Measuring frequency fluctuations in nonlinear nanomechanical resonators

Advances in nanomechanics within recent years have demonstrated an always expanding range of devices, from top-down structures to appealing bottom-up MoS$_2$ and graphene membranes, used for both sensing and component-oriented applications. One of the main concerns in all of these devices is frequency noise, which ultimately limits their applicability. This issue has attracted a lot of attention recently, and the origin of this noise remains elusive up to date. In this Letter we present a very simple technique to measure frequency noise in nonlinear mechanical devices, based on the presence of bistability. It is illustrated on silicon-nitride high-stress doubly-clamped beams, in a cryogenic environment. We report on the same $T/f$ dependence of the frequency noise power spectra as reported in the literature. But we also find unexpected {\it damping fluctuations}, amplified in the vicinity of the bifurcation points; this effect is clearly distinct from already reported nonlinear dephasing, and poses a fundamental limit on the measurement of bifurcation frequencies. The technique is further applied to the measurement of frequency noise as a function of mode number, within the same device. The relative frequency noise for the fundamental flexure $\delta f/f_0$ lies in the range $0.5 - 0.01~$ppm (consistent with literature for cryogenic MHz devices), and decreases with mode number in the range studied. The technique can be applied to {\it any types} of nano-mechanical structures, enabling progresses towards the understanding of intrinsic sources of noise in these devices.Comment: Published 7 may 201

On the nonlinear NMR and magnon BEC in antiferromagnetic materials with coupled electron-nuclear spin precession

We present a new study of nonlinear NMR and Bose-Einstein Condensation (BEC) of nuclear spin waves in antiferromagnetic MnCO3 with coupled electron and nuclear spins. In particular, we show that the observed behaviour of NMR signals strongly contradicts the conventional description of paramagnetic ensembles of noninteracting spins based on the phenomenological Bloch equations. We present a new theoretical description of the coupled electron-nuclear spin precession, which takes into account an indirect relaxation of nuclear spins via the electron subsystem. We show that the magnitude of the nuclear magnetization is conserved for arbitrary large excitation powers, which is drastically different from the conventional heating scenario derived from the Bloch equations. This provides strong evidence that the coherent precession of macroscopic nuclear magnetization observed experimentally can be identified with BEC of nuclear spin waves with k=0.Comment: 12 pages, 8 figure

Nanomechanical damping via electron-assisted relaxation of two-level systems

We report on measurements of dissipation and frequency noise at millikelvin temperatures of nanomechanical devices covered with aluminum. A clear excess damping is observed after switching the metallic layer from superconducting to the normal state with a magnetic field. Beyond the standard model of internal tunneling systems coupled to the phonon bath, here we consider the relaxation to the conduction electrons together with the nature of the mechanical dispersion laws for stressed/unstressed devices. With these key ingredients, a model describing the relaxation of two-level systems inside the structure due to interactions with electrons and phonons with well separated timescales captures the data. In addition, we measure an excess 1/f-type frequency noise in the normal state, which further emphasizes the impact of conduction electrons

Electromagnetic shield characteristics investigation for the calibration the NMR logging tool

The problem of electromagnetic shielding is relevant due to increasing number of electronic devices that interact with each other. It is known that shield, which is made of high conductivity materials, is widely used for controlling electromagnetic noise. Due to development of NMR logging tool two shielding Faraday cages have been made. The aim of the work was determination the frequency transmittance dependence of shielding in range from 100 kHz to 100 MHz. Transmitting and receiving devices were developed for an experiment. As a result, constructed shields are suitable for tuning and calibration NMR logging tools

On-chip thermometry for microwave optomechanics implemented in a demagnetization cryostat

We report on microwave optomechanics measurements performed on a nuclear adiabatic demagnetization cryostat, whose temperature is determined by accurate thermometry from below 500$~\mu$K to about 1$~$Kelvin. We describe a method for accessing the on-chip temperature, building on the blue-detuned parametric instability and a standard microwave setup. The capabilities and sensitivity of both the experimental arrangement and the developed technique are demonstrated with a very weakly coupled silicon-nitride doubly-clamped beam mode of about 4$~$MHz and a niobium on-chip cavity resonating around 6$~$GHz. We report on an unstable intrinsic driving force in the coupled microwave-mechanical system acting on the mechanics that appears below typically 100$~$mK. The origin of this phenomenon remains unknown, and deserves theoretical input. It prevents us from performing reliable experiments below typically 10-30$~$mK; however no evidence of thermal decoupling is observed, and we propose that the same features should be present in all devices sharing the microwave technology, at different levels of strengths. We further demonstrate empirically how most of the unstable feature can be annihilated, and speculate how the mechanism could be linked to atomic-scale two level systems. The described microwave/microkelvin facility is part of the EMP platform, and shall be used for further experiments within and below the millikelvin range.Comment: 14 pages with appendi

Beyond linear coupling in microwave optomechanics

We explore the nonlinear dynamics of a cavity optomechanical system. Our realization consisting of a drumhead nano-electro-mechanical resonator (NEMS) coupled to a microwave cavity, allows for a nearly ideal platform to study the nonlinearities arising purely due to radiation-pressure physics. Experiments are performed under a strong microwave Stokes pumping which triggers mechanical self-sustained oscillations. We analyze the results in the framework of an extended nonlinear optome-chanical theory, and demonstrate that quadratic and cubic coupling terms in the opto-mechanical Hamiltonian have to be considered. Quantitative agreement with the measurements is obtained considering only genuine geometrical nonlinearities: no thermo-optical instabilities are observed, in contrast with laser-driven systems. Based on these results, we describe a method to quantify nonlin-ear properties of microwave optomechanical devices. Such a technique, available now in the quantum electro-mechanics toolbox, but completely generic, is mandatory for the development of new schemes where higher-order coupling terms are proposed as a new resource, like Quantum Non-Demolition measurements, or in the search for new fundamental quantum signatures, like Quantum Gravity. We also find that the motion imprints a wide comb of extremely narrow peaks in the microwave output field, which could also be exploited in specific microwave-based measurements, potentially limited only by the quantum noise of the optical and the mechanical fields for a ground-state cooled NEMS device

Low temperature adsorption of 3He on silica aerogel surface and its influence on 3He spin kinetics

Significant influence of the aerogel surface heterogeneity on the processes of 3He nuclear magnetic relaxation at temperatures 1.5 - 4.2 K is discovered. This influence appears, for instance, in differences of the 3He T 1 relaxation times for small portion of 3He, adsorbed at different temperatures. Binding energy data of 3He and distributions of this energy in two types of aerogel were obtained experimentally. Adsorbed 3He molecules with binding energies 60 - 250 K play supreme role in processes of nuclear magnetic relaxation of gaseous and liquid 3He in aerogel

On the thermodynamic equilibrium in the 3He-aerogel system at low temperatures

A new method for studying the processes of the establishment of the thermodynamic equilibrium in the adsorbed 3He layers in highly porous media has been proposed. Using this method, the thermalization of adsorbed 3He on silica aerogel at a temperature of 1. 5 K has been studied. The process of the establishment of the thermodynamic equilibrium has been controlled by measuring the pressure in an experimental cell, the amplitude of the NMR signal, and the nuclear spin-spin and spin-lattice relaxation times of adsorbed 3He. It has been shown that the establishment of the thermodynamic equilibrium in the adsorbed 3He-aerogel system is characterized by a time of 26 min. © 2011 Pleiades Publishing, Ltd