Casimir Interaction Research Articles

Effects of Casimir force on high-order sideband generation in an optomechanical system

We introduce a Casimir force in a conventional optomechanical system to study the high-order sideband generation. In this system, a nanosphere is placed near the moveable mirror of the conventional optomechanical system. The moveable mirror is coupled to the cavity field and the nanosphere by the optomechanical interaction and the Casimir interaction, respectively. We find that the amplitude and cutoff order of the high-order sideband can be enhanced by decreasing the sphere–mirror separation (increasing the Casimir force) and increasing the optomechanical coupling strength. Our proposal provides an alternative method for generating the high-order sidebands and for measuring the Casimir force.

Simulation of lattice statistical models with defects: Critical Casimir Effect

The influence of lattice structure defects on phase transition phenomena was studied in framework of 2D spin model. Effective mass of defect was proposed for investigation of conformal properties of the model at critical point. The volume dependence of defect’s mass at critical point and the Critical Casimir interaction of two defects were studied. It was shown that this Casimir interaction is attraction for any value of hopping parameter. The confinement of the defect on the defects line and the process of defects line collapse were studied. Applications in nanophysics and biophysics were discussed.

Scattering formalism in the Casimir interaction of gratings and Chern-Simons layers

We describe scattering formalism to evaluate the Casimir energy of two gratings separated by a vacuum slit and the Casimir energy of two Chern- Simons layers in vacuum.

Fluctuation induced forces in critical films with disorder at their surfaces

We investigate the effect of quenched surface disorder on effective interactions between two planar surfaces immersed in fluids which are near criticality and belong to the Ising bulk universality class. We consider the case that, in the absence of random surface fields, the surfaces of the film belong to the surface universality class of the so-called ordinary transition. We find analytically that in the linear weak-coupling regime, i.e. upon including the mean-field contribution and Gaussian fluctuations, the presence of random surface fields with zero mean leads to an attractive, disorder-induced contribution to the critical Casimir interactions between the two confining surfaces. Our analytical, field-theoretic results are compared with corresponding Monte Carlo simulation data.

Electromagnetic δ -function sphere

We develop a formalism to extend our previous work on the electromagnetic $\delta$-function plates to a spherical surface. The electric ($\lambda_e$) and magnetic ($\lambda_g$) couplings to the surface are through $\delta$-function potentials defining the dielectric permittivity and the diamagnetic permeability, with two anisotropic coupling tensors. The formalism incorporates dispersion. The electromagnetic Green's dyadic breaks up into transverse electric and transverse magnetic parts. We derive the Casimir interaction energy between two concentric $\delta$-function spheres in this formalism and show that it has the correct asymptotic flat plate limit. We systematically derive expressions for the Casimir self-energy and the total stress on a spherical shell using a $\delta$-function potential, properly regulated by temporal and spatial point-splitting, which are different from the conventional temporal point-splitting. In strong coupling, we recover the usual result for the perfectly conducting spherical shell but in addition, there is an integrated curvature-squared divergent contribution. For finite coupling, there are additional divergent contributions; in particular, there is a familiar logarithmic divergence occurring in the third order of the uniform asymptotic expansion that renders it impossible to extract a unique finite energy except in the case of an isorefractive sphere, which translates into $\lambda_g=-\lambda_e$.

Casimir interaction between two smoothly deformed cylindrical surfaces

We generalize the derivative expansion (DE) approach to the interaction between almost-flat smooth surfaces, to the case of surfaces which are optimally described in cylindrical coordinates. As in the original form of the DE, the obtained method does not depend on the nature of the interaction. We apply our results to the study of the static, zero-temperature Casimir effect between two cylindrical surfaces, obtaining approximate expressions which are reliable under the assumption that the distance between those surfaces is always much smaller than their local curvature radii. To obtain the zero-point energy, we apply known results about the thermal Casimir effect for a planar geometry. To that effect, we relate the time coordinate in the latter to the angular variable in the cylindrical case, as well as the temperature to the radius of the cylinders. We study the dependence of the applicability of the DE on the kind of interaction, considering the particular cases where Dirichlet or Neumann conditions are applied to a scalar field.

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.

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.

Unifying Microscopic and Continuum Treatments of van der Waals and Casimir Interactions

We present an approach for computing long-range van der Waals (vdW) interactions between complex molecular systems and arbitrarily shaped macroscopic bodies, melding atomistic treatments of electronic fluctuations based on density functional theory in the former with continuum descriptions of strongly shape-dependent electromagnetic fields in the latter, thus capturing many-body and multiple scattering effects to all orders. Such a theory is especially important when considering vdW interactions at mesoscopic scales, i.e., between molecules and structured surfaces with features on the scale of molecular sizes, in which case the finite sizes, complex shapes, and resulting nonlocal electronic excitations of molecules are strongly influenced by electromagnetic retardation and wave effects that depend crucially on the shapes of surrounding macroscopic bodies. We show that these effects together can modify vdW interaction energies and forces, as well as molecular shapes deformed by vdW interactions, by orders of magnitude compared to previous treatments based on Casimir-Polder, nonretarded, or pairwise approximations, which are valid only at macroscopically large or atomic-scale separations or in dilute insulating media, respectively.

Constraints on axionlike particles and non-Newtonian gravity from measuring the difference of Casimir forces

We derive constraints on the coupling constants of axion-like particles to nucleons and on the Yukawa-type corrections to Newton's gravitational law from the results of recent experiment on measuring the difference of Casimir forces between a Ni-coated sphere and Au and Ni sectors of a structured disc. Over the wide range of axion masses from 2.61\,meV to 0.9\,eV the obtained constraints on the axion-to-nucleon coupling are up to a factor of 14.6 stronger than all previously known constraints following from experiments on measuring the Casimir interaction. The constraints on non-Newtonian gravity found here are also stronger than all that following from the Casimir and Cavendish-type experiments over the interaction range from 30\,nm to $5.4\,\mu$m. They are up to a factor of 177 stronger than the constraints derived recently from measuring the difference of lateral forces. Our constraints confirm previous somewhat stronger limits obtained from the isoelectronic experiment, where the contribution of the Casimir force was nullified.

Casimir interaction of strained graphene

We calculate the Casimir interaction of two freestanding graphene samples under uniaxial strain. Our approach fully takes retardation and dispersion into account and is based on quantum field theoretical expressions for conductivities in terms of the polarization operator. Contrary to some recent results the force shows a rather weak dependence on the realistic values of strain, changing just by a few percent in its maximum as compared to the non-strained case.

Nonperturbative Casimir effect and monopoles: Compact Abelian gauge theory in two spatial dimensions

We demonstrate that Casimir forces associated with zero-point fluctuations of quantum vacuum may be substantially affected by the presence of dynamical topological defects. In order to illustrate this nonperturbative effect we study the Casimir interactions between dielectric wires in a compact formulation of Abelian gauge theory in two spatial dimensions. The model possesses topological defects, instanton-like monopoles, which are known to be responsible for nonperturbative generation of a mass gap and for a linear confinement of electrically charged probes. Despite the model has no matter fields, the Casimir energy depends on the value of the gauge coupling constant. We show, both analytically and numerically, that in the strong coupling regime the Abelian monopoles make the Casimir forces short-ranged. Simultaneously, their presence increases the interaction strength between the wires at short distances for certain range of values of the gauge coupling. The wires suppress monopole density in the space between them compared to the density outside the wires. In the weak coupling regime the monopoles become dilute and the Casimir potential reduces to a known theoretical result which does not depend on the gauge coupling.

Thermal and nonthermal scaling of the Casimir-Polder interaction in a black hole spacetime

We study the Casimir-Polder force arising between two identical two-level atoms and mediated by a massless scalar field propagating in a black-hole background. We study the interplay of Hawking radiation and Casimir-Polder forces and find that, when the atoms are placed near the event horizon, the scaling of the Casimir-Polder interaction energy as a function of interatomic distance displays a transition from a thermallike character to a nonthermal behavior. We corroborate our findings for a quantum field prepared in the Boulware, Hartle-Hawking, and Unruh vacua. Our analysis is consistent with the nonthermal character of the Casimir-Polder interaction of two-level atoms in a relativistic accelerated frame [J. Marino et al., Phys. Rev. Lett. 113, 020403 (2014)], where a crossover from thermal scaling, consistent with the Unruh effect, to a nonthermal scaling has been observed. The two crossovers are a consequence of the noninertial character of the background where the field mediating the Casimir interaction propagates. While in the former case the characteristic crossover length scale is proportional to the inverse of the surface gravity of the black hole, in the latter it is determined by the inverse of the proper acceleration of the atoms.

From 2D to 3D: Critical Casimir interactions and phase behavior of colloidal hard spheres in a near-critical solvent.

Colloids dispersed in a binary solvent mixture experience long-ranged solvent-mediated interactions (critical Casimir forces) upon approaching the critical demixing point of the solvent mixture. The range of the interaction is set by the bulk correlation length of the solvent mixture, which diverges upon approaching the critical point. This presents a great opportunity to realize the reversible self-assembly of colloids by tuning the proximity to the critical point of the solvent. Here, we develop a rejection-free geometric cluster algorithm to study the full ternary mixture of colloidal hard spheres suspended in an explicit three-dimensional lattice model for the solvent mixture using extensive Monte Carlo simulations. The phase diagram displays stable colloidal gas, liquid, and crystal phases, as well as broad gas-liquid and gas-crystal phase coexistence, and pronounced fractionation of the solvent in the coexisting colloid phases. The topology of the phase diagram in our three-dimensional study shows striking resemblance to that of our previous studies carried out in two dimensions.

Casimir force phase transitions in the graphene family

The Casimir force is a universal interaction induced by electromagnetic quantum fluctuations between any types of objects. The expansion of the graphene family by adding silicene, germanene and stanene (2D allotropes of Si, Ge, and Sn), lends itself as a platform to probe Dirac-like physics in honeycomb staggered systems in such a ubiquitous interaction. We discover Casimir force phase transitions between these staggered 2D materials induced by the complex interplay between Dirac physics, spin-orbit coupling and externally applied fields. In particular, we find that the interaction energy experiences different power law distance decays, magnitudes and dependences on characteristic physical constants. Furthermore, due to the topological properties of these materials, repulsive and quantized Casimir interactions become possible.

Classical Casimir interaction of a perfectly conducting sphere and plate

We study the Casimir interaction between a perfectly conducting sphere and plate in the classical limit of high temperatures. By taking the small-distance expansion of the exact scattering formula, we compute the leading correction to the Casimir energy beyond the commonly employed proximity force approximation. We find that for a sphere of radius $R$ at a distance $d$ from the plate the correction is of the form ${\mathrm{ln}}^{2}(d/R)$, in agreement with indications from recent large-scale numerical computations. We develop a fast-converging numerical scheme for computing the Casimir interaction to high precision, based on bispherical partial waves, and we verify that the short-distance formula provides precise values of the Casimir energy also for fairly large distances.

On the static Casimir effect with parity-breaking mirrors

We study the Casimir interaction energy due to the vacuum fluctuations of the electromagnetic (EM) field in the presence of two mirrors, described by 2+1-dimensional, generally nonlocal actions, which may contain both parity-conserving and parity-breaking terms. We compare the results with the ones corresponding to Chern–Simons boundary conditions and evaluate the interaction energy for several particular situations.

Quantum thermal machines driven by vacuum forces.

We propose a quantum thermal machine composed of two nanomechanical resonators (two membranes suspended over a trench in a substrate) placed a few μm from each other. The quantum thermodynamical cycle is powered by the Casimir interaction between the resonators and the working fluid is the polariton resulting from the mixture of the flexural (out-of-plane) vibrations. With the help of piezoelectric cells, we select and sweep the polariton frequency cyclically. We calculate the performance of the proposed quantum thermal machines and show that high efficiencies are achieved thanks to (i) the strong coupling between the resonators and (ii) the large difference between the membrane stiffnesses. Our findings can be of particular importance for applications in nanomechanical technologies where a sensitive control of temperature is needed.

Nonmonotonic Casimir interaction: The role of amplifying dielectrics

The normal and the lateral Casimir interactions between corrugated ideal metallic plates in the presence of an amplifying or an absorptive dielectric slab has been studied by the path-integral quantization technique. The effect of the amplifying slab, which is located between corrugated conductors, is to increase the normal and lateral Casimir interactions, while the presence of the absorptive slab diminishes the interactions. These effects are more pronounced if the thickness of the slab increases, and also if the slab comes closer to one of the bounding conductors. When both bounding ideal conductors are flat, the normal Casimir force is non-monotonic in the presence of the amplifying slab and the system has a stable mechanical equilibrium state, while the force is attractive and is weakened by intervening the absorptive dielectric slab in the cavity. By replacing one of the flat conductors by a flat ideal permeable plate the force becomes non-monotonic and the system has an unstable mechanical equilibrium state in the presence of either an amplifying or an absorptive slab. When the left side plate is conductor and the right one is permeable, the force is non-monotonic in the presence of a double-layer DA (dissipative-amplifying) dielectric slab with a stable mechanical equilibrium state, while it is purely repulsive in the presence of a double-layer AD (amplifying-dissipative) dielectric slab.

Transient Casimir Forces from Quenches in Thermal and Active Matter.

We compute fluctuation-induced (Casimir) forces for classical systems after a temperature quench. Using a generic coarse-grained model for fluctuations of a conserved density, we find that transient forces arise even if the initial and final states are force free. In setups reminiscent of Casimir (planar walls) and van der Waals (small inclusions) interactions, we find comparable exact universal expressions for the force. Dynamical details only scale the time axis of transient force curves. We propose that such quenches can be achieved, for instance, in experiments on active matter, employing tunable activity or interaction protocols.