This thesis is concerned with the development of an intermediate magnetic field "clock-qubit" in 43Ca+ at 146G and techniques to manipulate this qubit using microwaves and lasers. While 43Ca+ has previously been used as a qubit, its relatively complicated level structure - with a nuclear spin of 7/2 and low-lying D-states -- makes cooling it in the intermediate field an intimidating prospect. As a result, previous experiments have used small magnetic fields of a few gauss where coherence times are limited and off-resonant excitation is a significant source of experimental error. We demonstrate a simple scheme that allows 43Ca+ to be cooled in the intermediate field without any additional experimental complexity compared with low fields. Using the clock-qubit, we achieve a coherence time of T*2 = 50 (10)s - the longest demonstrated in any single qubit. We also demonstrate a combined state preparation and measurement error of 6.8(6)x 10-4 - the lowest achieved for a hyperfine trapped ion qubit [NVG+13] - and single-qubit logic gates with average errors of 1.0(3) x 10-6 - more than an order of magnitude better than the previous record [BWC+11]. These results represent the state-of-the-art in the field of single-qubit control. Moreover, we achieve them all in a single scalable room-temperature ion trap using experimentally robust techniques and without relying on the use of narrow-linewidth lasers, magnetic field screening or dynamical decoupling techniques. We also present work on a recent scheme [OWC+11] to drive two-qubit gates using microwaves. We have constructed an ion trap with integrated microwave circuitry to perform these gates. Using this trap, we have driven motional sideband transitions, demonstrating the spin-motion coupling that underlies the two-qubit gate. We present an analysis of likely sources of experimental error during a future two-qubit gate and the design and preliminary characterisation of apparatus to minimise the main error contributions. Using this apparatus, we hope to perform a two-qubit gate in the near future.
This thesis is concerned with the development of an intermediate magnetic field "clock-qubit" in 43Ca+ at 146G and techniques to manipulate this qubit using microwaves and lasers. While 43Ca+ has previously been used as a qubit, its relatively complicated level structure - with a nuclear spin of 7/2 and low-lying D-states -- makes cooling it in the intermediate field an intimidating prospect. As a result, previous experiments have used small magnetic fields of a few gauss where coherence times are limited and off-resonant excitation is a significant source of experimental error. We demonstrate a simple scheme that allows 43Ca+ to be cooled in the intermediate field without any additional experimental complexity compared with low fields. Using the clock-qubit, we achieve a coherence time of T*2 = 50 (10)s - the longest demonstrated in any single qubit. We also demonstrate a combined state preparation and measurement error of 6.8(6)x 10-4 - the lowest achieved for a hyperfine trapped ion qubit [NVG+13] - and single-qubit logic gates with average errors of 1.0(3) x 10-6 - more than an order of magnitude better than the previous record [BWC+11]. These results represent the state-of-the-art in the field of single-qubit control. Moreover, we achieve them all in a single scalable room-temperature ion trap using experimentally robust techniques and without relying on the use of narrow-linewidth lasers, magnetic field screening or dynamical decoupling techniques. We also present work on a recent scheme [OWC+11] to drive two-qubit gates using microwaves. We have constructed an ion trap with integrated microwave circuitry to perform these gates. Using this trap, we have driven motional sideband transitions, demonstrating the spin-motion coupling that underlies the two-qubit gate. We present an analysis of likely sources of experimental error during a future two-qubit gate and the design and preliminary characterisation of apparatus to minimise the main error contributions. Using this apparatus, we hope to perform a two-qubit gate in the near future.
Quantum computers offer great potential for significant speedup in executing certain algorithms compared to their classical counterparts. One of the most promising physical systems in which implementing such a device seems viable are trapped atomic ions. All of the fundamental operations needed for quantum information processing have already been experimentally demonstrated in trapped ion systems. Today, the remaining two obstacles are to improve the fidelities of these operations up to the point where quantum error correction techniques can be successfully applied, as well as to scale up the present systems to a higher number of quantum bits (qubits). This thesis addresses both issues. On the one hand, it decribes the experimental implementation of a high-fidelity two-qubit quantum logic gate, which is the most technically demanding fundamental operation to realise in practice. On the other hand, the presented work is carried out in a microfabricated surface ion trap – an architecture that holds the promise of scalability. The gate is applied directly to hyperfine "atomic clock" qubits in 43Ca+ ions using the near-field microwave magnetic field gradient produced by an integrated trap electrode. To protect the gate against fluctuating energy shifts of the qubit states, as well as to avoid the need to null the microwave field at the position of the ions, a dynamically decoupled Mølmer-Sørensen scheme is employed. After accounting for state preparation and measurement errors, the achieved gate fidelity is 99.7(1)%. In previous work, the same apparatus has been used to demonstrate coherence times of T*2 ≈ 50 s and all single-qubit operations with fidelity > 99.95%. To gain access to the "atomic clock" qubit transition in 43Ca+, a static magnetic field of 146G is applied. The resulting energy level Zeeman-structure is spread over many times the linewidth of the atomic transition used for Doppler cooling. This thesis presents a simple and robust method for Doppler cooling and obtaining high fluorescence from this qubit in spite of the complicated level structure. A temperature of 0.3mK, slightly below the Doppler limit, is reached.
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.
We demonstrate a two-qubit logic gate driven by near-field microwaves in a room-temperature microfabricated surface ion trap. We introduce a dynamically decoupled gate method, which stabilizes the qubits against fluctuating energy shifts and avoids the need to null the microwave field. We use the gate to produce a Bell state with fidelity 99.7(1)%, after accounting for state preparation and measurement errors. The gate is applied directly to ^{43}Ca^{+} hyperfine "atomic clock" qubits (coherence time T_{2}^{*}≈50 s) using the oscillating magnetic field gradient produced by an integrated microwave electrode.
This thesis describes theoretical and experimental work whose main aim is the development of techniques for using trapped 43Ca⁺ ions for quantum information processing. I present a rate equations model of 43Ca⁺, and compare it with experimental data. The model is then used to investigate and optimise an electron-shelving readout method from a ground-level hyperfine qubit. The process is robust against common experimental imperfections. A shelving fidelity of up to 99.97% is theoretically possible, taking 100 μs. The laser pulse sequence can be greatly simplified for only a small reduction in the fidelity. The simplified method is tested experimentally with fidelities up to 99.8%. The shelving procedure could be applied to other commonly-used species of ion qubit. An entangling two-qubit quantum controlled-phase gate was attempted between a 40Ca⁺ and a 43Ca⁺ ion. The experiment did not succeed due to frequent decrystallisation of the ion pair, and strong motional decoherence. The source of the problems was never identified despite significant experimental effort, and the decision was made to suspend the experiments and continue them in an improved ion trap which is under construction. A sequence of pi-pulses, inspired by the Hahn spin-echo, was derived that is capable of greatly reducing dephasing of any qubit. If the qubit precession frequency varies with time as an nth-order polynomial, an (n+1) pulse sequence is theoretically capable of perfectly cancelling the resulting phase error. The sequence is used on a 43Ca+ magnetic-field-sensitive hyperfine qubit, with 20 pulses increasing the coherence time by a factor of 75 compared to an experiment without any spin-echo. In our ambient noise environment the well-known Carr-Purcell-Meiboom-Gill dynamic-decoupling method was found to be comparably effective.
Towards the goal of a large-scale quantum computer based on trapped ions, near-field microwaves represent a promising approach to perform the techni- cally challenging key operation of a two-qubit entangling gate. In this thesis we present the first microwave-driven two-qubit gate in 9Be+ ions employing a first-order field-independent qubit transition and a scalable surface-electrode ion trap at room temperature. We test the quality of the gate operation by producing a maximally entangled state and measuring the resulting state preparation fidelity in a reduced tomography procedure. For the best two- qubit gate achieved in the system we find this fidelity to be F = 98.2 ± 1.2 %. Following a comprehensive error analysis based on numerical simulations and experimentally determined input parameters, we identify current infidelity con- tributions of the apparatus. Here, the natural error source of the microwave near-field approach, namely fluctuating AC Zeeman shifts, could be reduced to the 10^−4 level due to the optimized design of the employed microwave con- ductor. As we find that the three largest errors can all be reduced upon purely technical improvements, higher fidelities are feasible in the future. Besides the gate realization, the thesis also comprises the initial characterization of the employed ion trap as well as the design and construction of a Raman laser at ∼ 313 nm which is utilized to perform near ground state cooling of radial modes of a single- and two-ion crystal. Here, ensuing heating rate measure- ments on a single-ion’s radial modes show good agreement with the electric- field noise spectral density expected from literature given the chosen mode frequency and nearest ion-to-electrode distance of 70 µm. Finally, we present the operation of a first multi-layer ion trap whose electrode layout features a 3-dimensional microwave conductor intended for performing microwave-driven two-qubit gates. Following a characterization of the resulting near-field pat- tern using a single ion as a local field probe, we find the multi-layer conductor to have significantly better field properties when compared to an equivalent single-layer design. Given these promising results, future work will focus on the integration of similar microwave circuitry in a multi-zone trap array as envisioned by the QCCD architecture.
This work describes the design and implementation of a new apparatus to achieve quantum information processing in trapped ions using microwave methods. The apparatus involves many design improvements over a previous quantum processing experiment which achieved the highest single-qubit gate fidelity, longest coherence time, and highest microwave based two-qubit fidelity. The goal of this new experiment is a two-qubit gate speed and a fidelity improvement of a factor of 10, making microwave based gates much more feasible as quantum processors. To this end, a novel clock qubit within 43Ca+ is chosen, and the ion height is nearly halved. An anticipated heating rate increase is counteracted by the use of cryogenics. A novel ion chip design is implemented via wafer-scale fabrication and subsequently attached using a novel eutectic bonding technique. The implementation required many design and fabrication problems to be solved; these are described. The vacuum system reaches < 10−11 mbar even at room temperature, lowering experimental difficulty and allowing for performance comparisons at a wide temperature range. A new experiment control system, ARTIQ, and corresponding Sinara hardware is used for control. Experimental results achieved so far include a study of contributing factors to the ion loading rate, and a comparison between the designed and measured microwave fields. All results achieved to date are compatible with the main speed and fidelity goal, which should be achieved in the near future.