We present a proposal for a versatile cold-atom-based quantum simulator of relativistic fermionic theories and topological insulators in arbitrary dimensions. The setup consists of a spin-independent optical lattice that traps a collection of hyperfine states of the same alkaline atom, to which the different degrees of freedom of the field theory to be simulated are then mapped. We show that the combination of bi-chromatic optical lattices with Raman transitions can allow the engineering of a spin-dependent tunneling of the atoms between neighboring lattice sites. These assisted-hopping processes can be employed for the quantum simulation of various interesting models, ranging from non-interacting relativistic fermionic theories to topological insulators. We present a toolbox for the realization of different types of relativistic lattice fermions, which can then be exploited to synthesize the majority of phases in the periodic table of topological insulators.

An Optical-Lattice-Based Quantum Simulator For Relativistic Field Theories and Topological Insulators

Individual addressing of qubits is essential for scalable quantum computation. Spatial addressing allows unlimited numbers of qubits to share the same frequency, while enabling arbitrary parallel operations. We demonstrate addressing of long-lived $^{43}\mathrm{Ca}^{+}$ ``atomic clock'' qubits held in separate zones ($960\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{m}$ apart) of a microfabricated surface trap with integrated microwave electrodes. Such zones could form part of a ``quantum charge-coupled device'' architecture for a large-scale quantum information processor. By coherently canceling the microwave field in one zone we measure a ratio of Rabi frequencies between addressed and nonaddressed qubits of up to 1400, from which we calculate a spin-flip probability on the qubit transition of the nonaddressed ion of $1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. Off-resonant excitation then becomes the dominant error process, at around $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. It can be prevented either by working at higher magnetic field, or by polarization control of the microwave field. We implement polarization control with error $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, which would suffice to suppress off-resonant excitation to the $\ensuremath{\sim}{10}^{\ensuremath{-}9}$ level if combined with spatial addressing. Such polarization control could also enable fast microwave operations.

High-fidelity spatial and polarization addressing of Ca-43 qubits using near-field microwave control

This thesis reports high-fidelity near-field spatial microwave addressing of long-lived 43Ca+ "atomic clock" qubits performed in a two-zone single-layer surface-electrode ion trap. Addressing is implemented by using two of the trap's integrated microwave electrodes, one in each zone, to drive single-qubit rotations in the zone we choose to address whilst interferometrically cancelling the microwave field at the neighbour (non-addressed) zone. Using this field-nulling scheme, we measure a Rabi frequency ratio between addressed and non-addressed zones of up to 1400, from which we calculate an addressing error (or a spin-flip probability on the qubit transition) of 1e-6. Off-resonant excitation out of the qubit state is a more significant source of error in this experiment, but we also demonstrate polarisation control of the microwave field at an error level of 2e-5, which, if combined with individual-ion addressing, would be sufficient to suppress off-resonant excitation errors to the 1e-9 level. Further, this thesis presents preliminary results obtained with a micron-scale coupled-microstrip differential antenna probe that can be scanned over an ion-trap chip to map microwave magnetic near fields. The probe is designed to enable the measurement of fields at tens of microns above electrode surfaces and to act as an effective characterisation tool, speeding up design-fabrication-characterisation cycles in the production of new prototype microwave ion-trap chips. Finally, a new multi-layer design for an ion-trap chip which displays, in simulations, a 100-fold improvement in addressing performance, is presented. The chip electrode structure is designed to use the cancelling effect of microwave return currents to produce Rabi frequency ratios of order 1000 between trap zones using a single microwave electrode (i.e. without the need for nulling fields). If realised, this chip could be used to drive individually addressed single-qubit operations on arrays of memory qubits in parallel and with high fidelity.

Diana Prado Lopes Aude Craik

Papers

Near-field microwave addressing of trapped-ion qubits for scalable quantum computation