[en] The optical Bloch equations, which give the time evolution of the elements of the density matrix of an atomic system subject to radiation, are generalized so that they can be applied when transitions between pairs of states can proceed by more than one stimulated route. The case considered is that for which the time scale of interest in the problem is long compared with that set by the differences in detuning of the radiation fields stimulating via the different routes. It is shown that the Bloch equations then reduce to the standard form of linear differential equations with constant coefficients. The theory is applied to a two-state system driven by two lasers with different intensities and frequencies and to a three-state Λ-system with one laser driving one transition and two driving the second. It is also shown that the theory reproduces well the observed response of a cold ⁴⁰Ca⁺ ion when subject to a single laser frequency driving the 4S_1/2-4P_1/2 transition and a laser with two strong sidebands driving 3D_3/2-4P_1/2

[en] We demonstrate simple and robust methods for Doppler cooling and obtaining high fluorescence from trapped "4"3Ca"+ ions at a magnetic field of 146 Gauss. This field gives access to a magnetic-field-independent ‘atomic clock’ qubit transition within the ground level hyperfine structure of the ion, but also causes the complex internal structure of the 64 states relevant to Doppler cooling to be spread over many times the atomic transition line-width. Using a time-dependent optical Bloch equation simulation of the system we develop a simple scheme to Doppler-cool the ion on a two-photon dark resonance, which is robust to typical experimental variations in laser intensities, detunings and polarizations. We experimentally demonstrate cooling to a temperature of 0.3 mK, slightly below the Doppler limit for the corresponding two-level system, and then use Raman sideband laser cooling to cool further to the ground states of the ion’s radial motional modes. These methods will enable two-qubit entangling gates with this ion, which is one of the most promising qubits so far developed. (paper)

[en] Laser cleaning of the electrodes in a planar micro-fabricated ion trap has been attempted using ns pulses from a tripled Nd:YAG laser at 355 nm. The effect of the laser pulses at several energy density levels has been tested by measuring the heating rate of a single ⁴⁰Ca⁺ trapped ion as a function of its secular frequency ω_z. A reduction of the electric-field noise spectral density by ∼50% has been observed and a change in the frequency dependence also noticed. This is the first reported experiment where the ‘anomalous heating’ phenomenon has been reduced by removing the source as opposed to reducing its thermal driving by cryogenic cooling. This technique may open up the way to better control of the electrode surface quality in ion microtraps. (paper)

[en] We describe a new electrode design for a surface-electrode Paul trap, which allows rotation of the normal modes out of the trap plane, and a technique for micromotion compensation in all directions using a two-photon process, which avoids the need for an ultraviolet laser directed to the trap plane. The fabrication and characterization of the trap are described, as well as its implementation for the trapping and cooling of single Ca⁺ ions. We also propose a repumping scheme that increases ion fluorescence and simplifies heating rate measurements obtained by time-resolved ion fluorescence during Doppler cooling.

[en] We present a general theory for laser-free entangling gates with trapped-ion hyperfine qubits, using either static or oscillating magnetic-field gradients combined with a pair of uniform microwave fields symmetrically detuned about the qubit frequency. By transforming into a ‘bichromatic’ interaction picture, we show that either ${\stackrel{^<!--\; ^\; -->}{\mathrm{\sigma <!--\; ??\; -->}}}_{\mathrm{\varphi <!--\; ??\; -->}}\otimes <!--\; ???\; -->{\stackrel{^<!--\; ^\; -->}{\mathrm{\sigma <!--\; ??\; -->}}}_{\mathrm{\varphi <!--\; ??\; -->}}$ or ${\stackrel{^<!--\; ^\; -->}{\mathrm{\sigma <!--\; ??\; -->}}}_z\otimes <!--\; ???\; -->{\stackrel{^<!--\; ^\; -->}{\mathrm{\sigma <!--\; ??\; -->}}}_z$ geometric phase gates can be performed. The gate basis is determined by selecting the microwave detuning. The driving parameters can be tuned to provide intrinsic dynamical decoupling from qubit frequency fluctuations. The ${\stackrel{^<!--\; ^\; -->}{\mathrm{\sigma <!--\; ??\; -->}}}_z\otimes <!--\; ???\; -->{\stackrel{^<!--\; ^\; -->}{\mathrm{\sigma <!--\; ??\; -->}}}_z$ gates can be implemented in a novel manner which eases experimental constraints. We present numerical simulations of gate fidelities assuming realistic parameters. (paper)