arXiv subjects

M. L. Roukes

Publications and source records attributed to M. L. Roukes.

At least 19 recordsLinked to original sources

arXiv2026

1/f frequency noise in mechanical resonators scales inversely with volume, not with quality factor

Mechanical frequency-shift sensors have never reached their fundamental thermomechanical or quantum limits. Every material, size, and transduction scheme yet examined yields a $1/f$ floor 1-3 orders higher, with a flicker-noise coefficient $h_{-1} \propto 1/V_{\varepsilon}$. Surveying the published record, I find the invariant $h_{-1}\,V_{\varepsilon} \equiv σ_A ^2\, V_{\varepsilon}/(2\ln 2)$ independent of device size across 13 decades; volume-independent noise is excluded by 9$σ$, site-averaging by 3.8$σ$. No $Q$ dependence appears: reported $Q^{-n}$ laws scale equivalently when $Q$ and volume co-vary; only volume scaling survives when they do not. Mass resolution follows as $|δm| \propto \sqrt{h_{-1}\,V_{\varepsilon} \cdot V}$.

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↗

arXiv2025

Frequency Fluctuations in Nanomechanical Resonators due to Quantum Defects

Nanomechanical resonators promise diverse applications ranging from mass spectrometry to quantum information processing, requiring long phonon lifetimes and frequency stability. Although two-level system (TLS) defects govern dissipation at millikelvin temperatures, the nature of frequency fluctuations remains poorly understood. In nanoscale devices, where acoustic fields are confined to sub-wavelength volumes, strong coupling to individual TLS should dominate over weak coupling to defect ensembles. In this work, we monitor fast frequency fluctuations of phononic crystal nanomechanical resonators, while varying temperature ($10$ mK$-1$ K), drive power ($10^2-10^5$ phonons), and the phononic band structure. We consistently observe random telegraph signals (RTS) which we attribute to state transitions of individual TLS. The frequency noise is well-explained by mechanical coupling to individual far off-resonant TLS, which are either thermally excited or strongly coupled to thermal fluctuators. Understanding this fundamental decoherence process, particularly its RTS structure, opens a clear path towards noise suppression for quantum and sensing applications.

cond-mat.mes-hall↗

arXiv2019

Resonantly induced friction in driven nanomechanical systems

We propose a new mechanism of friction in resonantly driven vibrational systems. The form of the friction force follows from the time- and spatial-symmetry arguments. We consider a microscopic mechanism of this resonant force in nanomechanical systems. The friction can be negative, leading to an instability of forced vibrations of a nanoresonator and the onset of self-sustained oscillations in the rotating frame.

cond-mat.mes-hall↗

arXiv2016

Nonlinear damping and dephasing in nanomechanical systems

We present a microscopic theory of nonlinear damping and dephasing of low-frequency eigenmodes in nano- and micro-mechanical systems. The mechanism of the both effects is scattering of thermally excited vibrational modes off the considered eigenmode. The scattering is accompanied by energy transfer of $2\hbarω_0$ for nonlinear damping and is quasieleastic for dephasing. We develop a formalism that allows studying both spatially uniform systems and systems with a strong nonuniformity, which is smooth on the typical wavelength of thermal modes but not their mean free path. The formalism accounts for the decay of thermal modes, which plays a major role in the nonlinear damping and dephasing. We identify the nonlinear analogs of the Landau-Rumer, thermoelastic, and Akhiezer mechanisms and find the dependence of the relaxation parameters on the temperature and the geometry of a system.

cond-mat.mes-hall↗

arXiv2013

Synchronization of two anharmonic nanomechanical oscillators

We investigate the synchronization of oscillators based on anharmonic nanoelectromechanical resonators. Our experimental implementation allows unprecedented observation and control of parameters governing the dynamics of synchronization. We find close quantitative agreement between experimental data and theory describing reactively coupled Duffing resonators with fully saturated feedback gain. In the synchronized state we demonstrate a significant reduction in the phase noise of the oscillators, which is key for sensor and clock applications. Our work establishes that oscillator networks constructed from nanomechanical resonators form an ideal laboratory to study synchronization given their high-quality factors, small footprint, and ease of co-integration with modern electronic signal processing technologies.

cond-mat.mes-hall↗

arXiv2013

Nonlinearity in nanomechanical cantilevers

Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro- and nano-cantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems development. In this article, we report the first highly controlled measurements of the nonlinear response of nanomechanical cantilevers using an ultra-linear detection system. This is performed for an extensive range of devices to probe the validity of Euler-Bernoulli theory in the nonlinear regime. We find that its predictions deviate strongly from our measurements for the nonlinearity of the fundamental flexural mode, which show a systematic dependence on aspect ratio (length/width) together with random scatter. This contrasts with the second mode, which is always found to be in good agreement with theory. These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation.

cond-mat.mes-hall↗

arXiv2012

Optimal operating points of oscillators using nonlinear resonators

We demonstrate an analytical method for calculating the phase sensitivity of a class of oscillators whose phase does not affect the time evolution of the other dynamic variables. We show that such oscillators possess the possibility for complete phase noise elimination. We apply the method to a feedback oscillator which employs a high Q weakly nonlinear resonator and provide explicit parameter values for which the feedback phase noise is completely eliminated and others for which there is no amplitude-phase noise conversion. We then establish an operational mode of the oscillator which optimizes its performance by diminishing the feedback noise in both quadratures, thermal noise, and quality factor fluctuations. We also study the spectrum of the oscillator and provide specific results for the case of 1/f noise sources.

cond-mat.other↗

arXiv2012

Surpassing fundamental limits of oscillators using nonlinear resonators

Self-sustained oscillators are ubiquitous and essential for metrology, communications, time reference, and geolocation. In its most basic form an oscillator consists of a resonator driven on-resonance, through feedback, to create a periodic signal sustained by a static energy source. The generation of a stable frequency, the basic function of oscillators, is typically achieved by increasing the amplitude of motion of the resonator while remaining within its linear, harmonic, regime. Contrary to this conventional paradigm, in this Letter we show that by operating the oscillator at special points in the resonators anharmonic regime we can overcome fundamental limitations of oscillator performance due to thermodynamic noise as well as practical limitations due to noise from the sustaining circuit. We develop a comprehensive model that accounts for the major contributions to the phase noise of the nonlinear oscillator. Using a nanoelectromechanical system (NEMS)-based oscillator, we experimentally verify the existence of a special region in the operational parameter space that enables a significant reduction of the oscillators phase noise, as predicted by our model.

cond-mat.mes-hall↗

arXiv2012

A Passive Phase Noise Cancellation Element

We introduce a new method for reducing phase noise in oscillators, thereby improving their frequency precision. The noise reduction device consists of a pair of coupled nonlinear resonating elements that are driven parametrically by the output of a conventional oscillator at a frequency close to the sum of the linear mode frequencies. Above the threshold for parametric response, the coupled resonators exhibit self-oscillation at an inherent frequency. We find operating points of the device for which this periodic signal is immune to frequency noise in the driving oscillator, providing a way to clean its phase noise. We present results for the effect of thermal noise to advance a broader understanding of the overall noise sensitivity and the fundamental operating limits.

cond-mat.mes-hall↗

arXiv2011

Detecting and characterizing frequency fluctuations of vibrational modes

We show how frequency fluctuations of a vibrational mode can be separated from other sources of phase noise. The method is based on the analysis of the time dependence of the complex amplitude of forced vibrations. The moments of the complex amplitude sensitively depend on the frequency noise statistics and its power spectrum. The analysis applies to classical and to quantum vibrations.

cond-mat.mes-hall↗

arXiv2008

Nonlinear Dynamics and Chaos in Two Coupled Nanomechanical Resonators

Two elastically coupled nanomechanical resonators driven independently near their resonance frequencies show intricate nonlinear dynamics. The dynamics provide a scheme for realizing a nanomechanical system with tunable frequency and nonlinear properties. For large vibration amplitudes the system develops spontaneous oscillations of amplitude modulation that also show period doubling transitions and chaos. The complex nonlinear dynamics are quantitatively predicted by a simple theoretical model.

cond-mat.mes-hall↗

arXiv2007

Basins of attraction of a nonlinear nanomechanical resonator

We present an experiment that systematically probes the basins of attraction of two fixed points of a nonlinear nanomechanical resonator and maps them out with high resolution. We observe a separatrix which progressively alters shape for varying drive strength and changes the relative areas of the two basins of attraction. The observed separatrix is blurred due to ambient fluctuations, including residual noise in the drive system, which cause uncertainty in the preparation of an initial state close to the separatrix. We find a good agreement between the experimentally mapped and theoretically calculated basins of attraction.

cond-mat.mes-hall↗

arXiv2007

Magnetotransport properties of strained (Ga0.95, Mn0.05)As epilayers close to the metal-insulator transition: Description using Aronov-Altshuler three-dimensional scaling theory

The magnitude of the anisotropic magnetoresistance (AMR) and the longitudinal resistance in compressively strained (Ga0.95, Mn0.05)As epilayers were measured for the first time down to temperatures as low as 30 mK. Below temperatures of 3K the conductivity decreases ~ T^1/3 over two orders of magnitude in temperature. The conductivity can be well described within the framework of a 3D scaling theory of Anderson's transition in the presence of spin scattering in semiconductors. It is shown that the samples are on the metallic side but very close to the metal-insulator transition (MIT). At lowest temperatures a decrease in the AMR effect is observed, which is assigned to changes in the coupling between the remaining itinerant carriers and the local Mn 5/2-spin moments.

cond-mat.other↗

arXiv2006

Dissipation in Single-Crystal 3C-SiC Ultra-High Frequency Nanomechanical Resonators

The energy dissipation 1/Q (where Q is the quality factor) and resonance frequency characteristics of single-crystal 3C-SiC ultrahigh frequency (UHF) nanomechanical resonators are measured, for a family of UHF resonators with resonance frequencies of 295MHz, 395MHz, 411MHz, 420MHz, 428MHz, and 482MHz. A temperature dependence of dissipation, 1/Q ~ T^(0.3) has been identified in these 3C-SiC devices. Possible mechanisms that contribute to dissipation in typical doubly-clamped beam UHF resonators are analyzed. Device size and dimensional effects on the dissipation are also examined. Clamping losses are found to be particularly important in these UHF resonators. The resonance frequency decreases as the temperature is increased, and the average frequency temperature coefficient is about -45ppm/K.

cond-mat.mes-hall↗

arXiv2005

Nanomechanical Measurements of Magnetostriction and Magnetic Anisotropy in (Ga,Mn)As

A (Ga,Mn)As nanoelectromechanical resonator is used to obtain the first direct measurement of magnetostriction in a dilute magnetic semiconductor. Field-dependent magnetoelastic stress induces shifts in resonance frequency that can be discerned with a high resolution electromechanical transduction scheme. By monitoring the field dependence, the magnetostriction and anisotropy field constants can be simultaneously mapped over a wide range of temperatures. These results, when compared with theoretical predictions, appear to provide insight into a unique form of magnetoelastic behavior mediated by holes.

cond-mat.soft↗

arXiv2005

Perturbation of magnetostatic modes observed by FMRFM

Magnetostatic modes of Yttrium Iron Garnet (YIG) films are investigated by ferromagnetic resonance force microscopy (FMRFM). A thin film ``probe'' magnet at the tip of a compliant cantilever introduces a local inhomogeneity in the internal field of the YIG sample. This influences the shape of the sample's magnetostatic modes, thereby measurably perturbing the strength of the force coupled to the cantilever. We present a theoretical model that explains these observations; it shows that tip-induced variation of the internal field creates either a local ``potential barrier'' or ``potential well'' for the magnetostatic waves. The data and model together indicate that local magnetic imaging of ferromagnets is possible, even in the presence of long-range spin coupling, through the induction of localized magnetostatic modes predicted to arise from sufficiently strong tip fields.

cond-mat.mtrl-sci↗

arXiv2005

Comment on recent Physical Review Letter by Gaidarzhy, et al. "Evidence for quantized displacement in macroscopic nanomechanical oscillator."

In a recent letter, Gaidarzhy et al. claim to have observed evidence for quantized displacements of a nanomechanical oscillator. We contend that the evidence, analysis, claims, and conclusions presented are contrary to expectations from fundamentals of quantum mechanics and elasticity theory, and that the method used by the authors is unsuitable in principle to observe the quantized energy states of a nanomechanical structure.

quant-ph↗