Casimir Interaction Research Articles

Impurities in graphene and their influence on the Casimir interaction

Impurities in graphene and their influence on the Casimir interaction

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.

Casimir Interaction of Chern–Simons Layers on Substrates via Vacuum Stress Tensor

We develop a Green’s functions scattering method for systems with Chern–Simons plane boundary layers on dielectric half-spaces. The Casimir pressure is derived by evaluation of the stress tensor in a vacuum slit between two half-spaces. The sign of the Casimir pressure on a Chern–Simons plane layer separated by a vacuum slit from the Chern–Simons layer at the boundary of a dielectric half-space is analyzed for intrinsic Si and SiO2 glass substrates.

Semi-Classical Electrodynamics and the Casimir Effect

From the late 1960s onwards, the groups of Barry Ninham and Adrian Parsegian, and their many collaborators, made a number of essential contributions to theory and experiment of intermolecular forces. In particular, they explored the semi-classical theory: Maxwell’s equations and Planck quantization of light leads to Lifshitz and Casimir interactions. We discuss some selected thought-provoking results from Ninham and his group. Some of the results have been conceived as controversial but, we would say, never uninteresting.

Universal Casimir attraction between filaments at the cell scale

The electromagnetic Casimir interaction between dielectric objects immersed in salted water includes a universal contribution that is not screened by the solvent and therefore long-ranged. Here, we study the geometry of two parallel dielectric cylinders. We derive the Casimir free energy by using the scattering method. We show that its magnitude largely exceeds the thermal energy scale for a large parameter range. This includes length scales relevant for actin filaments and microtubules in cells. We show that the Casimir free energy is a universal function of the geometry, independent of the dielectric response functions of the cylinders, at all distances of biological interest. While multiple interactions exist between filaments in cells, this universal attractive interaction should have an important role in the cohesion of bundles of parallel filaments.

Laser-induced heating for the experimental study of critical Casimir forces with optical trapping

Critical Casimir interactions represent a perfect example of bath-induced forces at mesoscales. These forces may have a relevant role in the living systems as well as a role in the design of nanomachines fueled by environmental fluctuations. Since the thermal fluctuations are enhanced in the vicinity of a demixing point of a second-order phase transition, we can modulate the magnitude and range of these Casimir-like forces by slight changes in the temperature. Here, we consider two optical trapped colloidal beads inside a binary mixture. The Casimir interaction is controlled by warming the mixture by laser-induced heating, whose local application ensures high reproducibility. Once this two-particle system is warmed, the critical behavior of different observables allows the system to become its self-thermometer. We use this experimental scheme for analyzing the energetics of a critical colloidal system under a non-equilibrium-driven protocol. We quantify how the injected work can be dissipated to the environment as heat or stored as free energy. Indeed, our system allows us to use the fluctuation theorems framework for analyzing the performance of this critically driven toy model. Our work paves the way for future experimental studies on the non-equilibrium features of bath-induced forces and the design of critically driven nanosystems.

Casimir force between semiconductor and metal and compensation of surface charges

Measurement of the Casimir forces is restricted by well-conducting materials, for which the residual electrostatic force can be compensated. For semiconductors and dielectrics, it is considered as impossible due to the effect of surface charging. In this paper, the possibility to compensate for the electrostatic interaction between a metal and poor conducting material is analyzed. It is shown that the electrostatic force can be compensated at certain conditions. For semiconductors, it is possible if the sign of the surface charges is opposite to that of the main carriers. Otherwise, the compensating potential is too large and distance dependent. For dielectrics, the surface charges can be compensated for a thin dielectric film deposited on a good conductor. These findings open the way to investigate the Casimir interaction for poor-conducting materials.

Thermal Casimir interactions in multiparticle systems: Scattering channel approach

Thermal Casimir interactions in multiparticle systems: Scattering channel approach

Giant enhancement of the axial Casimir force of a rotating particle near hyperbolic metasurface

We show that the axial Casimir force (ACF) acting on a rotating nanoparticle can also appear in the proximity of a hyperbolic metasurface made of graphene ribbons since it was first demonstrated existing near a bi-isotropic material. The ACF can be enhanced by several orders of magnitude compared with that in the bi-isotropic configuration. We numerically demonstrate that the largest ACF exerted on the particle can be achieved when the rotation direction of the nanoparticle is parallel to the hyperbolic metasurface. ACF is also determined by the azimuth angle between the rotating axis and the edge of the metasurface. The dependence of ACF on the chemical potential and ribbon width of graphene is also investigated in detail. ACF increases as the chemical potential increases for fixed ribbon width. For given chemical potential, ACF increases first and then decreases after reaching the maximum value when the ribbon width increases. The results extend the application of hyperbolic metasurfaces in regulating Casimir interactions.

Casimir interaction of finite-width strings

Casimir interaction of finite-width strings

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.

Effective binding potential from Casimir interactions: the case of the Bose gas

We consider the thermal Casimir effect in ideal Bose gases, where the dispersion relation involves both terms quadratic and quartic in momentum. We demonstrate that if macroscopic objects are immersed in such a fluid in spatial dimensionality and at the critical temperature , the Casimir force acting between them is characterized by a sign which depends on the separation D between the bodies and changes from attractive at large distances to repulsive at smaller separations. In consequence, an effective potential which binds the two objects at a finite separation arises. We demonstrate that for odd integer dimensionality , the Casimir energy is a polynomial of degree in D −2. We point out a very special role of dimensionality d = 3, where we derive a strikingly simple form of the Casimir energy as a function of D at Bose–Einstein condensation. We discuss crossover between monotonous and oscillatory decay of the Casimir interaction above the condensation temperature.

The Casimir interaction in a nonlocal electrolyte slab

In this paper, the Casimir force per unit area across a nonlocal slab of an electrolyte between two semispaces of ordinary materials has been studied through the scattering approach. Because of the insufficiency of Maxwell’s boundary conditions, additional boundary conditions are used as well. The numerical calculations show that for polystyrene semispaces at small separations, ascending the concentration causes intensifying the Casimir pressure. However, it is illustrated that in the case of silver substrates the Casimir pressure has the same amount for two electrolyte concentrations and this intensification does not occur by increasing the concentration. At small separations for polystyrene semispaces, the Hamaker coefficient has two different magnitudes corresponding to 90 and 0.9[Formula: see text]mM concentrations, but for silver substrates the Hamaker coefficient starts from the same value for both concentrations.

Multiple Scattering Expansion for Dielectric Media: Casimir Effect.

Recent measurements of Casimir forces have provided evidence of an intricate modification of quantum fluctuations of the electromagnetic field in complex geometries. Here we introduce a multiple scattering description for Casimir interactions between bodies of arbitrary shape and material composition, admitting an expansion as a sequence of inter- and intra-body wave scatterings. Interactions in complex geometries can be computed within the current experimental resolution from typically a few wave scatterings, notably without any apriori knowledge of the scattering amplitudes of the bodies. Some first applications demonstrate the power of the approach.

Effect of Epsilon-Near-Zero Modes on the Casimir Interaction between Ultrathin Films.

Vacuum fluctuation-induced interactions between macroscopic metallic objects result in an attractive force between them, a phenomenon known as the Casimir effect. This force is the result of both plasmonic and photonic modes. For very thin films, field penetration through the films will modify the allowed modes. Here, we theoretically investigate the Casimir interaction between ultrathin films from the perspective of force distribution over real frequencies for the first time. Pronounced repulsive contributions to the force are found due to the highly confined and nearly dispersion-free epsilon-near-zero (ENZ) modes that only exist in ultrathin films. These contributions persistently occur around the ENZ frequency of the film irrespective of the interfilm separation. We further associate the ENZ modes with a striking thickness dependence of a proposed figure of merit (FOM) for conductive thin films, suggesting that the motion of objects induced by Casimir interactions is boosted for deeply nanoscale sizes. Our results shed light on the correlation between special electromagnetic modes and the vacuum fluctuation-induced force as well as the resulting mechanical properties of ultrathin ENZ materials, which may create new opportunities for engineering the motion of ultrasmall objects in nanomechanical systems.

Comparison of the Lifshitz Theory Using the Nonconventional Fit of Response Functions with Precise Measurements of the Casimir Force

It is known that the fundamental Lifshitz theory, which is based on the first principles of thermal quantum field theory, experiences difficulties when compared with precise measurements of the Casimir force. We analyzed the nonconventional fit of the response functions of many materials along the imaginary frequency axis to the empirical model of “modified” oscillators, which was recently proposed in the literature. According to our results, this model is unacceptable because at high frequencies it leads to the asymptotic behavior of the response functions, which is in contradiction with that following from the fundamental physical principles. We calculated the Casimir interaction in the configurations of several precise experiments using the Lifshitz theory and the response functions to the quantized electromagnetic field expressed in terms of modified oscillators and demonstrated that the obtained results are excluded by the measurement data. This invalidated a claim made in the literature that the Casimir–van der Waals forces calculated using these response functions are in remarkable agreement with the experimental values. Possible reasons for a disagreement between experiment and theory are discussed, and the way to improve the situation is indicated.

Casimir interaction with black phosphorus sheets.

We calculate the Casimir interaction between isotropic plates (gold or graphene) and black phosphorus (BP) sheets with Lifshitz theory. It is found that the Casimir force with BP sheets is of the order of α times the perfect metal limit, and α is the fine structure constant. Strong anisotropy of the BP conductivity gives rise to a difference in the Casimir force contribution between the two principal axis. Furthermore, increasing the doping concentration both in BP sheets and graphene sheets can enhance the Casimir force. Moreover, introducing substrate and increased temperature can also enhance the Casimir force, by this way we reveal that the Casimir interaction can be doubled. The controllable Casimir force opens a new avenue for designing next generation devices in micro- and nano-electromechanical systems.

Coherent resonant coupling between atoms and a mechanical oscillator mediated by cavity-vacuum fluctuations

We show that an atom can be coupled to a mechanical oscillator via quantum vacuum fluctuations of a cavity field enabling energy transfer processes between them. In a hybrid quantum system consisting of a cavity resonator with a movable mirror and an atom, these processes are dominated by two pair-creation mechanisms: the counterrotating (atom-cavity system) and dynamical Casimir interaction terms (optomechanical system). Because of these two pair-creation mechanisms, the resonant atom-mirror coupling is the result of high-order virtual processes with different transition paths well described in our theoretical framework. We perform a unitary transformation to the atom-mirror system Hamiltonian, exhibiting two kinds of multiple-order transitions of the pair creation. By tuning the frequency of the atom, we show that photon frequency conversion can be realized within a cavity of multiple modes. Furthermore, when involving two atoms coupled to the same mechanical mode, a single vibrating excitation of the mechanical oscillator can be simultaneously absorbed by the two atoms. Considering recent advances in strong and ultrastrong coupling for cavity optomechanics and other systems, we believe our proposals can be implemented using available technology.

Electrically switchable Casimir forces using transparent conductive oxides

Casimir forces between charge-neutral bodies originate from quantum vacuum fluctuations of electromagnetic fields, which exhibit a critical dependence on material's electromagnetic properties. Over the years, in situ modulation of a material's optical properties has been enabled through various means and has been widely exploited in a plethora of applications such as electro-optical modulation, transient color generation, bio- or chemical sensing, etc. Yet Casimir force modulation has been hindered by difficulty in achieving high modulation signals due to the broadband nature of the Casimir interaction. Here we propose and investigate two configurations that allow for in situ modulation of Casimir forces through electrical gating of a metal-insulator-semiconductor junction comprised of transparent conductive oxide (TCO) materials. By switching the gate voltage on and off, a force modulation of >400 pN is predicted due to substantive charge carrier accumulation in the TCO layer, which can be easily measured using state-of-the-art force measurement techniques in an atomic force microscope. We further examine the influence of the oxide layer thickness on the force modulation, suggesting the importance of the fine control of the oxide layer deposition. Our work provides a promising pathway for modulating the Casimir effect in situ with experimentally measurable force contrast.

Universal van der Waals Force between Heavy Polarons in Superfluids.

We investigate the long-range behavior of the induced Casimir interaction between two spinless heavy impurities, or polarons, in superfluid cold atomic gases. With the help of effective field theory (EFT) of a Galilean invariant superfluid, we show that the induced impurity-impurity potential at long distance universally shows a relativistic van der Waals-like attraction (∼1/r^{7}) resulting from the exchange of two superfluid phonons. We also clarify finite temperature effects from the same two-phonon exchange process. The temperature T introduces the additional length scale c_{s}/T with the speed of sound c_{s}. Leading corrections at finite temperature scale as T^{6}/r for distances r≪c_{s}/T smaller than the thermal length. For larger distances the potential shows a nonrelativistic van der Waals behavior (∼T/r^{6}) instead of the relativistic one. Our EFT formulation applies not only to weakly coupled Bose or Fermi superfluids but also to those composed of strongly correlated unitary fermions with a weakly coupled impurity. The sound velocity controls the magnitude of the van der Waals potential, which we evaluate for the fermionic superfluid in the BCS-BEC crossover.