Demonstration of optically modulated dispersion forces

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.

Sensitivity of actuation dynamics on normal and lateral Casimir forces: Interaction of phase change and topological insulator materials

We investigated here the influence of the lateral and normal Casimir force on the actuation dynamics between sinusoidal corrugated surfaces undergoing both normal and lateral displacements. The calculations were performed for topological insulators and phase change materials that are of high interest for device applications. The results show that the lateral Casimir force becomes stronger by increasing the material conductivity and the corrugations toward similar sizes producing wider normal separation changes during lateral motion. In a conservative system, bifurcation and Poincaré portrait analysis shows that larger but similar in size corrugations and/or higher material conductivity favor stable motion along the lateral direction. However, in the normal direction, the system shows higher sensitivity on the optical properties for similar in size corrugations leading to reduced stable operation for higher material conductivity. Furthermore, in non-conservative systems, the Melnikov function with the Poincaré portrait analysis was combined to probe the possible occurrence of chaotic motion. During lateral actuation, systems with more conductive materials and/or the same but high corrugations exhibit lower possibility for chaotic motion. By contrast, during normal motion, chaotic behavior leading to stiction of the moving components is more likely to occur for systems with more conductive materials and similar in magnitude corrugations.

Casimir Puzzle and Casimir Conundrum: Discovery and Search for Resolution

This paper provides a review of the complicated problems in Lifshitz theory describing the Casimir force between real material plates composed of metals and dielectrics, including different approaches to their resolution. For both metallic plates with perfect crystal lattices and any dielectric plates, we show that the Casimir entropy calculated in the framework of Lifshitz theory violates the Nernst heat theorem when the well-approved dielectric functions are used in computations. The respective theoretical Casimir forces are excluded by the measurement data of numerous precision experiments. In the literature, this situation has been called the Casimir puzzle and the Casimir conundrum for the cases of metallic and dielectric plates, respectively. This review presents a summary of both the main theoretical and experimental findings on this subject. Next, a discussion is provided of the main approaches proposed in the literature to bring the Lifshitz theory into agreement with the measurement data and with the laws of thermodynamics. Special attention is paid to the recently suggested spatially nonlocal Drude-like response functions, which consider the relaxation properties of conduction electrons, as does the standard Drude model, but lead to the theoretical results being in agreement with both thermodynamics and the measurement data through the alternative response to quantum fluctuations of the mass shell. Further advances and trends in this field of research are discussed.

Casimir-Polder Interaction of an Atom with a Cavity Wall Made of Phase-Change Material out of Thermal Equilibrium

We consider the out-of-thermal-equilibrium Casimir-Polder interaction between atoms of He*, Na, Cs, and Rb and a cavity wall made of sapphire coated with a vanadium dioxide film which undergoes the dielectric-to-metal phase transition with increasing wall temperature. Numerical computations of the Casimir-Polder force and its gradient as the functions of atom-wall separation and wall temperature are made when the latter exceeds the temperature of the environment. The obtained results are compared with those in experiment on measuring the gradient of the Casimir-Polder force between 87Rb atoms and a silica glass wall out of thermal equilibrium. It is shown that the use of phase-change wall material significantly increases the force magnitude and especially the force gradient, as opposed to the case of a dielectric wall.

Chaotic motion due to lateral Casimir forces during nonlinear actuation dynamics

We investigated here the influence of the lateral Casimir force on the dynamical actuation of devices with interacting materials covering a broad range of optical properties ranging from poor to good conductors, such as, for example, nitrogen doped SiC and Au, respectively. The conservative actuating system shows a central heteroclinic orbit surrounded by a finite number of homoclinic orbits, because at higher periods, an increased lateral Casimir force will be necessary to counterbalance the restoring force. As a result, the conservative system reaches stable operation sooner for the higher conductivity materials (Au-Au), indicating the significant impact of the material optical properties on the lateral Casimir force. Furthermore, for the non-conservative driven systems, the decrement of the Melnikov parameter α leads to a faster disappearance of the satellite homoclinic orbits in the Poincaré portraits, followed by a strong shrinkage of the central heteroclinic orbit toward unstable chaotic motion. The latter is more pronounced for the lower conductivity materials since comparison shows the Au-Au system to be significantly more stable than the SiC-SiC system. Therefore, in actuating systems where the lateral Casimir force could play a significant role, the higher conductivity materials appear to be a better choice to ensure stable operation against a chaotic motion.

Sensitivity of nonequilibrium Casimir forces on low frequency optical properties toward chaotic motion of microsystems: Drude vs plasma model

Here, we investigate the sensitivity of nonequilibrium Casimir forces to optical properties at low frequencies via the Drude and plasma models and the associated effects on the actuation of microelectromechanical systems. The stability and chaotic motion for both autonomous conservative and nonconservative driven systems were explored assuming good, e.g., Au, and poor, e.g., doped SiC, interacting conductors having large static conductivity differences. For both material systems, we used the Drude and plasma methods to model the optical properties at low frequencies, where measurements are not feasible. In fact, for the conservative actuating system, bifurcation and phase space analysis show that the system motion is strongly influenced by the thermal nonequilibrium effects depending on the modeling of the optical properties at low frequencies, where also the presence of residual electrostatic forces can also drastically alter the actuating state of the system, depending strongly on the material conductivity. For nonconservative systems, the Melnikov function approach is used to explore the presence of chaotic motion rendering predictions of stable actuation or malfunction due to stiction on a long-term time scale rather impossible. In fact, the thermal effects produce the opposite effect for the emerging chaotic behavior for the Au-Au and SiC-SiC systems if the Drude model is used to model the low optical frequencies. However, using the plasma model, only for the poor conducting SiC-SiC system, the chance of chaotic motion is enhanced, while for the good conducting Au-Au system, the chaotic behavior will remain unaffected at relatively short separations (<2 μm).

Dependence of non-equilibrium Casimir forces on material optical properties toward chaotic motion during device actuation

The sensitivity of nonequilibrium Casimir forces on material optical properties can have strong impact on the actuation of devices. For this purpose, we considered nonequilibrium Casimir interactions between good and poor conductors, for example, gold (Au) and highly doped silicon carbide (SiC), respectively. Indeed, for autonomous conservative systems, the bifurcation and phase portrait analysis have shown that the nonequilibrium Casimir forces can have significant impact on the stable and unstable operating regimes depending on the material optical properties. At a few micrometer separations, for systems with high conductivity materials, an increasing temperature difference between the actuating components can enhance the stable operation range due to the reduction of the Casimir force, while for the poor conductive materials, the opposite takes place. For periodically driven dissipative systems, the Melnikov function and Poincare portrait analysis have shown that for poor conductive systems, the nonequilibrium Casimir forces lead to an increased possibility for chaotic behavior and stiction with an increasing temperature difference between the actuating components. However, for good conducting systems, the thermal contribution to Casimir forces reduces the possibility for chaotic behavior with increasing temperature, as comparison with systems without thermal fluctuations shows. Nevertheless, the positive benefit of good conductors toward increased actuation stability and reduced the chaotic behavior under nonequilibrium conditions can be easily compromised by any voltage application. Therefore, thermal, nonequilibrium Casimir forces can influence the actuation of devices toward unstable and chaotic behavior in strong correlation with their optical properties, and associated conduction state, as well as applied electrostatic potentials.

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.

Chaotic behavior in Casimir oscillators: A case study for phase-change materials

Casimir forces between material surfaces at close proximity of less than 200 nm can lead to increased chaotic behavior of actuating devices depending on the strength of the Casimir interaction. We investigate these phenomena for phase-change materials in torsional oscillators, where the amorphous to crystalline phase transitions lead to transitions between high and low Casimir force and torque states, respectively, without material compositions. For a conservative system bifurcation curve and Poincare maps analysis show the absence of chaotic behavior but with the crystalline phase (high force-torque state) favoring more unstable behavior and stiction. However, for a nonconservative system chaotic behavior can take place introducing significant risk for stiction, which is again more pronounced for the crystalline phase. The latter illustrates the more general scenario that stronger Casimir forces and torques increase the possibility for chaotic behavior. The latter is making it impossible to predict whether stiction or stable actuation will occur on a long-term basis, and it is setting limitations in the design of micronano devices operating at short-range nanoscale separations.

How to confirm and exclude different models of material properties in the Casimir effect

We formulate a method allowing us to confirm or exclude the alternative models of material properties at some definite confidence level in experiments on measuring the Casimir force. The method is based on the consideration of differences between the theoretical and mean measured quantities and the confidence intervals for these differences found at sufficiently high or low confidence probabilities. The developed method is applied to the data of four recent experiments on measuring the gradient of the Casimir force by means of a dynamic atomic force microscope. It is shown that in experiments with Au-Au and Ni-Ni test bodies, where the Drude model approach is excluded at a 95% confidence level, the plasma model approach agrees with the data at higher than 90% confidence. In experiments using an Au sphere interacting with either a Ni plate or a graphene-coated substrate, the measurement data agree with the common prediction of the Drude and plasma model approaches and theory using the polarization tensor at 90% and 80% confidence levels, respectively.

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.

How to modify the van der Waals and Casimir forces without change of the dielectric permittivity

We propose a new experiment on the measurement of the Casimir force and its gradient between a Au-coated sphere and two different plates made of doped semiconductors. The concentrations of charge carriers in the plates are chosen slightly below and above the critical density at which the Mott-Anderson insulator-metal transition occurs. We calculate changes in the Casimir force and the Casimir pressure due to the insulator-metal transition using the standard Lifshitz theory and the phenomenological approach neglecting the contribution of free charge carriers in the dielectric permittivity of insulator materials (this approach was recently supported by the measurement data of several experiments). It is demonstrated that for the special selection of semiconductor materials (S- or Se-doped Si, B-doped diamond) the calculation results using the two theoretical approaches differ significantly and the predicted effects are easily detectable using the existing laboratory setups. In the case that the prediction of the phenomenological approach is confirmed, this would open opportunities to modify the van der Waals and Casimir forces with almost no change of room temperature dielectric permittivity.

Reduction of the Casimir force from indium tin oxide film by UV treatment

A significant decrease in the magnitude of the Casimir force (from 21% to 35%) was observed after an indium tin oxide sample interacting with an Au sphere was subjected to the UV treatment. Measurements were performed by using an atomic force microscope in high vacuum. The experimental results are compared with theory and a hypothetical explanation for the observed phenomenon is proposed.

Casimir interaction from magnetically coupled eddy currents

We study the quantum and thermal fluctuations of eddy (Foucault) currents in thick metallic plates. A Casimir interaction between two plates arises from the coupling via quasistatic magnetic fields. As a function of distance, the relevant eddy current modes cross over from a quantum to a thermal regime. These modes alone reproduce previously discussed thermal anomalies of the electromagnetic Casimir interaction between good conductors. In particular, they provide a physical picture for the Casimir entropy whose nonzero value at zero temperature arises from a correlated, glassy state.

Application of the Lifshitz theory to poor conductors

The Lifshitz formula for dispersive forces is generalized to the materials, which cannot be described with the local dielectric response. The principal nonlocality of poor conductors is related to the finite screening length of the penetrating field and collisional relaxation; at low temperatures the role of collisions plays the Landau damping. Spatial dispersion makes the theory self-consistent. Our predictions are compared with the recent experiment. It is demonstrated that at low temperatures Casimir-Lifshitz entropy disappears as T in the case of degenerate plasma and as T2 for the nondegenerate one.

Collapse of optical binding under secondary irradiation

When an optically trapped and bound micrometer-sized chain of particles is subjected to a suitably oriented secondary laser beam above a threshold level of intensity, the structure will collapse. The effect arises from modifications to the interparticle energy landscapes owing to the superposition of optically induced potentials. From the theory it also emerges that, for particles separated by near-field distances, optically induced assemblies may be continuously transformed between linear, spherical, and lamellar forms. The results show scope for the optical fabrication of moldable nanoscale structures.