Attractive Casimir Force Research Articles

Casimir interaction driven by hyperbolic polaritons

Abstract Casimir interaction is an intriguing phenomenon that is induced by electromagnetic quantum fluctuations, which dominates the interaction between microstructures at small separations and is essential for micro- and nano-electromechanical systems (MEMS and NEMS). However, Casimir interaction driven by hyperbolic polaritons remains an unexplored frontier. In this work, we investigate the Casimir interaction between natural hyperbolic material hexagonal boron nitride from the perspective of force distribution with different optical axis orientations for the first time. The attractive Casimir force is remarkably enhanced due to the excitation of volume-confined hyperbolic polaritons (HPs). Furthermore, distinct repulsive contributions to the force are observed due to surface-confined HPs that only exist when the optical axis is in-plane. The HPs are associated with a striking thickness dependence of spectral force properties, suggesting that the discrete volume-confined HPs lead to the attractive-repulsive transition of Casimir force. This work sheds light on the relation between HPs and the vacuum fluctuation-induced force, which could offer new opportunities for the development of the MEMS and NEMS.

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.

Interplay between chiral media and perfect electromagnetic conductor plates: Repulsive vs. attractive Casimir force transitions

We determine the Casimir energies and forces in a variety of potentially experimentally viable setups, consisting of parallel plates made of perfect electromagnetic conductors (PEMCs), which generalize perfect electric conductors (PECs) and perfect magnetic conductors (PMCs), and Weyl semimetals (WSMs). Where comparison is possible, our results agree with the Casimir forces calculated elsewhere in the literature, albeit with different methods. We find a multitude of known but also new cases where repulsive Casimir forces are in principle possible, but restricting the setup to PECs combined with the aforementioned WSM geometry, results in purely attractive Casimir forces.

Sensitivity of actuation dynamics of Casimir oscillators on finite temperature with topological insulator materials: Response of repulsive vs attractive interactions

We explore the sensitivity of repulsive and attractive Casimir interactions on thermal fluctuations in topological insulator materials, and the associated effects on non-linear actuation towards chaotic motion. For system at low temperature and applied magnetization in the same direction, by increasing the temperature the sensitivity of the Casimir force to the magnetization, at large separations, weakens. Moreover, by increasing the temperature the repulsive force vanishes for weak magnetization. Furthermore, for conservative systems the stable actuation area for high temperature does not show strong sensitivity to changes of the magnetization and the magnetoelectric effect. For non-conservative system with weak magnetization in the same direction leading to attractive Casimir forces, increment of the temperature increases the possibility for occurrence of chaotic motion.

Massive fermion between two parallel chiral plates

Abstract We study the system of a massive fermion field confined between two parallel plates, where the properties of both plates are discussed under chiral MIT boundary conditions. We investigate the effects of the chiral angle on the Casimir energy for a massive fermion field with the general momentum. We find that the Casimir energy as a function of the chiral angle is generally symmetric, and the attractive Casimir force in the chiral case is stronger than that in the nonchiral case. In addition, we investigate the approximate Casimir energy for light and heavy mass cases. The behavior of the discrete momentum and changes of spin orientation are also discussed.

The Horava–Lifshitz modifications of the Casimir effect at finite temperature revisited

We investigate the Casimir force for parallel plates at finite temperature in the Horava–Lifshitz (HL) theory. We find that the HL exponent cannot be chosen as an integer, or the Casimir energy will be a constant, and further, the Casimir force between two parallel plates will vanish. The higher temperature causes the attractive Casimir force to weaken, which is consistent with the original results confirmed theoretically and experimentally. We can select the HL factor appropriately to obtain a thermally revised Casimir force similar to the standard results for the parallel plates.

Nonlinear actuation of micromechanical Casimir oscillators with topological insulator materials toward chaotic motion: Sensitivity on magnetization and dielectric properties.

We have investigated the dynamical actuation of micro-electromechanical systems under the influence of attractive and repulsive Casimir forces between topological insulator plates as a function of their dielectric function and coating magnetization. The analysis of the Casimir force in the limit of strong and weak magnetization shows that the attractive force, which is produced for plate magnetizations in the same direction, is greater than the repulsive force that is produced for opposite magnetizations. However, both forces remain comparable for intermediate magnetizations. Moreover, for weak magnetization, the attractive force becomes stronger for an increasing dielectric function, while the opposite occurs for the repulsive force. On the other hand, increasing magnetization decreases the influence of the dielectric function on both the repulsive and attractive forces. Furthermore, for conservative systems, bifurcation and phase portrait analysis revealed that increasing magnetization decreases the regime of stable operation for devices with attractive forces, while their operation remains always stable under the presence of repulsive forces. Finally, for non-conservative periodically driven systems, the Melnikov function and Poincaré portrait analysis show that for magnetizations in the same direction leading to strong attractive Casimir forces, chaotic motion toward stiction is highly likely to occur preventing the long-term prediction of actuating dynamics. A remedy for this situation is obtained by the application of any magnetization in opposite directions between the interacting surfaces since the repulsive force makes it possible to prevent stiction.

Quantum vacuum phenomena in various backgrounds

In this paper, we will review, through various examples, some ideas connecting the physics of the quantum vacuum and the Casimir effect with the mechanism of symmetry breaking in different backgrounds. In the first example, we will discuss how the quantum vacuum energy is altered by the presence of nonlinearities in the underlying quantum field theory in a way that depends on the spatial dimensionality, as dictated by the Mermin–Wagner–Hohenberg–Coleman theorem. In the second example, we will explore how the combination of boundary effects and (discrete) chiral symmetry breaking can affect the thermodynamical behavior of a system of interacting fermions, and how this is reflected on the Casimir force. Even in the simplest setup of two parallel plates, two interesting things happen: first, the order of the transition through which discrete chiral symmetry may be broken/restored changes from second-order for infinitely large separation to first-order for a finite separation between the boundaries. Second, a peculiar behavior in the fermion condensate occurs, resulting in the appearance of two different phases (massless and massive) in the Casimir force. In the third example, we will also be concerned with the Casimir effect on an interacting fermion background over a string of finite length. Using a self-consistent method, we will show how a nontrivial behavior in the Casimir force arises, displaying a switch from an attractive to a repulsive regime, as a result of the competing effects due to the usual attractive Casimir force and a repulsive component coming from the condensate.

GRAVITATIONAL CASIMIR EFFECT IN INSPIRALLING NEUTRON STAR BINARY

Currently, the discussions and investigations for the vacuum energy are drawing great both theoretical and experimental attention. The vacuum states of variety of fields, subject to special boundary conditions, may contribute to non-trivial macroscopic vacuum energy, i.e., the Casimir effect, which become an interdisciplinary subject and plays an important role in a variety of fields of physics. We adopt Schwingers source theory and study the quantization of gravitation contributions to the Casimir effect, i.e., the gravitational Casimir effect, in inspiraling neutron star binaries with wide separation of 109 m. By considering gravitoelectromagnetism (GEM) arising from the spiral-in orbital motion and evaluating the gravitoelectromagnetic contributions to the vacuum energy of gravitons radiated during the orbital decay, we demonstrate that, when the radial separation of the system decay a distance L, the GEM results in a small Casimir correction to the gravitational vacuum energy, which contributes to an attractive gravitational Casimir force to the binary, in addition to the gravitational force. We also discuss the possible detections for such gravitational Casimir effect from both the future space-based gravitational wave observatories and cosmological observations.

GRAVITATIONAL CASIMIR EFFECT IN INSPIRALLING NEUTRON STAR BINARY

Currently, the discussions and investigations for the vacuum energy is drawing great both theoretical and experimental attention. The vacuum states of variety of fields, subject to special boundary conditions, may contribute to non-trivial macroscopic vacuum energy, i.e. the Casimir effect, which become an interdisciplinary subject and plays an important role in a variety of fields of physics. We adopt Schwinger's source theory and study the Casimir effect due to the quantization of gravitation, i.e. the gravitational Casimir effect (GCE), in inspiraling neutron star (NS) binaries with wide separation of $10^9 \rm m$. By considering gravitoelectromagnetism (GEM) arising from the spiral-in orbital motion and evaluating the contributions of GEM to the vacuum energy of gravitons radiated during the orbital decay, we demonstrate that, when the orbital separation of the binary decay a distance of $L$ in radial direction, the GEM results in a small Casimir correction to the gravitational vacuum energy, which contributes to an attractive gravitational Casimir force to the binary, in addition the gravitational force. The gravitational waves (GWs), emitted from wide inspiraling NS binaries, locate in the low-frequency band of $10^{-4}-1$ Hz. For a characteristic GW frequency of $10^{-3}$ Hz, the gravitational Casimir correction to the signals is estimated as of the order of $\sim10^{-24}$, which corresponds to a force of $10^{-20}$ N. By considering that the sensitivity of space-based gravitational wave observatory, LISA/eLISA and Taiji, can be reduced to $10^{-24}$, we would expect that LISA/eLISA and Taiji with sensitivity improvements give the powerful tool to detect GCE in the near future.

Casimir Interactions from Infinite Range and Dilation Symmetry

The Casimir interaction energy for a class of discrete self-similar configuration of parallel plates is evaluated using existing methods. The similarities to characteristics of an attractive Casimir force is deduced only at infinite range of configuration. Further, the emergence of Casimir-like energy is qualitatively described for a Gaussian model of Landau-Ginzburg scalar field. Its relevance to self-similarity in the statistical field is shown at infinite range of fluctuations.

Comparing Classical and Quantum Electromagnetics: Part 3 [Special Series: Guest Editorial

Quantum technology is becoming increasingly important with the recent advancements in quantum computers. The article “Casimir Force: Vacuum Fluctuation, Zero-Point Energy, and Computational Electromagnetics,” by Xia et al., summarizes how to calculate the Casimir force in the simplest fashion. It gives a brief overview of quantum theory and quantum weirdness. It then explains the role of quantum theory in electromagnetics and how the Casimir energy is equal to the sum of the zero-point energies of different modes in a system. The zero-point energy gives rise to vacuum fluctuations that persist down to zero temperature. Next, the article shows how to find the electromagnetic modes of an electromagnetic system using computational electromagnetics. The authors discuss the use of the argument principle as a way of finding this sum of zero-point energies indirectly. Moreover, a broadband fast multipole algorithm is discussed that is error controllable from statics to microwave frequencies. As a result, both attractive and repulsive Casimir forces are demonstrated with some complex structures.

Tunable self-assembled Casimir microcavities and polaritons.

Spontaneous formation of ordered structures-self-assembly-is ubiquitous in nature and observed on different length scales, ranging from atomic and molecular systems to micrometre-scale objects and living matter1. Self-ordering in molecular and biological systems typically involves short-range hydrophobic and van der Waals interactions2,3. Here we introduce an approach to micrometre-scale self-assembly based on the joint action of attractive Casimir and repulsive electrostatic forces arising between charged metallic nanoflakes in an aqueous solution. This system forms a self-assembled optical Fabry-Pérot microcavity with a fundamental mode in the visible range (long-range separation distance about 100-200 nanometres) and a tunable equilibrium configuration. Furthermore, by placing an excitonic material in the microcavity region, we are able to realize hybrid light-matter states (polaritons4-6), whose properties, such as coupling strength and eigenstate composition, can be controlled in real time by the concentration of ligand molecules in the solution and light pressure. These Casimir microcavities could find future use as sensitive and tunable platforms for a variety of applications, including opto-mechanics7, nanomachinery8 and cavity-induced polaritonic chemistry9.

Statics and dynamics of a finite two-dimensional colloidal system with competing attractive critical Casimir and repulsive magnetic dipole interactions.

We continue our theoretical study of a recently proposed two-dimensional colloidal system with attractive critical Casimir and repulsive magnetic dipole forces that can be tuned easily and independently from each other via the temperature and the strength of an external magnetic field, respectively [K. Marolt, M. Zimmermann, and R. Roth, Phys. Rev. E 100, 052602 (2019)2470-004510.1103/PhysRevE.100.052602]. Using this freedom, it is possible to construct a competing interaction potential that causes microphase separation featuring spatially inhomogeneous cluster, stripe, and bubble phases in the bulk, i.e., in an infinite system without an external potential. In the present work, we demonstrate by means of density functional theory that microphase separation can also occur in finite geometries. In a square cell with a side length of 20 or 30 colloid diameters, we observe the emergence of highly structured cluster and ring phases at intermediate bulk densities in addition to almost uniform fluid phases for lower and higher bulk densities. We then employ dynamic density functional theory to determine how the system reacts when the temperature and the magnetic field are altered over time, and we show how to induce a transition from the liquid to the cluster/ring phase and also from the cluster directly to the ring phase. We find that often a slowly varying and nontrivial path in parameter space is required to reach a stable state, whereas abrupt changes are prone to lead to metastable configurations.

Thermal Casimir effect with general boundary conditions

In this paper we study the system of a scalar quantum field confined between two plane, isotropic, and homogeneous parallel plates at thermal equilibrium. We represent the plates by the most general lossless and frequency-independent boundary conditions that satisfy the conditions of isotropy and homogeneity and are compatible with the unitarity of the quantum field theory. Under these conditions we compute the thermal correction to the quantum vacuum energy as a function of the temperature and the parameters encoding the boundary condition. The latter enables us to obtain similar results for the pressure between plates and the quantum thermal correction to the entropy. We find out that our system is thermodynamically stable for any boundary conditions, and we identify a critical temperature below which certain boundary conditions yield attractive, repulsive, and null Casimir forces.

Pressure of the fluctuating vacuum: Interpretation of the attractive and repulsive Casimir force

We calculate the Casimir force between two magnetodielectric slabs. The force expression is expressed in terms of parameters with which the repulsive effect is more transparent and convenient for numerical analysis. Finally, we propose a physical interpretation of the effect which clarifies the sign of force properly.

Microphase separation in a two-dimensional colloidal system with competing attractive critical Casimir and repulsive magnetic dipole interactions.

We propose and study theoretically a colloidal system in two dimensions with attractive critical Casimir and repulsive magnetic dipole forces, wherein the strength of attraction and repulsion can be easily and independently tuned by adjusting the temperature and an external magnetic field, respectively. We expect this setup to be experimentally accessible and are confident that it can serve to deepen our understanding of the mechanisms behind microphase separation due to competing interactions. We develop a density functional theory for our model and present first results of our calculations in the form of a phase diagram for fixed temperature, but varying magnetic fields and bulk densities. For certain values of these parameters, we are able to confirm the existence of thermodynamically stable inhomogeneous density profiles in the bulk, such as parallel lamellar stripes, as well as clusters and voids on a hexagonal lattice.

Casimir interaction of two dielectric half spaces with Chern-Simons boundary layers

A diffraction problem for a flat Chern-Simons layer at plane boundary of a dielectric half space is solved. The Casimir energy of two dielectric half spaces with Chern-Simons layers at plane-parallel boundaries separated by a vacuum slit is derived. Crossing from the repulsive to the attractive Casimir force is analyzed for two Au and two Si half spaces with boundary Chern-Simons layers. Boundary quantum Hall layers in external magnetic field lead to Casimir repulsion at nanoscales. We discuss features that make systems with boundary quantum Hall layers unique for force measurements and search of long-range interactions beyond electromagnetism.

Casimir force for magnetodielectric media

Boyer showed that a perfect electrically conducting slab repels a perfect magnetically conducting slab, in contrast to the attractive Casimir force between two identical perfect electrically/magnetically conducting slabs. To gain insight for the difference between the Boyer force and the Casimir force, we present the derivation of the Boyer force using the stress tensor method and then using the method of variation in dielectric. The Green dyadic, in terms of electric and magnetic Green's functions, is presented for an electric medium filling half of space and another magnetic medium filling another half of space such that the two half-spaces are parallel and separated by a distance $a$. We make the observation that the spectral distribution of scattering in a Boyer cavity is that of Fermi-Dirac type, while the spectral distribution of scattering in a Casimir cavity is that of Bose-Einstein type. Based on this observation we conclude that the difference between the Boyer force and the Casimir force is governed by the statistics of the possible scattering in the respective cavities.

Optical Chopper Driven by the Casimir Force

We propose the experimental scheme and present detailed theory of the optical chopper which functionality is based on the balance between the Casimir and light pressures. The proposed device consists of two atomically thin metallic mirrors forming the Fabry-P\'{e}rot microfilter. One of the mirrors is deposited on a solid cube and another one on a thinner wall subjected to bending under the influence of the attractive Casimir force and repulsive force due to the pressure of light from a continuous laser amplified in the resonator of a microfilter. The separation distance between the mirrors should only slightly exceed the half wavelength of the laser light. It is shown that in this case the resonance condition in the microfilter alternatively obeys and breaks down resulting in the periodic pulses of the transmitted light. The Casimir pressure is calculated taking into account an anisotropy of the dielectric permittivity of a metal at several first Matsubara frequencies. The reflectivity properties of atomically thin metallic mirrors in the optical spectral range are found using the experimentally consistent phenomenological approach developed earlier in the literature. The specific values of all parameters, found for the microfilter made of quartz glass with Ag mirrors, demonstrate its workability. The proposed optical chopper may find prospective applications in the emerging field of nanotechnology exploiting the effects of quantum fluctuations.