Self-dressing in classical and quantum electrodynamics

A short review is presented of the theory of dressed states in nonrelativistic QED, encompassing fully and partially dressed states in atomic physics. This leads to the concept of the reconstruction of the cloud of virtual photons and of self-dressing. Finally some recent results on the classical counterpart of self-dressing are discussed and a comparison is made with the QED case. Attention is drawn to open problems and future lines of research are briefly outlined.

Spontaneous emission of an atom in a dynamical photonic crystal

A structured environment such as a photonic crystal can strongly affect radiative properties of an atomic system, for example the spontaneous emission process. Recently there has been also an increasing interest on dynamical photonic crystal, that is photonic crystals whose dielectric properties change on time. We consider the spontaneous emission of an atom placed inside a photonic crystal with time-dependent properties (dynamical photonic crystal). We investigate the atomic spontaneous emission in two different regimes, weak and strong coupling, assuming a small, periodic and adiabatic perturbation of the crystal. In the weak coupling case, we analytically obtain the spontaneous emission …

Collective spontaneous emission of two entangled atoms near an oscillating mirror

We consider the cooperative spontaneous emission of a system of two identical atoms, interacting with the electromagnetic field in the vacuum state and in the presence of an oscillating mirror. We assume that the two atoms, one in the ground state and the other in the excited state, are prepared in a correlated (symmetric or antisymmetric) {\em Bell}-type state. We also suppose that the perfectly reflecting plate oscillates adiabatically, with the field modes satisfying the boundary conditions at the mirror surface at any given instant, so that the time-dependence of the interaction Hamiltonian is entirely enclosed in the instantaneous atoms-wall distance. Using time-dependent perturbation …

Nonlocal field correlations and dynamical Casimir-Polder forces between one excited- and two ground-state atoms

The problem of nonlocality in the dynamical three-body Casimir-Polder interaction between an initially excited and two ground-state atoms is considered. It is shown that the nonlocal spatial correlations of the field emitted by the excited atom during the initial part of its spontaneous decay may become manifest in the three-body interaction. The observability of this new phenomenon is discussed.

Harmonic oscillator model for the atom-surface Casimir-Polder interaction energy

In this paper we consider a quantum harmonic oscillator interacting with the electromagnetic radiation field in the presence of a boundary condition preserving the continuous spectrum of the field, such as an infinite perfectly conducting plate. Using an appropriate Bogoliubov-type transformation we can diagonalize exactly the Hamiltonian of our system in the continuum limit and obtain non-perturbative expressions for its ground-state energy. From the expressions found, the atom-wall Casimir-Polder interaction energy can be obtained, and well-know lowest-order results are recovered as a limiting case. Use and advantage of this method for dealing with other systems where perturbation theory …

Optomechanical Rydberg-atom excitation via dynamic Casimir-Polder coupling

We study the optomechanical coupling of a oscillating effective mirror with a Rydberg atomic gas, mediated by the dynamical atom-mirror Casimir-Polder force. This coupling may produce a near-field resonant atomic excitation whose probability scales as $\propto (d^2\;a\;n^4\;t)^2/z_0^8$, where $z_0$ is the average atom-surface distance, $d$ the atomic dipole moment, $a$ the mirror's effective oscillation amplitude, $n$ the initial principal quantum number, and $t$ the time. We propose an experimental configuration to realize this system with a cold atom gas trapped at a distance $\sim 2\cdot10 \, \mu$m from a semiconductor substrate, whose dielectric constant is periodically driven by an ext…

Dynamical Casimir-Polder force between an atom and a conducting wall

The time-dependent Casimir-Polder force arising during the time evolution of an initially bare two-level atom, interacting with the radiation field and placed near a perfectly conducting wall, is considered. Initially the electromagnetic field is supposed to be in the vacuum state and the atom in its ground state. The analytical expression of the force as a function of time and atom-wall distance, is evaluated from the the time-dependent atom-field interaction energy. Physical features and limits of validity of the results are discussed in detail.

Spectroscopy of Alkali Atoms in Solid Matrices of Rare Gases: Experimental Results and Theoretical Analysis

We present an experimental and theoretical investigation of the spectroscopy of dilute alkali atoms in a solid matrix of inert gases at cryogenic temperatures, specifically Rubidium atoms in a solid Argon or Neon matrix, and related aspects of the interaction energies between the alkali atoms and the atoms of the solid matrix. The system considered is relevant for matrix isolation spectroscopy, and it is at the basis of a recently proposed detector of cosmological axions, exploiting magnetic-type transitions between Zeeman sublevels of alkali atoms in a magnetic field, tuned to the axion mass, assumed in the meV range. Axions are one of the supposed constituents of the dark matter (DM) of t…

Reply to "Comment on 'Dispersion Interaction between Two Hydrogen Atoms in a Static Electric Field' "

In their Comment on our Letter Dispersion Interaction between Two Hydrogen Atoms in a Static Electric Field, P. P. Abrantes et al. address one of the main points discussed in our Letter, that is, the possibility to manipulate interatomic interactions through an external static electric field. In our Letter, we have shown that the interaction between two ground-state atoms can be significantly modified, exploiting an external static electric field, and even turned from attractive to repulsive, depending on the strength of the external field and the geometrical configu- ration. In their Comment, Abrantes et al. point out that it is the electrostatic contribution between the electric dipoles i…

Vacuum fluctuations and radiation reaction contributions to the resonance dipole-dipole interaction between two atoms near a reflecting boundary

We investigate the resonance dipole-dipole interaction energy between two identical atoms, one in the ground state and the other in the excited state, interacting with the electromagnetic field in the presence of a perfectly reflecting plane boundary. The atoms are prepared in a correlated (symmetric or anti-symmetric) Bell-type state. Following a procedure due to Dalibard et. al. [J. Dalibard et. al., J. Phys. (Paris) {\bf 43}, 1617 (1982); {\bf 45}, 637 (1984)], we separate the contributions of vacuum fluctuations and radiation reaction (source) field to the resonance interaction energy between the two atoms, and show that only the source field contributes to the interatomic interaction, …

Resonant Interaction Energy between Two Identical Atoms in a Photonic Crystal

We consider the resonant interaction energy between two identical atoms, one in an excited state and the other in the ground state, placed inside a photonic crystal. We consider two different models of a photonic crystal: a one-dimensional crystal and an isotropic three-dimensional crystal. The two atoms, having the same orientation of their transition dipole moment, are supposed prepared in their entangled symmetrical state and interacting with the quantum electromagnetic field in the multipolar coupling scheme. We consider both the case of an atomic transition frequency outside the photonic band gap and the case of a transition frequency inside the gap. When the transition frequency is ou…

Vacuum Casimir energy densities and field divergences at boundaries

We consider and review the emergence of singular energy densities and field fluctuations at sharp boundaries or point-like field sources in the vacuum. The presence of singular energy densities of a field may be relevant from a conceptual point of view, because they contribute to the self-energy of the system. They should also generate significant gravitational effects. We first consider the case of the interface between a metallic boundary and the vacuum, and obtain the structure of the singular electric and magnetic energy densities at the interface through an appropriate limit from a dielectric to an ideal conductor. Then, we consider the case of a point-like source of the electromagneti…

Casimir-Polder force density between an atom and a conducting wall

In this paper we calculate the Casimir-Polder force density (force per unit area acting on the elements of the surface) on a metallic plate placed in front of a neutral atom. To obtain the force density we use the quantum operator associated to the electromagnetic stress tensor. We explicitly show that the integral of this force density over the plate reproduces the total force acting on the plate. This result shows that, although the force is obtained as a sum of surface element-atom contributions, the stress-tensor method includes also nonadditive components of Casimir-Polder forces in the evaluation of the force acting on a macroscopic object.

Casimir-Polder interatomic potential between two atoms at finite temperature and in the presence of boundary conditions

We evaluate the Casimir-Polder potential between two atoms in the presence of an infinite perfectly conducting plate and at nonzero temperature. In order to calculate the potential, we use a method based on equal-time spatial correlations of the electric field, already used to evaluate the effect of boundary conditions on interatomic potentials. This method gives also a transparent physical picture of the role of a finite temperature and boundary conditions on the Casimir-Polder potential. We obtain an analytical expression of the potential both in the near and far zones, and consider several limiting cases of interest, according to the values of the parameters involved, such as atom-atom d…

Nonperturbative approach for the electronic Casimir-Polder effect in a one-dimensional semiconductor

We present the electronic Casimir-Polder effect for a system consisting of two impurities on a one-dimensional semiconductor quantum wire. Due to the charge transfer from the impurity to a one-dimensional conduction band, the impurity states are dressed by a virtual cloud of the electron field. The attractive electronic Casimir force arises due to the overlap of the virtual clouds. The Van Hove singularity causes the persistent bound state (PBS) to appear below the band edge even when the bare impurity state energy is above the band edge. Since the decay rate of the virtual cloud of the PBS in space is small, the Casimir force can be of a very long range. While the overlap of the electronic…

Casimir-Polder force density between an atom and a conducting plate

The bound state in the spectrum of the Lee–Friedrichs Hamiltonian

Abstract The spectrum of the Lee–Friedrichs Hamiltonian, describing a two-level system embedded in a continuum, is considered. An appropriate discretization of the field modes is performed before taking the continuum limit. It is shown that the existence of an eigenstate with negative energy (bound state) is related to the nonanalyticity of the Friedrichs spectral representation. This negative energy state is a dressed state and its physical properties are studied in some significant cases.

Dynamical Casimir-Polder forces between an atom and a conducting wall

The Power of dressed atoms

Vacuum energy densities of a field in a cavity with a mobile boundary

We consider the zero-point field fluctuations, and the related field energy densities, inside a one-dimensional and a three-dimensional cavity with a mobile wall. The mechanical degrees of freedom of the mobile wall are described quantum mechanically and they are fully included in the overall system dynamics. In this optomechanical system, the field and the wall can interact with each other through the radiation pressure on the wall, given by the photons inside the cavity or even by vacuum fluctuations. We consider two cases: the one-dimensional electromagnetic field and the three-dimensional scalar field, and use the Green's functions formalism, which allows extension of the results obtain…

Casimir-Polder potential between two atoms near a conducting plate

Casimir Energies in a One-Dimensional Cavity with a Fluctuating Boundary

We consider a massless scalar field in a one-dimensional cavity with one fixed and one mobile wall. We assume that the mobile wall is also subjected to a harmonic potential, and its mechanical degrees of freedom are treated quantum-mechanically. The wall's position has thus quantum fluctuations around the equilibrium position. The possible motion of the wall makes the cavity length variable, and this gives rise to a wall-field interaction and an effective interaction between the modes of the cavity. We use an effective Hamiltonian, originally introduced by C. K. Law, to describe our system in terms of field modes relative to the equilibrium position of the mobile wall. We obtain by perturba…

Casimir Polder forces between two accelerating atoms and the Unruh effect

The Casimir-Polder force between two atoms with equal uniform acceleration and separated by a constant distance R is considered. We show that, in the low-acceleration limit, while the near-zone R-6 behavior of the interatomic interaction energy is not changed by the acceleration of the atoms, the far-zone interaction energy decreases as R-5 instead of the well-known R-7 behavior for inertial atoms. Possibility of an indirect detection of the Unruh effect through measurements of the Casimir-Polder force between the two accelerating atoms is also suggested. We also consider a heuristic model for calculating the Casimir-Polder potential energy between the two atoms in the high-acceleration lim…

Spatial correlations and dynamical Casimir-Polder forces between three atoms

Nonequilibrium dressing in a cavity with a movable reflecting mirror

We consider a movable mirror coupled to a one-dimensional massless scalar field in a cavity. Both the field and the mirror's mechanical degrees of freedom are described quantum-mechanically, and they can interact each other via the radiation pressure operator. We investigate the dynamical evolution of mirror and field starting from a nonequilibrium initial state, and their local interaction which brings the system to a stationary configuration for long times. This allows us to study the time-dependent dressing process of the movable mirror interacting with the field, and its dynamics leading to a local equilibrium dressed configuration. Also, in order to explore the effect of the radiation …

Resonance Dipole-Dipole Interaction Between Two Accelerated Atoms in the Presence of a Reflecting Plane Boundary

We study the resonant dipole-dipole interaction energy between two uniformly accelerated identical atoms, one excited and the other in the ground state, prepared in a correlated {\em Bell-type} state, and interacting with the scalar field or the electromagnetic field nearby a perfectly reflecting plate. We suppose the two atoms moving with the same uniform acceleration, parallel to the plane boundary, and that their separation is constant during the motion. We separate the contributions of vacuum fluctuations and radiation reaction field to the resonance energy shift of the two-atom system, and show that Unruh thermal fluctuations do not affect the resonance interaction, which is exclusivel…

Casimir-Polder interaction energy between two atoms in uniformly accelerated motion

Vacuum local and global electromagnetic self-energies for a point-like and an extended field source

We consider the electric and magnetic energy densities (or equivalently field fluctuations) in the space around a point-like field source in its ground state, after having subtracted the spatially uniform zero-point energy terms, and discuss the problem of their singular behavior at the source's position. We show that the assumption of a point-like source leads, for a simple Hamiltonian model of the interaction of the source with the electromagnetic radiation field, to a divergence of the renormalized electric and magnetic energy density at the position of the source. We analyze in detail the mathematical structure of such singularity in terms of a delta function and its derivatives. We als…

Enhanced resonant force between two entangled identical atoms in a photonic crystal

We consider the resonant interaction energy and force between two identical atoms, one in an excited state and the other in the ground state, placed inside a photonic crystal. The atoms, having the same orientation of their dipole moment, are supposed prepared in their symmetrical state and interact with the quantum electromagnetic field. We consider two specific models of photonic crystals: a one-dimensional model and an isotropic model. We show that in both cases the resonant interatomic force can be strongly enhanced by the presence of the photonic crystal, as a consequence of the modified dispersion relation and density of states, in particular if the transition frequency of the atoms i…

Nonthermal effects of acceleration in the resonance interaction between two uniformly accelerated atoms

We study the resonance interaction between two uniformly accelerated identical atoms, one excited and the other in the ground state, prepared in a correlated (symmetric or antisymmetric) state and interacting with the scalar field or the electromagnetic field in the vacuum state. In this case (resonance interaction), the interatomic interaction is a second-order effect in the atom-field coupling. We separate the contributions of vacuum fluctuations and radiation reaction to the resonance energy shift of the system, and show that only radiation reaction contributes, while Unruh thermal fluctuations do not affect the resonance interaction. We also find that beyond a characteristic length scal…

Fluctuations of the Casimir-Polder force between an atom and a conducting wall

Electromagnetic field fluctuations near a dielectric half-space and appearance of surface divergences in the ideal conductor limit

The electromagnetic field fluctuations in the vacuum state are considered in the region external to a half-space filled with a homogeneous non-dissipative dielectric. We discuss the appropriate limits to a real and an ideal metal, focusing on the renormalized field fluctuations (equivalent to energy densities) in the proximity of the dielectric-vacuum interface. We show that, whereas in presence of a real conductor the renormalized field fluctuations are finite in any point of space, surface divergences appear at the interface in the ideal conductor limit. The main features of such divergences are discussed in detail. We point out that the behavior of field fluctuations close to the interfa…

van der Waals interactions between excited atoms in generic environments

We consider the the van der Waals force involving excited atoms in general environments, constituted by magnetodielectric bodies. We develop a dynamical approach studying the dynamics of the atoms and the field, mutually coupled. When only one atom is excited, our dynamical theory suggests that for large distances the van der Waals force acting on the ground-state atom is monotonic, while the force acting in the excited atom is spatially oscillating. We show how this latter force can be related to the known oscillating Casimir--Polder force on an excited atom near a (ground-state) body. Our force also reveals a population-induced dynamics: for times much larger that the atomic lifetime the …

Spontaneous emission of an atom near an oscillating mirror

We investigate the spontaneous emission of one atom placed near an oscillating reflecting plate. We consider the atom modeled as a two-level system, interacting with the quantum electromagnetic field in the vacuum state, in the presence of the oscillating mirror. We suppose that the plate oscillates adiabatically, so that the time-dependence of the interaction Hamiltonian is entirely enclosed in the time-dependent mode functions, satisfying the boundary conditions at the plate surface, at any given time. Using time-dependent perturbation theory, we evaluate the transition rate to the ground-state of the atom, and show that it depends on the time-dependent atom-plate distance. We also show t…

Dynamical Casimir-Polder forces

We consider the dynamical (time-dependent) Casimir-Polder force between an atom and a perfectly conducting wall, as well as the dynamical Casimir-Polder force between two atoms in the presence of a boundary condition such as a conducting wall. The dynamical Casimir-Polder forces are obtained from iterative solutions of the Heisenberg equations for the time evolution of the electric and magnetic field operators around one atom in the presence of the conducting wall and related field energy densities, which are valid for any initial state. We consider both the case of an initially bare atomic state and of an initially partially dressed atomic state. The problem of relativistic causality in th…

van der Waals Interaction Energy Between Two Atoms Moving With Uniform Acceleration

We consider the interatomic van der Waals interaction energy between two neutral ground-state atoms moving in the vacuum space with the same uniform acceleration. We assume the acceleration orthogonal to their separation, so that their mutual distance remains constant. Using a model for the van der Waals dispersion interaction based on the interaction between the instantaneous atomic dipole moments, which are induced and correlated by the zero-point field fluctuations, we evaluate the interaction energy between the two accelerating atoms in terms of quantities expressed in the laboratory reference frame. We find that the dependence of the van der Waals interaction between the atoms from the…

Effect of boundaries on vacuum field fluctuations and radiation-mediated interactions between atoms

In this paper we discuss and review several aspects of the effect of boundary conditions and structured environments on dispersion and resonance interactions involving atoms or molecules, as well as on vacuum field fluctuations. We first consider the case of a perfect mirror, which is free to move around an equilibrium position and whose mechanical degrees of freedom are treated quantum mechanically. We investigate how the quantum fluctuations of the mirror's position affect vacuum field fluctuations for both a one-dimensional scalar and electromagnetic field, showing that the effect is particularly significant in the proximity of the moving mirror. This result can be also relevant for poss…

Casimir-Polder forces, boundary conditions and fluctuations

We review different aspects of the atom-atom and atom-wall Casimir-Polder forces. We first discuss the role of a boundary condition on the interatomic Casimir-Polder potential between two ground-state atoms, and give a physically transparent interpretation of the results in terms of vacuum fluctuations and image atomic dipoles. We then discuss the known atom-wall Casimir-Polder force for ground- and excited-state atoms, using a different method which is also suited for extension to time-dependent situations. Finally, we consider the fluctuation of the Casimir-Polder force between a ground-state atom and a conducting wall, and discuss possible observation of this force fluctuation.

Resonance energy transfer between two atoms in a conducting cylindrical waveguide

We consider the energy transfer process between two identical atoms placed inside a perfectly conducting cylindrical waveguide. We first introduce a general analytical expression of the energy transfer amplitude in terms of the electromagnetic Green's tensor; we then evaluate it in the case of a cylindrical waveguide made of a perfect conductor, for which analytical forms of the Green's tensor exist. We numerically analyse the energy transfer amplitude when the radius of the waveguide is such that the transition frequency of both atoms is below the lower cutoff frequency of the waveguide, so that the resonant photon exchange is strongly suppressed. We consider both cases of atomic dipoles p…

Dynamical Casimir-Polder force between an excited atom and a conducting wall

We consider the dynamical atom-surface Casimir-Polder force in the non-equilibrium configuration of an atom near a perfectly conducting wall, initially prepared in an excited state with the field in its vacuum state. We evaluate the time-dependent Casimir-Polder force on the atom, and find that it shows an oscillatory behavior from attractive to repulsive both in time and in space. We also investigate the asymptotic behavior in time of the dynamical force and of related local field quantities, showing that the static value of the force, as obtained by a time-independent approach, is recovered for times much larger than the timescale of the atomic self-dressing, but smaller than the atomic d…

Tuning the collective decay of two entangled emitters by means of a nearby surface

We consider the radiative properties of a system of two identical correlated atoms interacting with the electromagnetic field in its vacuum state in the presence of a generic dielectric environment. We suppose that the two emitters are prepared in a symmetric or antisymmetric superposition of one ground state and one excited state and we evaluate the transition rate to the collective ground state, showing distinctive cooperative radiative features. Using a macroscopic quantum electrodynamics approach to describe the electromagnetic field, we first obtain an analytical expression for the decay rate of the two entangled two-level atoms in terms of the Green's tensor of the generic external en…

Causality, non-locality and three-body Casimir–Polder energy between three ground-state atoms

The problem of relativistic causality in the time-dependent three-body Casimir–Polder interaction energy between three atoms, initially in their bare ground-state, is discussed. It is shown that the non-locality of the spatial correlations of the electromagnetic field emitted by the atoms during their dynamical self-dressing may become manifest in the dynamical three-body Casimir–Polder interaction energy between the three atoms.

Effects of a uniform acceleration on atom–field interactions

We review some quantum electrodynamical effects related to the uniform acceleration of atoms in vacuum. After discussing the energy level shifts of a uniformly accelerated atom in vacuum, we investigate the atom-wall Casimir-Polder force for accelerated atoms, and the van der Waals/Casimir-Polder interaction between two accelerated atoms. The possibility of detecting the Unruh effect through these phenomena is also discussed in detail.

Edwin Power and the birth of dressed atoms

This paper reviews the main results of a twenty year-long international collaborative effort led by the late E.A. Power on the physics of atoms dressed by the vacuum electromagnetic field. The presentation uses the historical, rather than the logical, order of development. This permits one to shed light on the influence of Power's personality and human qualities on the birth and evolution of the notion of the dressed atom, which is central to modern non-relativistic QED.

Dynamical Casimir-Polder energy between an excited- and a ground-state atom.

We consider the Casimir-Polder interaction between two atoms, one in the ground state and the other in its excited state. The interaction is time-dependent for this system, because of the dynamical self-dressing and the spontaneous decay of the excited atom. We calculate the dynamical Casimir-Polder potential between the two atoms using an effective Hamiltonian approach. The results obtained and their physical meaning are discussed and compared with previous results based on a time-independent approach which uses a non-normalizable dressed state for the excited atom.

Electromagnetic field fluctuations near a point-like and an extended field source

We investigate the field fluctuations near a point-like and an extended field source, such as an atom or a polarisable body, and discuss the problem of their singular behaviour at the position of the source. We consider a point-like source interacting with the electromagnetic field, in its dressed ground-state and investigate the local and global properties of the electric and magnetic energy densities in the space around the point-like source, after that the zero-point energy has been subtracted. We show that the assumption of a point-like source leads to a divergence of the renormalized electric and magnetic energy densities at the position of the source. We investigate in detail the math…

Nonlocal properties of dynamical three-body Casimir-Polder forces

We consider the three-body Casimir-Polder interaction between three atoms during their dynamical self-dressing. We show that the time-dependent three-body Casimir-Polder interaction energy displays nonlocal features related to quantum properties of the electromagnetic field and to the nonlocality of spatial field correlations. We discuss the measurability of this intriguing phenomenon and its relation with the usual concept of stationary three-body forces.

Dispersion Interactions between Neutral Atoms and the Quantum Electrodynamical Vacuum

Dispersion interactions are long-range interactions between neutral ground-state atoms or molecules, or polarizable bodies in general, due to their common interaction with the quantum electromagnetic field. They arise from the exchange of virtual photons between the atoms, and, in the case of three or more atoms, are not additive. In this review, after having introduced the relevant coupling schemes and effective Hamiltonians, as well as properties of the vacuum fluctuations, we~outline the main properties of dispersion interactions, both in the nonretarded (van der Waals) and retarded (Casimir--Polder) regime. We then discuss their deep relation with the existence of the vacuum fluctuation…

Non-Hermitian Hamiltonian for a Modulated Jaynes-Cummings Model with PT Symmetry

We consider a two-level system such as a two-level atom, interacting with a cavity field mode in the rotating wave approximation, when the atomic transition frequency or the field mode frequency is periodically driven in time. We show that in both cases, for an appropriate choice of the modulation parameters, the state amplitudes in a generic $n${-}excitation subspace obey the same equations of motion that can be obtained from a \emph{static} non-Hermitian Jaynes-Cummings Hamiltonian with ${\mathcal PT}$ symmetry, that is with an imaginary coupling constant. This gives further support to recent results showing the possible physical interest of ${\mathcal PT}$ symmetric non-Hermitian Hamilto…

Cloud of virtual photons in the ground state of the hydrogen atom.

A spinless, nonrelativistic hydrogen atom coupled to an electromagnetic field is considered. The interaction is taken in the minimal-coupling form, and the ground state of the coupled system is obtained by straightforward perturbation theory. The form of the cloud of virtual photons surrounding the atom is studied through the quantum-mechanical average on this state of an appropriately defined coarse-grained energy-density (CGED) operator W(r\ensuremath{\rightarrow}). The properties of W(r\ensuremath{\rightarrow}) are studied in order to show that this operator can give a reliable description of the shape of the virtual photon cloud. The quantum-mechanical average of W(r\ensuremath{\rightar…

Dynamical Casimir-Polder force on a partially dressed atom near a conducting wall

We study the time evolution of the Casimir-Polder force acting on a neutral atom in front of a perfectly conducting plate, when the system starts its unitary evolution from a partially dressed state. We solve the Heisenberg equations for both atomic and field quantum operators, exploiting a series expansion with respect to the electric charge and an iterative technique. After discussing the behaviour of the time-dependent force on an initially partially-dressed atom, we analyze a possible experimental scheme to prepare the partially dressed state and the observability of this new dynamical effect.

Resonance interaction energy between two accelerated identical atoms in a coaccelerated frame and the Unruh effect

We investigate the resonance interaction energy between two uniformly accelerated identical atoms, interacting with the scalar field or the electromagnetic field in the vacuum state, in the reference frame coaccelerating with the atoms. We assume that one atom is excited and the other in the ground state, and that they are prepared in their correlated symmetric or antisymmetric state. Using perturbation theory, we separate, at the second order in the atom-field coupling, the contributions of vacuum fluctuations and radiation reaction field to the energy shift of the interacting system. We show that only the radiation reaction term contributes to the resonance interaction between the two ato…

Van der Waals and resonance interactions between accelerated atoms in vacuum and the Unruh effect

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 dispersion interactions between atoms. We then consider the resonance interaction between two accelerat…

Effective Hamiltonians in Nonrelativistic Quantum Electrodynamics

In this paper, we consider some second-order effective Hamiltonians describing the interaction of the quantum electromagnetic field with atoms or molecules in the nonrelativistic limit. Our procedure is valid only for off-energy-shell processes, specifically virtual processes such as those relevant for ground-state energy shifts and dispersion van der Waals and Casimir-Polder interactions, while on-energy-shell processes are excluded. These effective Hamiltonians allow for a considerable simplification of the calculation of radiative energy shifts, dispersion, and Casimir-Polder interactions, including in the presence of boundary conditions. They can also provide clear physical insights int…

Spatial correlations of field observables in two half-spaces separated by a movable perfect mirror

We consider a system of two cavities separated by a reflecting boundary of finite mass that is free to move, and bounded to its equilibrium position by a harmonic potential. This yields an effective mirror-field interaction, as well as an effective interaction between the field modes mediated by the movable boundary. Two massless scalar fields are defined in each cavity. We consider the second-order interacting ground state of the system, that contains virtual excitations of both mirror's degrees of freedom and of the scalar fields. We investigate the correlation functions between field observables in the two cavities, and find that the squared scalar fields in the two cavities, in the inte…

Dynamical Casimir-Polder interaction between an atom and surface plasmons

We investigate the time-dependent Casimir-Polder potential of a polarizable two-level atom placed near a surface of arbitrary material, after a sudden change in the parameters of the system. Different initial conditions are taken into account. For an initially bare ground-state atom, the time-dependent Casimir-Polder energy reveals how the atom is "being dressed" by virtual, matter-assisted photons. We also study the transient behavior of the Casimir-Polder interaction between the atom and the surface starting from a partially dressed state, after an externally induced change in the atomic level structure or transition dipoles. The Heisenberg equations are solved through an iterative techni…

Fluctuations of the Casimir-Polder force between an atom and a conducting wall

We consider the quantum fluctuations of the Casimir-Polder force between a neutral atom and a perfectly conducting wall in the ground state of the system. In order to obtain the atom-wall force fluctuation we first define an operator directly associated to the force experienced by the atom considered as a polarizable body in an electromagnetic field, and we use a time-averaged force operator in order to avoid ultraviolet divergences appearing in the fluctuation of the force. This time-averaged force operator takes into account that any measurement involves a finite time. We also calculate the Casimir-Polder force fluctuation for an atom between two conducting walls. Experimental observabili…

Time-dependent Maxwell fields and energy densities for an atom in front of a conducting wall

Field Fluctuations in a One-Dimensional Cavity with a Mobile Wall

We consider a scalar field in a one-dimensional cavity with a mobile wall. The wall is assumed bounded by a harmonic potential and its mechanical degrees of freedom are treated quantum mechanically. The possible motion of the wall makes the cavity length variable, and yields a wall-field interaction and an effective interaction among the modes of the cavity. We consider the ground state of the coupled system and calculate the average number of virtual excitations of the cavity modes induced by the wall-field interaction, as well as the average value of the field energy density. We compare our results with analogous quantities for a cavity with fixed walls, and show a correction to the Casim…

Dynamical Casimir-Polder potentials in non-adiabatic conditions

In this paper we review different aspects of the dynamical Casimir¿Polder potential between a neutral atom and a perfectly conducting plate under nonequilibrium conditions. In order to calculate the time evolution of the atom¿wall Casimir¿Polder potential, we solve the Heisenberg equations describing the dynamics of the coupled system using an iterative technique. Different nonequilibrium initial states are considered, such as bare and partially dressed states. The partially dressed states considered are obtained by a sudden change of a physical parameter of the atom or of its position relative to the conducting plate. Experimental feasibility of detecting the considered dynamical effects i…

A microscopic approach to Casimir forces between metal bodies

We consider the Casimir interaction between macroscopic metallic objects in terms of the dispersion interactions (Casimir-Polder and van der Waals) between their constituents. Expressions for two- and three-body dispersion interactions between the microscopic parts of a metal are obtained, both in the retarded and non-retarded limits. They are then used to evaluate two- and three-body contributions of the Casimir force between two flat ideal metallic slabs. Our results show the non-applicability of the Hamaker approximation in this geometry. It is further seen that the three-body contributions give an overall repulsive contribution to the force, which is of the same order of magnitude as th…

Vacuum field correlations and three-body Casimir-Polder potential with one excited atom

The three-body Casimir-Polder potential between one excited and two ground-state atoms is evaluated. A physical model based on the dressed field correlations of vacuum fluctuations is used, generalizing a model previously introduced for three ground-state atoms. Although the three-body potential with one excited atom is already known in the literature, our model gives new insights on the nature of non-additive Casimir-Polder forces with one or more excited atoms.

Spatial correlations of vacuum fluctuations and the Casimir-Polder potential

We calculate the Casimir-Polder intermolecular potential using an effective Hamiltonian recently introduced. We show that the potential can be expressed in terms of the dynamical polarizabilities of the two atoms and the equal-time spatial correlation of the electric field in the vacuum state. This gives support to an interesting physical model recently proposed in the literature, where the potential is obtained from the classical interaction between the instantaneous atomic dipoles induced and correlated by the vacuum fluctuations. Also, the results obtained suggest a more general validity of this intuitive model, for example when external boundaries or thermal fields are present.

The limits of the rotating wave approximation in electromagnetic field propagation in a cavity

We consider three two-level atoms inside a one-dimensional cavity, interacting with the electromagnetic field in the rotating wave approximation (RWA), commonly used in the atom-radiation interaction. One of the three atoms is initially excited, and the other two are in their ground state. We numerically calculate the propagation of the field spontaneously emitted by the excited atom and scattered by the second atom, as well as the excitation probability of the second and third atom. The results obtained are analyzed from the point of view of relativistic causality in the atom-field interaction. We show that, when the RWA is used, relativistic causality is obtained only if the integrations …

Field fluctuations near a conducting plate and Casimir-Polder forces in the presence of boundary conditions

We consider vacuum fluctuations of the quantum electromagnetic field in the presence of an infinite and perfectly conducting plate. We evaluate how the change of vacuum fluctuations due to the plate modifies the Casimir-Polder potential between two atoms placed near the plate. We use two different methods to evaluate the Casimir-Polder potential in the presence of the plate. They also give new insights on the role of boundary conditions in the Casimir-Polder interatomic potential, as well as indications for possible generalizations to more complicated boundary conditions.

Exceptional points in a non-Hermitian extension of the Jaynes-Cummings Hamiltonian

We consider a generalization of the non-Hermitian \({\mathcal PT}\) symmetric Jaynes-Cummings Hamiltonian, recently introduced for studying optical phenomena with time-dependent physical parameters, that includes environment-induced decay. In particular, we investigate the interaction of a two-level fermionic system (such as a two-level atom) with a single bosonic field mode in a cavity. The states of the two-level system are allowed to decay because of the interaction with the environment, and this is included phenomenologically in our non-Hermitian Hamiltonian by introducing complex energies for the fermion system. We focus our attention on the occurrence of exceptional points in the spec…

Time-dependent Casimir-Polder forces and partially dressed states

A time-dependent Casimir–Polder force is shown to arise during the time evolution of a partially dressed two-level atom. The partially dressed atom is obtained by a rapid change of an atomic parameter such as its transition frequency, due to the action of some external agent. The electromagnetic field fluctuations around the atom, averaged over the solid angle for simplicity, are calculated as a function of time, and it is shown that the interaction energy with a second atom yields a dynamical Casimir–Polder potential between the two atoms.

Dispersion Interaction between Two Hydrogen Atoms in a Static Electric Field

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 atoms, it is possible to change the character of the dispersion force, turning it from attractive to re…

Dynamical Casimir-Polder interaction between an atom and a real surface

We discuss the dynamical (i.e. time-dependent) Casimir-Polder force between a neutral atom and a real surface of arbitrary material, under non-equilibrium conditions. More specifically, we consider a polarisable neutral atom placed near a surface with arbitrary dielectric properties and we investigate the dynamical dressing and the consequent dynamical Casimir-Polder potential after the non-adiabatic (sudden) change of parameters involved in the atom-field coupling, such as the atomic transition frequency or the transition dipole moment. Using time-dependent perturbation theory and the matter-assisted field approach, we discuss how the physical properties of the real surface can influence t…

Analysis of high-harmonic generation in terms of complex Floquet spectral analysis

Recent developments on intense laser sources is opening a new field of optical sciences. An intense coherent light beam strongly interacting with the matter causes a coherent motion of a particle, forming a strongly dressed excited particle. A photon emission from this dressed excited particle is a strong nonlinear process causing high-harmonic generation (HHG), where the perturbation analysis is broken down. In this work, we study a coherent photon emission from a strongly dressed excited atom in terms of complex spectral analysis in the extended Floquet-Hilbert-space. We have obtained the eigenstates of the total Hamiltonian with use of Feshbach-Brilloiun-Wigner projection method. In this…

Thermal and non-thermal signatures of the Unruh effect in Casimir-Polder forces

We show that Casimir-Polder forces between two relativistic uniformly accelerated atoms exhibit a transition from the short distance thermal-like behavior predicted by the Unruh effect, to a long distance non-thermal behavior, associated with the breakdown of a local inertial description of the system. This phenomenology extends the Unruh thermal response detected by a single accelerated observer to an accelerated spatially extended system of two particles, and we identify the characteristic length scale for this crossover with the inverse of the proper acceleration of the two atoms. Our results are derived separating at fourth order in perturbation theory the contributions of vacuum fluctu…

Dynamical three-body Casimir-Polder potential and nonlocality

Electromagnetic field fluctuations near a dielectric-vacuum boundary and surface divergences in the ideal conductor limit

We consider the electric and magnetic field fluctuations in the vacuum state in the region external to a half-space filled with a homogeneous non-dissipative dielectric. We discuss an appropriate limit to an ideal metal and concentrate our interest on the renormalized field fluctuations, or equivalently to renormalized electric and magnetic energy densities, in the proximity of the dielectric-vacuum interface. We show that surface divergences of field fluctuations arise at the interface in an appropriate ideal conductor limit, and that our limiting procedure allows to discuss in detail their structure. Field fluctuations close to the surface can be investigated through the retarded Casimir-…

Dynamical Casimir-Polder forces

We consider the dynamical Casimir-Polder force on an atom placed near an infinite conducting wall. The system is initially in a non equilibrium configuration such as a bare or a partially dressed state, and its time evolution is considered as well as the time dependence of the atom-wall Casimir-Polder interaction. A possible scheme to generate experimentally the initial partially dressed state and to detect the dynamical Casimir-Polder force is discussed.

Casimir-Polder force between an atom and surface elements of a conducting plate

Time-dependent Maxwell field operators and field energy density for an atom near a conducting wall

We consider the time evolution of the electric and magnetic field operators for a two-level atom, interacting with the electromagnetic field, placed near an infinite perfectly conducting wall. We solve iteratively the Heisenberg equations for the field operators and obtain the electric and magnetic energy density operators around the atom (valid for any initial state). Then we explicitly evaluate them for an initial state with the atom in its bare ground state and the field in the vacuum state. We show that the results can be physically interpreted as the superposition of the fields propagating directly from the atom and the fields reflected on the wall. Relativistic causality in the field …

Exactly solvable model of two three-dimensional harmonic oscillators interacting with the quantum electromagnetic field: The far-zone Casimir-Polder potential

We consider two three-dimensional isotropic harmonic oscillators interacting with the quantum electromagnetic field in the Coulomb gauge and within dipole approximation. Using a Bogoliubov-like transformation, we can obtain transformed operators such that the Hamiltonian of the system, when expressed in terms of these operators, assumes a diagonal form. We are also able to obtain an expression for the energy shift of the ground state, which is valid at all orders in the coupling constant. From this energy shift the nonperturbative Casimir-Polder potential energy between the two oscillators can be obtained. When approximated to the fourth order in the electric charge, the well-known expressi…

Dynamical Casimir-Polder interaction between a chiral molecule and a surface

We develop a dynamical approach to study the Casimir-Polder force between a initially bare molecule and a magnetodielectric body at finite temperature. Switching on the interaction between the molecule and the field at a particular time, we study the resulting temporal evolution of the Casimir-Polder interaction. The dynamical self-dressing of the molecule and its population-induced dynamics are accounted for and discussed. In particular, we find that the Casimir-Polder force between a chiral molecule and a perfect mirror oscillates in time with a frequency related to the molecular transition frequency, and converges to the static result for large times.

A microscopic approach to Casimir and Casimir-Polder forces between metallic bodies

We consider the Casimir-Polder interaction energy between a metallic nanoparticle and a metallic plate, as well as the Casimir interaction energy between two macroscopic metal plates, in terms of the many-body dispersion interactions between their constituents. Expressions for two- and three-body dispersion interactions between the microscopic parts of a real metal are first obtained, both in the retarded and non-retarded limits. These expressions are then used to evaluate, a compare each other, the overall two- and three-body contributions to the macroscopic Casimir-Polder and Casimir force, by summing up the contributions from the microscopic constituents of the bodies (metal nanoparticle…

Dynamical Casimir-Polder effect with Rydberg atoms

We investigate the dynamics of Rydberg atoms trapped in front of an oscillating conducting mirror, that can be simulated by a wall with a periodically driven dielectric constant (dynamical mirror). We focus our attention on the probability of atomic excitation due to a dynamical Casimir-Polder effect, related to the near field of the image atom whose distance periodically changes as a consequence of the mirror's motion. The theoretical analysis of this system also aims to an experimental proposal to detect this new dynamical effect exploiting Rydberg atoms trapped in the vicinity of the dynamical mirror. Our results indicate that the number of excited atoms is high enough to allow detection…

Nonlocal properties of the time-dependent Casimir-Polder interaction between three atoms

The Casimir-Polder potential from an exact diagonalization of the Hamiltonian of two three-dimensional harmonic oscillators interacting with the electromagnetic field

Control of spontaneous emission of a single quantum emitter through a time-modulated photonic-band-gap environment

We consider the spontaneous emission of a two-level quantum emitter, such as an atom or a quantum dot, in a modulated time-dependent environment with a photonic band gap. An example of such an environment is a dynamical photonic crystal or any other environment with a bandgap whose properties are modulated in time, in the effective mass approximation. After introducing our model of dynamical photonic crystal, we show that it allows new possibilities to control and tailor the physical features of the emitted radiation, specifically its frequency spectrum. In the weak coupling limit and in an adiabatic case, we obtain the emitted spectrum and we show the appearance of two lateral peaks due to…

Il vuoto: da Galileo al XXI secolo

Time-dependent resonance interaction energy between two entangled atoms under nonequilibrium conditions

We consider the time-dependent resonance interaction energy between two identical atoms, one in the ground state and the other in an excited state, and interacting with the vacuum electromagnetic field, during a nonequilibrium situation such as the dynamical atomic self-dressing process. We suppose the two atoms prepared in a correlated, symmetric or antisymmetric, state. Since the atoms start from a nonequilibrium conditions, their interaction energy is time dependent. We obtain, at second order in the atom-field coupling, an analytic expression for the time-dependent resonance interaction energy between the atoms. We show that this interaction vanishes when the two atoms are outside the l…

Resonance interaction energy between two entangled atoms in a photonic bandgap environment

We consider the resonance interaction energy between two identical entangled atoms, where one is in the excited state and the other in the ground state. They interact with the quantum electromagnetic field in the vacuum state and are placed in a photonic-bandgap environment with a dispersion relation quadratic near the gap edge and linear for low frequencies, while the atomic transition frequency is assumed to be inside the photonic gap and near its lower edge. This problem is strictly related to the coherent resonant energy transfer between atoms in external environments. The analysis involves both an isotropic three-dimensional model and the one-dimensional case. The resonance interaction…

Dynamical atom-wall Casimir-Polder forces

Temperature dependence of the magnetic Casimir-Polder interaction

We analyze the magnetic dipole contribution to atom-surface dispersion forces. Unlike its electrical counterpart, it involves small transition frequencies that are comparable to thermal energy scales. A significant temperature dependence is found near surfaces with a nonzero DC conductivity, leading to a strong suppression of the dispersion force at T > 0. We use thermal response theory for the surface material and discuss both normal metals and superconductors. The asymptotes of the free energy of interaction and of the entropy are calculated analytically over a large range of distances. Near a superconductor, the onset of dissipation at the phase transition strongly changes the interac…

New Trends in Quantum Electrodynamics

Quantum electrodynamics is one of the most successful physical theories, and its predictions agree with experimental results with exceptional accuracy. Nowadays, after several decades since its introduction, quantum electrodynamics is still a very active research field from both the theoretical and experimental points of view. The aim of this Special Issue is to present recent relevant advances in quantum electrodynamics, both theoretical and experimental, and related aspects in quantum field theory and quantum optics.