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Annual Meeting Optical Society of America

Steady-state population Inversion via quantized fields

Craig M. Savage, Markus Lindberg

Published Jan 1, 1988• 0 citations
Publisher

Abstract

Placing an optical cavity around a two-level atom modifies the electromagnetic vacuum to which it couples. Effects such as inhibited and enhanced spontaneous emission are known to result. Recently one of us predicted a new nonclassical effect of vacuum engineering.1 A two-level transition may be laser driven into an inverted steady state. Semiclassical theory forbids this fully quantum mechanical result. Unlike squeezing and antibunching, this inversion is not a property of the linearized quantum fluctuations. We present numerical and analytical results which clarify the physics of the inversion. The maximum inversion possible is determined. We attempt to identify obstacles to the experimental realization of steady-state inversion. Multiple atoms and multiple cavity modes do not destroy the effect. A significant difficulty appears to be localizing the atoms at the cavity beamwaist until they reach steady state. The inversion may be observed via fluorescence changes as the cavity is blocked and unblocked or via the presence of a fluoresence maximum as a function of the driving field intensity.

DOI
10.1364/oam.1988.ms8

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Placing an optical cavity around a two-level atom modifies the electromagnetic vacuum to which it couples. Effects such as inhibited and enhanced spontaneous emission are known to result. Recently one of us predicted a new nonclassical effect of vacuum engineering.1 A two-level transition may be laser driven into an inverted steady state. Semiclassical theory forbids this fully quantum mechanical result. Unlike squeezing and antibunching, this inversion is not a property of the linearized quantum fluctuations. We present numerical and analytical results which clarify the physics of the inversion. The maximum inversion possible is determined. We attempt to identify obstacles to the experimental realization of steady-state inversion. Multiple atoms and multiple cavity modes do not destroy the effect. A significant difficulty appears to be localizing the atoms at the cavity beamwaist until they reach steady state. The inversion may be observed via fluorescence changes as the cavity is blocked and unblocked or via the presence of a fluoresence maximum as a function of the driving field intensity.
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.
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.
We consider a single two-level atom in an optical cavity, in which the system is driven by a coherent driving field. In the bad-cavity limit, when the cavity loss rate is taken to be large compared to the atomic decay rate and atom-field coupling, the cavity field can be adiabatically eliminated from the equations of motion for the atomic operators. The main effect of the cavity in this limit is the enhancement of spontaneous emission into the cavity mode. For this model, the second-order intensity correlation function g(2)() has been shown to exhibit photon antibunching, sub-Poissonian photon number distributions, and other nonclassical effects.1 In this paper, analytic results are presented for g(2)() for both the transmitted and fluorescent light fields when broadband squeezed light is injected into the cavity. Effects of the squeezing on nonclassical behavior is examined.
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.
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.