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Journal of the Optical Society of America B

Monitoring quantum effects in cavity electrodynamics by atoms in semiclassical dressed states

G. S. Agarwal, Ravinder Rupchand Puri

Published Aug 1, 1988• 19 citations
Publisher

Abstract

Field quantization effects in cavity electrodynamics can be isolated by sending through the cavity those atoms prepared initially in semiclassical dressed states. Under such initial conditions the fully quantized theory predicts irregular evolution, whereas the semiclassical and neoclassical theories predict, respectively, no dynamical evolution and regular periodic evolution.

DOI
10.1364/josab.5.001669

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Field quantization effects in cavity electrodynamics can be isolated by sending through the cavity those atoms prepared initially in semiclassical dressed states. Under such initial conditions the fully quantized theory predicts irregular evolution, whereas the semiclassical and neoclassical theories predict, respectively, no dynamical evolution and regular periodic evolution.
Since the photon box gedanken experiments of several of the founding fathers of modern physics, considerable progress has been made in differentiating the quantum and classical worlds. In this pursuit, the cavity as an open quantum system has been indispensable. From the quantization of the atom and field within a superconducting cavity, a unique realm of EPR type entanglement has emerged. In this way, dynamical evolution of the system in the strong coupling regime is intimately tied with the coupling of an atom with a single resonant or non-resonant mode within the cavity. More specifically, the cavity can be prepared so that the atom is detected in a desired state. Here, the essentials of the strong coupling regime of Cavity Quantum Electrodynamics (QED) are reviewed for cavities tuned with a single atomic transition. A brief introduction of the systems is followed by an approach of the more striking effects, leading towards Ramsey Interferometry and Quantum Non-Demolition measurements as means for quantum gate protocol. Because the integrity of the atom and photon states is important for the advancement of quantum computation, a brief discussion of the decoherence problems is also presented. This document is meant to introduce the topic in a way that makes it easily accessible to those working in closely related areas of physics, and to highlight key applications and some basic questions concerning decoherence and the measurement problem.
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.
The neoclassical or semiclassical theory (NCT) of the radiative decay of an isolated atom predicts that the decay rate of an excited state is proportional to the atoms's population in the state to which the atom is decaying. For weak excitation of a two-level system, this prediction is consistent with observations and with the Weisskopf-Wigner theory of decay, which assumes a quantized electromagnetic field as in quantum electrodynamics (QED). But for weak excitation of a system with three or more levels, there can be gross disagreements between NCT and QED. NCT predicts that the lifetime of an excited state depends on the nuclear spin which determines the number of ground states between which the atom's unity population density is divided. Also NCT predicts no fluorescence to a third level not initially populated, even though the transition is highly allowed. Observations in Pb vapor are inconsistent with NCT and consistent with QED. The oscillator strengths of the 2833-, 3640-, and 4058-A transitions were determined to be 0.167(20), 0.061(04), and 0.146(10), respectively, by measuring the ratios of oscillator strengths and using the lifetime measurements of Happer and Saloman.
Solutions of the basic equations of a simplified model of the cavity quantum electrodynamics are presented under the condition that the single-photon Rabi frequency is much larger than the cavity decay rate. Such solutions are used to calculate the quantum-statistical properties of the field and atomic observables under a variety of initial conditions involving the states of the field and atom. Effects of increasing cavity damping and of the addition of thermal photons on collapse and revival phenomena are discussed. Phase-sensitive aspects of the cavity field are also treated. Quantum effects are shown to be most easily isolated by sending an atom initially prepared in a dressed state for such a state does not evolve further under the influence of a classical field. The appearance of squeezing in the cavity field is demonstrated. The squeezing is most prominent for a coherently prepared atom passing through an empty cavity. The quantum features of the complex dipole moment and their detectability are also discussed in detail.