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arXiv:quant-ph/0306159 · Physical Review Letters

Vacuum-Field Level Shifts in a Single Trapped Ion Mediated by a Single Distant Mirror

M. A. Wilson, Pavel A. Bushev, Jürgen Eschner, Ferdinand Schmidt‐Kaler, Christoph Becher, R. Blatt, U. Dorner

Published Nov 21, 2003• 79 citations
arXivHTMLPDF

Abstract

A distant mirror leads to a vacuum-induced level shift in a laser-excited atom. This effect has been measured with a single mirror 25 cm away from a single, trapped barium ion. This dispersive action is the counterpart to the mirror's dissipative effect, which has been shown earlier to effect a change in the ion's spontaneous decay [Nature (London) 413, 495 (2001)]]. The experimental data are well described by eight-level optical Bloch equations which are amended to take into account the presence of the mirror according to the model in Phys. Rev. A 66, 023816 (2002)]. Observed deviations from simple dispersive behavior are attributed to multilevel effects.

DOI
10.1103/physrevlett.91.213602

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A distant mirror leads to a vacuum-induced level shift in a laser-excited atom. This effect has been measured with a single mirror 25 cm away from a single, trapped barium ion. This dispersive action is the counterpart to the mirror's dissipative effect, which has been shown earlier to effect a change in the ion's spontaneous decay [Nature (London) 413, 495 (2001)]]. The experimental data are well described by eight-level optical Bloch equations which are amended to take into account the presence of the mirror according to the model in Phys. Rev. A 66, 023816 (2002)]. Observed deviations from simple dispersive behavior are attributed to multilevel effects.
An excited-state atom whose emitted light is backreflected by a distant mirror can experience trapping forces, because the presence of the mirror modifies both the electromagnetic vacuum field and the atom's own radiation reaction field. We demonstrate this mechanical action using a single trapped barium ion. We observe the trapping conditions to be notably altered when the distant mirror is translated across an optical wavelength. The well-localized barium ion enables the spatial dependence of the forces to be measured explicitly. The experiment has implications for quantum information processing and may be regarded as the most elementary optical tweezers.
A single Ba/sup +/ ion is confined in a miniature Paul trap and Doppler cooled with green laser light at 493 nm and red light at 650 nm. A theoretical description of the experiment predicts that a level shift of the upper (P/sub 1/2/) state is associated with the modified decay. This level shift is observed in the following way: as the frequency detuning of the red laser is scanned across resonance, the phase between green and red fringes is recorded. Varying the mirror-ion distance leads to high-visibility interference fringes in the green fluorescence (/spl sim/60%) whilst the red fluorescence, that is transmitted by the mirror and detected by photomultiplier, is seen to be modulated with the same period but with lower visibility (/spl sim/1-2%). The modulation of the red light indicates a modified decay rate on the green transition, showing that the mirror changes the vacuum field at the green wavelength and leads to enhancement and inhibition of spontaneous decay from the upper state.
The behavior of a two-level atom in a half-cavity, i.e., a cavity with one mirror, is studied within the framework of a one-dimensional model with respect to spontaneous decay and resonance fluorescence. The system under consideration corresponds to the setup of a recently performed experiment [J. Eschner et al., Nature (London) 413,413,413, 495 (2001)] where the influence of a mirror on a fluorescing single atom was revealed. In the present work special attention is paid to the regime of large atom-mirror distances where intrinsic memory effects can not longer be neglected. This is done with the help of delay-differential equations which contain, for small atom-mirror distances, the Markovian limit with effective level shifts and decay rates leading to the phenomenon of enhancement or inhibition of spontaneous decay. Several features are recovered beyond an effective Markovian treatment, appearing in experimentally accessible quantities like the intensity or emission spectra of the scattered light.
We describe a series of experiments showing how a single trapped ion, which interacts with its own resonance fluorescence via a distant mirror, exhibits cavity-QED effects such as modified spontaneous emission, level shifts, and even mechanical forces. The same interaction is used to establish feedback on the ion's quantum motion, providing additional cooling and phase stabilisation of its vibration in the trap. Based on these methods and results we present an experiment dedicated at creating entanglement between two distant ions by projective measurements.
By tightly focusing a laser field onto a single cold ion trapped in front of a far-distant dielectric mirror, we could observe a quantum electrodynamic effect whereby the ion behaves as the optical mirror of a Fabry-Pérot cavity. We show that the amplitude of the laser field is significantly altered due to a modification of the electromagnetic mode structure around the atom in a novel regime in which the laser intensity is already changed by the atom alone. We propose a direct application of this system as a quantum memory for single photons.