We study the resonant Casimir--Polder potential of an excited atom near a half space containing m... more We study the resonant Casimir--Polder potential of an excited atom near a half space containing magneto-electric meta-material of various kinds on the basis of macroscopic quantum electrodynamics. Analytical results are obtained in the nonretarded and retarded distance regimes and numerical examples are given. We compare our findings with the potential of an excited atom near a left-handed superlens.
We present a quantization scheme for the electromagnetic field interacting with atomic systems in... more We present a quantization scheme for the electromagnetic field interacting with atomic systems in the presence of dispersing and absorbing magnetodielectric media, including left-handed material having negative real part of the refractive index. The theory is applied to the spontaneous decay of a two-level atom at the center of a spherical free-space cavity surrounded by magnetodielectric matter of overlapping band-gap zones. Results for both big and small cavities are presented, and the problem of local-field corrections within the real-cavity model is addressed.
A general theory of the Casimir-Polder interaction of single atoms with dispersing and absorbing ... more A general theory of the Casimir-Polder interaction of single atoms with dispersing and absorbing magnetodielectric bodies is presented, which is based on QED in linear, causal media. Both ground-state and excited atoms are considered. Whereas the Casimir-Polder force acting on a ground-state atom can conveniently be derived from a perturbative calculation of the atom-field coupling energy, an atom in an excited state is subject to transient force components that can only be fully understood by a dynamical treatment based on the body-assisted vacuum Lorentz force. The results show that the Casimir-Polder force can be influenced by the body-induced broadening and shifting of atomic transitions — an effect that is not accounted for within lowest-order perturbation theory. The theory is used to study the Casimir-Polder force of a ground-state atom placed within a magnetodielectric multilayer system, with special emphasis on thick and thin plates as well as a planar cavity consisting of two thick plates. It is shown how the competing attractive and repulsive force components related to the electric and magnetic properties of the medium, respectively, can — for sufficiently strong magnetic properties — lead to the formation of potential walls and wells.
Journal of Optics B-quantum and Semiclassical Optics, 2004
Within the frame of macroscopic quantum electrodynamics in causal media, the van der Waals intera... more Within the frame of macroscopic quantum electrodynamics in causal media, the van der Waals interaction between an atomic system and an arbitrary arrangement of dispersing and absorbing dielectric bodies including metals is studied. It is shown that the minimal-coupling scheme and the multipolar-coupling scheme lead to essentially the same formula for the van der Waals potential. As an application, the vdW potential of an atom in the presence of a sphere is derived. Closed expressions for the long-distance (retardation) and short-distance (non-retardation) limits are given, and the effect of material absorption is discussed.
We establish a general relation between dispersion forces. First, based on QED in causal media, l... more We establish a general relation between dispersion forces. First, based on QED in causal media, leading-order perturbation theory is used to express both the single-atom Casimir-Polder and the two-atom van der Waals potentials in terms of the atomic polarizabilities and the Green tensor for the body-assisted electromagnetic field. Endowed with this geometry-independent framework, we then employ the Born expansion of the Green tensor together with the Clausius-Mosotti relation to prove that the macroscopic Casimir-Polder potential of an atom in the presence of dielectric bodies is due to an infinite sum of its microscopic many-atom van der Waals interactions with the atoms comprising the bodies. This theorem holds for inhomogeneous, dispersing, and absorbing bodies of arbitrary shapes and arbitrary atomic composition on an arbitrary background of additional magnetodielectric bodies.
An approximate treatment is given for the state evolution in the two-photon Jaynes-Cummings model... more An approximate treatment is given for the state evolution in the two-photon Jaynes-Cummings model with initial squeezed vacuum and chaotic state fields. Both initially pure and mixed atomic states are examined. Interesting features such as the evolution of the atom into unique ...
A formalism for studying spontaneous decay of an excited two-level atom in the presence of disper... more A formalism for studying spontaneous decay of an excited two-level atom in the presence of dispersing and absorbing dielectric bodies is developed. An integral equation, which is suitable for numerical solution, is derived for the atomic upper-state-probability amplitude. The emission pattern and the power spectrum of the emitted light are expressed in terms of the Green tensor of the dielectric-matter formation including absorption and dispersion. The theory is applied to the spontaneous decay of an excited atom at the center of a three-layered spherical cavity, with the cavity wall being modeled by a band-gap dielectric of Lorentz type. Both weak coupling and strong coupling are studied, the latter with special emphasis on the cases where the atomic transition is (i) in the normal-dispersion zone near the medium resonance and (ii) in the anomalous-dispersion zone associated with the band gap. In a single-resonance approximation, conditions of the appearance of Rabi oscillations and closed solutions to the evolution of the atomic state population are derived, which are in good agreement with the exact numerical results.
Within the framework of quantization of the macroscopic electromagnetic field, equations of motio... more Within the framework of quantization of the macroscopic electromagnetic field, equations of motion and an effective Hamiltonian for treating both the resonant dipole-dipole interaction between two-level atoms and the resonant atom-field interaction are derived, which can suitably be used for studying the influence of arbitrary dispersing and absorbing material surroundings on these interactions. The theory is applied to the study of the transient behavior of two atoms that initially share a single excitation, with special emphasis on the role of the two competing processes of virtual and real photon exchange in the energy transfer between the atoms. In particular, it is shown that for weak atom-field interaction there is a time window, where the energy transfer follows a rate regime of the type obtained by ordinary second-order perturbation theory. Finally, the resonant dipole-dipole interaction is shown to give rise to a doublet spectrum of the emitted light for weak atom-field interaction and a triplet spectrum for strong atom-field interaction.
We study the resonant Casimir--Polder potential of an excited atom near a half space containing m... more We study the resonant Casimir--Polder potential of an excited atom near a half space containing magneto-electric meta-material of various kinds on the basis of macroscopic quantum electrodynamics. Analytical results are obtained in the nonretarded and retarded distance regimes and numerical examples are given. We compare our findings with the potential of an excited atom near a left-handed superlens.
The influence of the local-field correction on the strong atom-field coupling regime are investig... more The influence of the local-field correction on the strong atom-field coupling regime are investigated using the real-cavity model. The atom is positioned at the center of a multilayer sphere. Three types of mirrors are considered: perfectly reflecting, Lorentz band gap, and Bragg-distributed ones, with special emphasis on experimental practicability. In particular, the influence of the local field on the spectral resonance lines, the Rabi oscillation frequency and decay rate, and the condition indicating the occurrence of the strong-coupling regime are studied in detail. It is shown that the local-field correction gives rise to a structureless plateau in the density of states of the electromagnetic field. The level of the plateau rises with increasing material density and/or absorption, which may eventually destroy the strong-coupling regime. The effect of the local field is especially pronounced at high-material densities due to direct energy transfer from the guest atom to the medium. At lower material density and/or absorption, variation of the material density does not seem to affect much the strong-coupling regime, except for a small shift in the resonance frequency.
Journal of Optics B-quantum and Semiclassical Optics, 2002
We study a scheme for entangling two-level atoms located close to the surface of a dielectric mic... more We study a scheme for entangling two-level atoms located close to the surface of a dielectric microsphere. The effect is based on medium-assisted spontaneous decay, rigorously taking into account dispersive and absorptive properties of the microsphere. We show that even in the weak-coupling regime, where the Markov approximation applies, entanglement up to 0.35 ebits between two atoms can be created. However, larger entanglement and violation of Bell's inequality can only be achieved in the strong-coupling regime.
Within the frame of macroscopic QED in linear, causal media, we study the radiation force of Casi... more Within the frame of macroscopic QED in linear, causal media, we study the radiation force of Casimir-Polder type acting on an atom which is positioned near dispersing and absorbing magnetodielectric bodies and initially prepared in an arbitrary electronic state. It is shown that minimal and multipolar coupling lead to essentially the same lowest-order perturbative result for the force acting on an atom in an energy eigenstate. To go beyond perturbation theory, the calculations are based on the exact center-of-mass equation of motion. For a nondriven atom in the weak-coupling regime, the force as a function of time is a superposition of force components that are related to the electronic density-matrix elements at a chosen time. Even the force component associated with the ground state is not derivable from a potential in the ususal way, because of the position dependence of the atomic polarizability. Further, when the atom is initially prepared in a coherent superposition of energy eigenstates, then temporally oscillating force components are observed, which are due to the interaction of the atom with both electric and magnetic fields.
The influence of the local-field correction on the strong atom-field coupling regime are investig... more The influence of the local-field correction on the strong atom-field coupling regime are investigated using the real-cavity model. The atom is positioned at the center of a multilayer sphere. Three types of mirrors are considered: perfectly reflecting, Lorentz band gap, and Bragg-distributed ones, with special emphasis on experimental practicability. In particular, the influence of the local field on the spectral
By making use of the Green function concept of quantization of the electromagnetic field in Krame... more By making use of the Green function concept of quantization of the electromagnetic field in Kramers--Kronig consistent media, a rigorous quantum mechanical derivation of the rate of intermolecular energy transfer in the presence of arbitrarily shaped, dispersing, and absorbing material bodies is given. Applications to bulk material, multi-slab planar structures, and microspheres are studied. It is shown that when the two molecules are near a planar interface, then surface-guided waves can strongly affect the energy transfer and essentially modify both the (F\"{o}rster) short-range $R^{-6}$ dependence of the transfer rate and the long-range $R^{-2}$ dependence, which are typically observed in free space. In particular, enhancement (inhibition) of energy transfer can be accompanied by inhibition (enhancement) of donor decay. Results for four- and five-layered planar structures are given and compared with experimental results. Finally, the energy transfer between two molecules located at diametrically opposite positions outside a microsphere is briefly discussed.
After giving a summary of the basic-theoretical concept of quantization of the electromagnetic fi... more After giving a summary of the basic-theoretical concept of quantization of the electromagnetic field in the presence of dispersing and absorbing (macroscopic) bodies, their effect on spontaneous decay of an excited atom is studied. Various configurations such as bulk material, planar half space media, spherical cavities, and microspheres are considered. In particular, the influence of material absorption on the local-field correction, the decay rate, the line shift, and the emission pattern are examined. Further, the interplay between radiative losses and losses due to material absorption is analyzed. Finally, the possibility of generating entangled states of two atoms coupled by a microsphere-assisted field is discussed.
The influence of the size and shape of a dispersing and absorbing dielectric body on the local-fi... more The influence of the size and shape of a dispersing and absorbing dielectric body on the local-field corrected spontaneous-decay of an excited atom embedded in the body is studied on the basis of the real-cavity model. By means of a Born expansion of the Green tensor of the system it is shown that to linear order in the susceptibility of the body the decay rate exactly follows Tomas's formula found for the special case of an atom at the center of a homogeneous dielectric sphere [Phys. Rev. A 63, 053811 (2001)]. It is further shown that for an atom situated at the interior of an arbitrary dielectric body this formula remains valid beyond the linear order. The case of an atom embedded in a weakly polarizable sphere is discussed in detail.
An effective Hamiltonian and equations of motion for treating both the resonant dipole-dipole int... more An effective Hamiltonian and equations of motion for treating both the resonant dipole-dipole interaction between two-level atoms and the resonant atom-field interaction are derived, which can suitably be used for studying the influence of arbitrary dispersing and absorbing material surroundings on these interactions. It is shown that the dipole-dipole interaction and the atom-field interaction, respectively, are closely related to the real part and the imaginary part of the (classical) Green tensor. The theory is applied to the study of the transient behavior of two atoms that initially share a single excitation, with special emphasis on the role of the two competing processes of virtual and real photon exchange in the energy transfer between the atoms. To illustrate the powerfulness of the theory, specific results for the case of the atoms being near a dispersing and absorbing microsphere are presented. In particular, the regimes of weak and strong atom-field coupling are addressed.
A scheme for nonconditional generation of long-living maximally entangled states between two spat... more A scheme for nonconditional generation of long-living maximally entangled states between two spatially well separated atoms is proposed. In the scheme, Λ -type atoms pass a resonatorlike equipment of dispersing and absorbing macroscopic bodies giving rise to body-assisted electromagnetic field resonances of well-defined heights and widths. Strong atom-field coupling is combined with weak atom-field coupling to realize entanglement transfer from the dipole-allowed transitions to the dipole-forbidden transitions, whereby the entanglement is preserved when the atoms depart from the bodies and from each other. The theory is applied to the case of atoms passing by a microsphere.
We study the resonant Casimir--Polder potential of an excited atom near a half space containing m... more We study the resonant Casimir--Polder potential of an excited atom near a half space containing magneto-electric meta-material of various kinds on the basis of macroscopic quantum electrodynamics. Analytical results are obtained in the nonretarded and retarded distance regimes and numerical examples are given. We compare our findings with the potential of an excited atom near a left-handed superlens.
We present a quantization scheme for the electromagnetic field interacting with atomic systems in... more We present a quantization scheme for the electromagnetic field interacting with atomic systems in the presence of dispersing and absorbing magnetodielectric media, including left-handed material having negative real part of the refractive index. The theory is applied to the spontaneous decay of a two-level atom at the center of a spherical free-space cavity surrounded by magnetodielectric matter of overlapping band-gap zones. Results for both big and small cavities are presented, and the problem of local-field corrections within the real-cavity model is addressed.
A general theory of the Casimir-Polder interaction of single atoms with dispersing and absorbing ... more A general theory of the Casimir-Polder interaction of single atoms with dispersing and absorbing magnetodielectric bodies is presented, which is based on QED in linear, causal media. Both ground-state and excited atoms are considered. Whereas the Casimir-Polder force acting on a ground-state atom can conveniently be derived from a perturbative calculation of the atom-field coupling energy, an atom in an excited state is subject to transient force components that can only be fully understood by a dynamical treatment based on the body-assisted vacuum Lorentz force. The results show that the Casimir-Polder force can be influenced by the body-induced broadening and shifting of atomic transitions — an effect that is not accounted for within lowest-order perturbation theory. The theory is used to study the Casimir-Polder force of a ground-state atom placed within a magnetodielectric multilayer system, with special emphasis on thick and thin plates as well as a planar cavity consisting of two thick plates. It is shown how the competing attractive and repulsive force components related to the electric and magnetic properties of the medium, respectively, can — for sufficiently strong magnetic properties — lead to the formation of potential walls and wells.
Journal of Optics B-quantum and Semiclassical Optics, 2004
Within the frame of macroscopic quantum electrodynamics in causal media, the van der Waals intera... more Within the frame of macroscopic quantum electrodynamics in causal media, the van der Waals interaction between an atomic system and an arbitrary arrangement of dispersing and absorbing dielectric bodies including metals is studied. It is shown that the minimal-coupling scheme and the multipolar-coupling scheme lead to essentially the same formula for the van der Waals potential. As an application, the vdW potential of an atom in the presence of a sphere is derived. Closed expressions for the long-distance (retardation) and short-distance (non-retardation) limits are given, and the effect of material absorption is discussed.
We establish a general relation between dispersion forces. First, based on QED in causal media, l... more We establish a general relation between dispersion forces. First, based on QED in causal media, leading-order perturbation theory is used to express both the single-atom Casimir-Polder and the two-atom van der Waals potentials in terms of the atomic polarizabilities and the Green tensor for the body-assisted electromagnetic field. Endowed with this geometry-independent framework, we then employ the Born expansion of the Green tensor together with the Clausius-Mosotti relation to prove that the macroscopic Casimir-Polder potential of an atom in the presence of dielectric bodies is due to an infinite sum of its microscopic many-atom van der Waals interactions with the atoms comprising the bodies. This theorem holds for inhomogeneous, dispersing, and absorbing bodies of arbitrary shapes and arbitrary atomic composition on an arbitrary background of additional magnetodielectric bodies.
An approximate treatment is given for the state evolution in the two-photon Jaynes-Cummings model... more An approximate treatment is given for the state evolution in the two-photon Jaynes-Cummings model with initial squeezed vacuum and chaotic state fields. Both initially pure and mixed atomic states are examined. Interesting features such as the evolution of the atom into unique ...
A formalism for studying spontaneous decay of an excited two-level atom in the presence of disper... more A formalism for studying spontaneous decay of an excited two-level atom in the presence of dispersing and absorbing dielectric bodies is developed. An integral equation, which is suitable for numerical solution, is derived for the atomic upper-state-probability amplitude. The emission pattern and the power spectrum of the emitted light are expressed in terms of the Green tensor of the dielectric-matter formation including absorption and dispersion. The theory is applied to the spontaneous decay of an excited atom at the center of a three-layered spherical cavity, with the cavity wall being modeled by a band-gap dielectric of Lorentz type. Both weak coupling and strong coupling are studied, the latter with special emphasis on the cases where the atomic transition is (i) in the normal-dispersion zone near the medium resonance and (ii) in the anomalous-dispersion zone associated with the band gap. In a single-resonance approximation, conditions of the appearance of Rabi oscillations and closed solutions to the evolution of the atomic state population are derived, which are in good agreement with the exact numerical results.
Within the framework of quantization of the macroscopic electromagnetic field, equations of motio... more Within the framework of quantization of the macroscopic electromagnetic field, equations of motion and an effective Hamiltonian for treating both the resonant dipole-dipole interaction between two-level atoms and the resonant atom-field interaction are derived, which can suitably be used for studying the influence of arbitrary dispersing and absorbing material surroundings on these interactions. The theory is applied to the study of the transient behavior of two atoms that initially share a single excitation, with special emphasis on the role of the two competing processes of virtual and real photon exchange in the energy transfer between the atoms. In particular, it is shown that for weak atom-field interaction there is a time window, where the energy transfer follows a rate regime of the type obtained by ordinary second-order perturbation theory. Finally, the resonant dipole-dipole interaction is shown to give rise to a doublet spectrum of the emitted light for weak atom-field interaction and a triplet spectrum for strong atom-field interaction.
We study the resonant Casimir--Polder potential of an excited atom near a half space containing m... more We study the resonant Casimir--Polder potential of an excited atom near a half space containing magneto-electric meta-material of various kinds on the basis of macroscopic quantum electrodynamics. Analytical results are obtained in the nonretarded and retarded distance regimes and numerical examples are given. We compare our findings with the potential of an excited atom near a left-handed superlens.
The influence of the local-field correction on the strong atom-field coupling regime are investig... more The influence of the local-field correction on the strong atom-field coupling regime are investigated using the real-cavity model. The atom is positioned at the center of a multilayer sphere. Three types of mirrors are considered: perfectly reflecting, Lorentz band gap, and Bragg-distributed ones, with special emphasis on experimental practicability. In particular, the influence of the local field on the spectral resonance lines, the Rabi oscillation frequency and decay rate, and the condition indicating the occurrence of the strong-coupling regime are studied in detail. It is shown that the local-field correction gives rise to a structureless plateau in the density of states of the electromagnetic field. The level of the plateau rises with increasing material density and/or absorption, which may eventually destroy the strong-coupling regime. The effect of the local field is especially pronounced at high-material densities due to direct energy transfer from the guest atom to the medium. At lower material density and/or absorption, variation of the material density does not seem to affect much the strong-coupling regime, except for a small shift in the resonance frequency.
Journal of Optics B-quantum and Semiclassical Optics, 2002
We study a scheme for entangling two-level atoms located close to the surface of a dielectric mic... more We study a scheme for entangling two-level atoms located close to the surface of a dielectric microsphere. The effect is based on medium-assisted spontaneous decay, rigorously taking into account dispersive and absorptive properties of the microsphere. We show that even in the weak-coupling regime, where the Markov approximation applies, entanglement up to 0.35 ebits between two atoms can be created. However, larger entanglement and violation of Bell's inequality can only be achieved in the strong-coupling regime.
Within the frame of macroscopic QED in linear, causal media, we study the radiation force of Casi... more Within the frame of macroscopic QED in linear, causal media, we study the radiation force of Casimir-Polder type acting on an atom which is positioned near dispersing and absorbing magnetodielectric bodies and initially prepared in an arbitrary electronic state. It is shown that minimal and multipolar coupling lead to essentially the same lowest-order perturbative result for the force acting on an atom in an energy eigenstate. To go beyond perturbation theory, the calculations are based on the exact center-of-mass equation of motion. For a nondriven atom in the weak-coupling regime, the force as a function of time is a superposition of force components that are related to the electronic density-matrix elements at a chosen time. Even the force component associated with the ground state is not derivable from a potential in the ususal way, because of the position dependence of the atomic polarizability. Further, when the atom is initially prepared in a coherent superposition of energy eigenstates, then temporally oscillating force components are observed, which are due to the interaction of the atom with both electric and magnetic fields.
The influence of the local-field correction on the strong atom-field coupling regime are investig... more The influence of the local-field correction on the strong atom-field coupling regime are investigated using the real-cavity model. The atom is positioned at the center of a multilayer sphere. Three types of mirrors are considered: perfectly reflecting, Lorentz band gap, and Bragg-distributed ones, with special emphasis on experimental practicability. In particular, the influence of the local field on the spectral
By making use of the Green function concept of quantization of the electromagnetic field in Krame... more By making use of the Green function concept of quantization of the electromagnetic field in Kramers--Kronig consistent media, a rigorous quantum mechanical derivation of the rate of intermolecular energy transfer in the presence of arbitrarily shaped, dispersing, and absorbing material bodies is given. Applications to bulk material, multi-slab planar structures, and microspheres are studied. It is shown that when the two molecules are near a planar interface, then surface-guided waves can strongly affect the energy transfer and essentially modify both the (F\"{o}rster) short-range $R^{-6}$ dependence of the transfer rate and the long-range $R^{-2}$ dependence, which are typically observed in free space. In particular, enhancement (inhibition) of energy transfer can be accompanied by inhibition (enhancement) of donor decay. Results for four- and five-layered planar structures are given and compared with experimental results. Finally, the energy transfer between two molecules located at diametrically opposite positions outside a microsphere is briefly discussed.
After giving a summary of the basic-theoretical concept of quantization of the electromagnetic fi... more After giving a summary of the basic-theoretical concept of quantization of the electromagnetic field in the presence of dispersing and absorbing (macroscopic) bodies, their effect on spontaneous decay of an excited atom is studied. Various configurations such as bulk material, planar half space media, spherical cavities, and microspheres are considered. In particular, the influence of material absorption on the local-field correction, the decay rate, the line shift, and the emission pattern are examined. Further, the interplay between radiative losses and losses due to material absorption is analyzed. Finally, the possibility of generating entangled states of two atoms coupled by a microsphere-assisted field is discussed.
The influence of the size and shape of a dispersing and absorbing dielectric body on the local-fi... more The influence of the size and shape of a dispersing and absorbing dielectric body on the local-field corrected spontaneous-decay of an excited atom embedded in the body is studied on the basis of the real-cavity model. By means of a Born expansion of the Green tensor of the system it is shown that to linear order in the susceptibility of the body the decay rate exactly follows Tomas's formula found for the special case of an atom at the center of a homogeneous dielectric sphere [Phys. Rev. A 63, 053811 (2001)]. It is further shown that for an atom situated at the interior of an arbitrary dielectric body this formula remains valid beyond the linear order. The case of an atom embedded in a weakly polarizable sphere is discussed in detail.
An effective Hamiltonian and equations of motion for treating both the resonant dipole-dipole int... more An effective Hamiltonian and equations of motion for treating both the resonant dipole-dipole interaction between two-level atoms and the resonant atom-field interaction are derived, which can suitably be used for studying the influence of arbitrary dispersing and absorbing material surroundings on these interactions. It is shown that the dipole-dipole interaction and the atom-field interaction, respectively, are closely related to the real part and the imaginary part of the (classical) Green tensor. The theory is applied to the study of the transient behavior of two atoms that initially share a single excitation, with special emphasis on the role of the two competing processes of virtual and real photon exchange in the energy transfer between the atoms. To illustrate the powerfulness of the theory, specific results for the case of the atoms being near a dispersing and absorbing microsphere are presented. In particular, the regimes of weak and strong atom-field coupling are addressed.
A scheme for nonconditional generation of long-living maximally entangled states between two spat... more A scheme for nonconditional generation of long-living maximally entangled states between two spatially well separated atoms is proposed. In the scheme, Λ -type atoms pass a resonatorlike equipment of dispersing and absorbing macroscopic bodies giving rise to body-assisted electromagnetic field resonances of well-defined heights and widths. Strong atom-field coupling is combined with weak atom-field coupling to realize entanglement transfer from the dipole-allowed transitions to the dipole-forbidden transitions, whereby the entanglement is preserved when the atoms depart from the bodies and from each other. The theory is applied to the case of atoms passing by a microsphere.
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