We load atoms into every site of an optical lattice and selectively spin flip atoms in a sublattice consisting of every other site. These selected atoms are separated from their unselected neighbors by less than an optical wavelength. We also show spin-dependent transport, where atomic wave packets are coherently separated into adjacent sites according to their internal state. These tools should be useful for quantum information processing and quantum simulation of lattice models with neutral atoms.

Favored schemes for trapped-ion quantum logic gates use bichromatic laser fields to couple internal qubit states with external motion through a "spin-dependent force." We introduce a new degree of freedom in this coupling that reduces its sensitivity to phase decoherence. We demonstrate bichromatic spin-dependent forces on a single trapped 111 Cd + ion, and show that phase coherence of the resulting "Schrödinger-cat" states of motion depends critically upon the spectral arrangement of the optical fields. This applies directly to the operation of entangling gates on multiple ions.PACS numbers: 42.50.Vk,03.67.Mn,03.67.Lx Trapped atomic ions have a number of desirable features that make them well suited for quantum information applications [1]. Pairs of hyperfine ground states provide an ideal host for quantum bits (qubits) that can be manipulated and entangled via optical Raman transitions [2]. Since the first proposal for entangling trapped ions [3], significant theoretical advances have relaxed the constraints on implementation to realize more robust entanglement schemes [4,5,6,7]. These schemes rely on a spin-dependent force acting on each ion where "spin" refers to the effective Pauli spin associated with the ionqubit's two-level system. Acting on a single ion, the force can entangle the ion's spin degree of freedom with its motion; following disentanglement, the ion acquires a net geometric phase that is spin dependent [6]. When the force is applied to two ions, the geometric phase depends nonlinearly on their spins through their mutual Coulomb interaction, generating entanglement.Optical Raman fields are a convenient way to create strong spin-dependent forces for hyperfine ion-qubits [8,9]. For example, an entangling gate based on aσ zdependent force has been realized with a state-dependent AC Stark shift from Raman fields [10], whereσ x,y,z are the Pauli operators. Unfortunately, suchσ z gates are not compatible with magnetic field insensitive (or "clock") qubit states [2,11], and are therefore open to qubit phase decoherence from fluctuating magnetic fields. An alternative solution is the Mølmer-Sørensen (MS) gate [4,12,13], which uses a more complicated arrangement of bichromatic fields to realize aσ φ -type force whereσ φ is a linear combination ofσ x andσ y operators. While the gate does work on clock states, it can have a significant phase instability due to the hyperfine coherences required to generate the spin dependence. All gates, whatever the spin dependence, are susceptible to fast phase fluctuations of the Raman fields during the course of gate evolution. However, the MS gate can also be susceptible to slow phase drifts, which cause changes in the spin dependence of the force and results in a phase instability between gates.In this Letter we show how to overcome phase drifts in the MS gate, allowing clock-state benefits to be realized for ion-based qubits. Such ideas may be useful in other experimental settings since the MS scheme is a general paradigm for entanglement [14]. A bichromatic for...

We report the implementation of Grover's quantum search algorithm in the scalable system of trapped atomic ion quantum bits. Any one of four possible states of a two-qubit memory is marked, and following a single query of the search space, the marked element is successfully recovered with an average probability of 60(2)%. This exceeds the performance of any possible classical search algorithm, which can only succeed with a maximum average probability of 50%. PACS numbers:Quantum computers promise dramatic speedup over conventional computers in some applications owing to the power of entangled superpositions [1]. Among the best-known quantum applications is Grover's search algorithm, which can search an unsorted database quadratically faster than any known classical search [2]. A common analogy for this searching algorithm is the problem of finding a person's name in a phone book given only their phone number [3]: for N entries in the phonebook, this requires of order N queries. However, if the correlation between name and phone number is encoded with quantum bits, the name can be found after only about √ N queries. While Grover's algorithm does not attain the exponential speedup of Shor's quantum factoring algorithm [4], it may be more versatile, by providing quadratic gains for almost any quantum algorithm [5] or accelerating NP-complete problems through exhaustive searches over possible solutions [6].We implement the Grover search algorithm over a space of N=4 elements using two trapped atomic ion qubits [7,8]. Grover's algorithm has been implemented with ensembles of molecules using nuclear magnetic resonance [9,10,11], with states of light using linear optical techniques [12,13], and with Rydberg states within individual atoms [14]. None of these systems are scalable however, as they require exponential resources as the number of qubits grows. The implementation of Grover's algorithm reported here complements the repertoire of multi-qubit quantum algorithms recently demonstrated in the scalable system of trapped atomic ions [15,16,17,18]. Unlike these earlier ion trap demonstrations, we use magnetically-insensitive "clock state" qubits and particular entangling gates that are uniquely suited to such qubits while remaining insensitive to external phase drifts between gates [19,20,21].At the heart of Grover's algorithm is the "oracle query," which quickly checks if a proposed input "x" is a solution to the search problem. The oracle marks a particular component of a quantum superposition by flipping the sign of its amplitude. Following the oracle, a number of quantum operations amplify the weighting of the marked state independent of which state is

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