Quantum coherence and population trapping in three-photon processes

The spectroscopic properties of a single, tightly trapped atom are studied, when the electronic levels are coupled by three laser fields in an $N$-shaped configuration of levels, whereby a $\Lambda$-type level system is weakly coupled to a metastable state. We show that depending on the laser frequencies the response can be tuned from coherent population trapping at two-photon resonance to novel behaviour at three photon resonance, where the metastable state can get almost unit occupation in a wide range of parameters. For certain parameter regimes the system switches spontaneously between dissipative and coherent dynamics over long time scales

Experiments towards quantum information with trapped Calcium ions

Ground state cooling and coherent manipulation of ions in an rf-(Paul) trap is the prerequisite for quantum information experiments with trapped ions. With resolved sideband cooling on the optical S1/2 - D5/2 quadrupole transition we have cooled one and two 40Ca+ ions to the ground state of vibration with up to 99.9% probability. With a novel cooling scheme utilizing electromagnetically induced transparency on the S1/2 - P1/2 manifold we have achieved simultaneous ground state cooling of two motional sidebands 1.7 MHz apart. Starting from the motional ground state we have demonstrated coherent quantum state manipulation on the S1/2 - D5/2 quadrupole transition at 729 nm. Up to 30 Rabi oscillations within 1.4 ms have been observed in the motional ground state and in the n=1 Fock state. In the linear quadrupole rf-trap with 700 kHz trap frequency along the symmetry axis (2 MHz in radial direction) the minimum ion spacing is more than 5 micron for up to 4 ions. We are able to cool two ions to the ground state in the trap and individually address the ions with laser pulses through a special optical addressing channel.Comment: Proceedings of the ICAP 2000, Firenz

Shot-noise limited monitoring and phase locking of the motion of a single trapped ion

We perform high-resolution real-time read-out of the motion of a single trapped and laser-cooled Ba ion. By using an interferometric setup we demonstrate shot-noise limited measurement of thermal oscillations with resolution of 4 times the standard quantum limit. We apply the real-time monitoring for phase control of the ion motion through a feedback loop, suppressing the photon recoil-induced phase diffusion. Due to the spectral narrowing in phase-locked mode, the coherent ion oscillation is measured with resolution of about 0.3 times the standard quantum limit

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

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 [J. Eschner et al., Nature 413, 495-498 (2001)]. The experimental data are well described by 8-level optical Bloch equations which are amended to take into account the presence of the mirror according to the model in [U. Dorner and P. Zoller, Phys. Rev. A 66, 023816 (2002)]. Observed deviations from simple dispersive behavior are attributed to multi-level effects.Comment: version accepted by PR

Feedback cooling of a single trapped ion

Based on a real-time measurement of the motion of a single ion in a Paul trap, we demonstrate its electro-mechanical cooling below the Doppler limit by homodyne feedback control (cold damping). The feedback cooling results are well described by a model based on a quantum mechanical Master Equation.Comment: 4 pages, 3 figure

Coupling a single atomic quantum bit to a high finesse optical cavity

The quadrupole S$_{1/2}$ -- D$_{5/2}$ optical transition of a single trapped Ca$^+$ ion, well suited for encoding a quantum bit of information, is coherently coupled to the standing wave field of a high finesse cavity. The coupling is verified by observing the ion's response to both spatial and temporal variations of the intracavity field. We also achieve deterministic coupling of the cavity mode to the ion's vibrational state by selectively exciting vibrational state-changing transitions and by controlling the position of the ion in the standing wave field with nanometer-precision

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

Time-separated entangled light pulses from a single-atom emitter

The controlled interaction between a single, trapped, laser-driven atom and the mode of a high-finesse optical cavity allows for the generation of temporally separated, entangled light pulses. Entanglement between the photon-number fluctuations of the pulses is created and mediated via the atomic center-of-mass motion, which is interfaced with light through the mechanical effect of atom-photon interaction. By means of a quantum noise analysis we determine the correlation matrix which characterizes the entanglement, as a function of the system parameters. The scheme is feasible in experimentally accessible parameter regimes. It may be easily extended to the generation of entangled pulses at different frequencies, even at vastly different wavelengths.Comment: 17 pages, 5 figures. Modified version, to appear in the New Journal of Physic

Quantum state engineering on an optical transition and decoherence in a Paul trap

A single Ca+ ion in a Paul trap has been cooled to the ground state of vibration with up to 99.9% probability. Starting from this Fock state |n=0> we have demonstrated coherent quantum state manipulation on an optical transition. Up to 30 Rabi oscillations within 1.4 ms have been observed. We find a similar number of Rabi oscillations after preparation of the ion in the |n=1> Fock state. The coherence of optical state manipulation is only limited by laser and ambient magnetic field fluctuations. Motional heating has been measured to be as low as one vibrational quantum in 190 ms.Comment: 4 pages, 5 figure

Motional sidebands and direct measurement of the cooling rate in the resonance fluorescence of a single trapped ion

Resonance fluorescence of a single trapped ion is spectrally analyzed using a heterodyne technique. Motional sidebands due to the oscillation of the ion in the harmonic trap potential are observed in the fluorescence spectrum. From the width of the sidebands the cooling rate is obtained and found to be in agreement with the theoretical prediction.Comment: 4 pages, 4 figures. Final version after minor changes, 1 figure replaced; to be published in PRL, July 10, 200