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Journal of Modern Optics

Quantum Optics with One Atom in an Optical Cavity

Craig M. Savage

Published Nov 1, 1990• 24 citations
Publisher

Abstract

The quantum mechanical master equation for a single two-level atom in a single-mode optical cavity is numerically solved in both the quantum and the semiclassical limits. The quantum limit of few cavity photons shows semiclassically forbidden behaviour such as steady state two-level population inversion. Qualitatively new fluorescent spectra, having sidebands broadened by the cavity interaction, also occur. The quantum theory of the single-atom laser with injected signal is presented. At the interface between its quantum and semiclassical dynamics we elucidate the signature of semiclassical limit cycles.

DOI
10.1080/09500349014551941

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The quantum mechanical master equation for a single two-level atom in a single-mode optical cavity is numerically solved in both the quantum and the semiclassical limits. The quantum limit of few cavity photons shows semiclassically forbidden behaviour such as steady state two-level population inversion. Qualitatively new fluorescent spectra, having sidebands broadened by the cavity interaction, also occur. The quantum theory of the single-atom laser with injected signal is presented. At the interface between its quantum and semiclassical dynamics we elucidate the signature of semiclassical limit cycles.
We investigate properties of a two-level atom coupled to a single cavity mode, and driven by a strong, in general off-resonance, external field. The cavity field is tuned to resonance with a Mollow sideband. We show that the steady-state atomic population may be highly (nearly totally) inverted, a phenomenon forbidden in semiclassical theory, and that a strong enhancement of the resonance fluorescence results. This system is suggested as an alternative approach to create the atomic inversion necessary for laser or maser generation without using additional atomic levels. We also investigate properties of the cavity field, derive an analytical expression for the photon number distribution in the good cavity or strong-coupling limit, and discuss the conditions under which this system acts as a single-atom dressed-state laser.
A two-level atom illuminated by a laser may be driven into a population-inverted steady state if it is coupled to a cavity. This is a result of the quantum nature of the electromagnetic field and is forbidden by the semiclassical theory. We numerically and analytically analyze this inversion. We find the maximum possible inversion and determine the rate of approach to the steady state. The quantized cavity modifies the electromagnetic vacuum seen by the atom; this connects our work to that on cavity-enhanced spontaneous emission and on dynamical line narrowing. Experimental signatures of the inversion and potential experimental difficulties are considered. For example, neither the presence of many atoms in the mode nor many modes in the cavity destroys the inversion.
The interaction of a two-level atom with a single mode of the radiation field is examined. The cavity mode is damped by coupling to a reservoir in a squeezed state, and the atom is also driven by an external laser field. A master equation for the atomic density operator in the bad-cavity limit is derived. The effect of the squeezing in the stationary population inversion and in the resonance spectrum of the light emitted by the atom into the background modes is studied. The results are compared with the numerical solution of the full master equation for the atom-plus-cavity mode-density operator.
The recent single-atom microlaser experiment [K. An et al., Phys. Rev. Lett. 73, 3375 (1994)], in which a stream of inverted two-level atoms is injected into an ultrahigh QQQ cavity, can be understood in the context of a semiclassical four-level laser model. Transit time broadening due to short atom-cavity interaction time effectively introduces nonradiative decay of the two levels in the model. The steady-state solution of semiclassical photon and atom rate equations for the intracavity mean photon number versus the intracavity atom number provides a good fit to the experimental data.
The mechanism of a four-level atom confined in a single-mode optical cavity with multiphoton transition is theoretically investigated in the steady-state. The behavior of the atom-cavity system is delineated by the master equation which in order to solve this equation, a set of expected values of a series of operators has been used. To numerically solve this set of coupled expectation values, the matrix continued fractions method is used. How the changes of the physical quantities including the atomic population inversion, mean photon number and second-order correlation function have been studied for any transition. Finally, the process of converting the four-level atom to a three-level one under several specific conditions is discussed for each transition.
A quantum mechanical analysis of a two-level atom in a coherently driven optical cavity is shown to predict steady-state atomic population inversion. Semi-classically this is forbidden because of the factorization of operator-product expectation values. The full quantum theory is much richer and different field states may be correlated with different atomic states. One consequence is that damping of the cavity field allows atomic polarization to be transferred from higher to lower field states and thus steady-state inversion becomes possible.