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.

Ground state laser cooling of a single trapped ion is achieved using a technique which tailors the absorption profile for the cooling laser by exploiting electromagnetically induced transparency in the Zeeman structure of a dipole transition. This new method is robust, easy to implement and proves particularly useful for cooling several motional degrees of freedom simultaneously, which is of great practical importance for the implementation of quantum logic schemes with trapped ions. PACS: 32.80.Pj, 42.50.Vk, 42.50.Gy, 03.67.Lx One of the most promising avenues towards implementing the fundamental ingredients of a scalable quantum computer is, as of today, based on trapped ions. With a string-like arrangement of several ions trapped in a radiofrequency (Paul) [5,7] and Raman sideband cooling [6], where a laser (or pair of lasers) exciting a narrow optical transition is detuned from the atomic resonance by the frequency of one motional quantum, thereby inducing transitions to lower-lying motional states until the ground state is reached.Although for quantum gate operation only one mode out of the 3N motional degrees of freedom of an Nion string is required to be cooled to the ground state, high-fidelity manipulation of the qubits requires the other modes to be deep inside the so-called Lamb-Dicke regime, where their residual vibrational amplitude is very small compared to the wavelength of the laser that induces optical transitions [8]. In conventional sideband and Raman sideband cooling, however, usually only one mode is cooled at a time, and the other modes are heated by spontaneous emission processes. A new cooling technique relying on electromagnetically induced transparency (EIT) [9] eliminates these difficulties largely by providing a larger cooling bandwidth, such that several modes can be cooled simultaneously, and by suppressing, through quantum interference, a large fraction of the heating processes. In this Letter we describe the first experimental demonstration of this technique and show that apart from its advantageous properties regarding heating and bandwidth it is also technically significantly simpler, thus making it a very favourable cooling method for quantum logic experiments with single ions.The theoretical background of the method as described in [9] has to be adapted only slightly to be applied to our experiment. We implemented the scheme on the S 1/2 → P 1/2 transition of a 40 Ca + ion, whose Zeeman sublevels form a four-level system. We denote the levels by |S, ± and |P, ± , see Fig.1. Three of the levels, |S, ± and |P, + , together with the σ + -and π-polarized laser beams, form a system of the kind considered in [9], and the main modification is the fourth level whose effect will be discussed below.The principle of the cooling is, briefly, that the stronger blue-detuned σ + light (the coupling laser) creates a Fanotype absorption profile for the π light (the cooling laser) which has a zero at ∆ π = ∆ σ (this is the EIT condition) and a bright resonance corresponding to the dressed...

We report measurements of the lifetimes of the 3d 2 D 5/2 and 3d 2 D 3/2 metastable states of a single laser-cooled 40 Ca + ion in a linear Paul trap. We introduce a new measurement technique based on high-efficiency quantum state detection after coherent excitation to the D 5/2 state or incoherent shelving in the D 3/2 state, and subsequent free, unperturbed spontaneous decay. The result for the natural lifetime of the D 5/2 state of 1168( 9) ms agrees excellently with the most precise published value. The lifetime of the D 3/2 state is measured with a single ion for the first time and yields 1176(11) ms which improves the statistical uncertainty of previous results by a factor of four. We compare these experimental lifetimes to high-precision ab initio all order calculations and find a very good agreement. These calculations represent an excellent test of high-precision atomic theory and will serve as a benchmark for the study of parity nonconservation in Ba + which has similar atomic structure.

We investigate theoretically the speed limit of quantum gate operations for ion trap quantum information processors. The proposed methods use laser pulses for quantum gates which entangle the electronic and vibrational degrees of freedom of the trapped ions. Two of these methods are studied in detail and for both of them the speed is limited by a combination of the recoil frequency of the relevant electronic transition, and the vibrational frequency in the trap. We have experimentally studied the gate operations below and above this speed limit. In the latter case, the fidelity is reduced, in agreement with our theoretical findings.