Casimir Interaction Research Articles

Twisted bilayered graphenes at magic angles and Casimir interactions: correlation-driven effects

Twisted bilayered graphenes (TBGs) at magic angles are systems housing long ranged periodicity of moiré patterns together with short ranged periodicity associated with the individual graphenes. Such materials are a fertile ground for novel states largely driven by electronic correlations. Here we find that the ubiquitous Casimir force can serve as a platform for macroscopic manifestations of the quantum effects stemming from the magic angle bilayered graphenes properties and their phases determined by electronic correlations. By utilizing comprehensive calculations for the electronic and optical response, we find that Casimir torque can probe anisotropy from the Drude conductivities in nematic states, while repulsion in the Casimir force can help identify topologically nontrivial phases in magic angle TBGs.

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.

Casimir self-entropy of nanoparticles with classical polarizabilities: Electromagnetic field fluctuations

Not only are Casimir interaction entropies not guaranteed to be positive, but also, more strikingly, Casimir self-entropies of bodies can be negative. Here, we attempt to interpret the physical origin and meaning of these negative self-entropies by investigating the Casimir self-entropy of a neutral spherical nanoparticle. After extracting the polarizabilities of such a particle by examining the asymptotic behavior of the scattering Green's function, we compute the corresponding free energy and entropy. Two models for the nanoparticle, namely a spherical plasma $\ensuremath{\delta}$-function shell and a homogeneous dielectric/diamagnetic ball, are considered at low temperature, because that is all that can be revealed from a nanoparticle perspective. The second model includes a contribution to the entropy from the bulk free energy, referring to the situation where the medium inside or outside the ball fills all space, which must be subtracted on physical grounds in order to maintain consistency with van der Waals interactions, corresponding to the self-entropy of each bulk. (The van der Waals calculation is described in Appendix A.) The entropies so calculated agree with known results in the low-temperature limit, appropriate for a small particle, and are negative. But we suggest that the negative self-entropy is simply an interaction entropy, the difference between the total entropy and the blackbody entropy of the two bulks, outside or inside of the nanosphere. The vacuum entropy is always positive and overwhelms the interaction entropy. Thus the interaction entropy can be negative, without contradicting the principles of statistical thermodynamics. Given the intrinsic electrical properties of the nanoparticle, the self-entropy arises from its interaction with the thermal vacuum permeating all space. Because the entropy of blackbody radiation by itself plays an important role, it is also discussed, including dispersive effects, in detail.

Universal Casimir Interaction between Two Dielectric Spheres in Salted Water.

We study the Casimir interaction between two dielectric spheres immersed in a salted solution at distances larger than the Debye screening length. The long distance behavior is dominated by the nonscreened interaction due to low-frequency transverse magnetic thermal fluctuations. It shows universality properties in its dependence on geometric dimensions and independence of dielectric functions of the particles, with these properties related to approximate conformal invariance. The universal interaction overtakes nonuniversal contributions at distances of the order of or larger than 0.1 μm, with a magnitude of the order of the thermal scale k_{B}T such as to make it important for the modeling of colloids and biological interfaces.

Engineering Casimir interactions with epsilon-near-zero materials

In this paper, we theoretically demonstrate the tunability of the Casimir force both in sign and magnitude between parallel plates coated with dispersive materials. We show that this force, existing between uncharged plates, can be tuned by carefully choosing the value of the plasma frequency (i.e., the epsilon-near-zero frequency) of the coating in the neighborhood of the resonance frequency of the cavity. The coating layer enables a continuous variation of the force between four limiting values when a coating is placed on each plate. We explore the consequences of such variation when pairs of electric and magnetic conductors (i.e., low and high impedance surfaces) are used as substrates on either side, showing that this continuous variation results in changes in the sign of the force, leading to both stable and unstable conditions, which could find interesting potential applications in nanomechanics, including nanoparticle tweezing.

The Casimir effect in graphene systems: Experiment and theory

The Casimir effect in graphene systems is reviewed with a emphasis made on the large thermal correction to the Casimir force predicted at short separations between the test bodies. The computational results for the Casimir pressure and for the thermal correction are presented for both pristine graphene and real graphene sheets, which possess nonzero energy gap and chemical potential, obtained by means of exact polarization tensor. Two experiments on measuring the gradient of the Casimir force between an Au-coated sphere and graphene-coated substrates performed by using a modified atomic force microscope cantilever-based technique are described. It is shown that the measurement data of both experiments are in agreement with theoretical predictions of the Lifshitz theory using the polarization tensor. Additionally, several important improvements made in the second experiment, allowed to demonstrate the predicted large thermal effect in the Casimir interaction at short separations. Possible implications of this result to the resolution of long-term problems of Casimir physics are discussed.

Universal Casimir interactions in the sphere–sphere geometry

We study universal Casimir interactions in two configurations which appear as dual to each other. The first involves spheres described by the Drude model and separated by vacuum while the second involves dielectric spheres immersed in a salted solution at distances larger than the Debye screening length. In both cases, the long-distance limit, equivalently the high-temperature limit, is dominated by the effect of low-frequency transverse magnetic thermal fluctuations. They are independent of the details of dielectric functions of materials, due to the finite conductivity of metals in the former case and of salted water in the latter one. They also show universality properties in their dependence on geometric dimensions in relation to an approximate conformal invariance of the reduced free energy.

Casimir effect between spherical objects: Proximity-force approximation and beyond using plane waves

For the Casimir interaction between two nearby objects, the plane-wave basis proves convenient for numerical calculations as well as for analytical considerations leading to an optical interpretation of the relevant scattering processes of electromagnetic waves. We review work on the proximity-force approximation (PFA) and corrections to it within the plane-wave basis for systems involving spherical objects. Previous work is extended by allowing for polarization mixing during the reflection at a sphere. In particular, explicit results are presented for perfect electromagnetic conductors. Furthermore, for perfect electric conductors at zero temperature, it is demonstrated that beyond the leading-order correction to the PFA, terms of half-integer order in the distance between the sphere surfaces appear.

From spatial to temporal patterns: cooperativity across ion channels in supercritical membranes

Theoretically predicted by Fisher and de Gennes in 1978, critical Casimir forces are the thermodynamic analogues of the Casimir-Polder attraction forces due to quantum fluctuations of confined electromagnetic field in vacuum. In the context of lipid membranes close to a miscibility transition, critical Casimir interactions are thought to be responsible for clustering of membrane proteins. Here we explore the hypothesis that these effective statistical-field mediated interactions can explain the observed ion channel cooperativity that has been suggested to promote multistability of the membrane potential and thus “cellular memory”.

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.

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 theoretically2,3 and experimentally4-9. The Casimir effect can dominate the interaction between microstructures at small separations and is essential for micro- and nanotechnologies10,11. It has been utilized to realize nonlinear oscillation12, quantum trapping13, phonon transfer14,15 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 point17-20 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.

Bulk contributions to the Casimir interaction of Dirac materials

Exploiting methods of Quantum Field Theory we compute the bulk polarization tensor and bulk dielectric functions for Dirac materials in the presence of a mass gap, chemical potential, and finite temperature. Using these results (and neglecting eventual boundary effects), we study the Casimir interaction of Dirac materials. We describe in detail the characteristic features of the dielectric functions and their influence on the Casimir pressure.

Trace singularities in obstacle scattering and the Poisson relation for the relative trace

We consider the case of scattering by several obstacles in {mathbb {R}}^d, d ge 2 for the Laplace operator Delta with Dirichlet boundary conditions imposed on the obstacles. In the case of two obstacles, we have the Laplace operators Delta _1 and Delta _2 obtained by imposing Dirichlet boundary conditions only on one of the objects. The relative operator g(Delta ) - g(Delta _1) - g(Delta _2) + g(Delta _0) was introduced in Hanisch, Waters and one of the authors in (A relative trace formula for obstacle scattering. arXiv:2002.07291, 2020) and shown to be trace-class for a large class of functions g, including certain functions of polynomial growth. When g is sufficiently regular at zero and fast decaying at infinity then, by the Birman–Krein formula, this trace can be computed from the relative spectral shift function xi _mathrm {rel}(lambda ) = -frac{1}{pi } {text {Im}}(Xi (lambda )), where Xi (lambda ) is holomorphic in the upper half-plane and fast decaying. In this paper we study the wave-trace contributions to the singularities of the Fourier transform of xi _mathrm {rel}. In particular we prove that {hat{xi }}_mathrm {rel} is real-analytic near zero and we relate the decay of Xi (lambda ) along the imaginary axis to the first wave-trace invariant of the shortest bouncing ball orbit between the obstacles. The function Xi (lambda ) is important in the physics of quantum fields as it determines the Casimir interactions between the objects.

Numerical study on stability of diamagnetic levitation of a single-layer graphene sheet

Strong diamagnetic interactions enable carbon materials such as graphite plates and organisms to levitate stably in the atmosphere without active control. Although the repulsive force caused by diamagnetism becomes weak as the size of the object decreases, the necessary force against gravity also decreases. Thus, a nanocarbon material such as a single-layer graphene sheet may be levitated by the diamagnetic force. However, the stability worsens as the dimensions of the sheet decrease. The dominant factors affecting the stability of the diamagnetic levitation of nanomaterials are the Brownian motion and attractive surface forces such as the Casimir interactions. We calculate the potential energy of a square graphene sheet in two states, vertical and horizontal to a magnet, and considered the transition rate between these states based on Kramers’ theory for the escape problem. Furthermore, the stiction of a single-layer graphene sheet onto a substrate caused by the Casimir force, which discontinues the levitation, is examined.

Experimental and theoretical investigation of the thermal effect in the Casimir interaction from graphene

We present the results of an experiment on measuring the gradient of the Casimir force between an Au-coated hollow glass microsphere and graphene-coated fused silica plate by means of a modified atomic force microscope cantilever-based technique operated in the dynamic regime. These measurements were performed in high vacuum at room temperature. The energy gap and the concentration of impurities in the graphene sample used have been measured utilizing scanning tunneling spectroscopy and Raman spectroscopy, respectively. The measurement results for the gradients of the Casimir force are found to be in a very good agreement with theory using the polarization tensor of graphene at nonzero temperature depending on the energy gap and chemical potential with no fitting parameters. The theoretical predictions of the same theory at zero temperature are experimentally excluded over the measurement region from 250 to 517 nm. We have also investigated a dependence of the thermal correction to the Casimir force gradient on the values of the energy gap, chemical potential, and on the presence of a substrate supporting the graphene sheet. It is shown that the observed thermal effect is consistent in size with that arising for pristine graphene sheets if the impact of real conditions such as nonzero values of the energy gap, chemical potential, and the presence of a substrate is included. Implications of the obtained results to the resolution of the long-standing problems in Casimir physics are discussed. In addition to the paper published previously [M. Liu et al., Phys. Rev. Lett. 126, 206802 (2021)], we present measurement results for the energy gap of the graphene sample, double the experimental data for the Casimir force, and perform a more complete theoretical analysis.

Chiral Anomaly-Enhanced Casimir Interaction between Weyl SemimetalsSupported by the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB28000000), the National Natural Science Foundation of China (Grant Nos. 61674145, 11974340, and 11504106), the National Key R&D Program of China (Grant Nos. 2017YFA0303400 and 2018YFA0306101), the Chinese Academy of Sciences (Grant No. QYZDJ-SSW-SYS001 and XDPB22).

We theoretically study the Casimir interaction between Weyl semimetals. When the distance a between semi-infinite Weyl semimetals is in the micrometer regime, the Casimir attraction can be enhanced by the chiral anomaly. The Casimir attraction depends sensitively on the relative orientations between the separations ( b 1, b 2) of Weyl nodes in the Brillouin zone and show anisotropic behavior for the relative orientation of these separations ( b 1, b 2) when they orient parallel to the interface. This anisotropy is quite larger than that in conventional birefringent materials. The Casimir force can be repulsive in the micrometer regime if the Weyl semimetal slabs are sufficiently thin and the direction of Weyl nodes separations ( b 1, b 2) is perpendicular to the interface. The Casimir attraction between Weyl semimetal slabs decays slower than 1/a 4 when the Weyl nodes separations b 1 and b 2 are both parallel to the interface.

A temperature-dependent critical Casimir patchy particle model benchmarked onto experiment.

Synthetic colloidal patchy particles immersed in a binary liquid mixture can self-assemble via critical Casimir interactions into various superstructures, such as chains and networks. Up to now, there are no quantitatively accurate potential models that can simulate and predict this experimentally observed behavior precisely. Here, we develop a protocol to establish such a model based on a combination of theoretical Casimir potentials and angular switching functions. Using Monte Carlo simulations, we optimize several material-specific parameters in the model to match the experimental chain length distribution and persistence length. Our approach gives a systematic way to obtain accurate potentials for critical Casimir induced patchy particle interactions and can be used in large-scale simulations.

The Casimir Effect in Topological Matter

We give an overview of the work done during the past ten years on the Casimir interaction in electronic topological materials, our focus being solids, which possess surface or bulk electronic band structures with nontrivial topologies, which can be evinced through optical properties that are characterizable in terms of nonzero topological invariants. The examples we review are three-dimensional magnetic topological insulators, two-dimensional Chern insulators, graphene monolayers exhibiting the relativistic quantum Hall effect, and time reversal symmetry-broken Weyl semimetals, which are fascinating systems in the context of Casimir physics. Firstly, this is for the reason that they possess electromagnetic properties characterizable by axial vectors (because of time reversal symmetry breaking), and, depending on the mutual orientation of a pair of such axial vectors, two systems can experience a repulsive Casimir–Lifshitz force, even though they may be dielectrically identical. Secondly, the repulsion thus generated is potentially robust against weak disorder, as such repulsion is associated with the Hall conductivity that is topologically protected in the zero-frequency limit. Finally, the far-field low-temperature behavior of the Casimir force of such systems can provide signatures of topological quantization.

Probing the screening of the Casimir interaction with optical tweezers

We measure the colloidal interaction between two silica microspheres in aqueous solution in the distance range from $0.2\,\mu$m to $0.5\,\mu$m with the help of optical tweezers. When employing a sample with a low salt concentration, the resulting interaction is dominated by the repulsive double-layer interaction which is fully characterized. The double-layer interaction is suppressed when adding $0.22\,$M of salt to our sample, thus leading to a purely attractive Casimir signal. When analyzing the experimental data for the potential energy and force, we find good agreement with theoretical results based on the scattering approach. At the distance range probed experimentally, the interaction arises mainly from the unscreened transverse magnetic contribution in the zero-frequency limit, with nonzero Matsubara frequencies providing a negligible contribution. In contrast, such unscreened contribution is not included by the standard theoretical model of the Casimir interaction in electrolyte solutions, in which the zero-frequency term is treated separately as an electrostatic fluctuational effect. As a consequence, the resulting attraction is too weak in this standard model, by approximately one order of magnitude, to explain the experimental data. Overall, our experimental results shed light on the nature of the thermal zero-frequency contribution and indicate that the Casimir attraction across polar liquids has a longer range than previously predicted.

Vacuum Interaction of Crossed Cosmic Strings

In this paper, we consider the vacuum energy of a scalar field in the spacetime of two non-parallel cosmic strings. To this end, we obtain metrics for orthogonal straight cosmic strings and for slightly nonparallel strings. In the first case, we derive the separation-dependent part of the vacuum energy in the leading order of string tension. The dependence of the vacuum energy on separation differs from that known for parallel strings. For two strings inclined at a small angle to each other, the approximation used simply reproduces the result for parallel strings, since the angle dependence enters the next to leading order. The results are compared with the Casimir interaction between two inclined cylinders.