The coherent dipole-dipole interactions of atoms in an atomic array are studied. It is found that the excitation probability of an atom in an array parallel to the direction of laser propagation (k) will either grow or decay logarithmically alongk, depending on the detuning of the laser. The symmetry of the system for atomic separations of δr = jλ/2, where j is an integer, causes the excitation distribution and scattered radiation to abruptly become symmetric about the center of the array. For atomic separations of δr < λ/2, the appearance of a collection of extremely subradiant states (Γ ∼ 0), disrupts the described trend. In order to interpret the results from a finite array of atoms, a band structure calculation in the N → ∞ limit is conducted where the decay rates and the collective Lamb shifts of the eigenmodes along the Brillouin zone are shown. Finally, the band structure of an array strongly affects its scattered radiation, allowing one to manipulate the collective Lamb shift as well as the decay rate (from superradiant to subradiant) by changing the angle of the driving laser.

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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 trueσ^ϕ⊗trueσ^ϕ or trueσ^z⊗trueσ^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 trueσ^z⊗trueσ^z gates can be implemented in a novel manner which eases experimental constraints. We present numerical simulations of gate fidelities assuming realistic parameters.

We present a new method of spin-motion coupling for trapped ions using microwaves and a magnetic field gradient oscillating close to the ions' motional frequency. We demonstrate and characterize this coupling experimentally using a single ion in a surface-electrode trap that incorporates current-carrying electrodes to generate the microwave field and the oscillating magnetic field gradient. Using this method, we perform resolved-sideband cooling of a single motional mode to its ground state.