Nonlinear micromechanical Casimir oscillator

Casimir Effect in MEMS: Materials, Geometries, and Metrologies-A Review

Casimir force densities, i.e., force per area, become very large if two solid material surfaces come closer together to each other than 10 nm. In most cases, the forces are attractive. In some cases, they can be repulsive depending on the solid materials and the fluid medium in between. This review provides an overview of experimental and theoretical studies that have been performed and focuses on four main aspects: (i) the combinations of different materials, (ii) the considered geometries, (iii) the applied experimental measurement methodologies and (iv) a novel self-assembly methodology based on Casimir forces. Briefly reviewed is also the influence of additional parameters such as temperature, conductivity, and surface roughness. The Casimir effect opens many application possibilities in microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS), where an overview is also provided. The knowledge generation in this fascinating field requires interdisciplinary approaches to generate synergetic effects between technological fabrication metrology, theoretical simulations, the establishment of adequate models, artificial intelligence, and machine learning. Finally, multiple applications are addressed as a research roadmap.

On Casimir and Helmholtz Fluctuation-Induced Forces in Micro- and Nano-Systems: Survey of Some Basic Results

Fluctuations are omnipresent; they exist in any matter, due either to its quantum nature or to its nonzero temperature. In the current review, we briefly cover the quantum electrodynamic Casimir (QED) force as well as the critical Casimir (CC) and Helmholtz (HF) forces. In the QED case, the medium is usually a vacuum and the massless excitations are photons, while in the CC and HF cases the medium is usually a critical or correlated fluid and the fluctuations of the order parameter are the cause of the force between the macroscopic or mesoscopic bodies immersed in it. We discuss the importance of the presented results for nanotechnology, especially for devising and assembling micro- or nano-scale systems. Several important problems for nanotechnology following from the currently available experimental findings are spelled out, and possible strategies for overcoming them are sketched. Regarding the example of HF, we explicitly demonstrate that when a given integral quantity characterizing the fluid is conserved, it has an essential influence on the behavior of the corresponding fluctuation-induced force.

Physical Limit of Nonlinear Brownian Oscillators in Quantum Trap

Quantum trap, a quantum and thermal fluctuations-induced nonmonotonous potential, offers a chance to build up microscopic mechanical systems completely dominated by fluctuations. Here, we explore the physical limit of the effective damping ratio of the nonlinear Brownian oscillator in a quantum trap, set by the finite separation for avoiding molecular-scale effects on the trap potential and the surface confinement effect-induced diverging damping and random forces. The quasiharmonic approximations and Langevin dynamics simulations show that the lowest effective damping ratios of the suspended Au plate and Au sphere upon a Teflon coating of 10 nm can be ∼210 and ∼145, respectively, at room temperature. Perforation is proposed as an effective route to reduce the damping ratio (down to 6.4) by attenuating the surface confinement effect. An unexpected result due to the temperature dependences of dielectric function and viscosity of ethanol is a further reduced damping ratio at 400 K (1.3). The nonlinear Brownian oscillator in the quantum trap shows promise of probing near-boundary hydrodynamics at nanoscale.

Large Casimir Flipping Torque in Quantum Trap

Casimir torque between parallel plates, a macroscopic quantum electrodynamics effect, is known to be induced by dielectric anisotropy and related to the rotational degree of freedom. We here reveal a different type of Casimir torque generated on a Au plate suspended in a quantum trap without recourse to materials anisotropy. As the Au plate deflects from the equilibrium plane with a nonzero flipping angle, the regions departing from and approaching the Teflon-coated Au substrate are subjected to attractive and repulsive Casimir forces, respectively, resulting in a restoring torque about the axis of flipping. For a quantum trap with an equilibrium separation of ∼10 nm, the stiffness per unit area of the Casimir flipping torque can be an order of magnitude larger than those of previously reported dielectric anisotropy-induced rotational torques at the same separation. The large Casimir flipping torque provides the possibility of designing a mechanical oscillator completely dominated by quantum and thermal fluctuations.

Influence of optical property contrast on the critical distribution of electrostatic torques in double-beam torsional Casimir actuators: Non-linear actuation toward chaotic motion

Here, we discuss how to achieve the stable actuation of a double beam torsional micro-actuator over the largest possible displacement of the moving component under the influence of Casimir and electrostatic torques, when the rotating component is constructed from different materials. The main part of this study is devoted to finding the optimal distribution of the electrostatic torque between the left and right sides of the micro-actuator to reach the maximum stable operation of the device. The latter is manifested by switching from homoclinic to heteroclinic orbits in the phase portraits. Indeed, the bifurcation curves and the phase portraits have been employed to show the sensitivity of the critical distribution of the electrostatic torque, beyond which the device does show stable performance, on the contrast of the optical properties of the moving component and the applied voltage in a conservative autonomous system. Moreover, for driven systems, the Melnikov function approach and the Poincaré portraits are used to study the presence of chaotic motion, which eventually leads to stiction. It is shown that the application of the optimal distribution of the electrostatic torque can significantly decrease the possibility of chaotic motion, and at this optimal level, the threshold curves reveal less difference between systems with different optical contrast.

Emergence of Synchronization in a Driven-Dissipative Hot Rydberg Vapor

We observe synchronization in a thermal (35-60 °C) atomic (Rb) ensemble driven to a highly excited Rydberg state (principle quantum number n ranging from 43 to 79). Synchronization in this system is unexpected due to the atomic motion; however, we show theoretically that sufficiently strong interactions via a global Rydberg density mean field cause frequency and phase entrainment. The emergent oscillations in the vapor's bulk quantities are detected in the transmission of the probe laser for a two-photon excitation scheme.

Attractive and Repulsive Fluctuation-Induced Pressure in Peptide Films Deposited on Semiconductor Substrates

We consider the fluctuation-induced (Casimir) pressure in peptide films deposited on GaAs, Ge, and ZnS substrates which are either in a dielectric or metallic state. The calculations of the Casimir pressure are performed in the framework of the fundamental Lifshitz theory employing the frequency-dependent dielectric permittivities of all involved materials. The electric conductivity of semiconductor substrates is taken into account within the experimentally and thermodynamically consistent approach. According to our results, the Casimir pressure in peptide films deposited on dielectric-type semiconductor substrates vanishes for some definite film thickness and is repulsive for thinner and attractive for thicker films. The dependence of this effect on the fraction of water in the film and on the static dielectric permittivity of the semiconductor substrate is determined. For the metallic-type semiconductor substrates, the Casimir pressure in peptide coatings is shown to be always repulsive. The possible applications of these results to the problem of stability of thin coatings in microdevices are discussed.

Observation and control of Casimir effects in a sphere-plate-sphere system

A remarkable prediction of quantum field theory is that there are quantum electromagnetic fluctuations (virtual photons) everywhere, which leads to the intriguing Casimir effect. While the Casimir force between two objects has been studied extensively for several decades, the Casimir force between three objects has not been measured yet. Here, we report the experimental demonstration of an object under the Casimir force exerted by two other objects simultaneously. Our Casimir system consists of a micrometer-thick cantilever placed in between two microspheres, forming a unique sphere-plate-sphere geometry. We also propose and demonstrate a three-terminal switchable architecture exploiting opto-mechanical Casimir interactions that can lay the foundations of a Casimir transistor. Beyond the paradigm of Casimir forces between two objects in different geometries, our Casimir transistor represents an important development for controlling three-body virtual photon interactions and will have potential applications in sensing and information processing.

Mechanical Bistability in Kerr-modified Cavity Magnomechanics

Bistable mechanical vibration is observed in a cavity magnomechanical system, which consists of a microwave cavity mode, a magnon mode, and a mechanical vibration mode of a ferrimagnetic yttrium-iron-garnet sphere. The bistability manifests itself in both the mechanical frequency and linewidth under a strong microwave drive field, which simultaneously activates three different kinds of nonlinearities, namely, magnetostriction, magnon self-Kerr, and magnon-phonon cross-Kerr nonlinearities. The magnon-phonon cross-Kerr nonlinearity is first predicted and measured in magnomechanics. The system enters a regime where Kerr-type nonlinearities strongly modify the conventional cavity magnomechanics that possesses only a radiation-pressure-like magnomechanical coupling. Three different kinds of nonlinearities are identified and distinguished in the experiment. Our Letter demonstrates a new mechanism for achieving mechanical bistability by combining magnetostriction and Kerr-type nonlinearities, and indicates that such Kerr-modified cavity magnomechanics provides a unique platform for studying many distinct nonlinearities in a single experiment.

Tuning the nonlinearity of graphene mechanical resonators by Joule heating

As an inherent property of the device itself, nonlinearity in micro-/nano- electromechanical resonators is difficult to eliminate, and it has shown a wide range of applications in basic research, sensing and other fields. While many application scenarios require tunability of the nonlinearity, inherent nonlinearity of a mechanical resonator is difficult to be changed. Here, we report the experimental observation of a Joule heating induced tuning effect on the nonlinearity of graphene mechanical resonators. We fabricated multiple graphene mechanical resonators and detected their resonant properties by an optical interference method. The mechanical vibration of the resonators will enter from the linear to the nonlinear intervals if we enhance the external driving power to a certain value. We found that at a fixed drive power, the nonlinearity of a mechanical resonator can be tuned by applying a dc bias current on the resonator itself. The tuning mechanism could be explained by the nonlinear amplitude-frequency dependence theory. Our results may provide a research platform for the study of mechanical nonlinearity by using atomic-thin layer materials.

Non-reciprocal energy transfer through the Casimir effect

One of the fundamental predictions of quantum mechanics is the occurrence of random fluctuations in a vacuum caused by the zero-point energy. Remarkably, quantum electromagnetic fluctuations can induce a measurable force between neutral objects, known as the Casimir effect¹, and it has been studied both theoretically^2,3 and experimentally^4-9. The Casimir effect can dominate the interaction between microstructures at small separations and is essential for micro- and nanotechnologies^10,11. It has been utilized to realize nonlinear oscillation¹², quantum trapping¹³, phonon transfer^14,15 and dissipation dilution¹⁶. However, a non-reciprocal device based on quantum vacuum fluctuations remains an unexplored frontier. Here we report quantum-vacuum-mediated non-reciprocal energy transfer between two micromechanical oscillators. We parametrically modulate the Casimir interaction to realize a strong coupling between the two oscillators with different resonant frequencies. We engineer the system's spectrum such that it possesses an exceptional point^17-20 in the parameter space and explore the asymmetric topological structure in its vicinity. By dynamically changing the parameters near the exceptional point and utilizing the non-adiabaticity of the process, we achieve non-reciprocal energy transfer between the two oscillators with high contrast. Our work demonstrates a scheme that employs quantum vacuum fluctuations to regulate energy transfer at the nanoscale and may enable functional Casimir devices in the future.

Path integral study of the Casimir effect in a chiral medium

The Casimir effect is a remarkable macroscopic feature of QED, while recent lattice studies have also shown its potential nontrivial consequences in QCD. In light of having a better understanding of the Casimir effect, it is advantageous to have a self-contained path integral formulation of the phenomenon. I will show how the Casimir effect between two uncharged plates in the presence of a chiral medium, modeled with an axion term θF͂μvFμv, can be formulated in terms of the path integral, and how such a formulation leads to a 3D effective action of the restricted electromagnetic field.

Analysis of a Casimir-driven parametric amplifier with resilience to Casimir pull-in for MEMS single-point magnetic gradiometry

The Casimir force, a quantum mechanical effect, has been observed in several microelectromechanical system (MEMS) platforms. Due to its extreme sensitivity to the separation of two objects, the Casimir force has been proposed as an excellent avenue for quantum metrology. Practical application, however, is challenging due to attractive forces leading to stiction and device failure, called Casimir pull-in. In this work, we design and simulate a Casimir-driven metrology platform, where a time-delay-based parametric amplification technique is developed to achieve a steady-state and avoid pull-in. We apply the design to the detection of weak, low-frequency, gradient magnetic fields similar to those emanating from ionic currents in the heart and brain. Simulation parameters are selected from recent experimental platforms developed for Casimir metrology and magnetic gradiometry, both on MEMS platforms. While a MEMS offers many advantages to such an application, the detected signal must typically be at the resonant frequency of the device, with diminished sensitivity in the low frequency regime of biomagnetic fields. Using a Casimir-driven parametric amplifier, we report a 10,000-fold improvement in the best-case resolution of MEMS single-point gradiometers, with a maximum sensitivity of 6 Hz/(pT/cm) at 1 Hz. Further development of the proposed design has the potential to revolutionize metrology and may specifically enable the unshielded monitoring of biomagnetic fields in ambient conditions.

Measurement of the Casimir Force between 0.2 and 8 μm: Experimental Procedures and Comparison with Theory

We present results on the determination of the differential Casimir force between an Au-coated sapphire sphere and the top and bottom of Au-coated deep silicon trenches performed by means of the micromechanical torsional oscillator in the range of separations from 0.2 to 8 μm. The random and systematic errors in the measured force signal are determined at the 95% confidence level and combined into the total experimental error. The role of surface roughness and edge effects is investigated and shown to be negligibly small. The distribution of patch potentials is characterized by Kelvin probe microscopy, yielding an estimate of the typical size of patches, the respective r.m.s. voltage and their impact on the measured force. A comparison between the experimental results and theory is performed with no fitting parameters. For this purpose, the Casimir force in the sphere-plate geometry is computed independently on the basis of first principles of quantum electrodynamics using the scattering theory and the gradient expansion. In doing so, the frequency-dependent dielectric permittivity of Au is found from the optical data extrapolated to zero frequency by means of the plasma and Drude models. It is shown that the measurement results exclude the Drude model extrapolation over the region of separations from 0.2 to 4.8 μm, whereas the alternative extrapolation by means of the plasma model is experimentally consistent over the entire measurement range. A discussion of the obtained results is provided.

A system for probing Casimir energy corrections to the condensation energy

In this article, we present a nanoelectromechanical system (NEMS) designed to detect changes in the Casimir energy. The Casimir effect is a result of the appearance of quantum fluctuations in an electromagnetic vacuum. Previous experiments have used nano- or microscale parallel plate capacitors to detect the Casimir force by measuring the small attractive force these fluctuations exert between the two surfaces. In this new set of experiments, we aim to directly detect the shifts in the Casimir energy in a vacuum due to the presence of the metallic parallel plates, one of which is a superconductor. A change in the Casimir energy of this configuration is predicted to shift the superconducting transition temperature (T c) because of the interaction between it and the superconducting condensation energy. In our experiment, we take a superconducting film, carefully measure its transition temperature, bring a conducting plate close to the film, create a Casimir cavity, and then measure the transition temperature again. The expected shifts are smaller than the normal shifts one sees in cycling superconducting films to cryogenic temperatures, so using a NEMS resonator in situ is the only practical way to obtain accurate, reproducible data. Using a thin Pb film and opposing Au surface, we observe no shift in T c >12 µK down to a minimum spacing of ~70 nm at zero applied magnetic field.

Sensitivity of chaotic behavior to low optical frequencies of a double-beam torsional actuator

We investigate here how the optical properties at low frequencies affect the actuation dynamics and emerging chaotic behavior in a double-beam torsion actuator at nanoscale separations (<200nm), where the Casimir forces and torques play a major role. In fact, we take into account differences of the Casimir force due to alternative modeling of optical properties at low frequencies, where measurements are not feasible, via the Drude and plasma models, and repercussions by different material preparation conditions. For conservative autonomous actuation, bifurcation and phase portrait analysis indicate that both factors affect the stability of an actuating device in such a way that stronger Casimir forces and torques will favor increased unstable behavior. The latter will be enhanced by unbalanced application of electrostatic voltages in double-beam actuating systems. For the case of a time-periodic driving force, we use a Melnikov function and a phase plane analysis to study the emerging chaotic behavior with respect to the Drude and plasma modeling and material preparation conditions. We find indications that any factor that leads to stronger Casimir interactions will aid chaotic behavior and prevent long term prediction of the actuating dynamics. Moreover, in a double-beam actuator chaoticity will be amplified by the application of unbalanced electrostatic voltages. Therefore, the details of modeling of optical properties and the material preparations conditions must be carefully considered in the design of actuating devices at nanoscale because here Casimir forces are omnipresent and broadband type interactions.

Building a Casimir metrology platform with a commercial MEMS sensor

The Casimir Effect is a physical manifestation of quantum fluctuations of the electromagnetic vacuum. When two metal plates are placed close together, typically much less than a micron, the long wavelength modes between them are frozen out, giving rise to a net attractive force between the plates, scaling as d -4 (or d -3 for a spherical-planar geometry) even when they are not electrically charged. In this paper, we observe the Casimir Effect in ambient conditions using a modified capacitive micro-electromechanical system (MEMS) sensor. Using a feedback-assisted pick-and-place assembly process, we are able to attach various microstructures onto the post-release MEMS, converting it from an inertial force sensor to a direct force measurement platform with pN (piconewton) resolution. With this system we are able to directly measure the Casimir force between a silver-coated microsphere and gold-coated silicon plate. This device is a step towards leveraging the Casimir Effect for cheap, sensitive, room temperature quantum metrology.

Dependence of chaotic behavior on optical properties and electrostatic effects in double-beam torsional Casimir actuation

We investigate the influence of Casimir and electrostatic torques on double-beam torsional microelectromechanical systems with materials covering a broad range of conductivities of more than three orders of magnitude. For the frictionless autonomous systems, bifurcation and phase space analysis shows a significant difference between stable and unstable operating regimes for equal and unequal applied voltages on both sides of the double torsional system giving rise to heteroclinic and homoclinic orbits, respectively. For equal applied voltages, only the position of a symmetric unstable saddle equilibrium point is dependent on the material optical properties and electrostatic effects, while in any other case stable and unstable equilibrium points are dependent on both factors. For the periodically driven system, a Melnikov function approach is used to show the presence of chaotic motion rendering predictions of whether stiction or stable actuation will take place over long times impossible. Chaotic behavior introduces significant risk for stiction, and it is more likely to occur for the more conductive systems that experience stronger Casimir forces and torques. Indeed, when unequal voltages are applied, the sensitive dependence of chaotic motion on electrostatics is more pronounced for the highest conductivity systems.

Distance-Dependent Sign Reversal in the Casimir-Lifshitz Torque

The Casimir-Lifshitz torque between two biaxially polarizable anisotropic planar slabs is shown to exhibit a nontrivial sign reversal in its rotational sense. The critical distance a_{c} between the slabs that marks this reversal is characterized by the frequency ω_{c}∼c/2a_{c} at which the in-planar polarizabilities along the two principal axes are equal. The two materials seek to align their principal axes of polarizabilities in one direction below a_{c}, while above a_{c} their axes try to align rotated perpendicular relative to their previous minimum energy orientation. The sign reversal disappears in the nonretarded limit. Our perturbative result, derived for the case when the differences in the relative polarizabilities are small, matches excellently with the exact theory for uniaxial materials. We illustrate our results for black phosphorus and phosphorene.

Sign change in the net force in sphere-plate and sphere-sphere systems immersed in nonpolar critical fluid due to the interplay between the critical Casimir and dispersion van der Waals forces

We study systems in which both long-ranged van der Waals and critical Casimir interactions are present. The latter arise as an effective force between bodies when immersed in a near-critical medium, say a nonpolar one-component fluid or a binary liquid mixture. They are due to the fact that the presence of the bodies modifies the order parameter profile of the medium between them as well as the spectrum of its allowed fluctuations. We study the interplay between these forces, as well as the total force (TF) between a spherical colloid particle and a thick planar slab and between two spherical colloid particles. We do that using general scaling arguments and mean-field-type calculations utilizing the Derjaguin and the surface integration approaches. They both are based on data of the forces between two parallel slabs separated at a distance L from each other, confining the fluctuating fluid medium characterized by its temperature T and chemical potential μ. The surfaces of the colloid particles and the slab are coated by thin layers exerting strong preference to the liquid phase of the fluid, or one of the components of the mixture, modeled by strong adsorbing local surface potentials, ensuring the so-called (+,+) boundary conditions. On the other hand, the core region of the slab and the particles influence the fluid by long-ranged competing dispersion potentials. We demonstrate that for a suitable set of colloids-fluid, slab-fluid, and fluid-fluid coupling parameters, the competition between the effects due to the coatings and the core regions of the objects involved result, when one changes T, μ, or L, in sign change of the Casimir force (CF) and the TF acting between the colloid and the slab, as well as between the colloids. This can be used for governing the behavior of objects, say colloidal particles, at small distances, say in colloid suspensions for preventing flocculation. It can also provide a strategy for solving problems with handling, feeding, trapping, and fixing of microparts in nanotechnology. Data for specific substances in support of the experimental feasibility of the theoretically predicted behavior of the CF and TF have been also presented.

Sign Flip in the Casimir Force for Interacting Fermion Systems

In this work we consider a fermionic chain of finite length ℓ. Fermions are allowed to interact and are forced to obey boundary conditions, thus altering the process of condensation. Our goal is to explore how this affects the quantum vacuum energy for this system. We approach this problem by using a self-consistent method and observe a nontrivial behavior in the Casimir force, displaying a switch from an attractive to a repulsive regime. This flip stems from the competition between the attractive contribution from the usual fermionic Casimir effect and a repulsive one coming from the condensate.

Strong Thermal and Electrostatic Manipulation of the Casimir Force in Graphene Multilayers

We show that graphene-dielectric multilayers give rise to an unusual tunability of the Casimir-Lifshitz forces and allow to easily realize completely different regimes within the same structure. Concerning thermal effects, graphene-dielectric multilayers take advantage of the anomalous features predicted for isolated suspended graphene sheets, even though they are considerably affected by the presence of the dielectric substrate. They can also achieve the anomalous nonmonotonic thermal metallic behavior by increasing the graphene sheets density and their Fermi level. In addition to a strong thermal modulation occurring at short separations, in a region where the force is orders of magnitude larger than the one occurring at large distances, the force can be also adjusted by varying the number of graphene layers as well as their Fermi levels, allowing for relevant force amplifications which can be tuned, very rapidly and in situ, by simply applying an electric potential. Our predictions can be relevant for both Casimir experiments and micro- or nanoelectromechanical systems and in new devices for technological applications.

Micromachined Resonators: A Review

This paper is a review of the remarkable progress that has been made during the past few decades in design, modeling, and fabrication of micromachined resonators. Although micro-resonators have come a long way since their early days of development, they are yet to fulfill the rightful vision of their pervasive use across a wide variety of applications. This is partially due to the complexities associated with the physics that limit their performance, the intricacies involved in the processes that are used in their manufacturing, and the trade-offs in using different transduction mechanisms for their implementation. This work is intended to offer a brief introduction to all such details with references to the most influential contributions in the field for those interested in a deeper understanding of the material.

Casimir rack and pinion as a miniaturized kinetic energy harvester

We study a nanoscale machine composed of a rack and a pinion with no contact, but intermeshed via the lateral Casimir force. We adopt a simple model for the random velocity of the rack subject to external random forces, namely, a dichotomous noise with zero mean value. We show that the pinion, even when it experiences random thermal torque, can do work against a load. The device thus converts the kinetic energy of the random motions of the rack into useful work.

Casimir switch: steering optical transparency with vacuum forces

The Casimir force, originating from vacuum zero-point energy, is one of the most intriguing purely quantum effects. It has attracted renewed interests in current field of nanomechanics, due to the rapid size decrease of on-chip devices. Here we study the optomechanically-induced transparency (OMIT) with a tunable Casimir force. We find that the optical output rate can be significantly altered by the vacuum force, even terminated and then restored, indicating a highly-controlled optical switch. Our result addresses the possibility of designing exotic optical nano-devices by harnessing the power of vacuum.

Generating giant and tunable nonlinearity in a macroscopic mechanical resonator from a single chemical bond

Nonlinearity in macroscopic mechanical systems may lead to abundant phenomena for fundamental studies and potential applications. However, it is difficult to generate nonlinearity due to the fact that macroscopic mechanical systems follow Hooke's law and respond linearly to external force, unless strong drive is used. Here we propose and experimentally realize high cubic nonlinear response in a macroscopic mechanical system by exploring the anharmonicity in chemical bonding interactions. We demonstrate the high tunability of nonlinear response by precisely controlling the chemical bonding interaction, and realize, at the single-bond limit, a cubic elastic constant of 1 × 10(20) N m(-3). This enables us to observe the resonator's vibrational bi-states transitions driven by the weak Brownian thermal noise at 6 K. This method can be flexibly applied to a variety of mechanical systems to improve nonlinear responses, and can be used, with further improvements, to explore macroscopic quantum mechanics.

Dynamical backaction cooling with free electrons

The ability to cool single ions, atomic ensembles, and more recently macroscopic degrees of freedom down to the quantum ground state has generated considerable progress and perspectives in fundamental and technological science. These major advances have been essentially obtained by coupling mechanical motion to a resonant electromagnetic degree of freedom in what is generally known as laser cooling. Here, we experimentally demonstrate the first self-induced coherent cooling mechanism that is not mediated by an electromagnetic resonance. Using a focused electron beam, we report a 50-fold reduction of the motional temperature of a nanowire. Our result primarily relies on the sub-nanometre confinement of the electron beam and generalizes to any delayed and spatially confined interaction, with important consequences for near-field microscopy and fundamental nanoscale dissipation mechanisms.

Cooling atoms and ions to the quantum ground state is generally achieved by resonantly coupling their mechanical motion to an electromagnetic wave. Here the authors report self-induced cooling based on sub-nanometre confinement with an electron beam, rather than an electromagnetic resonance.

Critical and near-critical phase behavior and interplay between the thermodynamic Casimir and van der Waals forces in a confined nonpolar fluid medium with competing surface and substrate potentials

We study, using general scaling arguments and mean-field type calculations, the behavior of the critical Casimir force and its interplay with the van der Waals force acting between two parallel slabs separated at a distance L from each other, confining some fluctuating fluid medium, say a nonpolar one-component fluid or a binary liquid mixture. The surfaces of the slabs are coated by thin layers exerting strong preference to the liquid phase of the fluid, or one of the components of the mixture, modeled by strong adsorbing local surface potentials ensuring the so-called (+,+) boundary conditions. The slabs, on the other hand, influence the fluid by long-range competing dispersion potentials, which represent irrelevant interactions in renormalization-group sense. Under such conditions, one usually expects attractive Casimir force governed by universal scaling function, pertinent to the extraordinary surface universality class of Ising type systems, to which the dispersion potentials provide only corrections to scaling. We demonstrate, however, that below a given threshold thickness of the system L(crit) for a suitable set of slabs-fluid and fluid-fluid coupling parameters the competition between the effects due to the coatings and the slabs can result in sign change of the Casimir force acting between the surfaces confining the fluid when one changes the temperature T, the chemical potential of the fluid μ, or L. The last implies that by choosing specific materials for the slabs, coatings, and the fluid for L≲L(crit) one can realize repulsive Casimir force with nonuniversal behavior which, upon increasing L, gradually turns into an attractive one described by a universal scaling function, depending only on the relevant scaling fields related to the temperature and the excess chemical potential, for L≫L(crit). We present arguments and relevant data for specific substances in support of the experimental feasibility of the predicted behavior of the force. It can be of interest, e.g., for designing nanodevices and for governing behavior of objects, say colloidal particles, at small distances. We formulate the corresponding criterion for determination of L(crit). The universality is regained for L≫L(crit). We also show that for systems with L≲L(crit), the capillary condensation phase diagram suffers modifications which one does not observe in systems with purely short-ranged interactions.

Quasi-polaritons in Bose-Einstein condensates induced by Casimir-Polder interaction with graphene

We consider the mechanical coupling between a two-dimensional Bose-Einstein condensate and a graphene sheet via the vacuum fluctuations of the electromagnetic field which are at the origin of the so-called Casimir-Polder potential. By deriving a self-consistent set of equations governing the dynamics of the condensate and the flexural (out-of-plane) modes of the graphene, we can show the formation of a new type of purely acoustic quasi-particle excitation, a quasi-polariton resulting from the coherent superposition of quanta of flexural and Bogoliubov modes.

Influence of materials' optical response on actuation dynamics by Casimir forces

The dependence of the Casimir force on the frequency-dependent dielectric functions of interacting materials makes it possible to tailor the actuation dynamics of microactuators. The Casimir force is largest for metallic interacting systems due to the high absorption of conduction electrons in the far-infrared range. For less conductive systems, such as phase change materials or conductive silicon carbide, the reduced force offers the advantage of increased stable operation of MEMS devices against pull-in instabilities that lead to unwanted stiction. Bifurcation analysis with phase portraits has been used to compare the sensitivity of a model actuator when the optical properties are altered.

Influence of surface roughness on dispersion forces

Surface roughness occurs in a wide variety of processes where it is both difficult to avoid and control. When two bodies are separated by a small distance the roughness starts to play an important role in the interaction between the bodies, their adhesion, and friction. Control of this short-distance interaction is crucial for micro and nanoelectromechanical devices, microfluidics, and for micro and nanotechnology. An important short-distance interaction is the dispersion forces, which are omnipresent due to their quantum origin. These forces between flat bodies can be described by the Lifshitz theory that takes into account the actual optical properties of interacting materials. However, this theory cannot describe rough bodies. The problem is complicated by the nonadditivity of the dispersion forces. Evaluation of the roughness effect becomes extremely difficult when roughness is comparable with the distance between bodies. In this paper we review the current state of the problem. Introduction for non-experts to physical origin of the dispersion forces is given in the paper. Critical experiments demonstrating the nonadditivity of the forces and strong influence of roughness on the interaction between bodies are reviewed. We also describe existing theoretical approaches to the problem. Recent advances in understanding the role of high asperities on the forces at distances close to contact are emphasized. Finally, some opinions about currently unsolved problems are also presented.

One-loop dominance in the imaginary part of the polarizability: application to blackbody and noncontact van der Waals friction

Phenomenologically important quantum dissipative processes include blackbody friction (an atom absorbs counterpropagating blueshifted photons and spontaneously emits them in all directions, losing kinetic energy) and noncontact van der Waals friction (in the vicinity of a dielectric surface, the mirror charges of the constituent particles inside the surface experience drag, slowing the atom). The theoretical predictions for these processes are modified upon a rigorous quantum electrodynamic treatment, which shows that the one-loop "correction" yields the dominant contribution to the off-resonant, gauge-invariant, imaginary part of the atom's polarizability at room temperature, for typical atom-surface interactions. The tree-level contribution to the polarizability dominates at high temperature.

Ultrahigh Casimir interaction torque in nanowire systems

We study the Casimir torque arising from the quantum electromagnetic fluctuations due to the interaction of two interfaces in a system formed by a dense array of metallic nanorods embedded in dielectric fluids. It is demonstrated that as a consequence of the ultrahigh density of photonic states in the nanowire array it is possible to channel the quantum fluctuations, and thereby boost the Casimir torque by several orders of magnitude as compared to other known systems (e.g., birefringent parallel plates).

Evidence for the role of normal-state electrons in nanoelectromechanical damping mechanisms at very low temperatures

We report on experiments performed at low temperatures on aluminum covered silicon nanoelectromechanical resonators. The substantial difference observed between the mechanical dissipation in the normal and superconducting states measured within the same device unambiguously demonstrates the importance of normal-state electrons in the damping mechanism. The dissipative component becomes vanishingly small at very low temperatures in the superconducting state, leading to exceptional values for the quality factor of such small silicon structures. A critical discussion is given within the framework of the standard tunneling model.

Optomechanical and photothermal interactions in suspended photonic crystal membranes

We present here an optomechanical system fabricated with novel stress management techniques that allow us to suspend an ultrathin defect-free silicon photonic-crystal membrane above a Silicon-on-Insulator (SOI) substrate with a gap that is tunable to below 200 nm. Our devices are able to generate strong attractive and repulsive optical forces over a large surface area with simple in- and out- coupling and feature the strongest repulsive optomechanical coupling in any geometry to date (gOM/2π ≈65 GHz/nm). The interplay between the optomechanical and photo-thermal-mechanical dynamics is explored, and the latter is used to achieve cooling and amplification of the mechanical mode, demonstrating that our platform is well-suited for potential applications in low-power mass, force, and refractive-index sensing as well as optomechanical accelerometry.

Variable-temperature device for precision Casimir-force-gradient measurement

We present the design and use of an instrument that is based on a microcantilever to perform precision force gradient measurements. We demonstrate its performance through measurements of the Casimir pressure at various temperatures. The instrument can operate in high vacuum environments and temperatures between 5 K and 300 K. It uses an all-fiber optical interferometer to detect the resonant-frequency shift of a customized microcantilever due to the presence of a force gradient. To measure this shift we use both, a technique of frequency-modulation atomic force microscopy and the direct recording of the thermomechanical resonant frequency.

Non-equilibrium Casimir force between vibrating plates

We study the fluctuation-induced, time-dependent force between two plates confining a correlated fluid which is driven out of equilibrium mechanically by harmonic vibrations of one of the plates. For a purely relaxational dynamics of the fluid we calculate the fluctuation-induced force generated by the vibrating plate on the plate at rest. The time-dependence of this force is characterized by a positive lag time with respect to the driving. We obtain two distinctive contributions to the force, one generated by diffusion of stress in the fluid and another related to resonant dissipation in the cavity. The relation to the dynamic Casimir effect of the electromagnetic field and possible experiments to measure the time-dependent Casimir force are discussed.

Casimir probe based upon metallized high Q SiN nanomembrane resonator

We present the instrumentation and measurement scheme of a new Casimir force probe that bridges Casimir force measurements at microscale and macroscale. A metallized high Q silicon nitride nanomembrane resonator is employed as a sensitive force probe. The high tensile stress present in the nanomembrane not only enhances the quality factor but also maintains high flatness over large area serving as the bottom electrode in a sphere-plane configuration. A fiber interferometer is used to readout the oscillation of the nanomembrane and a phase-locked loop scheme is applied to track the change of the resonance frequency. Because of the high quality factor of the nanomembrane and the high stability of the setup, a frequency resolution down to 2 × 10(-9) and a corresponding force gradient resolution of 3 μN/m is achieved. Besides sensitive measurement of Casimir force, our measurement technique simultaneously offers Kelvin probe measurement capability that allows in situ imaging of the surface potentials.

Strong Casimir force reduction through metallic surface nanostructuring

The Casimir force between bodies in vacuum can be understood as arising from their interaction with an infinite number of fluctuating electromagnetic quantum vacuum modes, resulting in a complex dependence on the shape and material of the interacting objects. Becoming dominant at small separations, the force has a significant role in nanomechanics and object manipulation at the nanoscale, leading to a considerable interest in identifying structures where the Casimir interaction behaves significantly different from the well-known attractive force between parallel plates. Here we experimentally demonstrate that by nanostructuring one of the interacting metal surfaces at scales below the plasma wavelength, an unexpected regime in the Casimir force can be observed. Replacing a flat surface with a deep metallic lamellar grating with sub-100 nm features strongly suppresses the Casimir force and for large inter-surfaces separations reduces it beyond what would be expected by any existing theoretical prediction.

Casimir force and in situ surface potential measurements on nanomembranes

We present Casimir force measurements in a sphere-plate configuration that consists of a high quality nanomembrane resonator and a millimeter sized gold coated sphere. The nanomembrane is fabricated from stoichiometric silicon nitride metallized with gold. A Kelvin probe method is used in situ to image the surface potentials to minimize the distance-dependent residual force. Resonance-enhanced frequency-domain measurements of the nanomembrane motion allow for very high resolution measurements of the Casimir force gradient (down to a force gradient sensitivity of 3  μN/m). Using this technique, the Casimir force in the range of 100 nm to 2  μm is accurately measured. Experimental data thus obtained indicate that the device system in the measured range is best described with the Drude model.

Effect of thermal noise on noncontact rack and pinion device

We study a nanoscale system composed of one corrugated plate (rack) and one corrugated cylinder (pinion) coupled via the lateral Casimir force. We assume that the rack moves uniformly. The axle of the pinion experiences frictional torque and random torque due to a surrounding fluid. We show that even in the presence of thermal noise, the device can work against external loads: The pinion rotates with a nonzero average velocity. The device operation becomes less influenced by the noise as the gap between rack and pinion decreases.

Dynamics of noncontact rack-and-pinion device: Periodic back-and-forth motion of the rack

We study a nanoscale system composed of one corrugated cylinder (pinion) and one corrugated plate (rack). The pinion and rack have no mechanical contact, but are coupled via the lateral Casimir force. We consider the case where the rack position versus time is a periodic triangular signal. We find that the device can rectify the periodic but nonsinusoidal motion of the rack. Using the typical values of parameters, we find that the pinion rotates with an average angular velocity Ω=1∼100 Hz . Experimental observation of the pinion rotation will show that the quantum vacuum can intermesh the noncontact parts of nanomachines.

Noncontact rack-pinion-rack device as a differential vibration sensor

We study a nanoscale system composed of one corrugated cylinder (pinion) placed between two corrugated plates (racks). The pinion and racks have no mechanical contact, but are coupled via the lateral Casimir force-one of the most spectacular consequences of quantum fluctuations of the electromagnetic field. The noncontact design of the device could help with the noteworthy wear problem in nanoscale mechanical systems. We consider the case where both racks undergo harmonic lateral motion. We assume that the amplitude, frequency, and phase of one of the racks are known. We show that probing the pinion motion, one can determine the vibration characteristics of the other rack.

Nonlinear dynamics of a rack-pinion-rack device powered by the Casimir force

Using the lateral Casimir force-a manifestation of the quantum fluctuations of the electromagnetic field between objects with corrugated surfaces-as the main force transduction mechanism, a nanomechanical device with rich dynamical behaviors is proposed. The device is made of two parallel racks that are moving in the same direction and a pinion in the middle that couples with both racks via the noncontact lateral Casimir force. The built-in frustration in the device causes it to be very sensitive and react dramatically to minute changes in the geometrical parameters and initial conditions of the system. The noncontact nature of the proposed device could help with the ubiquitous wear problem in nanoscale mechanical systems.

Measurement of the short-range attractive force between Ge plates using a torsion balance

We have measured the short-range attractive force between crystalline Ge plates, and found contributions from both the Casimir force and an electrical force possibly generated by surface patch potentials. Using a model of surface patch effects that generates an additional force due to a distance dependence of the apparent contact potential, the electrical force was parametrized using data at distances where the Casimir force is relatively small. Extrapolating this model, to provide a correction to the measured force at distances less than 5 microm, shows a residual force that is in agreement, within experimental uncertainty, with five models that have been used to calculate the Casimir force.

Halving the Casimir force with conductive oxides

The possibility to modify the strength of the Casimir effect by tailoring the dielectric functions of the interacting surfaces is regarded as a unique opportunity in the development of micro- and nanoelectromechanical systems. In air, however, one expects that, unless noble metals are used, the electrostatic force arising from trapped charges overcomes the Casimir attraction, leaving no room for exploitation of Casimir force engineering at ambient conditions. Here we show that, in the presence of a conductive oxide, the Casimir force can be the dominant interaction even in air, and that the use of conductive oxides allows one to reduce the Casimir force up to a factor of 2 when compared to noble metals.

Crossover from attractive to repulsive Casimir forces and vice versa

Systems described by an O(n) symmetrical varphi;{4} Hamiltonian are considered in a d-dimensional film geometry at their bulk critical points. The critical Casimir forces between the film's boundary planes B_{j}, j=1,2, are investigated as functions of film thickness L for generic symmetry-preserving boundary conditions partial differential_{n}phi=c[over composite function]_{j}phi. The L-dependent part of the reduced excess free energy per cross-sectional area takes the scaling form f_{res} approximately D(c_{1}L;{Phi/nu},c_{2}L;{Phi/nu})/L;{d-1} when d<4, where c_{i} are scaling fields associated with the variables c[over composite function]_{i} and Phi is a surface crossover exponent. Explicit two-loop renormalization group results for the function D(c_{1},c_{2}) at d=4- dimensions are presented. These show that (i) the Casimir force can have either sign, depending on c_{1} and c_{2}, and (ii) for appropriate choices of the enhancements c[over composite function]_{j}, crossovers from attraction to repulsion and vice versa occur as L increases.

Anomalous temperature dependence of the Casimir force for thin metal films

Within the framework of the Drude dispersive model, we predict an unusual nonmonotonic temperature dependence of the Casimir force for thin metal films. For certain conditions, this force decreases with temperature due to the decrease of the metallic conductivity, whereas the force increases at high temperatures due to the increase of the thermal radiation pressure. We consider the attraction of a film to: either (i) a bulk ideal metal with a planar boundary, or (ii) a bulk metal sphere (lens). The experimental observation of the predicted decreasing temperature dependence of the Casimir force can put an end to the long-standing discussion on the role of the electron relaxation in the Casimir effect.

Temperature correction to Casimir-Lifshitz free energy at low temperatures: semiconductors

The Casimir force and free energy at low temperatures have been the subject of focus for some time. We calculate the temperature correction to the Casimir-Lifshitz free energy between two parallel plates made of dielectric material possessing a constant conductivity at low temperatures, described through a Drude-type dielectric function. For the transverse magnetic (TM) mode such a calculation is made. A further calculation for the case of the TE mode is thereafter presented which extends and generalizes previous work for metals. A numerical study is undertaken to verify the correctness of the analytic results.