We obtain a general result for the Lamb shift of excited states of multilevel atoms in inhomogeneous electromagnetic structures and apply it to study atomic hydrogen in inverse-opal photonic crystals. We find that the photonic-crystal environment can lead to very large values of the Lamb shift, as compared to the case of vacuum. We also suggest that the position-dependent Lamb shift should extend from a single level to a miniband for an assembly of atoms with random distribution in space, similar to the velocity-dependent Doppler effect in atomic/molecular gases.
We obtain a general result for the Lamb shift of excited states of multilevel atoms in inhomogeneous electromagnetic structures and apply it to study atomic hydrogen in inverse-opal photonic crystals. We find that the photonic-crystal environment can lead to very large values of the Lamb shift, as compared to the case of vacuum. We also suggest that the position-dependent Lamb shift should extend from a single level to a miniband for an assembly of atoms with random distribution in space, similar to the velocity-dependent Doppler effect in atomic/molecular gases.
Motivated by the significant controversy between the two dispersion models and Weisskopf-Wigner approximation (WWA), for the first time to our knowledge, we introduce the position-dependent photon-atom interaction into the Green function method of the evolution operator and develop a universal theoretical treatment on spontaneous emission of atoms in photonic crystals (PCs). A position-sensitive generalized Lorentzian formulism (non-Lorentzian shape) for the decay of an excited atom in PCs is derived, an exact numerical method for calculating the local coupling strength, proportional to the photonic local density of state (LDOS), is presented. For weak interaction PCs with pseudo gaps, the generalized Lorentzian formulism may be reduced to the famous Lorentzian spectrum. In this case, we introduced a lifetime distribution function for an assembly of atoms and found that the lifetime distribution strongly depend on the spread configuration of these atoms in space, which clarifies successfully the tremendous discrepancy between different experiments. For the PCs with large full gaps, we found that the atomic position can fundamentally change the decay behavior of an excited atom: in strong interaction positions, the atomic decay is non-classical or exhibits an envelope-damped Rabi oscillation, while in weak interaction positions the WWA is valid. Recently, we also predicted giant Lamb shifts for hydrogen atoms in PCs, and revealed that in inhomogeneous electromagnetic environment, the dominant contribution to the Lamb shift comes from real photon emission, while the contribution from emission and reabsorption of virtual photon is negligible, in vast contrast with the case of free space where the virtual photon processes play a key role.
Being motivated by the controversial results based on two dispersion models and Weisskopf–Wigner approximation (WWA), we introduce, for the first time to our knowledge, the position-dependent photon-atom interaction into the Green function method of the evolution operator and develop a universal theoretical approach to study spontaneous emission of atoms in photonic crystals (PCs). A position-sensitive generalized Lorentzian formalism (non-Lorentzian shape) for the decay of an excited atom in PCs is derived, and an exact numerical method for calculating the local coupling strength, proportional to the photonic local density of state (LDOS), is presented. For weak interaction PCs with pseudo gaps, the generalized Lorentzian formalism may be reduced to the famous Lorentzian spectrum. In this case, we introduce a lifetime distribution function for an assembly of atoms and find that it depends strongly on the atomic configuration in space, which clarifies successfully the tremendous discrepancy between different experiments. For the PCs with large full gaps, we find that the atomic position can fundamentally change the decay behavior of an excited atom: in strong interaction positions, the atomic decay is non-classical or exhibits an envelope-damped Rabi oscillation, while in weak interaction positions the WWA is valid. Recently, we also predicted giant Lamb shifts for hydrogen atoms in PCs, and revealed that in inhomogeneous electromagnetic environment, the dominant contribution to the Lamb shift comes from real photon emission, while the contribution from emission and reabsorption of virtual photon is negligible, in vast contrast with the case of free space where the virtual photon processes play a key role.
We investigate spontaneous emission from a two-level atom embedded in a photonic crystals with three-dimensional dispersion relation, where the dependence of wave vectors on direction is taken into account. Due to the difference of the density of states of electromagnetic modes between a three-dimensional and a one-dimensional photonic crystal (lack of singularity), the dynamics of the population in the excited state and the emitted field are quite different from those of a one-dimensional photonic crystal. There is no quasi-oscillation for the population evolution. The localized field and the propagating field cannot coexist. When the upper level moves from the gap to the band, the emitted field changes from a localized field to a diffusion field and then to a propagating field. The energy of the diffusion and propagating fields propagates out incoherently and coherently, respectively. An analytical expression for the Lamb shift is obtained. The Lamb shift for the current case is smaller than that in an ordinary vacuum or in one-dimensional photonic crystals.
Spontaneous emission in photonic crystals with anisotropic three-dimensional dispersion relation is studied. If the upper level is below a characteristic frequency omega(1), or above omega(2), or between omega(1) and omega(2), the radiation is a localized field with a frequency in the band gap, or a propagating field with a frquency in the band, or a diffusion field, respectively. An analytical expression for the Lamb shift is obtained. The Lamb shift for the current case is small compared to that in an ordinary vacuum or in one- or two-dimensional photonic crystals due to lower density of states.
Dielectric studies with characteristics of a photonic crystal and a new expression of Lamb Shift including spatial average of dielectric constant for the material and its surrounding for odd parity of 2p/sub 1/2/ state of hydrogen for photon-atom interaction as a function of relative dispersion frequency, refractive index contrast and propagation vector using quadratic fluctuations and randomness in an anisotropic model of Brillouin Zone (BZ) for p-polarization are reported. The anomalous Lamb shift in 2p/sub 1/2/ level is significantly more than that obtained by using isotropic model which indicates that introducing anisotropic behaviour of BZ is important.
The study of Lamb shift plays a unique role in quantum electrodynamics because it provides an excellent test of the theory on photonic crystals (PCs). In this Letter, we present the first observation of large Lamb shift in the YBO(3):Eu(3+) inverse opals fabricated by the polystyrene templating method. In addition, it is very interesting to observe that the luminescent dynamics of Eu(3+) decayed with a faster power law (t(-3)), followed by a slower exponential process due to the coexistence of the diffusion field and the propagating field in the PCs.