Measurement of the Casimir Force between Two Spheres

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.

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.

Synergistic action in colloidal heat engines coupled by non-conservative flows

Colloidal heat engines are model systems to analyze mechanisms of transduction of heat to work at the mesoscale. While engines developed hitherto were realized using conservative potentials and operated in isolation, biological micromotors - their real counterparts - seldom perform under such simplifications. Here, we examine thermodynamics beyond such idealizations by constructing a pair of engines from two colloidal microspheres in optical traps at close separation. We demonstrate that at such proximity, non-conservative scattering forces that were hitherto neglected affect the particle motion. Hydrodynamics generated while dissipating these are hindered by the microsphere in the adjacent trap and energy that was otherwise rejected into the medium gets reused. Thus, despite being in contact with the same reservoir, the particles are driven out of equilibrium and can exchange energy, allowing cooperative behavior. Leveraging this in a manner analogous to microswimmers and active Brownian particles that utilize such flows to enhance propulsion, we construct two colloidal engines in close proximity. To estimate thermodynamic quantities, we develop a minimal model that is appropriate in the asymptotic limit and is similar to active Brownian particles. While complete theoretical frameworks to understand such scenarios remain to be developed, results based on our model demonstrate the intuitive idea that a pair of Stirling engines at close proximity outperform those that are well separated. Although these results explore the simplest case of two Stirling engines, the concepts unraveled could aid in designing larger collections akin to biological systems.

Analytical theory for the crossover from retarded to non-retarded interactions between metal plates

The van der Waals force established between two surfaces plays a central role in many phenomena, such as adhesion or friction. However, the dependence of this forces on the distance of separation between plates is very complex. Two widely different non-retarded and retarded regimes are well known, but these have been traditionally studied separately. Much less is known about the important experimentally accessible cross-over regime. In this study, we provide analytical approximations for the van der Waals forces between two plates that interpolates exactly between the short distance and long distance behavior, and provides new insight into the crossover from London to Casimir forces at finite temperature. At short distance, where the behavior is dominated by non-retarded interactions, we work out a very accurate simplified approximation for the Hamaker constant which adopts analytical form for both the Drude and Lorentz models of dielectric response. We apply our analytical expressions for the study of forces between metallic plates, and observe very good agreement with exact results from numerical calculations. Our results show that contributions of interband transitions remain important in the experimentally accessible regime of decades nm for several metals, including gold.

New type of autocollimator based on the normal tracing method and Risley prisms

In the present study, we proposed a new type of autocollimator for high-accuracy angular measurement within a large angle range. The new system comprises a traditional autocollimator and Risley prisms, and it employs the normal tracing method to measure the angle. By rotating the Risley prisms, the outgoing beam of the autocollimator can be deflected close to the normal direction of the reflecting mirror and then reflected back to the system by the mirror along the near normal direction to realize normal tracing. Based on the angle measured by the the autocollimator and the rotation angles of Risley prisms, we can calculate the tilt angle of the mirror. Since the beam returns to the system close to the original path, the angle error caused by aberration, optical component processing defects, nonuniform refractive index, and so on, can be ignored. Due to the normal tracing measurement method, theoretically, the angle error is not affected by the working distance. ZEMAX non-sequential simulation shows that the angle error caused by aberration in the new system can be significantly reduced.

Strong geometry dependence of the Casimir force between interpenetrated rectangular gratings

Quantum fluctuations give rise to Casimir forces between two parallel conducting plates, the magnitude of which increases monotonically as the separation decreases. By introducing nanoscale gratings to the surfaces, recent advances have opened opportunities for controlling the Casimir force in complex geometries. Here, we measure the Casimir force between two rectangular silicon gratings. Using an on-chip detection platform, we achieve accurate alignment between the two gratings so that they interpenetrate as the separation is reduced. Just before interpenetration occurs, the measured Casimir force is found to have a geometry dependence that is much stronger than previous experiments, with deviations from the proximity force approximation reaching a factor of ~500. After the gratings interpenetrate each other, the Casimir force becomes non-zero and independent of displacement. This work shows that the presence of gratings can strongly modify the Casimir force to control the interaction between nanomechanical components.

The geometry dependence of the Casimir force could enable applications in nanomechanical systems if the effects can be enhanced. Here, the authors demonstrate that the Casimir force between two interpenetrating nanoscale gratings can exceed the proximity force approximation by a factor of 500.

Nonadditive Enhancement of Nonequilibrium Atom-Surface Interactions

The motion-induced drag force acting on a particle moving parallel to an arrangement of N objects is analyzed. Particular focus is placed on the nonequilibrium statistics of the interaction and on the interplay between the system's geometry and the different dissipative processes occurring in realistic setups. We show that the drag force can exhibit a markedly nonadditive enhancement with respect to the corresponding additive approximation. The specific case of a planar cavity-a relevant configuration for many experiments-is calculated, showing an enhancement of about one order of magnitude. This and similar configurations are of significant potential interest for future measurements that aim to detect the drag force.

Impact of nuclear vibrations on van der Waals and Casimir interactions at zero and finite temperature

Recent advances in measuring van der Waals (vdW) interactions have probed forces on molecules at nanometric separations from metal surfaces and demonstrated the importance of infrared nonlocal polarization response and temperature effects, yet predictive theories for these systems remain lacking. We present a theoretical framework for computing vdW interactions among molecular structures, accounting for geometry, short-range electronic delocalization, dissipation, and collective nuclear vibrations (phonons) at atomic scales, along with long-range electromagnetic interactions in arbitrary macroscopic environments. We primarily consider experimentally relevant low-dimensional carbon allotropes, including fullerenes, carbyne, and graphene, and find that phonons couple strongly with long-range electromagnetic fields depending on molecular dimensionality and dissipation, especially at nanometric scales, creating delocalized phonon polaritons that substantially modify infrared molecular response. These polaritons, in turn, alter vdW interaction energies between molecular and macroscopic structures, producing nonmonotonic power laws and nontrivial temperature variations at nanometric separations feasible in current experiments.

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.

Multiscale Functional Imaging of Interfaces through Atomic Force Microscopy Using Harmonic Mixing

The spatial resolution of atomic force microscopy (AFM) needed to resolve material interfaces is limited by the tip-sample separation ( d) dependence of the force used to record an image. Here, we present a new multiscale functional imaging technique that allows for in situ tunable spatial resolution, which can be applied to a wide range of inhomogeneous materials, devices, and interfaces. Our approach uses a multifrequency method to generate a signal whose d-dependence is controlled by mixing harmonics of the cantilever's oscillation with a modulated force. The spatial resolution of the resulting image is determined by the signal's d-dependence. Our measurements using harmonic mixing (HM) show that we can change the d-dependence of a force signal to improve spatial resolution by up to a factor of two compared to conventional methods. We demonstrate the technique with both Kelvin probe force microscopy (KPFM) and bimodal AFM to show its generality. Bimodal AFM with harmonic mixing actuation separates conservative from dissipative forces and is used to identify the regions of adhesive residue on exfoliated graphene. Our electrostatic measurements with open-loop KPFM demonstrate that multiple force modulations may be applied at once. Further, this method can be applied to any tip-sample force that can be modulated, for example, electrostatic, magnetic, and photoinduced forces, showing its universality. Because HM enables in situ switching between high sensitivity and high spatial resolution with any periodic driving force, we foresee this technique as a critical advancement for multiscale functional imaging.

Sensing Static Forces with Free-Falling Nanoparticles

Miniaturized mechanical sensors rely on resonant operation schemes, unsuited to detect static forces. We demonstrate a nanomechanical sensor for static forces based on an optically trapped nanoparticle in vacuum. Our technique relies on an off-resonant interaction of the particle with a weak static force, and a resonant readout of the displacement caused by this interaction. We demonstrate a sensitivity of 10 aN to static gravitational and electric forces. Our work provides a tool for the closer investigation of short-range forces, and marks an important step towards the realization of matter-wave interferometry with macroscopic objects.