Trapped ions are among the most promising systems for practical quantum computing (QC). The basic requirements for universal QC have all been demonstrated with ions and quantum algorithms using few-ion-qubit systems have been implemented. We review the state of the field, covering the basics of how trapped ions are used for QC and their strengths and limitations as qubits. In addition, we discuss what is being done, and what may be required, to increase the scale of trapped ion quantum computers while mitigating decoherence and control errors. Finally, we explore the outlook for trapped-ion QC. In particular, we discuss near-term applications, considerations impacting the design of future systems of trapped ions, and experiments and demonstrations that may further inform these considerations. CONTENTS

We demonstrate the production of ultracold polar RbCs molecules in their vibronic ground state, via photoassociation of laser-cooled atoms followed by a laser-stimulated state transfer process. The resulting sample of X 1 Σ + (v = 0) molecules has a translational temperature of ∼ 100 µK and a narrow distribution of rotational states. With the method described here it should be possible to produce samples even colder in all degrees of freedom, as well as other bi-alkali species.PACS numbers: 33.80. Ps, 39.25.+k, 33.80.Wz, 33.70.Ca Samples of ultracold, polar molecules (UPMs) can provide access to new regimes in many phenomena. Ultracold temperatures allow trapping, and polarity can be used to engineer large, anisotropic, and tunable interactions between molecules. These features make UPMs attractive as qubits for quantum computation [1], as building blocks for novel types of many-body systems [2], and for the study of chemistry in the ultracold regime [3]. Furthermore, UPMs can be used as uniquely sensitive probes of phenomena beyond the Standard Model of particle physics [4].Methods such as buffer-gas cooling [5], Stark-slowing [6], billiard-like collisions [7], and velocity filtering [8] have produced samples of polar molecules at temperatures of ∼ 10-100 mK. Formation of heteronuclear molecules from pre-cooled atoms via photoassociation (PA) [9,10,11,12] or Feshbach resonance techniques [13] promises access to much lower temperatures; however, these processes leave molecules in highly excited vibrational levels, which have vanishingly small polarity [14] and are unstable to collisions [15,16]. The possibility of transferring such molecules to their vibronic ground state, via optical processes such as stimulated Raman transitions, has been discussed extensively (see e.g. [1,17,18,19,20]); however, insufficient data on the structure of experimentally accessible molecules has made it difficult to identify specific pathways for efficient transfer.Here we report the production of UPMs via PA of laser-cooled Rb and Cs atoms, followed by a two-step stimulated emission pumping (SEP) process. This yields RbCs molecules in their absolute vibronic ground state X 1 Σ + (v = 0). These polar molecules (calculated electric dipole moment µ ≈ 1.3 D [21]) have a translational temperature of ∼ 100 µK. The distribution of rotational states is also quite narrow, so the resulting sample of X 1 Σ + state molecules is cold in all degrees of freedom. Figure 1 shows the methods by which we produce and detect UPMs. A pair of colliding, ultracold Rb and Cs atoms is photoassociated, i.e., the pair absorbs a photon and is driven to an electronically excited molecular level [22]. This level decays rapidly, with branching fraction of ∼ 7% into the long-lived a 3 Σ + (v = 37) level [9]. After a period of PA, a resonant laser pulse ("pump" pulse) transfers these metastable, vibrationally excited molecules to an intermediate, electronically excited state (i). The population of state i is monitored by applying an intense laser pulse ("ionizat...

We have produced ultracold, polar RbCs * molecules via photoassociation in a laser-cooled mixture of Rb and Cs atoms. Using a model of the RbCs * molecular interaction which reproduces the observed rovibrational structure, we infer decay rates in our experiments into deeply bound X 1 Σ + ground state RbCs vibrational levels as high as 5×10 5 s −1 per level. Population in such deeply bound levels could be efficiently transferred to the vibrational ground state using a single stimulated Raman transition, opening the possibility to create large samples of stable, ultracold polar molecules.PACS numbers: 32.80. Pj, 33.80.Ps, 34.50.Gb, 34.50.Rk Ultracold polar molecules, due to their strong, longrange, anisotropic dipole-dipole interactions, may provide access to qualitatively new regimes previously inaccessible to ultracold atomic and molecular systems. For example, they might be used as the qubits of a scalable quantum computer [1]. New types of highly-correlated many-body quantum states could become accessible such as BCS-like superfluids [2], supersolid and checkerboard states [3], or "electronic" liquid crystal phases [4]. Ultracold chemical reactions between polar molecules have been discussed [5], and might be controlled using electric fields [6]. Finally, the sensitivity of current moleculebased searches for violations of fundamental symmetries [7] might be increased to unprecedented levels.Cold, trapped polar molecules have so far only been produced using either buffer-gas cooling [8] or Starkslowing [9], at temperatures of ∼10-100 mK [8,9]. This is much higher than the ∼1-100 µK accessible with atoms, and attempts to bridge this gap with evaporative cooling may run afoul of predicted molecular Feshbach resonances [10] or inelastic losses [11].Another approach is to extend well-known techniques for producing ultracold (non-polar) homonuclear diatomic molecules in binary collisions of ultracold atoms, either through photoassociation [12,13,14,15,16], or Feshbach resonance [17,18]. In these methods, the translational and rotational temperatures of the molecules are limited only by the initial atomic sample, possibly providing access all the way to the quantum-degenerate regime [15,18]. An important limitation, however, is that the molecules are typically formed in weakly bound vibrational levels near dissociation, which may have vanishing electric dipole moments [19], and are unstable with respect to inelastic collisions [10,11,15]; therefore, a method for transferring them to the vibrational ground state is desirable [14].Several authors have discussed the extension of these methods to the formation of (heteronuclear) polar molecules in collisions between different atomic species [20,21,22,23]. In recent experiments NaCs + and RbCs + ions formed in the presence of near-resonant light have indeed been observed in small numbers [21]; however, these observations did not permit an analysis of their formation mechanism, nor demonstrate a method for producing neutral, ultracold polar molecules.In this Letter, we ...

We propose new experiments with high sensitivity to a possible variation of the electron-to-proton mass ratio mu identical with m(e)/m(p). We consider a nearly degenerate pair of molecular vibrational levels, each associated with a different electronic potential. With respect to a change in mu, the change in the splitting between such levels can be large both on an absolute scale and relative to the splitting. We demonstrate the existence of such pairs of states in Cs2, where the narrow spectral lines achievable with ultracold molecules make the system promising for future searches for small variations in mu.