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arXiv:0807.0978 · Journal of Physics A Mathematical and Theoretical

Emergent radiation in an atom–field system at twice resonance

Brijesh Kumar

Published May 29, 2009• 2 citations
arXivHTMLPDF

Abstract

A two-level atom interacting with a single mode of quantized electromagnetic radiation is discussed using a new representation in which the atom and the radiation are unified into a single canonical Bose field. At the twice resonance , when the frequency of the original radiation is twice the atomic transition frequency (ω = 2 ), the emergent unified field in the non-interacting atom–field system resembles a free radiation of frequency . This free emergent radiation is further shown to exist in the presence of an interaction which looks similar to the atom–field interaction in the dipole approximation. The one-photon correlation and the population inversion are discussed as the possible means of observing the emergent radiation. The entanglement properties of the emergent radiation are also discussed.

DOI
10.1088/1751-8113/42/24/245307

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A two-level atom interacting with a single mode of quantized electromagnetic radiation is discussed using a new representation in which the atom and the radiation are unified into a single canonical Bose field. At the twice resonance , when the frequency of the original radiation is twice the atomic transition frequency (ω = 2 ), the emergent unified field in the non-interacting atom–field system resembles a free radiation of frequency . This free emergent radiation is further shown to exist in the presence of an interaction which looks similar to the atom–field interaction in the dipole approximation. The one-photon correlation and the population inversion are discussed as the possible means of observing the emergent radiation. The entanglement properties of the emergent radiation are also discussed.
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In the preceding chapters concerning the interaction of a radiation field with matter, we assumed the field to be classical. In many situations this assumption is valid. There are, however, many instances where a classical field fails to explain experimentally observed results and a quantized description of the field is required. This is, for example, true of spontaneous emission in an atomic system which was described phenomenologically in Chapter 5. For a rigorous treatment of the atomic level decay in free space, we need to consider the interaction of the atom with the vacuum modes of the universe. Even in the simplest system involving the interaction of a single-mode radiation field with a single two-level atom, the predictions for the dynamics of the atom are quite different in the semiclassical theory and the fully quantum theory. In the absence of the decay process, the semiclassical theory predicts Rabi oscillations for the atomic inversion whereas the quantum theory predicts certain collapse and revival phenomena due to the quantum aspects of the field. These interesting quantum field theoretical predictions have been experimentally verified. In this chapter we discuss the interaction of the quantized radiation field with the two-level atomic system described by a Hamiltonian in the dipole and the rotating-wave approximations. For a single-mode field it reduces to a particularly simple form. This is a very interesting Hamiltonian in quantum optics for several reasons. First, it can be solved exactly for arbitrary coupling constants and exhibits some true quantum dynamical effects such as collapse followed by periodic revivals of the atomic inversion.
The quantum-electrodynamical problem of N identical two-level atoms interacting with M field modes is considered, and an exact solution for the case of spontaneous emission from a single atom is obtained. The behavior of this system is shown to be quite different from the exponential decay of a single excited atom radiating into free space. A ``ringing'' behavior at the enigmatic frequency \ensuremath{\sim} \ensuremath{\surd}N which occurs when only one mode is accessible to the field persists when many modes are present. When a continuum of modes is accessible, the long-time limit shows that the energy of the originally excited atom is equally likely to be shared by the N-1 originally unexcited atoms and the electromagnetic field when M/N\ensuremath{\rightarrow}1. ``Radiation suppression'' occurs whenever N\ensuremath{\gg}1 and M\ensuremath{\ll}N, when the originally excited atom does not emit its energy. When M=N\ensuremath{\gg}1, the single atom decays monotonically to zero (and approximately exponentially) but with a decay rate that is \ensuremath{\surd}N times the Rabi frequency. Such unexpected effects are presently within experimental range.
The quantum mechanical analysis for a non-resonant case of a single radiation mode interacting with a two-level atom in a cavity is studied. Expressions for the mean value of photon number and the time evolution of the atomic motion are given. The frequency of exchange energy between the atomic levels and the radiation field systems for non- resonant and resonant interactions is obtained. Results for all initial states of the atom-radiation field are presented. Results for resonant and non-resonant interactions are compared.
The strong resonance interaction of a two-level atom with the continuum of quantized electromagnetic modes falling within the contour of a resonance mode of a dielectric microsphere is considered within the framework of quantum electrodynamics. Analytical solutions are derived. As an initial condition, we consider the case when, at time t = 0, the atom is excited and the resonance modes of the microsphere contain a single-photon wavepacket. It is shown that the properties of the emitted photon pair depend crucially on space-time properties of the photon wavepacket contained in the resonator. When the mean square of the electric field of the photon wavepacket at the initial instant of time at the atom position is close to the vacuum value, the radiation of an atom is similar to a spontaneous one and the emitted photon pair has no correlations. On the contrary, if the mean square of the electric field of the photon wavepacket at the initial instant of time at the atom position is substantially greater than the vacuum value, the radiation of an atom has a stimulated nature and the emitted photon pair has very complicated strong correlations. The relationship between the results obtained and the predictions of the dressed states theory are briefly discussed. The results obtained are of a general character and can be applied to the description of the resonant interaction of an excited atom and an excited resonator of an arbitrary shape.
We study the interaction of two-level atoms with correlated two-mode states of the quantized electromagnetic field. We assume that only one of the modes is near resonance with the atomic transition so that the second mode does not interact directly with the atom. However, we find that the presence of the second field does produce a kind of nonlocal effect in that if the atom is initially in the excited or the ground state no atomic dipole moment develops. We consider two kinds of correlated field state, namely, the correlated SU(1, 1) coherent states, which are generalizations of the two-mode squeezed vacuum states, and the so-called pair coherent states. We study the atomic inversions and the evolutions of the field statistics and of the squeezing properties of the initial field.