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Physical Review A

Decay of a two-level atom

M. P. Sharma, David A. Cardimona, A. Gavrielides

Published May 1, 1990• 5 citations
Publisher

Abstract

We have reexamined the two-level atom with decay from the excited state out of the system and have noticed a rather surprising result. The intuitive exponential decay of the ground state at the damping rate of the excited state is actually reduced substantially when this damping rate is much greater than the Rabi frequency between the two states.

DOI
10.1103/physreva.41.5237

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We have reexamined the two-level atom with decay from the excited state out of the system and have noticed a rather surprising result. The intuitive exponential decay of the ground state at the damping rate of the excited state is actually reduced substantially when this damping rate is much greater than the Rabi frequency between the two states.
We examine the exponential decay law for an excited quantum system in the case where the state amplitude has a “memory,” that is, where the rate at which the amplitude is decaying at a particular time depends to some extent on values of the amplitude at previous times. For a particular choice of memory, characterized by a memory time τ, the amplitude obeys the differential equation of a damped harmonic oscillator. When τ is greater than a certain critical memory time τc, comparable to the natural lifetime of the state, the amplitude becomes an exponentially damped oscillation in time. When τ is less than τc, the decay is nearly exponential with a decay rate somewhat greater than that calculated from standard theory. By comparing theory with experiment, we can place an upper limit on the memory time for the radiative decay of atoms.
The radiative decay of an atom with two excited states coupled by an external perturbation is investigated. The differential equations of motion are Fourier transformed and the probability amplitudes are obtained by contour integration. The real parts of the poles in the complex plane are the perturbed energies of the excited states, and the imaginary parts yield the decay characteristics. The decay probabilities of the excited states contain three different decay terms; two exponential decays and one modulated exponential decay. The probabilities of the final states give the frequency distribution of the emitted photons as a function of time. In an Appendix, the Heitler-Ma formalism is used to eliminate the final states of the system, and the resulting equations which contain damping terms are compared with the phenomenological method.
Atomic radiative decay behavior is frequently treated as if it were an inherent property of the atoms involved. Excited atomic states are ascribed specific exponential rates of decay to lower lying levels, and the dynamics of driven atoms are calculated assuming that radiative damping proceeds at the same invariant rate with or without excitation. The frequent assumption of fixed radiative decay properties is legitimized through it generally successful predictive power. 78 refs., 11 figs., 1 tab.