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Physical Review A

Squeezing in resonance fluorescence from a trapped ion

R. L. de Matos Filho, W. Vogel

Published Apr 1, 1994• 15 citations
Publisher

Abstract

Squeezing of the fluorescence light from a single trapped and laser-cooled ion is studied for atomic localization conditions far from the Lamb-Dicke limit. The quantum center-of-mass motion significantly influences the quantum fluctuations of the fluorescence light field. Both for traveling- and standing-wave excitation squeezing is found to depend on the observation direction.

DOI
10.1103/physreva.49.2812

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Chinese Physics•Jun 1, 2007•1 citation
Squeezing of the fluorescence light from a single trapped and laser-cooled ion is studied for atomic localization conditions far from the Lamb-Dicke limit. The quantum center-of-mass motion significantly influences the quantum fluctuations of the fluorescence light field. Both for traveling- and standing-wave excitation squeezing is found to depend on the observation direction.
The spectrum of resonance fluorescence of a single trapped and laser-cooled ion is studied theoretically. The quantum motion of the trapped particle manifests itself in the form of narrow motional sidebands in the fluorescence spectrum. For our calculations it is assumed that the ion is confined to dimensions much smaller than the optical wavelength (Lamb-Dicke limit) and the approach is valid for multilevel systems, general trapping potentials, and for both traveling-wave and standing-wave configurations. The motional sidebands in the spectrum have asymmetric amplitudes and this asymmetry is shown to depend on the ion energy, the detector position, and the choice of standing- or traveling-wave laser excitation.
The spectrum of resonance fluorescence of a single trapped and laser-cooled ion is studied theoretically. The quantum motion of the trapped particle manifests itself in the form of narrow motional sidebands in the fluorescence spectrum. For our calculations it is assumed that the ion is confined to dimensions much smaller than the optical wavelength (Lamb-Dicke limit) and the approach is valid for multilevel systems, general trapping potentials, and for both traveling-wave and standing-wave configurations. The motional sidebands in the spectrum have asymmetric amplitudes and this asymmetry is shown to depend on the ion energy, the detector position, and the choice of standing- or traveling-wave laser excitation.
Starting from the Jaynes-Cummings(J-C) model describing the interaction of a trapped ion with a standing wave laser field,we derive the interaction Hamiltonian on the nonlinear J-C model of the trapped ion excited resonantly with single quantum vibrational mode.After solving the time dependent states of this model,we study the ion centroid motion of squeezing effects by utilizing the ion numerical model.It is shown that the ion squeezing effects is related with the Lamb-Dicke parameter and the position of the ion in the standing wave laser field.
The resonant heating of a harmonically trapped ion by a standing-wave light field is described as a quantum stochastic process combining a coherent Schrödinger evolution with Bohr-Einstein quantum jumps. The dependence of the center-of-mass motion on Lamb-Dicke parameter is studied. For Lamb-Dicke parameters greater than unity we demonstrate significant departures from the diffusion process that holds in the limit of small momentum “kicks”; a strong inhibition of the heating of the ion (fluorescence) occurs. Heating rates are calculated as a Monte-Carlo average from both the full quantum stochastic process and its semi-quantum approximation.
The resonance fluorescence spectrum of a laser-cooled trapped ion is theoretically studied in the Lamb-Dicke limit. Angular averaged spectrum around the elastic peak and the motional sidebands is calculated. The widths of the sidebands are shown to be given by the cooling rate of the ion in the trap. In the limit when the trapping force is strong a possibility of dispersive line shapes is predicted. The spectrum derived is also shown to reproduce in the low-intensity limit the earlier perturbative results.