Control of neutral atoms in optical lattices
Neutral atoms are promising candidates to store and manipulate quantum information. In this thesis we examine several problems related to the control of neutral atoms for quantum computation and simulation. In the first problem we show how the transport of atoms in an optical lattice can be controlled through variation of the polarization of the optical lattice and the application of global microwave pulses. This type of control control is a first step in many of the schemes for quantum computation and quantum simulation. We show that with the available tools for global control, the synthesis of any unitary transformation, consistent with translational invariance, may be performed and provide an explicit method for carrying this out. In the second problem, we study a spectroscopic method for probing atomic interactions that may form the basis for two-qudit quantum logic gates. The confinement of atoms required to perform quantum computation can strongly affect how they interact. Probing the nature of those confinement-induced effects is a first step towards quantum computing with neutral atoms. Transport of the atoms to overlapping wells is achieved through microwave pulses that drive population between hyperfine levels in a lin-perp-lin polarization-gradient lattice. By measuring the amount of population transferred into certain excited states, we can detect changes in the spectrum of the two-atom system induced by the interaction. In the third problem, we consider a cloud of cold atoms driven by both microwave and radio-frequency magnetic fields. The large number of spin sublevels available in individual atoms makes them candidates for a qudit-based quantum computer. Because the applied fields that drive the system may be inhomogeneous, the collection of atoms forms an ensemble of different qudits. Borrowing ideas developed for NMR control, we show how to drive the ensemble through a given evolution. We show that even in the presence of large experimental errors, state preparation may be achieved with high fidelities. We also show that intentionally applied variations in spatial magnetic fields can be used to synthesize different states in different regions of space.
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