We prepare arbitrary patterns of neutral atoms in a one-dimensional (1D) optical lattice with single-site precision using microwave radiation in a magnetic field gradient. We give a detailed account of the current limitations and propose methods to overcome them. Our results have direct relevance for addressing of planes, strings or single atoms in higher dimensional optical lattices for quantum information processing or quantum simulations with standard methods in current experiments. Furthermore, our findings pave the way for arbitrary single qubit control with single site resolution.

Spin-dependent optical potentials allow us to use microwave radiation to manipulate the motional state of trapped neutral atoms Phys. Rev. Lett. 103, 233001). Here, we discuss this method in greater detail, comparing it to the widely-employed Raman sideband coupling method. We provide a simplified model for sideband cooling in a spin-dependent potential, and we discuss it in terms of the generalized Lamb-Dicke parameter. Using a master equation formalism, we present a quantitative analysis of the cooling performance for our experiment, which can be generalized to other experimental settings. We additionally use microwave sideband transitions to engineer motional Fock states and coherent states, and we devise a technique for measuring the population distribution of the prepared states.

Engineering quantum particle systems, such as quantum simulators and quantum cellular automata, relies on full coherent control of quantum paths at the single particle level. Here we present an atom interferometer operating with single trapped atoms, where single particle wave packets are controlled through spin-dependent potentials. The interferometer is constructed from a sequence of discrete operations based on a set of elementary building blocks, which permit composing arbitrary interferometer geometries in a digital manner. We use this modularity to devise a space-time analogue of the well-known spin echo technique, yielding insight into decoherence mechanisms. We also demonstrate mesoscopic delocalization of single atoms with a separation-to-localization ratio exceeding 500; this result suggests their utilization beyond quantum logic applications as nano-resolution quantum probes in precision measurements, being able to measure potential gradients with precision 5 × 10 −4 in units of gravitational acceleration g.single atom manipulation | atom interferometry | quantum engineering Localized ParticlesParticle interferometry has yielded numerous important results from the advent of quantum mechanics until now; counting only the most recent ones, they range from precision measurements (1) and fundamental tests of quantum mechanics (2, 3) to applications in optical and superconducting magnetometry (4, 5). Whereas other architectures provide a natural way to engineer, guide, and confine interfering paths, e.g., by means of optical waveguides for photons or superconducting circuits for electrons, one key challenge for atoms consists in realizing a flexible platform that is capable of providing complex interfering geometries where the atoms remain localized at all times. Unprecedented control over atomic states has been obtained in optical lattice potentials; designed to mimic solid state systems they resemble engineered circuits. To construct interfering paths in these systems, an additional quantum number is needed-that has to be decoupled from motional states-for the atomic wave packet's motion to be steered in a coherent and state-dependent manner. This additional control is achieved by leaving the simple scalar concept of an atom and taking advantage of its vector nature endowed by electronic and nuclear spin. Mediated by the spin-orbit interaction, optical dipole forces yield a state-dependent force, offering the right handle for steering atomic paths. Therefore, an effective magnetic field coupled to the atomic magnetic moment makes position control of the interfering paths possible, albeit at the expense of an increased sensitivity to magnetic fields (6-8). Even though this direct coupling to magnetic fields is not a fundamental limitation, it represents a technical hurdle that demands efficient shielding against stray magnetic field fluctuations; accepting this price, digital engineering of atomic paths in optical potentials can bring atom interferometry to a unique level of control. Particle localization...

We investigate the possible superconducting pairing symmetries which would account for the latest experimental results on the Bechgaard salts. Using a renormalization group (R.G) technique we calculate the couplings of the singlet and triplet interactions in the quasi 1D Hamiltonian. In the presence of interchain interactions, the singlet and triplet couplings are of the same order of magnitude. The renormalized couplings are then used in an RPA calculation to evaluate the critical fields of superconductivity for the two dominant order parameter symmetries in the R.G flow, i.e, the d x 2 −y 2 and fy symmetries. It is shown that, for the standard values of the anisotropy ratio of the Fermi surface, the critical fields of the singlet symmetry are strongly reduced. A reentrant superconductivity is however still present for the triplet state.

We propose a theoretical model of quasi-one-dimensional superconductors, with attractive electron-electron interactions dominant in the singlet d-wave channel and sub-dominant in the pwave channel. We discuss, in the mean field approximation, the effect of a magnetic field applied perpendicularly to the direction of the lowest conductivity. The lowest free energy phase corresponds to a singlet d-wave symmetry in low fields, but to a triplet symmetry in high fields. A first order singlet-triplet phase transition is expected at moderate applied fields of a few teslas. We propose to ascribe the recent critical field and NMR experimental data, observed in superconducting (T M T SF )2ClO4 to such an effect.PACS numbers: 74.70. Tx, 74.25.Op, 74.20.Rp The nature of superconductivity in the family of the quasi-1D organic superconductors [1, 2, 3] (T M T SF ) 2 X (X = P F 6 , ClO 4 ,...) has been a long standing issue for the last three decades. There is still a debate whether it is a conventional superconductivity, with a completely gapped Fermi surface, or an unconventional one with points or lines of nodes on the gap. Many experiments have tried to address this question using different techniques such as NMR relaxation rate, thermal conductivity, non magnetic impurity effect on T c , Knight Shift and upper critical field measurements.The temperature dependence of the proton spin lattice relaxation rate, measured by Takigawa et al. [6] studied the effect of non magnetic impurities on the superconducting critical temperature T c [7], and showed unequivocally that the order parameter changes sign on the Fermi surface and that consequently the gap has nodes where it is zero on the Fermi surface. This is in complete agreement with a model of unconventional superconductivity in these organic materials.However, whether the pairing of the electrons in the superconducting state is in the singlet or the triplet symmetry remains an unsolved question. Measurements of the upper critical field of superconductivity in these materials [8,9,10] showed a superconducting state surviving up to a field as high as 9 T in the case of the P F 6 compounds [8], and at least 5 T in the case of the ClO 4 compounds [9]. These fields exceed by far the Clogston-Pauli paramagnetic limit [11] for homogeneous singlet superconductivity, which is estimated to be of the order of 1.84 T c , with a T c around 1.1 K in these materials. This result is a strong indication that at high magnetic fields superconductivity could not be of a homogeneous singlet type. Many theories [12,13,14] have been proposed to explain this behaviour by a triplet superconducting state, which is a non Pauli limited state. At low magnetic fields, however, besides the observation by Andres et al.[15] of a diamagnetic signal when the field is perpendicular to the chains indicating a singlet state, measurements of the Knight-Shift [16] showed a significant variation from the normal state behaviour of the spin susceptibility of Cooper pairs which decreased with decreasing temperatur...

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