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Physical Review A

Spatially dependent spontaneous emission and Rabi oscillations of atoms in an open cavity with nonorthogonal eigenmodes

Yuh‐Jen Cheng

Published Mar 19, 2008• 0 citations
Publisher

Abstract

The spatial dependence of the cavity modified spontaneous emission of an atom in a cavity with finite output coupling loss is analyzed. The analysis is based on the quantized nonorthogonal eigenmodes defined by the open cavity boundary condition. The spatial dependence of the Rabi oscillation frequency in the strong coupling regime is also analyzed. For spontaneous decay, the spatial dependence is a sinusoidal modulation on top of a dc value, where the interaction with all cavity modes is considered. For Rabi oscillations, where the atom interacts mainly with only one cavity mode, the oscillation frequency also has a sinusoidal spatial dependence.

DOI
10.1103/physreva.77.033835

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The spatial dependence of the cavity modified spontaneous emission of an atom in a cavity with finite output coupling loss is analyzed. The analysis is based on the quantized nonorthogonal eigenmodes defined by the open cavity boundary condition. The spatial dependence of the Rabi oscillation frequency in the strong coupling regime is also analyzed. For spontaneous decay, the spatial dependence is a sinusoidal modulation on top of a dc value, where the interaction with all cavity modes is considered. For Rabi oscillations, where the atom interacts mainly with only one cavity mode, the oscillation frequency also has a sinusoidal spatial dependence.
The spontaneous emission of an excited atom in a lossy cavity with nonorthogonal eigenmodes is analyzed. The quantum Langevin formalism is used to describe the dynamics of the spontaneous decay. The analysis shows that the spontaneous decay is modified by the Q value and the effective mode volume factor of each cavity eigenmode. The effective mode volume is generalized for cavities with nonorthogonal modes, which can be a very significant modification in the microcavity regime. It is shown that the spontaneous decay is not enhanced by the excess noise factor as claimed by other analyses.
We revisit the problem of spontaneous emission by a two-level system in a cavity, concentrating in particular on those aspects associated with the finite propagation time of light between the atom and the cavity boundaries. We find that spontaneous emission always occurs first at the free space rate and there is then an abrupt change in these dynamics when light reflected by the cavity mirrors returns to the atom, leading to interference effects that result either in an enhancement or a reduction of this rate or in a periodic exchange of excitation between the atom and the cavity field. From this point of view, reversible spontaneous emission in terms of single-mode ``vacuum Rabi oscillations'' can be interpreted as resulting from the interference between the multimode partial waves reflected at the cavity mirrors and the instantaneously radiated light. \textcopyright{} 1996 The American Physical Society.
Spontaneous emission competes with stimulated emission in many interactions of light with matter. In the usual analyses which describe the interaction of an atom with a coherent optical field, the spontaneous emission characteristics, e.g., probability and spectral distribution, are not determined. The spontaneous emission from an atom which interacts with a coherent light wave is considered. The competition between coherent photons and spontaneous photons is treated in detail for a system consisting of a stationary atom, an open cavity and spatial fields. In the model chosen, a multilevel atom which spontaneously decays by interacting with spatial fields has two nondegenerate states coupled by an interaction with a single mode of the cavity. The Laplace-transformed Schrodinger equation is solved for specified initial conditions of the system. It is found that the interaction with the coherent field modifies the spectral distribution of spontaneous radiation from the atom. For spontaneous transitions involving an atomic state which interacts with the coherent field, the spectral distributions can no longer be described by Lorentzian functions. The new distributions exhibit a broadening and splitting for strong interactions between the atom and the coherent field. It is shown that the qualitative features of these distributions can be predicted from the energy-level diagram of the atom-cavity system. The net probability of the system gaining a coherent or cavity photon is calculated by integrating over the emitted spontaneous frequencies. The equivalence of this approach to the method of computing probabilities by integrating over time is demonstrated by using Parseval's theorem.
A quantum theory of spontaneous emission from an initially excited two-level atom in a one-dimensional optical cavity with output coupling from both sides is developed. Orthonormal mode functions with a continuous spectrum are employed, which are derived by imposing a periodic boundary condition on the whole space with a period much larger than the cavity length. The delay differential equation of the atomic state of Cook and Milonni [Phys. Rev. A 35, 5081 (1987)] is re-derived in a strict manner, where the reflectivity of the cavity mirrors is included naturally in the mode functions. An approximate solution at a single-resonant-mode limit shows the results of ``vacuum'' Rabi oscillation in an underdamped cavity and enhanced spontaneous emission rate in an overdamped cavity. For the latter case, it is found that in the optical range the spontaneous emission rate is enhanced by a factor F (finesse of the cavity).
The role of spontaneous emission in the interaction between a two-level atom and a pumped microcavity in the strong-coupling regime is discussed. In particular, using a quantum Monte Carlo simulation, we investigate atomic spatial coherence. It is found that atomic spontaneous emission destroys the coherence between neighboring lattice sites, while cavity decay does not. Furthermore, our computation of the spatial coherence function shows that the in-site locality is little affected by the cavity decay but greatly depends on the cavity pump amplitude.
A spontaneously decaying two-level atom in an evacuated high-Q cavity undergoes Rabi oscillations. This phenomenon has been observed experimentally as enhanced or inhibited spontaneous emission. In the standard Jaynes-Cummings model the atom is assumed to interact with only a single cavity mode. By retaining the infinite set of cavity modes the propagation of the spontaneously emitted radiation may be calculated. Such an analysis yields a clear physical picture of Rabi oscillations. These vacuum-field Rabi oscillations are compared with Rabi oscillations of a one-electron atom induced by coherent radiation. We show that the same wave packet analysis explains both types of Rabi oscillation. The limit in which a multimode cavity may be approximated as a single-mode cavity is discussed.