Casimir Polder Research Articles

Casimir Forces in CFT with Defects and Boundaries

We investigate the quantum forces occurring between the defects and/or boundaries of a conformal field theory (CFT). We propose to model imperfect defects and boundaries as localized relevant double-trace operators that deform the CFT. Our focus is on pointlike and codimension-one planar defects. In the case of two parallel membranes, we point out that the CFT 2-point function tends to get confined and develops a tower of resonances with a constant decay rate when the operator dimension approaches the free field dimension. Using a functional formalism, we compute the quantum forces induced by the CFT between a variety of configurations of pointlike defects, infinite plates and membranes. Consistency arguments imply that these quantum forces are attractive at any distance. Forces of the Casimir–Polder type appear in the UV (ultraviolet), while forces of the Casimir type appear in the IR (infrared), in which case the CFT gets repelled from the defects. Most of the forces behave as a non-integer power of the separation, controlled by the dimension of the double-trace deformation. In the Casimir regime of the membrane–membrane configuration, the quantum pressure behaves universally as 1/ℓd; however, information about the double-trace nature of the defects still remains encoded in the strength of the pressure.

Nonequilibrium Casimir–Polder Force between Nanoparticles and Graphene-Coated Silica Plate: Combined Effect of the Chemical Potential and Mass Gap

The Casimir–Polder force between spherical nanoparticles and a graphene-coated silica plate is investigated in situations out of thermal equilibrium, i.e., with broken time-reversal symmetry. The response of the graphene coating to the electromagnetic field is described on the basis of first principles of quantum electrodynamics at nonzero temperature using the formalism of the polarization tensor in the framework of the Dirac model. The nonequilibrium Casimir–Polder force is calculated as a function of the mass-gap parameter, the chemical potential of graphene, and the temperature of the graphene-coated plate, which can be both higher or lower than that of the environment. It is shown that the force value increases with the increasing chemical potential, and this increase is more pronounced when the temperature of a graphene-coated plate is lower than that of the environment. The nonequilibrium force also increases with increasing temperature of the graphene-coated plate. This increase is larger when the plate is hotter than the environment. The effect is revealed that the combined impact of the chemical potential, μ, and mass gap, Δ, of the graphene coating depends on the relationship between Δ and 2μ. If 2μ>Δ, the magnitude of the nonequilibrium force between nanoparticles and a cooled graphene-coated plate becomes much larger than for a graphene coating with μ=0. The physical reasons explaining this effect are elucidated. Possible applications of the obtained results are discussed.

Neutrino mass and nature through its mediation in atomic clock interference

The absolute mass of neutrinos and their nature are presently unknown. Aggregate matter has a coherent weak charge leading to a repulsive interaction mediated by a neutrino pair. The virtual neutrinos are non-relativistic at micron distances, giving a distinct behavior for Dirac versus Majorana mass terms. This effective potential allows for the disentanglement of the Dirac or Majorana nature of the neutrino via magnitude and distance dependence. We propose an experiment to search for this potential based on the concept that the density-dependent interaction of an atomic probe with a material source in one arm of an atomic clock interferometer generates a differential phase. The appropriate geometry of the device is selected using the saturation of the weak potential as a guide. The proposed experiment has the added benefit of being sensitive to gravity at micron distances. A strategy to suppress the competing Casimir–Polder interaction, depending on the electronic structure of the material source, as well as a way to compensate the gravitational interaction in the two arms of the interferometer is discussed.

Casimir Physics beyond the Proximity Force Approximation: The Derivative Expansion

We review the derivative expansion (DE) method in Casimir physics, an approach which extends the proximity force approximation (PFA). After introducing and motivating the DE in contexts other than the Casimir effect, we present different examples which correspond to that realm. We focus on different particular geometries, boundary conditions, types of fields, and quantum and thermal fluctuations. Besides providing various examples where the method can be applied, we discuss a concrete example for which the DE cannot be applied; namely, the case of perfect Neumann conditions in 2+1 dimensions. By the same example, we show how a more realistic type of boundary condition circumvents the problem. We also comment on the application of the DE to the Casimir–Polder interaction which provides a broader perspective on particle–surface interactions.

Correction: Klimchitskaya et al. Nonequilibrium Casimir–Polder Interaction between Nanoparticles and Substrates Coated with Gapped Graphene. Symmetry 2023, 15, 1580

The authors wish to make the following corrections in their paper [...]

Surface Scattering Expansion of the Casimir–Polder Interaction for Magneto-Dielectric Bodies: Convergence Properties for Insulators, Conductors, and Semiconductors

Fluctuation-induced forces are a hallmark of the interplay between fluctuations and geometry. We recently proved the existence of a multi-parametric family of exact representations of Casimir and Casimir–Polder interactions between bodies of arbitrary shape and material composition, admitting a multiple scattering expansion (MSE) as a sequence of inter-body and intra-body multiple wave scatterings. The approach requires no knowledge of the scattering amplitude (T-matrix) of the bodies. In this paper, we investigate the convergence properties of the MSE for the Casimir–Polder interaction of a polarizable particle with a macroscopic body. We consider representative materials from different classes, such as insulators, conductors, and semiconductors. Using a sphere and a cylinder as benchmarks, we demonstrate that the MSE can be used to efficiently and accurately compute the Casimir–Polder interaction for bodies with smooth surfaces.

Photonic Crystal Surface Modes for Trapping and Waveguiding of Ultracold Atoms.

The design of a photonic system for the trapping and waveguiding of ultracold atoms far above a dielectric surface is proposed and analyzed. The system consists of an optical rib waveguide deposited on a planar one-dimensional photonic crystal, which sustains two wavelengths of photonic crystal surface modes tuned in the red and blue sides relative to the atomic transition of the neutral atom. The addition of a third blue-tuned wavelength to the system allows the neutral atoms to be stabilized in the lateral dimension above the rib waveguide. Trapping atoms at relatively large distances, more than 600 nm above the dielectric surface, allows to reduce the influence of Casimir-Polder forces in this system. The detailed design methodology and specifications of the photonic system are provided. The presented design can be employed in atomic chips and quantum sensors.

Electromagnetic Casimir–Polder Interaction for a Conducting Cone

Using the formulation of the electromagnetic Green’s function of a perfectly conducting cone in terms of analytically continued angular momentum, we compute the Casimir–Polder interaction energy of a cone with a polarizable particle. We introduce this formalism by first reviewing the analogous approach for a perfectly conducting wedge, and then demonstrate the calculation through numerical evaluation of the resulting integrals.

Excitation of 87Rb Rydberg atoms to nS and nD states (n≤68) via an optical nanofiber

Cold Rydberg atoms are a promising platform for quantum technologies, and combining them with optical waveguides has the potential to create robust quantum information devices. Here, we experimentally observe the excitation of cold rubidium atoms to a large range of Rydberg S and D states through interaction with the evanescent field of an optical nanofiber. We develop a theoretical model to account for experimental phenomena present such as the AC Stark shifts and the Casimir–Polder interaction. This work strengthens the knowledge of Rydberg atom interactions with optical nanofibers and is a critical step toward the implementation of all-fiber quantum networks and waveguide quantum electrodynamics (QED) systems using highly excited atoms.

Excitation of 87Rb Rydberg atoms to nS and nD states (n≤68) via an optical nanofiber

Cold Rydberg atoms are a promising platform for quantum technologies, and combining them with optical waveguides has the potential to create robust quantum information devices. Here, we experimentally observe the excitation of cold rubidium atoms to a large range of Rydberg S and D states through interaction with the evanescent field of an optical nanofiber. We develop a theoretical model to account for experimental phenomena present such as the AC Stark shifts and the Casimir–Polder interaction. This work strengthens the knowledge of Rydberg atom interactions with optical nanofibers and is a critical step toward the implementation of all-fiber quantum networks and waveguide quantum electrodynamics (QED) systems using highly excited atoms.

Large-Separation Behavior of the Casimir–Polder Force from Real Graphene Sheet Deposited on a Dielectric Substrate

The Casimir–Polder force between atoms or nanoparticles and graphene-coated dielectric substrates is investigated in the region of large separations. Graphene coating with any value of the energy gap and chemical potential is described in the framework of the Dirac model using the formalism of the polarization tensor. It is shown that the Casimir–Polder force from a graphene-coated substrate reaches the limit of large separations at approximately 5.6 μm distance between an atom or a nanoparticle and graphene coating independently of the values of the energy gap and chemical potential. According to our results, however, the classical limit, where the Casimir–Polder force no longer depends on the Planck constant and the speed of light, may be attained at much larger separations depending on the values of the energy gap and chemical potential. In addition, we have found a simple analytic expression for the Casimir–Polder force from a graphene-coated substrate at large separations and determined the region of its applicability. It is demonstrated that the asymptotic results for the large-separation Casimir–Polder force from a graphene-coated substrate are in better agreement with the results of numerical computations for the graphene sheets with larger chemical potential and smaller energy gap. Possible applications of the obtained results in nanotechnology and bioelectronics are discussed.

Nonequilibrium Casimir–Polder Interaction between Nanoparticles and Substrates Coated with Gapped Graphene

The out-of-thermal-equilibrium Casimir–Polder force between nanoparticles and dielectric substrates coated with gapped graphene is considered in the framework of the Dirac model using the formalism of the polarization tensor. This is an example of physical phenomena violating the time-reversal symmetry. After presenting the main points of the used formalism, we calculate two contributions to the Casimir–Polder force acting on a nanoparticle on the source side of a fused silica glass substrate coated with gapped graphene, which is either cooler or hotter than the environment. The total nonequilibrium force magnitudes are computed as a function of separation for different values of the energy gap and compared with those from an uncoated plate and with the equilibrium force in the presence of graphene coating. According to our results, the presence of a substrate increases the magnitude of the nonequlibrium force. The force magnitude becomes larger with higher and smaller with lower temperature of the graphene-coated substrate as compared to the equilibrium force at the environmental temperature. It is shown that, with increasing energy gap, the magnitude of the nonequilibrium force becomes smaller, and the graphene coating makes a lesser impact on the force acting on a nanoparticle from the uncoated substrate. Possible applications of the obtained results are discussed.

Casimir–Polder Force on Atoms or Nanoparticles from Gapped and Doped Graphene: Asymptotic Behavior at Large Separations

The Casimir–Polder force acting on atoms and nanoparticles spaced at large separations from real graphene sheets possessing some energy gaps and chemical potentials is investigated in the framework of the Lifshitz theory. The reflection coefficients expressed via the polarization tensor of graphene, found based on the first principles of thermal quantum field theory, are used. It is shown that for graphene the separation distances, starting from which the zero-frequency term of the Lifshitz formula contributes more than 99% of the total Casimir–Polder force, are less than the standard thermal length. According to our results, however, the classical limit for graphene, where the force becomes independent of the Planck constant, may be reached at much larger separations than the limit of the large separations determined by the zero-frequency term of the Lifshitz formula, depending on the values of the energy gap and chemical potential. The analytic asymptotic expressions for the zero-frequency term of the Lifshitz formula at large separations are derived. These asymptotic expressions agree up to 1% with the results of numerical computations starting from some separation distances that increase with increasing energy gaps and decrease with increasing chemical potentials. The possible applications of the obtained results are discussed.

Casimir-Polder interactions of S -state Rydberg atoms with graphene

We investigate the thermal Casimir-Polder (CP) potential of $^{87}\mathrm{Rb}$ atoms in Rydberg $nS$-states near single- and double-layer graphene, and briefly look into the lifetimes near graphene-hexagonal boron nitride (hBN) multilayered structures. The dependence of the CP potential on parameters such as atom-surface distance, temperature, principal quantum number $n$, and graphene Fermi energy are explored. Through large-scale numerical simulations, we show that, in the nonretarded regime, the CP potential is dominated by the nonresonant and evanescent-wave terms which are monotonic, and that, in the retarded regime, the CP potential exhibits spatial oscillations. We identify that the most important contributions to the resonant component of the CP potential come from the $nS\text{\ensuremath{-}}nP$ and $nS\text{\ensuremath{-}}(n\ensuremath{-}1)P$ transitions. Scaling of the CP potential as a function of the principal quantum number and temperature is obtained. A heterostructure comprising hexagonal boron nitride layers sandwiched between two graphene layers is also studied. When the boron nitride layer is sufficiently thin, the CP potential can be weakened by changing the Fermi energy of the top graphene layer. Our study provides insights for understanding and controlling CP potentials experienced by Rydberg atoms near single- and multilayer graphene-based van der Waals heterostructures.

Quantum thermal field fluctuation induced corrections to the interaction between two ground-state atoms

We generalize the formalism proposed by Dalibard, Dupont-Roc, and Cohen-Tannoudji (the DDC formalism) in the fourth order for two atoms in interaction with scalar fields in vacuum to a thermal bath at finite temperature T, and then calculate the interatomic interaction energy of two ground-state atoms separately in terms of the contributions of thermal fluctuations and the radiation reaction of the atoms and analyze in detail the thermal corrections to the van der Waals and Casimir–Polder interactions. We discover a particular region, i.e. with L, β and λ denoting the interatomic separation, the wavelength of thermal photons and the transition wavelength of the atoms respectively, where the thermal corrections remarkably render the van der Waals force, which is usually attractive, repulsive, leading to an interesting crossover phenomenon of the interatomic interaction from attractive to repulsive as the temperature increases. We also find that the thermal corrections cause significant changes to the Casimir–Polder force when the temperature is sufficiently high, resulting in an attractive force proportional to TL −3 in the λ ≪ β ≪ L region, and a force that can be either attractive or repulsive and even vanishing in the β ≪ λ ≪ L region depending on the interatomic separation.

The nature of nothing: exploring the quantum vacuum in microgravity

In this paper we discuss a number of investigations of the quantum vacuum that could potentially take advantage of a microgravity environment. Ultra-cold atoms are exquisite sensors of the electro-magnetic vacuum, and microgravity aids our ability to precisely position and control them in the vicinity of surfaces and cavity modes. Measurements of Casimir–Polder force, Anderson localization and the possibilities for confining atoms with vacuum forces are amongst the intriguing possibilities discussed.

An excited atom interacting with a Chern insulator: toward a far-field resonant Casimir–Polder repulsion

We consider the resonant Casimir-Polder interaction of an excited alkali-type atom which has a single (electric dipole) transition with a Chern insulator. The Chern insulator has a nonzero, time reversal symmetry breaking Hall conductance, leading to an additional contribution to the resonant Casimir-Polder interaction which depends on the coupling between the Hall conductance and the circular polarization state of the atomic transition. We find that the resonant Casimir-Polder shift can be significantly enhanced for de-excitation frequencies near values associated with the van Hove singularities of the Chern insulator. Furthermore, we find that the resonant Casimir-Polder force can become monotonically decaying and repulsive for a relatively large atom-surface distance, if the atomic dipole transition is right circularly polarized and the Chern number of the Chern insulator is $-1$ or the atomic dipole transition is left circularly polarized and the Chern number is $1$.

Indirect detection of Cosmological Constant from interacting open quantum system

We study the indirect detection of Cosmological Constant from an open quantum system of interacting spins, weakly interacting with a thermal bath, a massless scalar field minimally coupled with the static de Sitter background, by computing the spectroscopic shifts. By assuming pairwise interaction between spins, we construct states using a generalization of the superposition principle. The corresponding spectroscopic shifts, caused by the effective Hamiltonian of the system due to Casimir Polder interaction, are seen to play a crucial role in predicting a very tiny value of the Cosmological Constant, in the static patch of de Sitter space, which is consistent with the observed value from the Planck measurements of the cosmic microwave background (CMB) anisotropies.

Dynamical Casimir–Polder force in a semi-infinite rectangle waveguide

In this paper, we study the dynamical Casimir–Polder force between an ensemble of identical two-level atoms and the wall of a rectangle waveguide with semi-infinite length. With the presence of both the rotating wave and counter rotating wave terms in the light–matter interaction Hamiltonian, we utilize the perturbation theory to solve the Heisenberg equation. Up to the seconder of coupling strength, we obtain the energy shift analytically and the Casimir–Polder force numerically. Our result shows that the dynamical behavior of the Casimir force is closely connected to the photon propagation in the waveguide. Therefore, we hope this work will stimulate the studies about the quantum effect in waveguide scenario.

Dynamical Casimir-Polder force between a two-level atom with different initial states and a dissipative cavity

In this paper, a model of interaction between a two-level atom and a dissipative cavity is considered. The dynamical Casimir–Polder forces between the atom and the cavity wall in different initial states are discussed and analyzed. The quasimode theory is used to describe the electromagnetic field. The results show that the magnitude and properties of the dynamical Casimir–Polder force are different in different initial states of atoms. By adjusting the initial state of the atom properly, the dynamical Casimir–Polder force can also reach zero. This conclusion has important reference significance for the application of quantum information.