Publications by Christopher Ballance


Fast quantum logic gates with trapped-ion qubits.

Nature 555 (2018) 75-78

VM Schäfer, CJ Ballance, K Thirumalai, LJ Stephenson, TG Ballance, AM Steane, DM Lucas

Quantum bits (qubits) based on individual trapped atomic ions are a promising technology for building a quantum computer. The elementary operations necessary to do so have been achieved with the required precision for some error-correction schemes. However, the essential two-qubit logic gate that is used to generate quantum entanglement has hitherto always been performed in an adiabatic regime (in which the gate is slow compared with the characteristic motional frequencies of the ions in the trap), resulting in logic speeds of the order of 10 kilohertz. There have been numerous proposals of methods for performing gates faster than this natural 'speed limit' of the trap. Here we implement one such method, which uses amplitude-shaped laser pulses to drive the motion of the ions along trajectories designed so that the gate operation is insensitive to the optical phase of the pulses. This enables fast (megahertz-rate) quantum logic that is robust to fluctuations in the optical phase, which would otherwise be an important source of experimental error. We demonstrate entanglement generation for gate times as short as 480 nanoseconds-less than a single oscillation period of an ion in the trap and eight orders of magnitude shorter than the memory coherence time measured in similar calcium-43 hyperfine qubits. The power of the method is most evident at intermediate timescales, at which it yields a gate error more than ten times lower than can be attained using conventional techniques; for example, we achieve a 1.6-microsecond-duration gate with a fidelity of 99.8 per cent. Faster and higher-fidelity gates are possible at the cost of greater laser intensity. The method requires only a single amplitude-shaped pulse and one pair of beams derived from a continuous-wave laser. It offers the prospect of combining the unrivalled coherence properties, operation fidelities and optical connectivity of trapped-ion qubits with the submicrosecond logic speeds that are usually associated with solid-state devices.


High-fidelity elementary qubit operations with trapped ions

Optics InfoBase Conference Papers Part F73-QIM 2017 (2017)

DM Lucas, TP Harty, CJ Ballance, DPL Aude Craik, MA Sepiol, VM Schäfer, K Thirumalai, JE Tarlton, L Stephenson, J Wolf, JF Goodwin, A Hughes, C Loschnauer, TG Ballance, AM Steane

© OSA 2017. I will describe recent experimental work at Oxford on implementing elementary one- and two-qubit operations with the high fidelities (99.9% or more) required for the implementation of quantum error correction, using trapped-ion “atomic clock“ qubits.


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

PHYSICAL REVIEW A 95 (2017) ARTN 022337

DPLA Craik, NM Linke, MA Sepiol, TP Harty, JF Goodwin, CJ Ballance, DN Stacey, AM Steane, DM Lucas, DTC Allcock


Minimally complex ion traps as modules for quantum communication and computing

NEW JOURNAL OF PHYSICS 18 (2016) ARTN 103028

R Nigmatullin, CJ Ballance, N de Beaudrap, SC Benjamin


Dark-resonance Doppler cooling and high fluorescence in trapped Ca-43 ions at intermediate magnetic field

NEW JOURNAL OF PHYSICS 18 (2016) ARTN 023043

DTC Allcock, TP Harty, MA Sepiol, HA Janacek, CJ Ballance, AM Steane, DM Lucas, DN Stacey


High-Fidelity Trapped-Ion Quantum Logic Using Near-Field Microwaves.

Physical review letters 117 (2016) 140501-

TP Harty, MA Sepiol, DTC Allcock, CJ Ballance, JE Tarlton, DM Lucas

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.


High-Fidelity Quantum Logic Gates Using Trapped-Ion Hyperfine Qubits.

Physical review letters 117 (2016) 060504-

CJ Ballance, TP Harty, NM Linke, MA Sepiol, DM Lucas

We demonstrate laser-driven two-qubit and single-qubit logic gates with respective fidelities 99.9(1)% and 99.9934(3)%, significantly above the ≈99% minimum threshold level required for fault-tolerant quantum computation, using qubits stored in hyperfine ground states of calcium-43 ions held in a room-temperature trap. We study the speed-fidelity trade-off for the two-qubit gate, for gate times between 3.8  μs and 520  μs, and develop a theoretical error model which is consistent with the data and which allows us to identify the principal technical sources of infidelity.


Hybrid quantum logic and a test of Bell's inequality using two different atomic isotopes.

Nature 528 (2015) 384-386

CJ Ballance, VM Schäfer, JP Home, DJ Szwer, SC Webster, DTC Allcock, NM Linke, TP Harty, DPL Aude Craik, DN Stacey, AM Steane, DM Lucas

Entanglement is one of the most fundamental properties of quantum mechanics, and is the key resource for quantum information processing (QIP). Bipartite entangled states of identical particles have been generated and studied in several experiments, and post-selected or heralded entangled states involving pairs of photons, single photons and single atoms, or different nuclei in the solid state, have also been produced. Here we use a deterministic quantum logic gate to generate a 'hybrid' entangled state of two trapped-ion qubits held in different isotopes of calcium, perform full tomography of the state produced, and make a test of Bell's inequality with non-identical atoms. We use a laser-driven two-qubit gate, whose mechanism is insensitive to the qubits' energy splittings, to produce a maximally entangled state of one (40)Ca(+) qubit and one (43)Ca(+) qubit, held 3.5 micrometres apart in the same ion trap, with 99.8 ± 0.6 per cent fidelity. We test the CHSH (Clauser-Horne-Shimony-Holt) version of Bell's inequality for this novel entangled state and find that it is violated by 15 standard deviations; in this test, we close the detection loophole but not the locality loophole. Mixed-species quantum logic is a powerful technique for the construction of a quantum computer based on trapped ions, as it allows protection of memory qubits while other qubits undergo logic operations or are used as photonic interfaces to other processing units. The entangling gate mechanism used here can also be applied to qubits stored in different atomic elements; this would allow both memory and logic gate errors caused by photon scattering to be reduced below the levels required for fault-tolerant quantum error correction, which is an essential prerequisite for general-purpose quantum computing.


Optical injection and spectral filtering of high-power ultraviolet laser diodes.

Optics letters 40 (2015) 4265-4268

VM Schäfer, CJ Ballance, CJ Tock, DM Lucas

We demonstrate injection locking of high-power laser diodes operating at 397 nm. We achieve stable operation with an injection power of ∼100  μW and a slave laser output power of up to 110 mW. We investigate the spectral purity of the slave laser light via photon scattering experiments on a single trapped (40)Ca(+) ion. We show that it is possible to achieve a scattering rate indistinguishable from that of monochromatic light by filtering the laser light with a diffraction grating to remove amplified spontaneous emission.


High-Fidelity Preparation, Gates, Memory, and Readout of a Trapped-Ion Quantum Bit.

Physical review letters 113 (2014) 220501-

TP Harty, DTC Allcock, CJ Ballance, L Guidoni, HA Janacek, NM Linke, DN Stacey, DM Lucas

We implement all single-qubit operations with fidelities significantly above the minimum threshold required for fault-tolerant quantum computing, using a trapped-ion qubit stored in hyperfine "atomic clock" states of ^{43}Ca^{+}. We measure a combined qubit state preparation and single-shot readout fidelity of 99.93%, a memory coherence time of T_{2}^{*}=50  sec, and an average single-qubit gate fidelity of 99.9999%. These results are achieved in a room-temperature microfabricated surface trap, without the use of magnetic field shielding or dynamic decoupling techniques to overcome technical noise.


Microwave control electrodes for scalable, parallel, single-qubit operations in a surface-electrode ion trap

APPLIED PHYSICS B-LASERS AND OPTICS 114 (2014) 3-10

DPLA Craik, NM Linke, TP Harty, CJ Ballance, DM Lucas, AM Steane, DTC Allcock


Injection locking of two frequency-doubled lasers with 3.2 GHz offset for driving Raman transitions with low photon scattering in <sup>43</sup>Ca+

Optics Letters 38 (2013) 5087-5089

NM Linke, CJ Ballance, DM Lucas

We describe the injection locking of two infrared (794 nm) laser diodes that are each part of a frequency-doubled laser system. An acousto-optic modulator in the injection path gives an offset of 1.6 GHz between the lasers for driving Raman transitions between states in the hyperfine split (by 3.2 GHz) ground level of 43Ca+. The offset can be disabled for use in 40Ca+. We measure the relative linewidth of the frequency-doubled beams to be 42 mHz in an optical heterodyne measurement. The use of both injection locking and frequency doubling combines spectral purity with high optical power. Our scheme is applicable for providing Raman beams across other ion species and neutral atoms where coherent optical manipulation is required. © 2013 Optical Society of America.


A microfabricated ion trap with integrated microwave circuitry

ArXiv (0)

DTC Allcock, TP Harty, CJ Ballance, BC Keitch, NM Linke, DN Stacey, DM Lucas

We describe the design, fabrication and testing of a surface-electrode ion trap, which incorporates microwave waveguides, resonators and coupling elements for the manipulation of trapped ion qubits using near-field microwaves. The trap is optimised to give a large microwave field gradient to allow state-dependent manipulation of the ions' motional degrees of freedom, the key to multiqubit entanglement. The microwave field near the centre of the trap is characterised by driving hyperfine transitions in a single laser-cooled 43Ca+ ion.


Heating rate and electrode charging measurements in a scalable, microfabricated, surface-electrode ion trap

Applied Physics B: Lasers and Optics (2011) 1-7

DTC Allcock, TP Harty, HA Janacek, NM Linke, CJ Ballance, AM Steane, DM Lucas, RL Jarecki Jr, SD Habermehl, MG Blain, D Stick, DL Moehring

We characterise the performance of a surface-electrode ion "chip" trap fabricated using established semiconductor integrated circuit and micro-electro-mechanical-system (MEMS) microfabrication processes, which are in principle scalable to much larger ion trap arrays, as proposed for implementing ion trap quantum information processing. We measure rf ion micromotion parallel and perpendicular to the plane of the trap electrodes, and find that on-package capacitors reduce this to ≲10 nm in amplitude. We also measure ion trapping lifetime, charging effects due to laser light incident on the trap electrodes, and the heating rate for a single trapped ion. The performance of this trap is found to be comparable with others of the same size scale. © 2011 Springer-Verlag.


Background-free detection of trapped ions

Applied Physics B: Lasers and Optics 107 (2012) 1175-1180

NM Linke, DTC Allcock, DJ Szwer, CJ Ballance, TP Harty, HA Janacek, DN Stacey, AM Steane, DM Lucas

We demonstrate a Doppler cooling and detection scheme for ions with low-lying D levels which almost entirely suppresses scattered laser light background, while retaining a high fluorescence signal and efficient cooling. We cool a single ion with a laser on the 2S1/2 ?2P1/2 transition as usual, but repump via the 2P3/2 level. By filtering out light on the cooling transition and detecting only the fluorescence from the 2P3/2 → 2S1/2 decays, we suppress the scattered laser light background count rate to 1 s-1 while maintaining a signal of 29000 s-1 with moderate saturation of the cooling transition. This scheme will be particularly useful for experiments where ions are trapped in close proximity to surfaces, such as the trap electrodes in microfabricated ion traps, which leads to high background scatter from the cooling beam.


Heating rate and electrode charging measurements in a scalable, microfabricated, surface-electrode ion trap

Applied Physics B: Lasers and Optics 107 (2012) 913-919

DTC Allcock, TP Harty, HA Janacek, NM Linke, CJ Ballance, AM Steane, DM Lucas, RL Jarecki, SD Habermehl, MG Blain, D Stick, DL Moehring

We characterise the performance of a surfaceelectrode ion "chip" trap fabricated using established semiconductor integrated circuit and micro-electro-mechanicalsystem (MEMS) microfabrication processes, which are in principle scalable to much larger ion trap arrays, as proposed for implementing ion trap quantum information processing. We measure rf ion micromotion parallel and perpendicular to the plane of the trap electrodes, and find that on-package capacitors reduce this to <~10 nm in amplitude.We also measure ion trapping lifetime, charging effects due to laser light incident on the trap electrodes, and the heating rate for a single trapped ion. The performance of this trap is found to be comparable with others of the same size scale. © Springer-Verlag 2011.


Background-free detection of trapped ions

Applied Physics B: Lasers and Optics (2011) 1-6

NM Linke, DTC Allcock, DJ Szwer, CJ Ballance, TP Harty, HA Janacek, DN Stacey, AM Steane, DM Lucas

We demonstrate a Doppler cooling and detection scheme for ions with low-lying D levels which almost entirely suppresses scattered laser light background, while retaining a high fluorescence signal and efficient cooling. We cool a single ion with a laser on the {Mathematical expression} transition as usual, but repump via the {Mathematical expression} level. By filtering out light on the cooling transition and detecting only the fluorescence from the {Mathematical expression} decays, we suppress the scattered laser light background count rate to 1 s -1 while maintaining a signal of 29000 s -1 with moderate saturation of the cooling transition. This scheme will be particularly useful for experiments where ions are trapped in close proximity to surfaces, such as the trap electrodes in microfabricated ion traps, which leads to high background scatter from the cooling beam. © 2011 Springer-Verlag.


Reduction of heating rate in a microfabricated ion trap by pulsed-laser cleaning

NEW JOURNAL OF PHYSICS 13 (2011) ARTN 123023

DTC Allcock, L Guidoni, TP Harty, CJ Ballance, MG Blain, AM Steane, DM Lucas