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Physical Review A

Steady-state two-level atomic population inversion via a quantized cavity field

Markus Lindberg, Craig M. Savage

Published Nov 1, 1988• 43 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.38.5182

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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.
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 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.
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 classically and quantum-mechanically the coherent interaction between a single mode of the electromagnetic field and a stream of two-level atoms under the assumptions that only one atom at a time is coupled to the field and that the interaction times are all equal. This is a quantum-optics analog of a coherently kicked harmonic oscillator. We find that the classical system always evolves toward a marginally stable steady state at the threshold of type-1 intermittency, independently of the initial state of inversion of the atoms. But there are infinitely many such steady states, and which one is reached may depend sensitively on the initial conditions. In contrast, in the case of inverted atoms the quantized system usually does not reach a steady state: The intrinsic quantum fluctuations of the field almost always force it eventually to grow past the classical fixed points. A notable exception occurs under conditions such that the sequence of inverted atoms injected into the cavity leads to the preparation of a highly excited Fock state of the cavity mode.
The steady-state behavior of two-level atoms, driven by a strong field and relaxing into a frequency-dependent vacuum reservoir, has been studied in an experiment involving Ba atoms in a confocal cavity. Enhancement or suppression of the atomic excitation is observed when the cavity is tuned to either of the strong-field fluorescence sidebands. These effects result from a redistribution of the population among the dressed atom-field states induced by the cavity-modified vacuum field. The enhancement effect may be useful in achieving significant steady-state inversion.
A cavity-modified master equation is derived for a coherently driven, V-type three-level atom coupled to a single-mode cavity in the bad-cavity limit. We show that population inversion in both the bare- and dressed-state bases may be achieved, originating from the enhancement of the atom-cavity interaction when the cavity is resonant with an atomic dressed-state transition. The atomic populations in the dressed-state representation are analyzed in terms of the cavity-modified transition rates. The atomic fluorescence spectrum and probe absorption spectrum are also investigated, and it is found that the spectral profiles may be controlled by adjusting the cavity frequency. Peak suppression and line narrowing occur under the appropriate conditions.