# Publications

### Journal Publications

#### 2019

**Probing qubit memory errors at the part-per-million level**

M. A. Sepiol, A. C. Hughes, J. E. Tarlton, D. P. Nadlinger, C. J. Ballance, T. P. Harty, A. M. Steane, J. F. Goodwin, D. M. Lucas

(Preprint)

#### 2018

**Magnetic field stabilization system for atomic physics experiments**

B. Merkel, K. Thirumalai, J. E. Tarlton, V. M. Schäfer, C. J. Ballance, T. P. Harty, D. M. Lucas

Rev. Sci. Instrum., Vol. 90, 044702

(Article, Preprint)

#### 2017

**A short response-time atomic source for trapped ion experiments**

T. G. Ballance, J. F. Goodwin, B. Nichol, L. J. Stephenson, C. J. Ballance, D. M. Lucas

Rev. Sci. Instrum., Vol. 89, 053102

(Article, Preprint)

**Fast quantum logic gates with trapped-ion qubits**

V. M. Schäfer, C. J. Ballance, K. Thirumalai, L. J. Stephenson, T. G. Ballance, A. M. Steane and D. M. Lucas

Nature, Vol. 555, pp. 75-78

(Article, Preprint, Nature "News & Views" by Prof. Tobias Schaetz)

**The effect of atomic response time in the theory of Doppler cooling of trapped ions**

H. Janacek, A. M. Steane, D. M. Lucas, and D. N. Stacey

Journal of Modern Optics, Vol. 65, pp. 577-584

(Article, Preprint)

#### 2016

**High-fidelity trapped-ion quantum logic using near-field microwaves**

T. P. Harty, M. A. Sepiol, D. T. C. Allcock, C. J. Ballance, J. E. Tarlton, D. M. Lucas

Phys. Rev. Lett. 117, 140501

(Article, Preprint)

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

D. P. L. Aude Craik, N. M. Linke, M. A. Sepiol, T. P. Harty, J. F. Goodwin, C. J. Ballance, D. N. Stacey, A. M. Steane, D. M. Lucas, and D. T. C. Allcock

Phys. Rev. A 95, 022337

(Article, Preprint)

#### 2015

**High-fidelity quantum logic gates using trapped-ion hyperfine qubits**

C. J. Ballance, T. P. Harty, N. M. Linke, M. A. Sepiol, D. M. Lucas

Phys. Rev. Lett. 117, 060504

(Article, Preprint)

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

D. T. C. Allcock, T. P. Harty, M. A. Sepiol, H. A. Janacek, C. J. Ballance, A. M. Steane, D. M. Lucas, D. N. Stacey

New J. Phys., Vol. 18, pp. 023043

(Article, Preprint)

**Optical injection and spectral filtering of high-power UV laser diodes**

V. M. Schäfer, C. J. Ballance, C. J. Tock, D. M. Lucas

Opt. Lett., Vol. 40, pp. 4265-4268

(Article, Preprint)

**Hybrid quantum logic and a test of Bell's inequality using two different atomic species**

C. J. Ballance, V. M. Schäfer, J. P. Home, D. J. Szwer, S. C. Webster, D. T. C. Allcock, N. M. Linke, T. P. Harty, D. P. L. Aude Craik, D. N. Stacey, A. M. Steane, D. M. Lucas

Nature, Vol. 528, pp. 384–386

(Article, Preprint, Nature "News & Views" by Prof. Tobias Schaetz)

#### 2014

**Pulsed force sequences for fast phase-insensitive quantum gates in trapped ions **

A. M. Steane, G. Imreh, J. P. Home, D. Leibfried

New J. Phys., Vol. 16, pp. 053049

(Article, Preprint)

**High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions**

C. J. Ballance, T. P. Harty, N. M. Linke, D. M. Lucas

(Preprint)

**High-fidelity preparation, gates, memory and readout of a trapped-ion quantum bit**

T. P. Harty, D. T. C. Allcock, C. J. Ballance, L. Guidoni, H. A. Janacek, N. M. Linke, D. N. Stacey, D. M. Lucas

Phys. Rev. Lett., Vol. 113, Issue 22, pp. 220501

(Article, Preprint, "Viewpoint: Trapped Ions Make Impeccable Qubits" by Prof. Jungsang Kim, phys.org, Nature - research highlights)

#### 2013

**Experimental Recovery of a Qubit from Partial Collapse**

J. A. Sherman, M. J. Curtis, D. J. Szwer, D. T. C. Allcock, G. Imreh, D. M. Lucas, A. M. Steane

Phys. Rev. Lett., Vol. 111, Issue 18, pp. 180501

(Article, Preprint, phys.org, gaianews.it)

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

N. M. Linke, C. J. Ballance, D. M. Lucas

Optics Letters, Vol. 38, Issue 23, pp. 5087-5089

(Article, Preprint)

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

D. P. L. Aude Craik, N. M. Linke, T. P. Harty, C. J. Ballance, D. M. Lucas, A. M. Steane, D. T. C. Allcock

Applied Physics B, Vol. 114, Issue 1-2, pp. 3-10

(Article, Preprint)

**Injection locking of violet laser diodes with a 3.2 GHz offset frequency for driving Raman transitions in 43Ca+**

B. C. Keitch, N. R. Thomas, D. M. Lucas

Optics Letters, Vol. 38, Issue 6, pp. 830-832

(Article, Preprint)

#### 2012

**A microfabricated ion trap with integrated microwave circuitry**

D. T. C. Allcock, T. P. Harty, C. J. Ballance, B. C. Keitch, N. M. Linke, D. N. Stacey, D. M. Lucas

Applied Physics Letters, Vol. 102, No. 4, pp. 044103

(Article, Preprint)

**Background-free detection of trapped ions**

N. M. Linke, D. T. C. Allcock, D. J. Szwer, C. J. Ballance, T. P. Harty, H. A. Janacek, D. N. Stacey, A. M. Steane, D. M. Lucas

Applied Physics B, Vol. 107, Issue 4, pp. 1175-1180

(Article, Preprint)

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

D. T. C. Allcock, T. P. Harty, H. A. Janacek, N. M. Linke, C. J. Ballance, A. M. Steane, D. M. Lucas, R. L. Jarecki Jr., S. D. Habermehl, M. G. Blain, D. Stick, D. L. Moehring

Applied Physics B, Vol. 107, Issue 4, pp. 913-919

(Article, Preprint)

#### 2011

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

D. T. C. Allcock, L. Guidoni, T. P. Harty, C. J. Ballance, M. G. Blain, A. M. Steane, D. M. Lucas

New J. Phys., Vol. 13, pp. 123023

(Article, Preprint)

**Keeping a single qubit alive by experimental dynamic decoupling**

D. J. Szwer, S. C. Webster, A. M. Steane and D. M. Lucas

J. Phys. B: At. Mol. Opt. Phys., Vol. 44, No. 2, pp. 025501

(Article, Preprint)

#### 2010

**Scalable simultaneous multi-qubit readout with 99.99% single-shot fidelity**

A. H. Burrell, D. J. Szwer, S. C. Webster and D. M. Lucas

Phys. Rev. A, Vol. 81, Issue 4, pp. 040302

(Article, Preprint)

**Implementation of a symmetric surface electrode ion trap with field compensation using a modulated Raman effect**

D. T. C. Allcock, J. A. Sherman, D. N. Stacey, A. H. Burrell, M. J. Curtis, G.Imreh, N. M. Linke, D. J. Szwer, S. C. Webster, A. M. Steane and D. M. Lucas

New J. Phys., Vol. 12, pp. 053026

(Article, Preprint)

#### 2009

**Memory coherence of a sympathetically cooled trapped-ion qubit**

J. P. Home, M. J. McDonnell, D. J. Szwer, B. C. Keitch, D. M. Lucas, D. N. Stacey, and A. M. Steane

Phys. Rev. A., Vol. 79, Issue 5, pp. 050305

(Article, Preprint)

#### 2008

**High-fidelity readout of trapped-ion qubits**

A. H. Myerson, D. J. Szwer, S. C. Webster, D. T. C. Allcock, M. J. Curtis, G. Imreh, J. A. Sherman, D. N. Stacey, A. M. Steane, and D. M. Lucas

Phys. Rev. Lett., Vol. 100, Issue 20, pp. 200502

(Article, Preprint)

**Optical Bloch Equations with Multiply-Connected States**

D.N. Stacey, D.T.C. Allcock, D.M. Lucas, D.J. Szwer, S.C. Webster

J. Phys. B., Vol. 41, No. 8, pp. 085502

(Article)

#### 2007

**A long-lived memory qubit on a low-decoherence quantum bus**

D. M. Lucas, B. C. Keitch, J. P. Home, G. Imreh, M. J. McDonnell, D. N. Stacey, D. J. Szwer and A. M. Steane

(Preprint)

**Context, spacetime loops and the interpretation of quantum mechanics**

A. M. Steane

J. Phys. A: Math. Theor., Vol. 40, No. 12, pp. 3223-3243

(Article, Preprint)

**Long-lived mesoscopic entanglement outside the Lamb-Dicke regime**

M. J. McDonnell, J. P. Home, D. M. Lucas, G. Imreh, B. C. Keitch, D. J. Szwer, N. R. Thomas, S. C. Webster, D. N. Stacey, A. M. Steane

Phys. Rev. Lett., Vol. 98, Issue 6, pp. 063603

(Article, Preprint)

**How to build a 300 bit, 1 Giga-operation quantum computer**

A. M. Steane

Quantum Information and Computation, Vol. 7, No.3, pp. 171-183.

(Article, Preprint)

#### 2006

**Deterministic entanglement and tomography of ion spin qubits**

J. P. Home, M. J. McDonnell, D. M. Lucas, G. Imreh, B. C. Keitch, D. J. Szwer, N. R. Thomas, S. C. Webster, D. N. Stacey, A. M. Steane

New J. Phys., Vol. 8, pp. 188

(Article, Preprint)

**Electrode Configurations for Fast Separation of Trapped Ions**

J. P. Home, A. M. Steane

Quantum Information and Computation, Vol. 6, Issue 4, pp. 289-325

(Article, Preprint)

#### 2004

**Laser linewidth effects in quantum state discrimination by electromagnetically induced transparency**

M. J. McDonnell, D. N. Stacey, A. M. Steane

Phys. Rev. A, Vol. 70, Issue 5, pp. 053802

(Article, Preprint)

**High-Efficiency Detection of a Single Quantum of Angular Momentum by Suppression of Optical Pumping**

M. J. McDonnell, J.-P. Stacey, S. C. Webster, J. P. Home, A. Ramos, D. M. Lucas, D. N. Stacey, A. M. Steane

Phys. Rev. Lett., Vol. 93, Issue 15, pp. 153601

(Article)

**Further quantum-gate methods using selective displacement of trapped ions**

M. Sasura, A. M. Steane

(Preprint)

#### 2003

**Isotope-selective photo-ionization for calcium ion trapping**

D. M. Lucas, A. Ramos, J. P. Home, M. J. McDonnell, S. Nakayama, J.-P. Stacey, S. C. Webster, D. N. Stacey, A. M. Steane

Phys. Rev. A, Vol. 69, Issue 1, pp. 012711

(Article,Preprint)

**Oxford ion-trap quantum computing project**

D. M. Lucas, C. J. S. Donald, J. P. Home, M. J. McDonnell, A. Ramos, D. N. Stacey, J.-P. Stacey, A. M. Steane, S. C. Webster

Philos. Transact. A Math Phys Eng Sci. 361, 1401-8

(Article)

**Extracting entropy from quantum computers**

A. M. Steane

Ann. Henri Poincare 4 supplement 2, pp. 799-809

(Article)

**Overhead and noise threshold of fault-tolerant quantum error correction**

A. M. Steane

Phys. Rev. A, Vol. 68, Issue 4, pp. 042322

(Article, Preprint)

**Fast quantum logic by selective displacement of hot trapped ions**

M. Sasura, A. M. Steane

Phys. Rev. A, Vol. 67, Issue 6, pp. 062318

(Article, Preprint)

#### 2002

**Quantum computer architecture for fast entropy extraction**

A. M. Steane

Quantum Information and Computation 2, pp. 297-306

(Article, Preprint)

#### 2001

**Development of a linear ion trap for quantum computing**

D. M. Lucas

Proc. First Int. Conf. on Experimental Implementation of Quantum Computation, pp. 91-98

(Article)

#### 2000

**Speed of ion-trap quantum information processors**

A. M. Steane, C. F. Roos, D. Stevens, A. Mundt, D. Leibfried, F. Schmidt-Kaler, R. Blatt

Phys. Rev. A, Vol. 62, Issue 4, pp. 042305

(Article, Preprint)

**Search for correlation effects in linear chains of trapped Ca+ ions**

C. J. S. Donald, D. M. Lucas, P. A. Barton, M. J. McDonnell, J. P. Stacey, D. A. Stevens, D. N. Stacey, A. M. Steane

Europhys. Lett. 51, pp. 388-394

(Article, Preprint)

**Quantum computing and error correction**

A. M. Steane

(Preprint)

**Quantum computing with trapped ions, atoms and light**

A. M. Steane, D.M. Lucas

Fortschritte der Physik, Vol. 48, Issue 9-11, pp. 839–858

(Preprint)

#### 1999

**Measurement of the lifetime of the 3d ^{2}D_{5/2} state in ^{40}Ca^{+}**

P. A. Barton, C. J. S. Donald, D. M. Lucas, D. A. Stevens, A. M. Steane, D. N. Stacey

Phys. Rev. A, Vol. 62, Issue 3, pp. 032503

(Article, Preprint)

#### 1998

**Space, time, parallelism and noise requirements for reliable quantum computing**

A. M. Steane

Fortsch.Phys., Vol. 46, pp. 443

(Preprint)

**Simple experimental methods for trapped-ion quantum processors**

D. Stevens, J. Brochard, A. M. Steane

Phys. Rev. A Vol. 58, Issue 4, pp. 2750

(Article, Preprint)

#### 1997

**Active stabilisation, quantum computation and quantum state synthesis**

A. M. Steane

Phys.Rev.Lett., Vol. 78, Issue 11, pp. 2252-2255

(Article, Preprint)

**The ion trap quantum information processor**

A. M. Steane

Applied Physics B , Vol. 64, Issue 6, pp. 623-643

(Article, Preprint)

#### 1996

**Simple Quantum Error Correcting Codes**

A. M. Steane

Phys.Rev. A, Vol. 54, Issue 6, pp. 4741

(Article, Preprint)

### Doctoral Theses

#### Vera Schäfer, 2018

Fast entangling gates using amplitude-shaped pulses on ^{43}Ca^{+}, reaching a fidelity of 99.8% in 1.6us and 60% in 480ns. Bell test experiment on ^{43}Ca^{+}-^{40}Ca^{+} mixed-species crystal and demonstration of mixed species entangling gate on ^{88}Sr^{+}-^{43}Ca^{+}.

#### James Tarlton, 2018

Direct measurement of qubit memory errors in a calcium-43 "atomic clock" qubit. Randomized memory benchmarking is used to measure the memory error of a single qubit down to the few 10^{-6} level. The error is found to remain below the 10^{-3} level for up to 400ms. Surface trap designs for near-field microwave-driven two-qubit gates are explored.

#### Martin Sepiol, 2016

Experimental implementation of a microwave-driven two-qubit quantum logic gate in a room-temperature microfabricated surface ion trap. The gate scheme involves dynamical decoupling methods, which stabilise the qubits against fluctuations of the motional mode frequency and fluctuating energy shifts, and avoid the need to null the microwave field. The gate is applied directly to hyperfine "atomic clock" qubits in ^{43}Ca^{+} using the near-field microwave magnetic field gradient produced by an integrated trap electrode. The achieved gate fidelity is 99.7(1)%, after accounting for state preparation and measurement errors.

#### Diana Prado Lopes Aude Craik, 2016

Demonstration of high-fidelity spatial and polarization addressing of trapped-ion "atomic clock" memory qubits using near-field microwaves. Addressing is performed by interfering fields from integrated microwave electrodes to address a chosen trap zone whilst nulling crosstalk fields in the neighbour zone. Design of a next-generation ion trap which can perform near-field microwave addressing in a quantum CCD architecture without the need for nulling fields. Demonstration of a prototype micro-fabricated loop antenna for microwave characterization of chip ion traps.

#### Hugo Janacek, 2015

Modelling temperature and fluorescence of a trapped ion using the optical Bloch equations. Development of efficient simulations that solve the time-dependent and time-independent problems for systems with large numbers of states. Introduction of a routine designed to model the approach to the steady state. Analysis of Doppler cooling incorporating motion of a trapped ion and the effects of repumping from a D state. Development of cooling schemes for ^{43}Ca^{+} at 146G and comparison with experiment. Demonstration of Doppler cooling below the Doppler limit for this isotope. Analysis of resonant effects in systems with more than three levels and comparison with experiment. Download both portions of the compressed file to extract.

Full Text (part one)

Full Text (part two)

#### Sarah Woodrow (M.Sc. thesis), 2015

Design of a new linear 'blade' trap, with improved optical access. Review of linear Paul trap theory. Discussion of axial micromotion and its use for ion addressing. Numerical simulations of trap fields. Technical drawings of trap components.

#### Christopher Ballance, 2014

High-fidelity single- and two-qubit laser-driven logic gates in ^{43}Ca^{+} hyperfine qubits. Theoretical and experimental study of speed/fidelity trade-off for two-qubit gates. Achievement of single-qubit gate fidelities above 99.99%, and two-qubit gate fidelities ranging between 97.1(2)% (for a gate time of 3.8µs) and 99.9(1)% (at 100µs), after accounting for single-qubit operation and readout errors (each at the 0.1% level). Demonstration of a mixed-species (^{43}Ca^{+} and ^{40}Ca^{+}) entangling gate with a fidelity of 99.8(5)%.

#### Thomas Harty, 2013

Development of an intermediate magnetic field "atomic clock" qubit in ^{43}Ca^{+} at 146G and high-fidelity techniques to manipulate this qubit using microwaves and lasers in a microfabricated surface-electrode ion trap. Randomized benchmarking of a single qubit. Work towards microwave-driven two-qubit gates including a theoretical analysis of likely sources of experimental error.

#### Norbert Linke, 2012

Assembly and testing of a microstructured 3D ion trap. Background-free detection and read-out of trapped ions. Raman laser system consisting of two injection-locked frequency-doubled lasers. Ground-state cooling and coherent manipulation of a mixed-species crystal in a macroscopic ion trap.

#### David Allcock, 2011

Design, fabrication and testing of microfabricated surface-electrode ion traps. Pulsed laser cleaning of ion traps to reduce anomalous heating. An intermediate-field hyperfine "atomic clock" qubit in 43Ca+. Design, construction and testing of an ion trap incorporating microwave resonators for microwave-driven quantum logic gates.

#### Alice Burrell, 2010

High-fidelity readout of trapped ion qubits. Demonstration of time-arrival resolved discrimination of ion states (TARDIS) with a photomultiplier detector to perform single-shot readout of a single ^{40}Ca^{+} optical qubit with 99.991(1)% fidelity. Replacing the photomultipler by an electron-multiplying CCD camera, the TARDIS method allows discrimination in both spatial and temporal dimensions, enabling achievement of the same 99.99% readout fidelity for a 4-ion "qunybble", despite 4% optical cross-talk between neighbouring ions.

#### Michael Curtis, 2010

Segmented ion trap modelling; measurement-selected ensembles (weak measurement); operation of planar and 7-electrode traps; implementation of a qubit in D5/2 state of 40Ca; partial collapse and `uncollapse' experiments.

#### David Szwer, 2009

Rate equations programs for simulation of 43Ca+; comparison with experiment and Bloch equations. Simulation and optimisation of a robust, high-fidelity readout method from 43Ca+; experimental implementation. Attempted two-qubit gate with 40Ca+ and 43Ca+ mixed crystal; problems with crystallisation; electrode noise; measurement of heating rate, motional decoherence and "Schrodinger Cat" states. Derivation of Uhrig Dynamical Decoupling (UDD); review of the literature; experimental implementation of UDD and CPMG on 43Ca+ hyperfine ground-state qubits.

#### Gergely Imreh 2008

Numerical modelling of multiple-electrode traps. Ion shuttling and loading theory. Set-up of apparatus (including vacuum system, lasers and optics and control electronics) for trapping and experimenting with microfabricated "Sandia trap". Detailed evaluation of "Sandia trap": loading and micro-motion compensation; measurement of ion lifetime, motional frequency and heating rate; demonstration of ion shuttling.

#### Benjamin Keitch 2007

Design and construction of various experimental apparatus: Laser Control Unit for precise pulse timing; master-slave 398nm laser system for Raman transitions in the hyperfine ground states of 43Ca+; KILL-110 system for PDH locking of lasers to optical cavities. Investigation of magnetic field fluctuations, using microwaves and 43Ca+ hyperfine states; Spicer SC20 field cancelling system tested. Demonstration of long T2 coherence time of 43Ca+ hyperfine clock state qubit.

#### Jonathan Home 2006

Careful study of sideband cooling and temperature diagnostics for one and two ions. Motional coherence measurements. Coherent manipulation of two ions. Spin state tomography for two ions. Quantum logic gate by oscillating force; deterministic entanglement. For electrode configurations for trap arrays, see Home and Steane paper, above.

#### Simon Webster 2005

Photoionisation, Rabi/Ramsay experiments on single spin qubits by magnetic resonance and stimulated Raman transitions, continuous Raman sideband cooling using bright/dark resonance, pulsed Raman sideband cooling to the motional ground state, temperature diagnostics for 1 and 2 ions, rate equations for Ca-43.

#### Matthew McDonnell, 2003

MOPA 397 laser system, servo theory, Pound-Drever-Hall (and other) locking, optical Bloch equations, dark resonance fits, dark resonance cooling/heating, spin state readout: various methods, EIT method proposed and implemented.

#### John-Patrick Stacey 2003

Reference cavities, improved photon counting, photon arrival time correlation method for micromotion compensation, new 850 laser, AOM optics, r.f. study towards helical resonator, magnetic field coils, dark resonances, isotope-selective photoionisation in detail.

#### Marek Sasura 2002

Survey of ion/laser coupling theory, theoretical study of "pushing" gate method.

#### Charles Donald 2000

Some space charge ideas, general apparatus development, imaging, spectroscopy of blue laser diodes, field compensation drift, precise D5/2 lifetime measurement, upper bound on 2- and 3-ion quantum jump correlations and statistical analysis.

#### David Stevens 1999

Construction from scratch of our ion trap, some Mathieu equation and Doppler cooling theory, optogalvanic spectroscopy, frequency doubling, observations of crystals and quantum jumps, first look at D5/2 lifetime measurement.

### Posters

**ECTI 2018:**

A two-node ion-photon quantum network

Single-qubit memory error metrology at short timescales

**NACTI 2017:**

Development of a photonically-linked ion trap network

Qubit decoherence metrology over short timescales

Quantum logic gates driven by near-field microwaves

**ECTI 2016:** Two-qubit near-field microwave gates on 43Ca+

**QCMC 2016:** Two-qubit near-field microwave gates on 43Ca+

**ECTI 2012:** Ion trap quantum information processing using Ca+ at Oxford

**ICAP 2012:** Quantum logic operations in 40Ca+ and 43Ca+ trapped ion qubits, Laser cleaning and background-free detection in microfabricated ion traps

**Siegen 2012:** Quantum logic operations in 40Ca+ and 43Ca+ using microwaves and lasers

**Obergurgl 2012:** Oxford planar traps

**Boulder 2011:** Oxford planar traps; Two-qubit microwave gates

**ETCI 2010:** High-fidelity simultaneous multiqubit readout; Oxford planar traps; Uncollapse; Dynamical decoupling

**SCALA 2009:** Uncollapse; Dynamical Decoupling; High-fidelity qunybble readout; Segmented traps

**Rome 2009:** Oxford planar traps

**ICAP 2008:** Segmented Traps; High-fidelity readout

**QPCR 2007:** Entanglement and high-fidelity readout; Microfabricated trap arrays

**ICAP 2006:** Deterministic entanglement and Schrodinger-cat states; Ca43 qubits

**ARDA Review 2005:** Long-lived coherence; Deterministic entanglement

**Warwick 2005:** Deterministic entanglement

**Michigan 2004:** Talk Presentation; Trapped calcium ions; A 'push and wobble' gate and octopole traps