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European Quantum Electronics Conference (EQEC)

Vacuum-field level shifts in a single atom mediated by a single distant mirror

Alex Wilson, PAVEL BOUCHEV, Jürgen Eschner, Christoph Becher, Ferdinand Schmidt‐Kaler, R. Blatt

Published Jan 1, 2003• 0 citations

Abstract

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.

DOI: 10.1109/eqec.2003.1314180

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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.

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.

The paper summarizes on the results of several experiments on single trapped ions which have been used to map optical fields. In these experiments, the ion was placed either in front of a (distant) mirror or in an optical cavity. Sub-wavelength resolution is achieved because the position of the ion relative to the mirror(s) is well-controlled and the ion's spatial wavefunction is confined to a region much smaller than the optical wavelength (400 to 800 nm). This strong localization is due to the trapping potential of a Paul-type ion trap, and laser cooling. In the three experiments the ions were Doppler-cooled, and a resolution between about 10 and 50 nm was achieved. With this resolution, the spatial variation of an optical standing-wave field was detected by shifting the single ion through the field structure.

Laser-cooled trapped ion crystals offer a unique opportunity to study the interactions between atoms. We have previously developed a microscopic planar Paul trap1 which is small and strong enough to bring the ion separation into the sub-micron region where quantum collective effects become important. A search is underway for the superradiant coupling of two atoms which manifests itself as a variation of the spontaneous emission rate with the ion-ion distance. We have produced an ion crystal with a separation of 1.1 microns in an 80 micron radius planar Paul trap. At this distance, equal to 2.2 wavelengths of the 493 nm Ba + transition, superradiant effects should alter the decay rate by about 10%. The two-ion crystal is imaged with sub-micron resolution by a new diffraction-limited vacuum-compatible microscope. The spontaneous emission rate is measured by a high repetition-rate transient spectrometer with an error of less than 1% for a single ion in a few minutes. Efficient extinction of the exciting laser light is provided by a new nonlinear electrooptic sideband switch.

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.

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,

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.