Casimir Effect Research Articles

Phonon-photon conversion as mechanism for cooling and coherence transfer

The dynamical Casimir effect is the physical phenomenon where the mechanical energy of a movable wall of a cavity confining a quantum field can be converted into quanta of the field itself. This effect has been recognized as one of the most astonishing predictions of quantum field theory. At the quantum scale, the energy conversion can also occur incoherently, namely, without a physical motion of the wall. By means of quantum thermodynamics, we show that this phenomenon can be employed as a tool to cool down the wall when there is a nonvanishing temperature gradient between the wall and the cavity. At the same time, the mechanism responsible for the heat transfer enables sharing the coherence from one cavity mode, driven by a laser, to the wall, thereby forcing its coherent oscillation. Finally, we show how to employ one laser drive to cool the entire system, including the case when it is composed of other subsystems. Published by the American Physical Society 2024

Casimir effect and holographic dual of wedges

This paper investigates the Casimir effect of a wedge and its holographic dual. We prove that the displacement operator universally determines the wedge Casimir effect in the smooth limit. Besides, we argue that the wedge Casimir energy increases with the opening angle and test it with several examples. Furthermore, we construct the holographic dual of wedges in AdS/BCFT in general dimensions. We verify that our proposal can produce the expected Casimir effect within smooth and singular limits. We observe that the Casimir energy density of a wedge increases with the brane tension. Next, we discuss the wedge contribution to holographic entanglement entropy and find it increases with the opening angle, similar to the wedge Casimir energy. Finally, we briefly discuss the holographic polygon in AdS3/BCFT2 and its generalization to higher dimensions.

Casimir wormholes in Brans–Dicke theory

In recent years there has been a growing interest in the field of wormhole physics in the presence of Casimir effect. As this effect provides negative energy density, it can be utilized as an ideal candidate for the exotic matter required for creating a traversable wormhole. In the context of modified theories of gravity such as Brans–Dicke (BD) theory (Brans and Dicke 1961 Phys. Rev. 124 925), wormhole geometries have been vastly investigated. However, the scientific literature is silent on the issue of BD wormholes in the presence of Casimir energy. Our aim in the present study is to seek for static spherically symmetric solutions representing wormhole configurations in BD theory with Casimir energy as the supporting matter. The Casimir setup we assume comprises two electrically neutral, infinitely large parallel planes placed in a vacuum. We then consider the Casimir vacuum energy density of a scalar field in such a configuration with Dirichlet and mixed boundary conditions. In the former case the corresponding Casimir force is attractive and in the latter this force is repulsive. We present exact zero tidal force wormhole solutions as well as those with non vanishing redshift function for both types of Casimir energies. The conditions on wormhole solutions along with the weak (WEC) and null (NEC) energy conditions put constraints on the values of BD coupling parameter. These constraints are also subject to the value of BD scalar field at the throat and the throat radius. We therefore find that BD wormholes in the presence of Casimir energy can exist without violating NEC and WEC (for the repulsive Casimir force). Finally, we examine the equilibrium condition for stability of the obtained solutions using Tolman–Oppenheimer–Volkoff equation.

Nanoalignment by critical Casimir torques

The manipulation of microscopic objects requires precise and controllable forces and torques. Recent advances have led to the use of critical Casimir forces as a powerful tool, which can be finely tuned through the temperature of the environment and the chemical properties of the involved objects. For example, these forces have been used to self-organize ensembles of particles and to counteract stiction caused by Casimir-Liftshitz forces. However, until now, the potential of critical Casimir torques has been largely unexplored. Here, we demonstrate that critical Casimir torques can efficiently control the alignment of microscopic objects on nanopatterned substrates. We show experimentally and corroborate with theoretical calculations and Monte Carlo simulations that circular patterns on a substrate can stabilize the position and orientation of microscopic disks. By making the patterns elliptical, such microdisks can be subject to a torque which flips them upright while simultaneously allowing for more accurate control of the microdisk position. More complex patterns can selectively trap 2D-chiral particles and generate particle motion similar to non-equilibrium Brownian ratchets. These findings provide new opportunities for nanotechnological applications requiring precise positioning and orientation of microscopic objects.

A Brief Review of Some Recent Precision Casimir Force Measurements

Here, we review recent advances in precision Casimir force measurements with both non-magnetic and magnetic materials. In addition, the measurement of the geometric dependence of the Casimir force, both lateral and normal, using uniformly corrugated surfaces is briefly presented. Finally, the measurement of the thermal Casimir force in graphene is discussed.

Optomechanical Backreaction of Quantum Field Processes in Dynamical Casimir Effect

Optomechanical Backreaction of Quantum Field Processes in Dynamical Casimir Effect

Examining the Electron Phase Transformation Theory in the Context of Atomic Structure

The shortcomings of the Rutherford atomic model can be eliminated by the suggested phase transformation of the electrons from point to non-revolving surface charge in the vicinity of the nucleus. The energy balance investigations of this atom model indicated that the stability of the surface charge valence electron shell is ensured by the one-dimensional Casimir effect. If this theoretical prediction is correct then the first ionization energies of the elements should correlate linearly to the inverse of atomic diameter. Classical physics approach, the electrostatic attraction of the nucleus and the repulsion of the surface charge electron shell result in an identical relationship. The problem with the classical physics approach is that it does not offer an adequate explanation for the photoelectric effect and the free electrons inside the metal. Therefore, classical electrostatics cannot be considered the right physical process responsible for the stability of the valence electron/s in neutral atoms. The derived theoretical relationship, between atomic diameter and ionization energy, was tested up to 86 elements of the periodic table. The correlation coefficient is 0.9187. The correlation is stronger for individual periods. The empirical relationship between the ionization energy and atomic radii is well known, resulting in the same correlation coefficients. However, the correlation to the atomic radii does not reproduce the theoretically derived constant multiplier, contrarily to the atomic diameter relationship. Thus, the first ionization energy is the function of the atomic diameter. The uncertainties in the reported atomic sizes are relatively high. Therefore, the correlation between theory and experiments should be considered as excellent. The theoretically derived relationship between the first ionization energy and atomic diameter is the consequence of the proposed phase transformation of the electron. Thus the detected strong correlation between theory and experiments adds further support to the proposed atomic structure.

Towards a realistic setup for a dynamical measurement of deviations from Newton’s 1/r2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1/r^2$$\\end{document} law: the impact of air viscosity

A novel experimental setup to measure deviations from the 1/r2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1/r^2$$\\end{document} distance dependence of Newtonian gravity was proposed in Donini and Marimón (Eur Phys J C 76:696, 2016). The underlying theoretical idea was to study the orbits of a microscopically-sized planetary system composed of a “Satellite”, with mass mS∼O(10-9)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_{\ extrm{S}} \\sim {\\mathcal {O}}(10^{-9})$$\\end{document} g, and a “Planet”, with mass MP∼O(10-5)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_{\ extrm{P}} \\sim {\\mathcal {O}} (10^{-5}) $$\\end{document} g at an initial distance of hundreds of microns. The detection of precession of the orbit in this system would be an unambiguous indication of a central potential with terms that scale with the distance differently from 1/r. This is a huge advantage with respect to the measurement of the absolute strength of the attraction between two bodies, as most electrically-induced background potentials do indeed scale as 1/r. Detection of orbit precession is unaffected by these effects, allowing for better sensitivities. In Baeza-Ballesteros et al. (Eur Phys J C 82:154, 2022), the impact of other subleading backgrounds that may induce orbit precession, such as, e.g., the electrical Casimir force or general relativity, was studied in detail. It was found that the proposed setup could test Yukawa-like corrections, α×exp(-r/λ),\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \ imes \\exp (-r/\\lambda ),$$\\end{document} to the 1/r potential with couplings as low as α∼10-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \\sim 10^{-2}$$\\end{document} for distances as small as λ∼10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda \\sim 10$$\\end{document}μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu $$\\end{document}m, improving by roughly an order of magnitude present bounds. In this paper, we start to move from a theoretical study of the proposal to a more realistic implementation of the experimental setup. As a first step, we study the impact of air viscosity on the proposed setup and see how the setup should be modified in order to preserve the theoretical sensitivity achieved in Donini and Marimón (2016) and Baeza-Ballesteros et al. (2022).

Anti-de Sitter → de Sitter transition driven by Casimir forces and mitigating tensions in cosmological parameters

Over the last few years, low- and high-redshift observations set off tensions in the measurement of the present-day expansion rate H0 and in the determination of the amplitude of the matter clustering in the late Universe (parameterized by S8). It was recently noted that both these tensions can be resolved if the cosmological constant parametrizing the dark energy content switches its sign at a critical redshift zc∼2. However, the anti-de Sitter (AdS) swampland conjecture suggests that the postulated switch in sign of the cosmological constant at zero temperature seems unlikely because the AdS vacua are an infinite distance apart from de Sitter (dS) vacua in moduli space. We provide an explanation for the required AdS → dS crossover transition in the vacuum energy using the Casimir forces of fields inhabiting the bulk. We then use entropy arguments to claim that any AdS → dS transition between metastable vacua must be accompanied by a reduction of the species scale where gravity becomes strong. We provide a few examples supporting this AdS → dS uplift conjecture.

Non-Hermitian Casimir effect of magnons

There has been a growing interest in non-Hermitian quantum mechanics. The key concepts of quantum mechanics are quantum fluctuations. Quantum fluctuations of quantum fields confined in a finite-size system induce the zero-point energy shift. This quantum phenomenon, the Casimir effect, is one of the most striking phenomena of quantum mechanics in the sense that there are no classical analogs and has been attracting much attention beyond the hierarchy of energy scales, ranging from elementary particle physics to condensed matter physics, together with photonics. However, the non-Hermitian extension of the Casimir effect and the application to spintronics have not yet been investigated enough, although exploring energy sources and developing energy-efficient nanodevices are its central issues. Here we fill this gap. By developing a magnonic analog of the Casimir effect into non-Hermitian systems, we show that this non-Hermitian Casimir effect of magnons is enhanced as the Gilbert damping constant (i.e., the energy dissipation rate) increases. When the damping constant exceeds a critical value, the non-Hermitian Casimir effect of magnons exhibits an oscillating behavior, including a beating one, as a function of the film thickness and is characterized by the exceptional point. Our result suggests that energy dissipation serves as a key ingredient of Casimir engineering.

Role of the Casimir force in micro- and nanoelectromechanical pressure sensors

The Casimir force caused by the electromagnetic fluctuations is computed in the configurations of micro- and nanoelectromechanical pressure sensors using Si membranes and either Si or Au-coated Si substrates. It is shown that if, under the influence of external pressure, the membrane-substrate separation drops to below 100 nm, the Casimir force makes a profound effect on the sensor functioning. There exists the maximum value of external pressure depending on the sensor parameters such that it finds itself in a state of unstable equilibrium. For this and larger pressures, the Casimir force leads to a collapse of the sensor, which loses its functionality. For any smaller external pressures, there exist two equilibrium positions, one of which is unstable and another one is stable, at smaller and larger membrane-substrate separations, respectively. The latter can be safely used for the pressure measurements. Possible applications of the obtained results in the design of micro- and nanoelectromechanical pressure sensors of next generations with further decreased dimensions are discussed.

Casimir energy for Lorentz-violating scalar field with helical boundary condition in d spatial dimensions

Delving into spring-like helical configurations, such as DNA within our cells, motivates physicists to inquire about the effects of such structures in the realm of quantum field theory, specifically unraveling their manifestation of effectiveness in Casimir energy. To explore this, we initiated our investigation with the Casimir effect and proceeded to calculate the Casimir energy, along with its thermal and radiative corrections, for massive and massless Lorentz-violating scalar fields across (d+1)-dimensional spacetime. Adhering to the principle that the renormalization program should be consistent with the boundary conditions applied to the quantum fields was paramount. Accordingly, one-loop correction to the Casimir energy for both massive and massless scalar fields under helical boundary conditions by employing a position-dependent counterterm was performed. Our results, spanning across spatial dimensions, exhibited convergence and coherence with established physical grounds. Additionally, we presented the Casimir energy density using graphical plots for systems featuring time-like and space-like Lorentz violations across all spatial dimensions, followed by a comprehensive discussion of the obtained results.

Dimensional reduction formulae for spectral traces and Casimir energies

This short letter considers the case of acoustic scattering by several obstacles in Rd+r\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^{d+r}$$\\end{document} for r,d≥1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r,d \\ge 1$$\\end{document} of the form Ω×Rr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega \ imes \\mathbb {R}^r$$\\end{document}, where Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega $$\\end{document} is a smooth bounded domain in Rd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^d$$\\end{document}. As a main result, a von Neumann trace formula for the relative trace is obtained in this setting. As a special case, we obtain a dimensional reduction formula for the Casimir energy for the massive and massless scalar fields in this configuration Ω×Rr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega \ imes \\mathbb {R}^r$$\\end{document} per unit volume in Rr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^r$$\\end{document}.

Magnetic-field tuning of the Casimir force

Magnetic-field tuning of the Casimir force

High-temperature modifications of charged Casimir wormholes

In this work, we extend the investigation of the consequences of thermal fluctuations on the Casimir effect within the context of a traversable wormhole, recently proposed by Garattini & Faizal, arXiv:2403.15174 [gr-qc], subject to charge contributions. Specifically, we focus on scenarios where the plates exhibit both constant and radial variations. In our analysis, we initially concentrate on the high temperature approximation, considering solely the influence of charge on the thermal Casimir wormholes. Additionally, upon incorporating Generalized Uncertainty Principle (GUP) corrections to the Casimir energy, we obtain a new class of wormhole solutions. Notably, we establish that the flare-out condition remains consistently satisfied. Intriguingly, our findings reveal that both the charge and GUP contributions serve to further enlarge the throat's size in the radial variation.

Quantum field theory at finite temperature for 3D periodic backgrounds

The one-loop quantum corrections to the internal energy of some lattices due to the quantum fluctuations of the scalar field of phonons are studied. The band spectrum of the lattice is characterised in terms of the scattering data, allowing to compute the quantum vacuum interaction energy between nodes at zero temperature, as well as the total Helmholtz free energy, the entropy, and the Casimir pressure between nodes at finite non-zero temperature. Some examples of periodic potentials built from the repetition in one of the three spatial dimensions of the same punctual or compact supported potential are addressed: a stack of parallel plates constructed by positioning δδ′ -functions at the lattice nodes, and an ‘upside-down tiled roof’ of parallel two-dimensional Pöschl–Teller wells centred at the nodes. They will be called generalised Dirac comb and Pöschl–Teller comb, respectively. Positive one-loop quantum corrections to the entropy appear for both combs at non-zero temperatures. Moreover, the Casimir force between the lattice nodes is always repulsive for both chains when non-trivial temperatures are considered, implying that the primitive cell increases its size due to the quantum interaction of the phonon field.

Switching the sign of the Casimir force between two perfect electromagnetic conductor spheres

Switching the sign of the Casimir force between two perfect electromagnetic conductor spheres

First- and Second-Order Forces in the Asymmetric Dynamical Casimir Effect for a Single δ − δ′ Mirror

Here, we consider an asymmetric δ−δ′ mirror undergoing time-dependent interactions with a massless scalar field in 1 + 1 dimensions. Using fluctuation-dissipation theory for a mirror in vacuum, we compute the force on a moving δ−δ′ mirror with time-dependent material properties. We investigate the first-order forces arising from the two distinct fluctuation sources and calculate the linear susceptibility in each case. We then plot the resulting forces. At the second order, we also find the independent contributions to the total force as well as the force that arises from the interference phenomena between the two fluctuation sources.

Gauge field fluctuation corrected QED3 effective action by fermionic particle-vortex duality

We present a non-perturbative framework for incorporating gauge field fluctuations into effective actions of QED3 in the infrared using fermionic particle-vortex duality. This approach is demonstrated through the applications to models containing N species of 2-component Dirac fermions in solvable and interpretable electromagnetic backgrounds, focusing on N = 1 or 2. For the N = 1 model, we establish a correspondence between fermion Casimir energy at finite density and the magnetic Euler-Heisenberg Lagrangian, and further evaluate the corrections to their amplitudes. This predicts amplification of charge susceptibility and reduction of magnetic permeability. We additionally provide physical interpretations for each component of our calculation and offer alternative derivations based on energy density measurements in different characteristic lengths. For N = 2, we show that magnetic catalysis is erased in a U(1) × U(1) QED3, indicating no breakdown of chiral symmetry. Reasoning is offered based on the properties of the lowest Landau level wave functions.

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.