Dark resonances as a probe for the motional state of a single ion

Single, rf-trapped ions find various applications ranging from metrology to quantum computation. High-resolution interrogation of an extremely weak transition under best observation conditions requires an ion almost at rest. To avoid line-broadening effects such as the second order Doppler effect or rf heating in the absence of laser cooling, excess micromotion has to be eliminated as far as possible. In this work the motional state of a confined three-level ion is probed, taking advantage of the high sensitivity of observed dark resonances to the trapped ion's velocity. Excess micromotion is controlled by monitoring the dark resonance contrast with varying laser beam geometry. The influence of different parameters such as the cooling laser intensity has been investigated experimentally and numerically

Raman cooling and heating of two trapped Ba+ ions

We study cooling of the collective vibrational motion of two 138Ba+ ions confined in an electrodynamic trap and irradiated with laser light close to the resonances S_1/2-P_1/2 (493 nm) and P_1/2-D_3/2 (650 nm). The motional state of the ions is monitored by a spatially resolving photo multiplier. Depending on detuning and intensity of the cooling lasers, macroscopically different motional states corresponding to different ion temperatures are observed. We also derive the ions' temperature from detailed analytical calculations of laser cooling taking into account the Zeeman structure of the energy levels involved. The observed motional states perfectly match the calculated temperatures. Significant heating is observed in the vicinity of the dark resonances of the Zeeman-split S_1/2-D_3/2 Raman transitions. Here two-photon processes dominate the interaction between lasers and ions. Parameter regimes of laser light are identified that imply most efficient laser cooling.Comment: 8 pages, 5 figure

Cooling atomic motion with quantum interference

We theoretically investigate the quantum dynamics of the center of mass of trapped atoms, whose internal degrees of freedom are driven in a $\Lambda$-shaped configuration with the lasers tuned at two-photon resonance. In the Lamb-Dicke regime, when the motional wave packet is well localized over the laser wavelenght, transient coherent population trapping occurs, cancelling transitions at the laser frequency. In this limit the motion can be efficiently cooled to the ground state of the trapping potential. We derive an equation for the center-of-mass motion by adiabatically eliminating the internal degrees of freedom. This treatment provides the theoretical background of the scheme presented in [G. Morigi {\it et al}, Phys. Rev. Lett. {\bf 85}, 4458 (2000)] and implemented in [C.F. Roos {\it et al}, Phys. Rev. Lett. {\bf 85}, 5547 (2000)]. We discuss the physical mechanisms determining the dynamics and identify new parameters regimes, where cooling is efficient. We discuss implementations of the scheme to cases where the trapping potential is not harmonic.Comment: 11 pages, 3 figure

Resonance fluorescence of a trapped three-level atom

We investigate theoretically the spectrum of resonance fluorescence of a harmonically trapped atom, whose internal transitions are $\Lambda$--shaped and driven at two-photon resonance by a pair of lasers, which cool the center--of--mass motion. For this configuration, photons are scattered only due to the mechanical effects of the quantum interaction between light and atom. We study the spectrum of emission in the final stage of laser--cooling, when the atomic center-of-mass dynamics is quantum mechanical and the size of the wave packet is much smaller than the laser wavelength (Lamb--Dicke limit). We use the spectral decomposition of the Liouville operator of the master equation for the atomic density matrix and apply second order perturbation theory. We find that the spectrum of resonance fluorescence is composed by two narrow sidebands -- the Stokes and anti-Stokes components of the scattered light -- while all other signals are in general orders of magnitude smaller. For very low temperatures, however, the Mollow--type inelastic component of the spectrum becomes visible. This exhibits novel features which allow further insight into the quantum dynamics of the system. We provide a physical model that interprets our results and discuss how one can recover temperature and cooling rate of the atom from the spectrum. The behaviour of the considered system is compared with the resonance fluorescence of a trapped atom whose internal transition consists of two-levels.Comment: 11 pages, 4 Figure

Quantum jumps induced by the center-of-mass motion of a trapped atom

We theoretically study the occurrence of quantum jumps in the resonance fluorescence of a trapped atom. Here, the atom is laser cooled in a configuration of level such that the occurrence of a quantum jump is associated to a change of the vibrational center-of-mass motion by one phonon. The statistics of the occurrence of the dark fluorescence period is studied as a function of the physical parameters and the corresponding features in the spectrum of resonance fluorescence are identified. We discuss the information which can be extracted on the atomic motion from the observation of a quantum jump in the considered setup

Resonance Fluorescence Spectrum of a Trapped Ion Undergoing Quantum Jumps

We experimentally investigate the resonance fluorescence spectrum of single 171Yb and 172Yb ions which are laser cooled to the Lamb-Dicke regime in a radiofrequency trap. While the fluorescence scattering of 172Yb is continuous, the 171Yb fluorescence is interrupted by quantum jumps because a nonvanishing rate of spontaneous transitions leads to electron shelving in the metastable hyperfine sublevel 2D3/2(F=2). The average duration of the resulting dark periods can be varied by changing the intensity of a repumping laser field. Optical heterodyne detection is employed to analyze the fluorescence spectrum near the Rayleigh elastic scattering peak. It is found that the stochastic modulation of the fluorescence emission by quantum jumps gives rise to a Lorentzian component in the fluorescence spectrum, and that the linewidth of this component varies according to the average duration of the dark fluorescence periods. The experimental observations are in quantitative agreement with theoretical predictions.Comment: 14 pages including 4 figures, pdf file, fig.1 replace

The spectrum of single-atom resonance fluorescence

The emission spectrum of the bichromatically excited resonance fluorescence of a single atomic particle, i.e. of a permanently trapped and cooled ${\rm Ba}^+$ ion has been recorded. It shows up to five peaks, two of them partially resolved, in agreement with fluorescence spectra of three-level atoms calculated from sets of parameters separately measured from recorded excitation spectra of the integrated fluorescence

An atom and a photon

10.1134/S1054660X0707016XLaser Physics1771007-101