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Radiative decay of densely confined atoms

Kristian Helmerson, M. Xiao, David E. Pritchard

Published May 21, 1990• 5 citations
OpenAlex

Abstract

The decay rate of an excited state atom into a ground state atom and a photon of momentum k depends on the photon mode structure1,2 and also the number of photons present in those modes.3 We consider the extent to which the rate of spontaneous emission may be altered by the mode structure of the atom (caused, e.g., by a trap) and in particular by the presence of other ground state atoms in the modes. We predict that this rate is enhanced in the presence of occupied atom modes for boson atoms and strongly suppressed for Fermi atoms.

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The decay rate of an excited state atom into a ground state atom and a photon of momentum k depends on the photon mode structure1,2 and also the number of photons present in those modes.3 We consider the extent to which the rate of spontaneous emission may be altered by the mode structure of the atom (caused, e.g., by a trap) and in particular by the presence of other ground state atoms in the modes. We predict that this rate is enhanced in the presence of occupied atom modes for boson atoms and strongly suppressed for Fermi atoms.
Spontaneous emission of photons by an atom placed near the dielectric waveguide is analyzed using global free electromagnetic modes, satisfying necessary continuity conditions at the waveguide boundaries 1. These modes include modes extended over the whole space (travelling) and modes trapped to the waveguide. To describe angular properties of the spontaneous emission, a parameterization of the travelling modes by the outgoing waves has been proposed. Otherwise, using a more common parameterization of these modes by the incoming waves, one has to take into account the interference of different reflected and transmitted waves accompanying photons incoming from both sides of the waveguide 2, what was overlooked in 3. Angular characteristics of the travelling photon emission (a), distributions of the trapped photon emission (b), as well as global decay rates (c), have been calculated using the quantum approach and standard perturbation theory. Enhancement and suppression of radiative decay rates in various configurations have been shown. A certain calculational error, in the treatment of the density of trapped states, in an earlier paper by Khosravi and Loudon 4, affecting emission rates for thin waveguides, has been corrected.
The long-time behavior of the number of photons in a mode of the electromagnetic field is given in closed form in terms of elementary functions when there is initially one (two-level) atom excited in the presence of NNN unexcited identical atoms and MMM field modes. The radiation trapping which occurs with only one mode disappears when the number of modes MMM approaches the total number of atoms in the continuum mode approximation.
The spontaneous emission of photons by an atom placed near the dielectric slab is analyzed using global free electromagnetic modes, satisfying necessary continuity conditions at the slab boundaries. These modes include the modes extended over the whole space (traveling) and the modes trapped to a waveguide formed by the slab (trapped). To describe angular properties of spontaneous emission a parametrization of the traveling modes by the outgoing waves has been proposed. Angular characteristics of the traveling photon emission, distributions of the trapped photon emission, as well as global decay rates have been calculated using the quantum approach and standard perturbation theory. Enhancement and suppression of radiative decay rates in various configurations have been shown. A certain calculational error in an earlier paper by Khosravi and Loudon [Proc. R. Soc. London Ser. A 436, 373 (1992)] affecting thin slabs and results near waveguide-mode thresholds has been improved.
The problem of the spontaneous emission from a single excited two-level atom in the presence of N unexcited similar atoms is discussed. A formalism is presented for evaluation of the time-development operator (and thus the density matrix) which has certain desirable features for time-dependent problems in the area, e.g. of atom-field interactions, when the off-diagonal elements are large compared to the diagonal elements of the Hamiltonian. By use of this formalism, it is shown that the spontaneous emission from a single atom is often drastically altered in the presence of unexcited atoms with similar resonances. When the number of atoms present becomes very large relative to the number of modes of the electromagnetic field, the excited atom becomes trapped in its excited state.>
Radiation can change the energy state of matter via three optical processes: spontaneous emission, absorption and stimulated emission. In spontaneous emission, an excited atomic or molecular state decays to a lower energy state with the emission of a photon of energy equal to the difference in the quantum state energies. Photon absorption is the reverse process, with a photon causing excitation from a lower to an excited quantum state. Stimulated emission was first proposed by Einstein in a paper published in 1917. He attempted to balance spontaneous emission and photon absorption, but could not get the correct balance without the postulated process of stimulated emission (see Section 4.2). With stimulated emission, an excited quantum state is stimulated to decay to a lower quantum state by an impinging photon. The existing photon survives with another identical photon being created (so that energy is conserved). The rates at which radiative transitions occur can be calculated using quantum mechanics. The time-dependent Schrodinger equation is used with the system wavefunction comprising time-varying linear combinations of the two wavefunctions for the lower and upper quantum states. In semi-classical treatments, an atom is treated quantum mechanically with the radiation field treated classically. There is a perturbation in energy associated with, say, the electric field of the radiation interacting with the electric dipole of the atom, though other interactions can be significant if the electric dipole interaction energy is small. In absorption, for example, a differential equation representing the change in ‘weighting’ of the wavefunction from the lower to upper state is obtained. A ‘time constant’ for the speed of change represents the rate of the radiative process. We examine the quantum mechanical nature of radiation absorption in Section 10.1 before discussing (Section 10.3) another important parameter arising with radiative transitions between discrete bound quantum states: the lineshape function. Quantum Theory of the Atom–Radiation Interaction An expression for the Einstein B-coefficient for photo-absorption is derived using quantum mechanics in this section. Einstein determined the detailed balance relationship between the rates of spontaneous emission, photo-absorption and stimulated emission when light interacts with an atom by considering an atomic system of two energy levels which are in equilibrium with a black-body radiation field. We use a semi-classical treatment where the atom is treated quantum mechanically and the radiation field is treated as a classical oscillating electric field.
Over the last few decades, the predominant strategies for controlling spontaneous emission have involved tailoring the spatial surroundings of quantum emitters or atoms to create resonant or spatially periodic photonic structures. However, the rise of time-varying photonics has prompted a reevaluation of spontaneous emission in dynamically changing environments, especially within photonic time crystals, where optical properties undergo time-periodic modulation. Here, we apply classical light-matter interaction theory together with Floquet analysis to reveal a substantial enhancement of the spontaneous emission decay rate at the momentum gap frequency in photonic time crystals. Moreover, our findings suggest that photonic time crystals enable a nonequilibrium light-matter interaction process: the spontaneous excitation of an atom from its ground state to an excited state, accompanied by the concurrent emission of a photon, referred to as spontaneous emission excitation.