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Physical Review A

Vibrational amplification by stimulated emission of radiation

Sascha Wallentowitz, W. Vogel, Ingo Siemers, P. E. Toschek

Published Jul 1, 1996• 42 citations
Publisher

Abstract

We propose the use of a single trapped and laser-cooled ion for vibrational amplification assisted by stimulated emission of radiation. This quantum-mechanical counterpart of the micromaser allows one to modify the fundamental vibronic coupling externally. In particular, a vibrational number state can be prepared in a coherent interaction regime, whereas incoherent interaction may yield a sub-Poissonian, binomial number distribution. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.943

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We propose the use of a single trapped and laser-cooled ion for vibrational amplification assisted by stimulated emission of radiation. This quantum-mechanical counterpart of the micromaser allows one to modify the fundamental vibronic coupling externally. In particular, a vibrational number state can be prepared in a coherent interaction regime, whereas incoherent interaction may yield a sub-Poissonian, binomial number distribution. \textcopyright{} 1996 The American Physical Society.
We propose a model for a single-trapped-ion vibronic Raman laser and study its dynamics by using quantum-trajectory methods. In our treatment, it is essential that both the cavity field of the high-finesse optical cavity and the center-of-mass vibrational motion of the trapped ion be quantized. A transition from a super-Poissonian light source to a Poissonian lasing regime is obtained by increasing the Raman coupling constant. Furthermore, we demonstrate that a nonclassical regime can be realized, where the photon statistics becomes sub-Poissonian and the photons leak out of the cavity in an antibunched manner. This is achieved by exploiting nonlinear Stark shifts inherent in the model, which depend on both the number of cavity photons and the number of vibrational quanta.
Introduction Previous discussions (see Section 10.4) suggested that stimulated emission can be used to generate optical gain, that is, to amplify radiation. The reader certainly has experience in the amplification of electronic signal. For example, radio receivers capture faint radio waves and turn them into a signal that is powerful enough to drive large speakers. This electronic amplification increases the amplitude of the signal while faithfully preserving its acoustic frequencies and modulation characteristics. Similarly, optical amplification is expected to increase the amplitude of an optical signal while preserving its frequency, its modulation characteristics, and its coherence. The latter requirement is of particular significance for optical radiation, where the coherence of naturally occurring radiation rarely exceeds one micrometer. Lasers are the primary source for coherent radiation. They depend on stimulated emission for amplification and for the generation of coherent radiation (the word laser is the acronym of Light Amplification by Stimulated Emission of Radiation). For amplification, an atomic system that is part of the laser medium must be prepared with a sufficiently large number of particles in the excited state. (The term atomic system is used here to describe all microscopic systems including molecules and free electrons.) Radiation passing through that excited medium encounters multiple events of stimulated emission, each event contributing one photon that is added coherently to the propagating beam. When the number of events of stimulated emission exceed all losses by absorption or scattering, the incident radiation is amplified.
We consider ultracold atoms in a far detuned optical lattice across a high-QQQ optical resonator. Applying an external driving laser to the atoms red detuned from the cavity mode by one vibrational quantum induces cavity-enhanced sideband cooling. For a dense and cold enough atomic ensemble we predict an oscillation threshold for optical Raman sideband lasing concurrent with coherent matter-wave amplification. Above threshold, photons and atoms in the lowest band are dominantly created pairwise via stimulated emission with a strong suppression of competing spontaneous processes. In close analogy to a nondegenerate parametric oscillator, we find sub-Poissonian photon statistics and almost perfect nonclassical atom-photon number correlations. Injecting atoms in higher vibrational bands via tunneling or incoherent scattering then leads to continuous, simultaneous generation of a coherent atom beam and laser light with nonclassical atom-field correlations.
Highly excited eigenstates of the motion of an individual spatially confined atom may be prepared making use of a “trapping” mechanism based on the nonlinearity of the laser-mediated coupling of internal excitation and center-of-mass vibration of the atom. In contrast to micromaser-type trapping states, these states are insensitive to laser-phase fluctuations, and a long sequence of laser pulses may be applied to the atom with little degradation only of the atomic motion. Thus, vibrational number states of high quantum numbers are achievable.