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.
A Bose-Einstein condensate may be prepared in a highly elongated harmonic trap with negligible interatomic interactions using a Feshbach resonance. If a strong repulsive interatomic interaction is switched on and the axial trap is removed to let the condensate evolve freely in the axial direction, a time dependent quantum interference pattern takes place in the short time (Thomas-Fermi) regime, in which the number of peaks of the momentum distribution increases one by one, whereas the spatial density barely changes.
Mainly on nano-scale, but maybe not exclusively, it can be imagined a spontaneous charge disjunction inside certain media due to the fluctuations, collisions, wall effects, radiation or/and other presently unknown interactions. The repulsive Casimir-Lifshitz force may be also a good candidate as a source of this kind of phenomenon. To cover this assumption mathematically an additional term should appear in the Maxwell equations. As a consequence of this term, similar Klein-Gordon equations with a negative mass term will be obtained for the electric and magnetic fields. These equations may have…
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., $\sqrt[4]{λ^3β}\ll L\ll λ$ with $L$, $β$ and $λ$ de…
We explore the interplay between tunneling and interatomic interactions in the dynamics of a bosonic Josephson junction. We tune the scattering length of an atomic $^{39}$K Bose-Einstein condensate confined in a double-well trap to investigate regimes inaccessible to other superconducting or superfluid systems. In the limit of small-amplitude oscillations, we study the transition from Rabi to plasma oscillations by crossing over from attractive to repulsive interatomic interactions. We observe a critical slowing down in the oscillation frequency by increasing the strength of an attractive inte…
We investigate the behavior of two quantum emitters (two-level atoms) embedded in a linear waveguide, in a quasi-one-dimensional configuration. Since the atoms can emit, absorb and reflect radiation, the pair can spontaneously relax towards an entangled bound state, under conditions in which a single atom would instead decay. We analyze the properties of these bound states, which occur for resonant values of the interatomic distance, and discuss their relevance with respect to entanglement generation. The stability of such states close to the resonance is studied, as well as the properties of …
We study the Casimir effect in axion electrodynamics. A finite $θ$-term affects the energy dispersion relation of photon if $θ$ is time and/or space dependent. We focus on a special case with linearly inhomogeneous $θ$ along the $z$-axis. Then we demonstrate that the Casimir force between two parallel plates perpendicular to the $z$-axis can be either attractive or repulsive, dependent on the gradient of $θ$. We call this repulsive component in the Casimir force induced by inhomogeneous $θ$ the anomalous Casimir effect.
An excited two-atom system can decay via different competing relaxation processes. If the excess energy is sufficiently high the system may not only relax via spontaneous emission but can also undergo interatomic Coulombic decay (ICD) or even Auger decay. We provide analytical expressions for the rates by including them into the same quantum optical framework on the basis of macroscopic quantum electrodynamics. By comparing the rates in free space we derive the atomic properties determining which decay channel dominates the relaxation. We show that by modifying the excitation propagation of th…
We analytically investigate the ground-state properties of two-component Bose-Einstein condensates with few ⁸⁷Rb atoms inside a high-quality cavity quantum electrodynamics. In the SU(2) representation for atom, this quantum system can be realized a generalized Dicke model with a quadratic term arising from the interatomic interactions, which can be controlled experimentally by Feshbach resonance technique. Moreover, this weak interspecies interaction can give rise to an important zero-temperature quantum phase transition from the normal to the superradiant phases, where the atomic …
Manipulating Excitation Dynamics in Structured Waveguide Quantum Electrodynamics
Molecular Science and Technology Program, Taiwan International Graduate Program, Academia Sinica（台湾国际研究生学院分子科学与技术项目，中央研究院）；Department of Physics, National Central University（国立中央大学物理系）；Institute of Atomic and Molecular Sciences, Academia Sinica（中央研究院原子与分子科学研究所）；Department of Physics, National Taiwan University（国立台湾大学物理系）；Physics Division, National Center for Theoretical Sciences（国家理论科学中心物理组）
The Casimir force between two parallel thick plates, one perfectly dielectric, the other purely magnetic, has been calculated long ago by Boyer [T. H. Boyer, Phys. Rev. A {\bf 9}, 2078 (1974)]. Its most characteristic property is that it is repulsive. The problem is actually delicate and counterintuitive, since it implies, for instance, that in the boundary layer of the electric plate the square $E^2$ of the electric field becomes a negative quantity. In the present paper we analyze the problem by first considering the simple harmonic oscillator model introduced by us earlier [J. S. Høye {\it …
Identification and understanding of the evolution of interference patterns in two-particle momentum correlations as a function of the strength of interatomic interactions are important in explorations of the nature of quantum states of trapped particles. Together with the analysis of two-particle spatial correlations, they offer the prospect of uncovering fundamental symmetries and structure of correlated many-body states, as well as opening vistas into potential control and utilization of correlated quantum states as quantum information resources. With the use of the second-order density matr…
We consider inter-atomic forces due to resonant dipole-dipole interactions within a dimer of highly excited Rydberg atoms, embedded in an ultra-cold gas. These forces rely on a coherent superposition of two-atom electronic states, which is destroyed by continuous monitoring of the dimer state through a detection scheme utilizing controllable interactions with the background gas atoms. We show that this intrinsic decoherence of the molecular energy surface can gradually deteriorate a repulsive dimer state, causing a mixing of attractive and repulsive character. For sufficiently strong decoheren…
We investigate the mean-field phase diagram of the Bose-Hubbard model with infinite-range interactions in two dimensions. This model describes ultracold bosonic atoms confined by a two-dimensional optical lattice and dispersively coupled to a cavity mode with the same wavelength as the lattice. We determine the ground-state phase diagram for a grand-canonical ensemble by means of analytical and numerical methods. Our results mostly agree with the ones reported in Dogra et al. [PRA 94, 023632 (2016)], and have a remarkable qualitative agreement with the quantum Monte Carlo phase diagrams of Flo…
We investigate the many-body state and the static and the dynamic behaviour of the pair-correlation function of a Bose-Einstein condensate with a finite atom number, which is confined in a quasi-one-dimensional toroidal/annular potential, both for repulsive, and for attractive interactions. We link the dynamic pair-correlation function that we evaluate with the problem of quantum time crystals. For weak repulsive interatomic interactions and a finite number of atoms the pair-correlation function shows a periodic temporal behaviour, which disappears in the limit of a large atom number, in agree…
The retarded dispersion interaction (Casimir interaction) between two dilute dielectric media at high temperatures is considered. The excited atoms are taken into account. It is shown that the perturbation technique can not be applied to this problem due to the divergence of integrals. A non-perturbative approach based on kinetic Green functions is implemented. We consider interaction between two atoms (one of them is excited0 embedded in an absorbing dielectric medium. We take into account possible absorption of photons in the medium, which solves the problem of divergence. The force between …
We consider the influence of the inclusion of interatomic interactions on the delta-kicked accelerator model. Our analysis concerns in particular quantum accelerator modes, namely quantum ballistic transport near quantal resonances. The atomic interaction is modelled by a Gross-Pitaevskii cubic nonlinearity, and we address both attractive (focusing) and repulsive (defocusing) cases. The most remarkable effect is enhancement or damping of the accelerator modes, depending on the sign of the nonlinear parameter. We provide arguments showing that the effect persists beyond mean-field description, …
We theoretically explore manipulation of interactions between excited and ground state atoms at nanoscale separations by cavity quantum electrodynamics (CQED). We develop an adiabatic molecular dressed state formalism and show that it is possible to generate Fano-Feshbach resonances between ground and long-lived excited-state atoms inside a cavity. The resonances are shown to arise due to non-adiabatic coupling near a pseudo-crossing between the dressed state potentials. We illustrate our results with a model study using fermionic $^{171}$Yb atoms in a two-modal cavity. Our study is important …
We propose an approach for investigation of interaction of thin material films with quantum electrodynamic fields. Using main principles of quantum electrodynamics (locality, gauge invariance, renormalizability) we construct a single model for Casimir-like phenomena arising near the film boundary on distances much larger then Compton wavelength of the electron where fluctuations of Dirac fields are not essential. In this model the thin film is presented by a singular background field concentrated on a 2-dimensional surface. All properties of the film material are described by one dimensionless…
The parity-preserving $U(1)\times U(1)$ massless QED$_3$ is proposed as a pristine graphene-like planar quantum electrodynamics model. The spectrum content, the degrees of freedom, spin, masses and charges of the quasiparticles (electron-polaron, hole-polaron, photon and Néel quasiparticles) which emerge from the model are discussed. The four-fold broken degeneracy of the Landau levels, similar as the one experimentally observed in pristine graphene submitted to high applied external magnetic fields, is obtained. Furthermore, the model exhibits zero-energy Landau level indicating a kind of ano…
We consider the dispersion interaction between two ground-state hydrogen atoms, interacting with the quantum electromagnetic field in the vacuum state, in the presence of an external static electric field, both in the nonretarded and in the retarded Casimir-Polder regime. We show that the presence of the external field strongly modifies the dispersion interaction between the atoms, changing its space dependence. Moreover, we find that, for specific geometrical configurations of the two atoms with respect to the external field and/or the relative orientation of the fields acting on the two atom…
The transmission of an interacting Bose-Einstein condensate incident on a repulsive Gaussian barrier is investigated through numerical simulation. The dynamics associated with interatomic interactions are studied across a broad parameter range not previously explored. Effective 1D Gross-Pitaevskii equation (GPE) simulations are compared to classical Boltzmann-Vlasov equation (BVE) simulations in order to isolate purely coherent matterwave effects. Quantum tunneling is then defined as the portion of the GPE transmission not described by the classical BVE. An exponential dependence of transmissi…
By cyclic adiabatic change of two control parameters of an optical trap one can induce a circulating current of condensed bosons. The amount of particles that are transported per period depends on the "radius" of the cycle, and this dependence can be utilized in order to probe the interatomic interactions. For strong repulsive interaction the current can be regarded as arising from a sequence of Landau-Zener crossings. For weaker interaction one observes either gradual or coherent mega crossings, while for attractive interaction the particles are glued together and behave like a classical ball…
Cavity modification of material properties and phenomena is a novel research field largely motivated by the advances in strong light-matter interactions. Despite this progress, exact solutions for extended systems strongly coupled to the photon field are not available, and both theory and experiments rely mainly on finite-system models. Therefore a paradigmatic example of an exactly solvable extended system in a cavity becomes highly desireable. To fill this gap we revisit Sommerfeld's theory of the free electron gas in cavity quantum electrodynamics (QED). We solve this system analytically in…
We investigate interplay between external field and interatomic interaction and its applications to coherent control of quantum tunneling for two repulsive bosons confined in a high-frequency driven double well. A full solution of the system is generated analytically as a coherent non-Floquet state by using the Floquet states as a set of complete bases. It is demonstrated that the photon resonance of interaction leads to translation of the Floquet level-crossing points, and the non-resonant interaction causes avoided crossing of partial levels. In the non-Floquet states, the bosons beyond the …
Theory of Dispersion and Exchange Interactions Subjected to Surface Roughness in Application to Signal Transmission through a Nanoswitch
Central Astronomical Observatory at Pulkovo of the Russian Academy of Sciences（俄罗斯科学院普尔科沃中央天文台）；Peter the Great Saint Petersburg Polytechnic University（彼得大帝圣彼得堡理工大学）
The scattering between light and individual saturable quantum emitters can induce strong optical nonlinearities and correlations between individual light quanta. Typically, this leads to an effective attraction that can generate exotic bound states of photons, which form quantum mechanical precursors of optical solitons, as found in many optical media. Here, we study the propagation of light through an optical waveguide that is chirally coupled to three-level quantum emitters. We show that the additional laser-coupling to a third emitter state not only permits to control the properties of the …
Cavity quantum electrodynamics (QED) manipulates the coupling of light with matter, and allows for several emitters to couple coherently with one light mode. However, even in a many-body system, the light-matter coupling mechanism was so far restricted to one body processes. Leveraging cavity QED for the quantum simulation of complex, many-body systems has thus far relied on multi-photon processes, scaling down the light-matter interaction to the low energy and slow time scales of the many-body problem. Here we report on cavity QED experiments using molecular transitions in a strongly interact…
We discuss different physical effects related to the uniform acceleration of atoms in vacuum, in the framework of quantum electrodynamics. We first investigate the van der Waals/Casimir-Polder dispersion and resonance interactions between two uniformly accelerated atoms in vacuum. We show that the atomic acceleration significantly affects the van der Waals force, yielding a different scaling of the interaction with the interatomic distance and an explicit time dependence of the interaction energy. We argue how these results could allow for an indirect detection of the Unruh effect through disp…
