctuations of the TLS on and off resonance with the mode induces switching between dressed and bare states; this elucidates the complex quantum nature of TLS-like defects in mesoscopic systems. These quintessential quantum effects emerge directly from the intrinsic material properties of mechanical systems - without need for complex, external quantum circuits. Our work provides long-sought insight into mesoscopic dynamics and offers a new direction to harness nanomechanics for quantum measurements.

cond-mat.mes-hall↗

arXiv2024

Resonant-force induced symmetry breaking in a quantum parametric oscillator

A parametrically modulated oscillator has two opposite-phase vibrational states at half the modulation frequency. An extra force at the vibration frequency breaks the symmetry of the states. The effect can be extremely strong due to the interplay between the force and the quantum fluctuations resulting from the coupling of the oscillator to a thermal bath. The force changes the rates of the fluctuation-induced walk over the quantum states of the oscillator. If the number of the states is large, the effect accumulates to an exponentially large factor in the rate of switching between the vibrational states. We find the factor and analyze it in the limiting cases including the prebifurcation regime where the system is close but not too close to the bifurcation point.

cond-mat.stat-mech↗

arXiv2024

Revealing inadvertent periodic modulation of qubit frequency

The paper describes the means to reveal and characterize slow periodic modulation of qubit frequency. Such modulation can come from different sources and can impact qubit stability. We show that the modulation leads to very sharp peaks in the power spectrum of outcomes of periodically repeated Ramsey measurements. The positions and shapes of the peaks allow finding both the frequency and the amplitude of the modulation. We also explore how additional slow fluctuations of the qubit frequency and fluctuations of the modulation frequency affect the spectrum. The analytical results are in excellent agreement with extensive simulations.

quant-ph↗

arXiv2024

Frequency stabilization of self-sustained oscillations in a sideband-driven electromechanical resonator

We present a method to stabilize the frequency of self-sustained vibrations in micro- and nanomechanical resonators. The method refers to a two-mode system with the vibrations at significantly different frequencies. The signal from one mode is used to control the other mode. In the experiment, self-sustained oscillations of micromechanical modes are excited by pumping at the blue-detuned sideband of the higher-frequency mode. Phase fluctuations of the two modes show near perfect anti-correlation. They can be compensated in either one of the modes by a stepwise change of the pump phase. The phase change of the controlled mode is proportional to the pump phase change, with the proportionality constant independent of the pump amplitude and frequency. This finding allows us to stabilize the phase of one mode against phase diffusion using the measured phase of the other mode. We demonstrate that phase fluctuations of either the high or low frequency mode can be significantly reduced. The results open new opportunities in generating stable vibrations in a broad frequency range via parametric downconversion in nonlinear resonators.

eess.SY↗

arXiv2023

Controlled asymmetric Ising model implemented with parametric micromechanical oscillators

Asymmetric Ising model, in which coupled spins affect each other differently, plays an important role in diverse fields, from physics to biology to artificial intelligence. We show that coupled parametric oscillators provide a well-controlled and fully characterizable physical system to implement the model. Such oscillators are bistable. The coupling changes the rate of interstate switching of an oscillator depending on the state of other oscillators. Our experiment on two coupled micromechanical resonators reveals unusual features of asymmetric Ising systems, including the onset of a probability current that circulates in the stationary state. We relate the asymmetry to the exponentially strong effect of a periodic force on the switching rates of an individual parametric oscillator, which we measure. Our findings open the possibilities of constructing and exploring asymmetric Ising systems with controlled parameters and connectivity.

cond-mat.mes-hall↗

arXiv2023

Nonergodic measurements of qubit frequency noise

Slow fluctuations of a qubit frequency are one of the major problems faced by quantum computers. To understand their origin it is necessary to go beyond the analysis of their spectra. We show that characteristic features of the fluctuations can be revealed using comparatively short sequences of periodically repeated Ramsey measurements, with the sequence duration smaller than needed for the noise to approach the ergodic limit. The outcomes distribution and its dependence on the sequence duration are sensitive to the nature of noise. The time needed for quantum measurements to display quasi-ergodic behavior can strongly depend on the measurement parameters.

quant-ph↗

arXiv2022

Spin dynamics in quantum dots on liquid helium

Liquid He-4 is free from magnetic defects, making it an ideal substrate for electrons with long-lived spin states. Such states can serve as qubit states. Here we consider the spin states of electrons electrostatically localized in quantum dots on a helium surface. Efficient gate operations in this system require spin-orbit coupling. It can be created by a nonuniform magnetic field from a current-carrying wire, can be turned on and off, and allows one to obtain large electro-dipole moment and comparatively fast coupling of spins in neighboring dots. Of central importance is to understand the spin decay due to the spin-orbit coupling. We establish the leading mechanism of such decay and show that the decay is sufficiently slow to enable high-fidelity single- and two-qubit gate operations

cond-mat.mes-hall↗

arXiv2022

Frequency comb from a single driven nonlinear nanomechanical mode

Phononic frequency combs have been attracting an increasing attention both as a qualitatively new type of nonlinear phenomena in vibrational systems and from the point of view of applications. It is commonly believed that at least two modes must be involved in generating a comb. In this paper we demonstrate that a comb can be generated by a single nanomechanical mode driven by a resonant monochromatic drive. The comb emerges where the drive is still weak, so that the anharmonic part of the mode potential energy remains small. We relate the effect to a negative nonlinear friction induced by the resonant drive, which makes the vibrations at the drive frequency unstable. We directly map the trajectories of the emerging oscillations in the rotating frame and show how these oscillations lead to the frequency comb in the laboratory frame. The results go beyond nanomechanics and suggest a qualitatively new approach to generating tunable frequency combs in single-mode vibrational systems.

cond-mat.mes-hall↗

arXiv2022

Characterizing low-frequency qubit noise

Fluctuations of the qubit frequencies are one of the major problems to overcome on the way to scalable quantum computers. Of particular importance are fluctuations with the correlation time that exceeds the decoherence time due to decay and dephasing by fast processes. The statistics of the fluctuations can be characterized by measuring the correlators of the outcomes of periodically repeated Ramsey measurements. This work suggests a method that allows describing qubit dynamics during repeated measurements in the presence of evolving noise. It made it possible, in particular, to evaluate the two-time correlator for the noise from two-level systems and obtain two- and three-time correlators for a Gaussian noise. The explicit expressions for the correlators are compared with simulations. A significant difference of the three-time correlators for the noise from two-level systems and for a Gaussian noise is demonstrated. Strong broadening of the distribution of the outcomes of Ramsey measurements, with a possible fine structure, is found for the data acquisition time comparable to the noise correlation time.

quant-ph↗

arXiv2022

Mesoscopic physics of nanomechanical systems

Nanomechanics has brought mesoscopic physics into the world of vibrations. Because nanomechanical systems are small, fluctuations are significant, the vibrations become nonlinear already for comparatively small amplitudes, and new mechanisms of dissipation come into play. At the same time, the exquisite control of these systems makes them a platform for studying many problems of classical and quantum physics far from thermal equilibrium in a well-characterized setting. This review describes, at a conceptual level, basic theoretical ideas and explicative experiments pertaining to mesoscopic physics of nanomechanical systems. Major applications of nanomechanics in science and technology are also outlined. A broad range of phenomena related to the conservative as well as dissipative nonlinearity and fluctuations are discussed within a unifying framework. They include the linear response of single and coupled vibrational modes as well as nonlinear effects of periodic driving. Such driving breaks the continuous time-translation symmetry and the detailed balance, with conspicuous consequences for fluctuations, particularly in the presence of the driving-induced bi- and multistability. Mathematical techniques are described in the appendices to streamline the reading, but also to provide an introduction to the theory. The goal of the review is to show the richness of the physics at work. The continuous experimental and theoretical advances make nanomechanical systems a vibrant area of research, with many new phenomena to discover.

cond-mat.mes-hall↗

arXiv2022

Learning Noise via Dynamical Decoupling of Entangled Qubits

Noise in entangled quantum systems is difficult to characterize due to many-body effects involving multiple degrees of freedom. This noise poses a challenge to quantum computing, where two-qubit gate performance is critical. Here, we develop and apply multi-qubit dynamical decoupling sequences that characterize noise that occurs during two-qubit gates. In our superconducting system comprised of Transmon qubits with tunable couplers, we observe noise that is consistent with flux fluctuations in the coupler that simultaneously affects both qubits and induces noise in their entangling parameter. The effect of this noise on the qubits is very different from the well-studied single-qubit dephasing. Additionally, steps are observed in the decoupled signals, implying the presence of non-Gaussian noise.

quant-ph↗

arXiv2021

Resonant nonlinear response of a nanomechanical system with broken symmetry

We study the response of a weakly damped vibrational mode of a nanostring resonator to a moderately strong resonant driving force. Because of the geometry of the experiment, the studied flexural vibrations lack inversion symmetry. As we show, this leads to a nontrivial dependence of the vibration amplitude on the force parameters. For a comparatively weak force, the response has the familiar Duffing form, but for a somewhat stronger force, it becomes significantly different. Concurrently there emerge vibrations at twice the drive frequency, a signature of the broken symmetry. Their amplitude and phase allow us to establish the cubic nonlinearity of the potential of the mode as the mechanism responsible for both observations. The developed theory goes beyond the standard rotating-wave approximation. It quantitatively describes the experiment and allows us to determine the nonlinearity parameters.

cond-mat.mes-hall↗

arXiv2021

Amplification and spectral evidence of squeezing in the response of a strongly driven nanoresonator to a probe field

Because of their small decay rates, nanomechanical modes enable studying strongly nonlinear phenomena for a moderately strong resonant driving. Here we study the response of a driven resonator to an additional probe field. We experimentally demonstrate resonant amplification and resonant absorption of the probe field. The corresponding spectral peaks lie on the opposite sides of the strong-drive frequency. Even though the fluctuation-dissipation theorem does not apply, we show that the response to the probe field allows us to characterize the squeezing of fluctuations about the stable states of forced oscillations. Our two-tone experiment is done in the classical regime, but our findings should equally apply to quantum fluctuations as well. In quantum terms, the observed response is due to multiphoton processes. The squeezing parameter extracted from the spectra of the response is in excellent agreement with the calculated value with no free parameters.

cond-mat.mes-hall↗