Interactions between objects can be classified as fundamental or emergent. Fundamental interactions are either extremely short-range or decay inversely with the separation distance, such as the Coulomb potential between charges or the gravitational attraction between masses. In contrast, emergent quantum van der Waals (vdW) and Casimir interactions decay considerably faster ($R^{-6}$ or $R^{-7}$) with distance $R$. Here we apply perturbative quantum electrodynamics (QED) to a many-body (MB) system of atoms modeled as charged harmonic oscillators, and reveal a persistent inverse-distance MB-QED interaction stemming from the coupling between virtual photons and molecular plasmons in the non-retarded regime. This interaction, scaling with the third power of the fine-structure constant, is reminiscent of the Lamb shift for a single atom. Although weaker than vdW forces, this MB-QED $R^{-1}$ interaction may substantially surpass gravitational attraction in future experiments probing quantum gravity at microscopic scales.
Interactions between objects can be classified as fundamental or emergent. Fundamental interactions are either extremely short-range or decay inversely with the separation distance, such as the Coulomb potential between charges or the gravitational attraction between masses. In contrast, emergent quantum van der Waals (vdW) and Casimir interactions decay considerably faster (R−6 or R−7) with distance R. Here we apply perturbative quantum electrodynamics (QED) to a many-body (MB) system of atoms modeled as charged harmonic oscillators, and reveal a persistent inverse-distance MB-QED interaction stemming from the coupling between virtual photons and molecular plasmons in the non-retarded regime. This interaction, scaling with the third power of the fine-structure constant, is reminiscent of the Lamb shift for a single atom. Although weaker than vdW forces, this MB-QED R−1 interaction may substantially surpass gravitational attraction in future experiments probing quantum gravity at microscopic scales.
Conventionally, dispersion forces mediated by quantum vacuum fluctuations are known to exhibit universal distance scalings, with retardation typically leading to a faster decay of the interaction. Here, we show that this expectation fails for intrinsically discrete systems. Using the microscopic scattering approach, we study the Casimir-Polder interaction between two atomic arrays, and uncover an unconventional distance scaling in which the force crosses over from a faster decay at short separations to a slower decay in the retarded regime. This behavior originates from the discrete lattice structure and can be consistently understood within the scattering picture. Extending our analysis to Rydberg atomic arrays, we predict an even stronger deviation from conventional scaling and propose an experimentally feasible scheme for direct measurement. Our results provide a new platform for exploring dispersion forces beyond the continuum limit.
The structure and stability of atomic and molecular systems with van der Waals (vdW) bonding are often determined by the interplay between attractive dispersion interactions and repulsive interactions caused by electron confinement. Arising due to different mechanisms---electron correlation for dispersion and the Pauli exclusion principle for exchange repulsion---these interactions do not appear to have a straightforward connection. In this paper, we use a coarse-grained approach for evaluating the exchange energy for two coupled quantum Drude oscillators and investigate the mutual compensation of the attractive and repulsive forces at the equilibrium distance within the multipole expansion of the Coulomb potential. This compensation yields a compact formula relating the vdW radius of an atom to its multipole polarizabilities, ${R}_{\mathrm{vdW}}={A}_{l}^{\phantom{\rule{0.16em}{0ex}}}\phantom{\rule{0.16em}{0ex}}{\ensuremath{\alpha}}_{l}^{2/7(l+1)}$, where l is the multipole rank and Al is a conversion factor. Such a relation is compelling because it connects an electronic property of an isolated atom (atomic polarizability) with an equilibrium distance in a dimer composed of two closed-shell atoms. We assess the accuracy of the revealed formula for noble-gas, alkaline-earth, and alkali atoms and show that Al can be assumed to be universal constants. Besides a seamless definition of vdW radii, the proposed relation can also be used for the efficient determination of atomic multipole polarizabilities solely based on the corresponding dipole polarizability and the vdW radius. Finally, our work provides a basis for the construction of efficient and minimally empirical interatomic potentials by combining multipolar interatomic exchange and dispersion forces on an equal footing.
) between closely spaced atoms and molecules are related to real photon and virtual photon exchange between them and decrease in the near field connected with the characteristic Coulombic dipole field law. The control and modification of this marked scaling with distance have become a long-standing theme in quantum engineering since dipole-dipole interactions govern Van der Waals forces, collective Lamb shifts, atom blockade effects, and Förster resonance energy transfer. We show that metamaterials can fundamentally modify these interactions despite large physical separation between interacting quantum emitters. We demonstrate a two orders of magnitude increase in the near-field resonant dipole-dipole interactions at intermediate field distances (10 times the near field) and observe the distance scaling law consistent with a super-Coulombic interaction theory curtailed only by absorption and finite size effects of the metamaterial constituents. We develop a first-principles numerical approach of many-body dipole-dipole interactions in metamaterials to confirm our theoretical predictions and experimental observations. In marked distinction to existing approaches of engineering radiative interactions, our work paves the way for controlling long-range dipole-dipole interactions using hyperbolic metamaterials and natural hyperbolic two-dimensional materials.
In the field of cavity quantum materials, vacuum fluctuations of optical cavities are used for modifying ground-state properties of quantum materials without external driving. Here, one example is the van der Waals (vdW)/dispersion interaction in layered 2D vdW materials, where non-additive long-range correlations can dominate the interlayer binding. While cavity-induced changes of such interactions have been predicted and described using ab initio methods for molecular systems, no efficient description exists yet for extended materials. In this Letter, we close this gap by introducing a periodic formulation of the photon many-body dispersion (pMBD) functional within quantum electrodynamical density-functional theory (QEDFT). Applying this method with efficient q-point sampling to bilayer hBN and graphene, we predict cavity-modified stacking, increased equilibrium interlayer distances, and softened layer breathing modes with increasing light-matter coupling strength. Our results establish cavity vacuum fluctuations as a tuning knob for the structural properties of vdW materials.
Over the past ten years, our group has investigated the effects of confinement on atoms inside metallic micron–sized cavities in order to elucidate some basic phenomena in the field of cavity quantum electrodynamics (QED). The first of these was the inhibition of spontaneous emission from an atom inside a cavity. This was followed by a laser spectroscopic measurement of the van der Waals interaction between a single Rydberg atom and a gold cavity, which showed that a simple electrostatic model of the atom–cavity interaction is correct when the cavity is small enough. More recently, the retarded Casimir–Polder force was measured between a ground state sodium atom and a large cavity, demonstrating that the van der Waals potential fails at long enough range and that the vacuum fluctuations of the field then have an important role in the interaction of the atom with the cavity. Our group is now pushing forward these investigations to study cavities whose walls have losses and dispersion, where the theory of cavity QED is significantly more complicated. With real surfaces, we have to deal with the complex dielectric response ε(ω) of the material, which exhibits frequency–dependent absorption and dispersion. One particularly interesting case is when a downward transition in the atom is resonant with an excitation of the cavity walls. This opens a new branch for the atomic decay: as an alternative to creating a photon within the space surrounded by the cavity walls the atomic decay can now create an electromagnetic excitation of the walls themselves. Another novel feature of our experiments is that the Bohr frequencies of the atom are close to the kT/h, where T is room temperature. We therefore expect to be able to measure effects associated with QED at finite temperature; in other words, to study how the blackbody radiation affects our experiments. By conducting experiments with real surfaces, we hope to elucidate and perhaps simplify the theoretical models used to describe these systems.
We have investigated, by separating the contributions from thermal fluctuations (tf) and the radiation reaction (rr), the gravitational Casimir-Polder interaction between a gravitationally polarizable two-level object and an infinite gravitational Dirichlet boundary in a thermal bath at a temperature T. The results indicate that the rr-contribution to the interaction potential is independent of the temperature, whereas the tf-contribution is generally governed by a nontrivial interplay between the thermal corrections and the polarization effect. Here, the object-to-boundary distance, the characteristic transition wavelength of the object and the thermal wavelength of gravitons are denoted by L, λ and β, respectively. In contrast to the vacuum case, where the interaction potential scales as L−5 for L≪λ and L−6 for L≫λ, corresponding to an always repulsive force, qualitatively new behaviors emerge at high temperatures. Particularly, when 4βλ3≪L≪λ and the object is polarizable within the plane perpendicular to the boundary, a novel scaling of TL−1 arises; when βλ≪L≪λ and the object is polarizable along the vertical-to-boundary axis, the interaction force becomes surprisingly attractive. At extremely high temperatures and large distances, i.e. when β≪λ≪L, the potential oscillates with the distance L and thus an attractive or repulsive and even vanishing force can be resulted, depending on the exact values of L. Our work demonstrates that thermal gravitons can act as an active control mechanism for quantum gravitational interactions, and temperature, polarization configuration, and object-to-boundary distance jointly determine the magnitude, scaling law, and even the attractive or repulsive nature of the interaction force.