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Quantum optics of driven atoms in colored vacua

THOMAS W. MOSSBERG, Maciej Lewenstein

Published Dec 31, 1994• 0 citations
OpenAlex

Abstract

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.

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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.
Several calculations have been carried out using the transition operator technique. The radiative decay in a two-level quantum system with excited state coupled by an external perturbation has been investigated and an expression obtained for P(t), the probability of finding the atom in its excited state at time t. This is seen to possess a steady value for yt >> 1 and a third term which decays at nearly half the rate of its second. Next radiative decay of an atom with two close-lying excited states is considered and |bq| 2 , the spectral density for spontaneous emission from the uppermost level, calculated. This shows that the proximity of the upper two levels makes the line-shape non-Lorentxian. Heisenberg equations of motion were then derived for the transitions operators of an ℓ-level atom undergoing radiative decay, the possibility of overlapping pairs of levels being ignored. These master equations were then used to obtain the spectral profiles of certain atomic lines, employing the so-far avoided Markoff approximation. First the spectral density of the scattered radiation was found for transitions between levels 5P3/2 and 4S (ground state), and 6S and 5P 3/2, in the potassium atom when driving fields of arbitrary strength coupled levels 6S and 4P3/2, and 4P 3/2 and 4S. Triple-peaked profiles were obtained. Spectral profiles for emission were then derived for transitions between levels 3P and (ground state), and 3P and in the hydrogen atom when a driving field of arbitrary strength coupled levels The former profile was double the latter quadruple-peaked. Lastly master equations were derived for an atom, with two excited levels undergoing radiative decay, when allowance was made for thepossibility of their overlapping. A driving field of arbitrary magnitude coupled the uppermost and ground states. The spectrum for the scattered light resulting from transitions between the uppermost and ground state was found and graphs computed for various field strengths and separations of the excited states.
Quantum electrodynamics (QED) tells us that the electromagnetic field is, on a mode-by-mode basis, quantized according to the harmonic oscillator model. Each mode is ascribed a lowest energy (or dark) state possessing one half quanta of non-removable energy plus an infinite ladder of equally spaced excited states accessed through the addition or removal of energy quanta from the mode. In the optical regime and under normal thermal conditions, electromagnetic field modes are typically in their dark state. Nevertheless, a residual dark-state atom-field coupling remains, and it is this coupling that mediates shifts and spontaneous radiative decay of atomic states. The experimental reality of dark-state atom-field coupling is frequently interpreted as proof of the quantum description of light.
In this paper we present a study of the radiative decay of coherently excited, closely spaced, molecular (or atomic) levels. Interference effects in the decay process cannot be treated in general by displaying the damping matrix in a diagonal form, so that each decay channel is assumed to be characterized by its own lifetime. The problem of the radiative decay of coherently excited indistinguishable levels (characterized by the same symmetry) is treated by a self-consistent extension of the Wigner-Weisskopf method, or alternatively, by the ‘unitarity relations’ method, developed in elementary particles physics. Finally, the Fano configuration interaction method is applied for the decay of a manifold of states characterized by the same polarization. General expressions for photon counting rates are derived and the nature of a general quantum beat experiment is discussed.
The absorbed/emitted radiation will be treated classically, as a monochromatic plane wave, whereas the atomic system that can absorb/emit such radiation will be described quantum-mechanically. However, no incident radiation beam is needed, and the atom “falls down” after a certain time interval to the ground state without any external reason. In the spontaneous emission processes the emitting atom can be thought of as a classical oscillating dipole, whose amplitude decreases due to the energy loss through the radiation. If an ensemble of identical atoms is considered and if, for simplicity, each atom emits radiation with the same spectral shape and full width at half maximum, it is impossible to ascribe a definite spectral component with intensity to a definite atom. In this case, such a broadening is identical for all atoms in the ensemble. On the microscopic scale, absorption of radiation is reduced to the transitions between pairs of energy levels of a discrete atomic spectrum.