[Research Papers] [Review Articles] [PhD Theses]

Research Papers

Magnetically induced electron shelving in a trapped Ca+ ion
D. R. Crick, S. Donnellan, R. C. Thompson1, and D. M. Segal Phys. Rev. A 81, 052503 (2010)

Fast shuttling of ions in a scalable Penning trap array
D. R. Crick, S. Donnellan, S. Ananthamurthy, R. C. Thompson1, and D. M. Segal Review of Scientific Instruments, vol.81, pp.013111-013111-5 (2010)

Two-ion Coulomb crystals of Ca+ in a Penning trap
D. R. Crick, H. Ohadi, I. Bhatti, R. C. Thompson, and D. M. Segal Optics Express, Vol. 16, Issue 4, pp. 2351-2362 (2008)

Laser spectroscopy of hyperfine structure in highly-charged ions: a test of QED at high fields
D.F.A. Winters, M. Vogel, D.M. Segal, R.C. Thompson, W. Noertershaeuser Can. J. Phys. 85, 403 (2007)

Novel designs for Penning ion traps
J.R. Castrejón-Pita, H. Ohadi, D.R. Crick, D.F.A. Winters, D.M. Segal and R.C. Thompson J. Mod. Opt 54, 1581 (2007)

Electronic detection of charged particle effects in a Penning trap
D.F.A. Winters, M. Vogel, D.M. Segal, and R.C. Thompson J. Phys. B: At. Mol. Opt. Phys. 39 3131-3143 (2006)

A proposed precision laser spectrometer for trapped highly charged ions
M. Vogel, D.F.A. Winters, D.M. Segal, and R.C. Thompson accepted for publication in Rev. Sci. Instr. (2005)

Proposal for a planar Penning ion trap
J. R. Castrejón-Pita and R. C. Thompson Physical Review A 71, 1 (2005)

Plans for laser spectroscopy of trapped cold hydrogen-like HCI
D.F.A Winters, A.M. Abdulla, J.R. Castrejon Pita, A. de Lange, D.M. Segal, R.C. Thompson Nucl Instr Meth Phys Res B 235, 201 (2005)

Doppler cooling of Ca+ ions in a Penning trap
K. Koo, J. Sudbery, D. M. Segal, and R. C. Thompson Physical Review A 69, 043402 (2004)

Improvement of Laser Cooling of Ions in a Penning Trap by use of the Axialisation Technique
H. F. Powell, S. R. de Echaniz, E. S. Phillips, D. M. Segal, and R. C. Thompson J. Phys. B: At. Mol. Opt. Phys. 36 1 (2003)

Axialization of Laser Cooled Magnesium Ions in a Penning Trap
H F Powell, D M Segal, and R C Thompson Physics Review Letters 89 93003 (2002)

Quantum jumps in singly ionized magnesium
H F Powell, M A van Eijkelenborg, W Irvine, D M Segal and R C Thompson Journal of Physics: B 35 205 (2002)

Simple model for the laser cooling of an ion in a Penning trap
R C Thompson and J Papadimitriou Journal of Physics B 33 3393 (2000)

Ion dynamics in a novel linear combined trap
M.A. van Eijkelenborg, M.E.M. Storkey, D.M. Segal, R.C. Thompson International Journal of Mass Spectrometry 188 155 (1999)

The quantum Zeno effect in trapped ions
R C Thompson, J-L Hernandez-Pozos, J Hoffges CP457, Trapped Charged Particles and Fundamental Physics 388 (1999)

A driven, trapped, laser cooled ion cloud: a forced damped oscillator
M A van Eijkelenborg, K Dholokia, M E M Storkey, D M Segal, R C Thompson Optics Communications 159 169 (1999)

Sympathetic cooling and detection of molecular ions in a Penning trap
M A van Eijkelenborg, M E M Storkey, D M Segal and R C Thompson Physical Review A 60 (1999)

Laser cooling of ions stored in a Penning trap: A phase space picture
G Zs K Horvath and R C Thompson Physical Review A 59 4530 (1999)

Ion dynamics in perturbed qudrupole ion traps
G. Zs. K. Horvat, J.-L. Hernandez-Pozos, K. Dholakia, J. Rink, D. M. Segal and R. C. Thompson Physical Review A 57 1944 (1998)

The motion of small numbers of ions in a Penning trap
R. C. Thompson and D. C. Wilson Zeitschrift für Physik D 42 271 (1997)

Inhibition of spontaneous decay by continuous measurements: Proposal for realizable experiment
M B Plenio, P L Knight and R C Thompson Optics Communications 123 278 (1996)

Laguerre-Gaussian laser beams and ion traps
W L Power and R C Thompson Optics Communications 132 371 (1996)

Investigation of ion dynamics in a Penning trap using a pulse-probe technique
K Dholakia, G Zs K Horvath, W Power, D M Segal and R C Thompson Applied Physics B 60 375 (1995)

Spectroscopy of laser cooled ions
R C Thompson, K Dholakia, G Zs K Horvath, W Power, D M Segal (refereed article) Journal of Modern Optics 41 1087 (1994)

Quantum state diffusion theory and a quantum jump experiment
N Gisin, P L Knight, I C Percival, R C Thompson and D C Wilson Journal of Modern Optics 40 1663 (1993)

Photon correlation detection of ion oscillation frequencies in quadrupole ion traps
K Dholakia, G Zs K Horvath, D M Segal, R C Thompson, D M Warrington and D C Wilson Physical Review A 47 441 (1993)

Ion oscillation frequencies in a combined trap
D J Bate, K Dholokia, R C Thompson and D C Wilson Journal of Modern Optics 39 305 (1992)

Photon correlation measurement of ion oscillation frequencies in a combined trap
K Dholakia, G Zs K Horvath, D M Segal and R C Thompson Journal of Modern Optics 39 2179 (1992)

Review Articles

Applications of laser cooled ions in a Penning trap
R C Thompson J. Phys. B: At. Mol. Opt. Phys. 42 154003 (2009)

Spectroscopy and quantum optics with trapped ions
R C Thompson Nathiagali Summer College, Pakistan (1999)

Fundamental physics with trapped ions
G Zs K Horvath, R C Thompson and P L Knight Contemporary Physics 38 25 (1997)

Spectroscopy of trapped ions
R C Thompson Advances in Atomic, Molecular and Optical Physics 31 63 (1993)

Spectroscopy and quantum optics of trapped ions
R C Thompson Comments on Atomic and Molecular Physics 29 349 (1992)

Current perspectives on the physics of trapped ions
R Blatt, P Gill and R C Thompson Journal of Modern Optics 39 193 (1992)

PhD Theses

Spectroscopy and Dynamics of Laser-Cooled Ca⁺ Ions in a Penning Trap
[PDF] [GZipped PS]
R.J. Hendricks (2006)

Controlled Dynamics of Laser-Cooled Ions in a Penning Trap
[PDF] [GZipped PS]
E. Phillips (2004)

Submission expected Oct 2003
P Blythe (2003)

Laser Cooling and Trapping of Ca+ Ions in a Penning Trap
[PDF] [GZipped PS]
K Koo (2003)

Studies of Laser Cooled Calcium Ions in the Penning and Combined Traps
[PDF] [GZipped PS]
J Sudbery (2003)

Entanglement and geometric phases in quantum information
I Fuentes (2002)

Quantum optics of a single trapped ion
[PDF]
H F Powell (2002)

Dynamics of trapped ions and progress towards the study of the quantum Zeno effect
J Vincent (2002)

Studies of laser cooled trapped ions
M. Storkey (2001)

Dynamics of Mg⁺ and Be⁺ trapped ions and design and construction of a cylindrical Penning trap
J. L. Hernández Pozos (2001)

Towards caity QED using trapped ions
T Walker (2000)

Miniature ion trap for cavity QED
X Feng (2000)

Spectroscopy of a single Yb⁺ ion
M Roberts (1996)

Dynamics and laser cooling of ions stored in a Penning trap
G Zs K Horvath (1995)

Dynamics of laser-atom interactions
W Power (1995)

The dynamics of laser cooled ions in a quadrupole ion trap
K Dholakia (1993)

Quantum optics and ion dynamics in a quadrupole trap
D C Wilson (1992)

Spectroscopy of Yb⁺, towards an optical frequency standard based on trapped ions
A S Bell, PRI student at NPL (1992)

Studies of trapped and laser cooled magnesium ions
D J Bate (1991)

Abstracts of above articles

Research Papers

Two-ion Coulomb crystals of Ca+ in a Penning trap. [Link] D. R. Crick, H. Ohadi, I. Bhatti, R. C. Thompson, and D. M. Segal Optics Express, Vol. 16, Issue 4, pp. 2351-2362 (2008)

Results demonstrating laser cooling and observation of individual calcium ions in a Penning trap are presented. We show that we are able to trap, cool, image and manipulate the shape of very small ensembles of ions sufficiently well to produce two-ion Coulomb crystal aligned along the magnetic field of a Penning trap. Images are presented which show the individual ions to be resolved in a two-ion crystal. A distinct change in the configuration of such a crystal is observed as the experimental parameters are changed. These structures could eventually be used as building blocks in a Penning trap based quantum computer.

Laser spectroscopy of hyperfine structure in highly-charged ions: a test of QED at high fields [arxiv.org] D.F.A. Winters, M. Vogel, D.M. Segal, R.C. Thompson, W. Noertershaeuser Can. J. Phys. 85, 403 (2007)

An overview is presented of laser spectroscopy experiments with cold, trapped, highly-charged ions, which will be performed at the HITRAP facility at GSI in Darmstadt (Germany). These high-resolution measurements of ground state hyperfine splittings will be three orders of magnitude more precise than previous measurements. Moreover, from a comparison of measurements of the hyperfine splittings in hydrogen- and lithium-like ions of the same isotope, QED effects at high electromagnetic fields can be determined within a few percent. Several candidate ions suited for these laser spectroscopy studies are presented.

Novel designs for Penning ion traps [PDF] J.R. Castrejón-Pita, H. Ohadi, D.R. Crick, D.F.A. Winters, D.M. Segal and R.C. Thompson J. Mod. Opt 54, 1581 (2007)

We present a number of alternative designs for Penning ion traps suitable for quantum information processing (QIP) applications with atomic ions. The first trap design is a simple array of long straight wires which allows easy optical access. A prototype of this trap has been built to trap Ca⁺ and a simple electronic detection scheme has been employed to demonstrate the operation of the trap. Another trap design consists of a conducting plate with a hole in it situated above a continuous conducting plane. The final trap design is based on an array of pad electrodes. Although this trap design lacks the open geometry of the traps described above, the pad design may prove useful in a hybrid scheme in which information processing and qubit storage take place in different types of trap. The behaviour of the pad traps is simulated numerically and techniques for moving ions rapidly between traps are discussed. Future experiments with these various designs are discussed. All of the designs lend themselves to the construction of multiple trap arrays, as required for scalable ion trap QIP.

Electronic detection of charged particle effects in a Penning trap [PDF] D.F.A. Winters, M. Vogel, D.M. Segal, and R.C. Thompson J. Phys. B: At. Mol. Opt. Phys. 39 3131-3143 (2006)

We present calculations and simulations of space charge and image charge effects on the motion of charged particles confined in a Penning trap. A quantitative prediction of these effects is of great importance in experiments which involve the trapping, manipulation, electronic detection and cooling of large numbers of charged particles, especially when high precision in the motional frequencies is required. The most prominent effect is a significant shift of the motional frequencies due to the charges' influence on the effective trapping potential. We derive expressions for the shifted motional frequencies from first principles, perform corresponding simulations and compare our results to previous experimental findings. We also study the possibility of electronic detection of frequency-shifted particle motions and discuss the consequences for their resistive cooling.

A proposed precision laser spectrometer for trapped highly charged ions [PDF] M. Vogel,D.F.A. Winters, D.M. Segal, and R.C. Thompson Review Of Scientific Instruments 76, 103102 (2005)

We propose a novel type of precision laser spectrometer for trapped, highly charged ions nearly at rest. It consists of a cylindrical open-endcap Penning trap in which an externally produced bunch of highly charged ions can be confined and investigated by means of laser spectroscopy. The combination of confinement, cooling and compression of a dense ion cloud will allow the ground state hyperfine splitting in highly charged ions to be measured with an accuracy three orders of magnitude better than in any previous experiment. A systematic study of different charge states and different isotopes of the same element allows for highly sensitive tests of bound-state QED and for a precision determination of nuclear properties. Apart from stable isotopes, also radioactive species with half-lives longer than about one hour can be investigated.

Proposal for a planar Penning ion trap [PDF] J. R. Castrejón-Pita and R. C. Thompson Physical Review A 71 (2005)

An alternative design for a planar Penning ion trap is presented. Although the analytical trapping potential is not exactly quadratic, approximate values for the characteristic frequencies around the equilibrium point can be found. An array of traps can be formed simply using long straight wires, and the open geometry of this design means that the structure can be miniaturized using well-known techniques. Consequently, these traps should be considered as excellent candidates for applications in quantum computation.

Plans for laser spectroscopy of trapped cold hydrogen-like HCI [PDF] [GZipped PS]
D.F.A Winters, A.M. Abdulla, J.R. Castrejon Pita, A. de Lange, D.M. Segal, R.C. Thompson Nucl Instr Meth Phys Res B 235 201 (2005) on 19 January 2005

Laser spectroscopy studies are being prepared to measure the 1s ground state hyperfine splitting in trapped cold highly charged ions. The purpose of such experiments is to test quantum electrodynamics in the strong electric feild regime. These experiments form part of the HITRAP project at GSI. A brief review of the planned experiments is presented.

Doppler cooling of Ca+ ions in a Penning trap [PDF] [GZipped PS]
K. Koo, J. Sudbery, D. M. Segal, and R. C. Thompson Physical Review A 69, 043402 (2004)

We have laser cooled a small cloud of ⁴⁰Ca⁺ ions stored in a Penning trap. The large Zeeman splittings that result from the presence of the imposed magnetic field necessitate the use of two cooling lasers tuned to the ²S_1/2-²P_1/2 transition near 397 nm (whereas only a single blue laser frequency is required in an rf trap). The 397 nm radiation is provided by a pair of blue diode lasers operated in extended cavities. Ions can escape from the cooling cycle by falling into a ²D_3/2 state. There is also a small probability that ions can be pumped into a ²D_5/2 state. The presence of large Zeeman splittings complicates the provision of repumper radiation to empty the D states. We describe two repumping schemes. The first scheme employs five infrared extended cavity diode lasers (ECDL's). The second scheme employs three infrared ECDL's, two of which have their injection current modulated to produce sidebands. An upper bound to the temperature of 1K is inferred from the linewidth of the 397-nm fluorescence for a small cloud of ⁴⁰Ca⁺ ions in our Penning trap. This work is part of a program aimed at using atomic ions in a Penning trap for decoherence studies and quantum information processing.

Improvement of Laser Cooling of Ions in a Penning Trap by use of the Axialisation Technique [PDF]
H. F. Powell, S. R. de Echaniz, E. S. Phillips, D. M. Segal, and R. C. Thompson J. Phys. B: At. Mol. Opt. Phys. 36 961 (2003)

We report a study of the axialisation and laser cooling of single ions and small clouds of ions in a Penning trap. A weak radiofrequency signal applied to a segmented ring electrode couples the magnetron motion to the cyclotron motion, which results in improved laser cooling of the magnetron motion. This allows us to approach the trapping conditions of a Paul trap, but without any micromotion. Using an ICCD camera we show that the motion of a single ion can be confined to dimensions of the order of 10 um. We have measured increased magnetron cooling rates using an rf-photon correlation technique. For certain laser cooling conditions, the magnetron motion of the centre of mass of the cloud grows and stabilises at a large value. This results in the ions orbiting the centre of the trap together in a small cloud, as confirmed by photon-photon correlation measurements.

Axialization of Laser Cooled Magnesium Ions in a Penning Trap [PDF] [GZipped PS]
H. F. Powell, D. M. Segal, and R. C. Thompson Physical Review Letters 89 93003 (2002)

We report the first demonstration of the axialization of laser cooled ions in a Penning trap. Axialization involves the application of a small radial quadrupole drive which couples the cyclotron and magnetron motions. This enhances the laser cooling, allowing tighter confinement of the ions to the central axis of the trap than is otherwise possible. Using an intensified charge-coupled device (ICCD) camera we have imaged the axialization process for the first time. For a single ion, we recorded a large decrease of the magnetron amplitude corresponding to a reduction in ion temperature of approximately 2 orders of magnitude to an upper limit of order 10 mK. We have discovered dynamics specific to the laser cooled system which depend critically on the axial drive frequency and amplitude.

Quantum jumps in singly ionized magnesium [PDF] [GZipped PS]
H F Powell, M A van Eijkelenborg, W Irvine, D M Segal and R C Thompson Journal of Physics: B 35 205 (2002)

The quantum jump statistics for the three stable isotopes of Mg⁺ have been studied experimentally. Single ions of magnesium were held and laser cooled in a Penning trap. Quantum jumps were observed by collecting the resonance fluorescence near 280 nm from the cooled ion.

The jump rate was analysed to find ratios of the average time the ion spends fluorescing, `on' time, to the average time it spends in the dark state, `off' time: for both ²⁴Mg⁺ and ²⁶Mg⁺ this value was found to be 15.9±1.2, in agreement with a theoretical value of 16.0. The presence of hyperfine structure in ²⁵Mg⁺ means that while the jump rate for ²⁴Mg⁺ and ²⁶Mg⁺ remains unaltered for both available cooling transitions, for the odd isotope the on to off ratio is predicted to be 11.8 and 22.8 for the lower and upper transitions respectively. Experimental values for these ratios were found to be 10.2 ± 0.7 and 22.0 ± 0.6.

The occurrence of so-called nuclear jumps in ²⁵Mg⁺ is investigated qualitatively. These rare jumps are produced as a result of the hyperfine splitting, which is only present in the odd isotope. Although the data indicate some evidence for this type of jump, it is not possible to draw any firm conclusions due to the small number of events observed.

Simple model for the laser cooling of an ion in a Penning trap [PDF] [GZipped PS]
R C Thompson and J Papadimitriou Journal of Physics B 33 3393 (2000)

We present a model for laser cooling of a single ion in the Penning trap. The model solves the equations of motion in the presence of the damping caused by the interaction with the laser beam, and predicts for the first time the dependence of the cooling rates for the two radial degrees of freedom of the trap as a function of the laser beam detuning, laser beam offset and saturation parameter. The conditions derived for both radial degrees of freedom to be cooled simultaneously agree with those found in earlier studies. The results indicate that under conditions where both motions are cooled simultaneously, the cooling rates are both significantly smaller than the maximum rate for either motion considered in isolation. Furthermore, the magnetron cooling rate is typically much lower than the cyclotron cooling rate, as has been found in experiments. The model indicates how the cooling rate for a single ion may be optimised.

Ion dynamics in a novel linear combined trap [PDF]
M.A. van Eijkelenborg, M.E.M. Storkey, D.M. Segal, R.C. Thompson International Journal of Mass Spectrometry v188 155 (1999)

We have studied the motional dynamics of ions stored in an ion trap of novel geometry, a linear combined trap, which combines the trapping fields of a linear rf trap and a Penning trap. The motional frequencies of trapped Mg/sup +/ ions are measured as a function of the trapping fields, and we find good agreement with theory

The quantum Zeno effect in trapped ions [PDF]
R C Thompson, J-L Hernandez-Pozos, J Hoffges CP457, Trapped Charged Particles and Fundamental Physics 388 (1999)

The quantum Zeno effect is the slowing down of the rate of a quantum mechanical transition by the frequent application of measurements to the system. Following the original suggestion of an experiment to test this in trapped ions, Itano et al performed an experiment in 1990. This was followed by several detailed theoretical treatments of the problem, making new predictions and giving a better understanding of what was happening. Also since then, suggestions for new types of experiment to test the quantum Zeno effect have been made. At Imperial College we are currently setting up an experiment to study the quantum Zeno effect of a single ion, incorporating some of these new ideas. Details of this experiment are discussed in the paper.

A driven, trapped, laser cooled ion cloud: a forced damped oscillator [PDF]
M A van Eijkelenborg, K Dholokia, M E M Storkey, D M Segal, R C Thompson Optics Communications 159 169 (1999)

We have studied the efficiency of laser cooling on clouds of magnesium and beryllium ions held in a Penning trap. We applied a driving voltage to the trap electrodes to drive the ions near one of their motional resonances, and studied the difference between the phase of the applied driving voltage and that of the resultant ion motion. Just as expected for a forced damped oscillator, we find that the phase difference changes by pi when the driving frequency is scanned through resonance. From the width of the measured phase change curves we determine the relative strength of the laser cooling on each of the three characteristic ion motions.

Sympathetic cooling and detection of molecular ions in a Penning trap [PDF]
M A van Eijkelenborg, M E M Storkey, D M Segal and R C Thompson Physical Review A 60 3903 (1999)

We have trapped and sympathetically cooled the molecular ions HCO⁺ and N₂H⁺ in a Penning trap. Through their Coulomb interaction with laser cooled Mg⁺ ions the molecules were sympathetically cooled to cryogenic temperatures. We identify the molecules through a measurement of their characteristic mass-dependent breathing mode frequencies. From a measurement of the temperature of the Mg⁺ ions we estimate that the final temperature of the sympathetically cooled molecules is 4K.

Laser cooling of ions stored in a Penning trap: A phase space picture [PDF]
G Zs K Horvath and R C Thompson Physical Review A 59 4530 (1999)

We present a phase-space picture of laser cooling of the radial motion of ions in a Penning trap. This picture enables a particularly simple derivation of the condition for simultaneous cooling of all degrees of freedom of a single ion to be obtained. It also allows a physically intuitive approach to be taken to the cooling process. Using this approach, we discuss different aspects of the cooling of a single ion in a Penning trap, including the formation of "trapped" states where the steady-state motion amplitude is non-zero for either the magnetron or modified cyclotron motion. We use an analytical approach where the approximation of small-amplitude motions can be made, and we use numerical calculations for larger-amplitude motions. The best procedure to use for effective laser cooling is derived. A similar approach is then used to treat the laser cooling of two ions in the Penning trap. We show that the use of the phase-space approach allows new insights into many aspects of the laser cooling process to be gained, and we indicate how these insights may be applied in experimental investigations.

Ion dynamics in perturbed qudrupole ion traps [PDF]
G. Zs. K. Horvat, J.-L. Hernandez-Pozos, K. Dholakia, J. Rink, D. M. Segal and R. C. Thompson Physical Review A 57 1944 (1998)

We use the results of a Lagrangian formulation of the dynamics of ions in a Penning trap to calculate the motional frequencies of the ions as a function of the trapping parameters. We then add realistic perturbations to the ideal trapping fields in the formalism and deduce the effects of these perturbations on the ion motion. For an ideal trap there exist values of the applied trapping fields that result in a degeneracy in the ion oscillation frequencies associated with different types of motion. We show that this motional frequency degeneracy is lifted by the inclusion of the effect of a tilt of the trap axis with respect to the axis of the applied magnetic field, leading to an "avoided crossing" between the oscillation frequencies. We calculate typical ion orbits for trap parameters that give oscillation frequencies near the avoided crossing between the axial and modified cyclotron frequencies. We generalize the analysis to include the motion of ions in a combined (Penning-Paul) trap and perform an experiment to test the predictions of the theory for a degeneracy between the modified cyclotron frequency and the axial frequency for Mg ions held in a tilted combined trap. The oscillation frequencies are measured for a range of tilt angles using a photon-photon correlation technique. There is good agreement between the experimental results and the theoretical predictions. The method we describe may prove to be a useful means by which trap imperfections can be identified and subsequently removed.

The motion of small numbers of ions in a Penning trap [PDF]
R. C. Thompson and D. C. Wilson Zeitschrift für Physik D 42 271 (1997)

An analysis is given of the motion of small num-bers of ions (up to three) in the Penning trap. It is shown that the motion is best described in the frame rotating at half the cyclotron frequency, in which the effect of the magnetic field can be described in terms of an effective electrostatic potential. The oscillation frequencies in this frame are cal-culated for 1, 2 and 3 ions and related to the frequencies observed in the laboratory frame. The orientations of 2- and 3-ion crystals are calculated as a function of the trap param-eters.

Inhibition of spontaneous decay by continuous measurements: Proposal for realizable experiment [PDF]
M B Plenio, P L Knight and R C Thompson Optics Communications 123 278 (1996)

We present several multilevel systems that should make possible the experimental verification of the quantum Zeno effect, ie the inhibition of exponential decay of the population of an atomic level rather than the suppression of a coherent transition. Both numerical and analytical results are presented. Possible ions that realize the required level configurations are presented and we verify for realistic parameters that the quantum Zeno effect should be observable.

Laguerre-Gaussian laser beams and ion traps [PDF]
W L Power and R C Thompson Optics Communications 132 371 (1996)

Light possessing orbital angular momentum is believed to exert a torque on atomic particles during resonant interactions. In this paper we suggest that trapped ions may be used to measure this effect. We present the results of simulations of trapped ions interacting with a Laguerre-Gaussian laser beam, and discuss the practical considerations of doing such an experiment.

Quantum state diffusion theory and a quantum jump experiment [PDF]
N Gisin, P L Knight, I C Percival, R C Thompson and D C Wilson Journal of Modern Optics 40 1663 (1993)

We use a recent stochastical diffusion model of quantum evolution to represent the evolution of a three-level quantum system undergoing quantum jumps. This is possible because the continuous change in the quantum state in this diffusion model is so rapid that it appears to be instantaneous in comparison with the time between transitions. Experimental data from a study of the intermittent fluoresence of a single trapped ²⁴Mg⁺ ion and equivalent theoretical data are shown to be strikingly similar. Statistical comparisons of the data are also made.

Investigation of ion dynamics in a Penning trap using a pulse-probe technique [PDF]
K Dholakia, G Zs K Horvath, W Power, D M Segal and R C Thompson Applied Physics B 60 375 (1995)

We demonstrate a pulse-probe method for measuring the ion-cloud rotation frequency in a Penning trap. We show that it is useful over a range of parameters not accessible to the photon correlation method of Dholakia et al. In particular, the pulse-probe method works for larger clouds than the photon-correlation method. We show that the pulse-probe method measures the space-charge-shifted frequency and gives us the optical pumping times within clouds. Furthermore, we show that, for Mg⁺ ions, it is capable of measuring much higher degrees of space-charge shift than the photon-correlation method. Improvements to the method may enable its use in measuring diffusion rates for ions in clouds.

Spectroscopy of laser cooled ions [PDF]
R C Thompson, K Dholakia, G Zs K Horvath, W Power, D M Segal (refereed article) Journal of Modern Optics 41 1087 (1994)

This paper is a written version of an invited review talk given at the 11th national Quantum Electronics Conference in Belfast in September 1993. It discusses the use of trapped ions for spectroscopy in both the optical and microwave regions of the spectrum. After introductory comments on the advantages offered by ion traps and laser cooling for spectroscopy, we take the example of mercury ions to show how many different types of experiment can be performed, with striking results. We also discuss our recent work at Imperial College, which can be seen as spectroscopy of the ion trap itself, giving information on the dynamics of trapped ions.

Photon correlation detection of ion oscillation frequencies in quadrupole ion traps [PDF]
K Dholakia, G Zs K Horvath, D M Segal, R C Thompson, D M Warrington and D C Wilson Physical Review A 47 441 (1993)

We present a method for measuring ion-oscillation frequencies in quadrupole traps (Paul, Penning, and combined traps). The method depends on a statistical analysis of the delays between detected fluoresence photons. We have used the method to verify the oscillation frequencies for magnesium ions in a Penning trap as a function of the dc voltage applied to the trap electrodes. We demonstrate that, as expected, the method can measure the space-charge shifted (individual ion) oscillation frequency rather than the frequency at which the ion cloud as a whole moves. However, our data suggest that for most of our operating conditions, any space-charge shift is negligible. We also discuss the effect of the contact potential arising from areas of the trap electrodes that are coated with excess Mg from the atomic beam used. We show that this extra potential shifts the center of the Penning trap and makes it unstable for low values of applied voltage.

Ion oscillation frequencies in a combined trap [PDF]
D J Bate, K Dholokia, R C Thompson and D C Wilson Journal of Modern Optics 39 305 (1992)

A combined trap is a quadrupole trap to which the fields of both the Paul and the Penning traps are applied. In this paper, equations of motion for ions confined in a combined trap are derived from first principles. The equations of motion are shown to give well-understood solutions for the Paul and Penning traps in the appropriate cases before they are solved to yield axial and radial oscillation frequencies on the applied fields is investigated.

The theoretical predictions were tested in an ion trap an Imperial College using very small numbers of ions, in some cases single ions. The single-ion cases were identified by the observation of quantum jumps in the fluoresence, which is characteristic of a single ion under these conditions. The agreement between the theory and experiment is good.

Photon correlation measurement of ion oscillation frequencies in a combined trap [PDF]
K Dholakia, G Zs K Horvath, D M Segal and R C Thompson Journal of Modern Optics 39 2179 (1992)

We present experimental verification of the oscillation frequencies of magnesium ions in a combined trap for a wide range of a.c. voltages and magnetic fields. We employ a new technique to measure these trap resonances using the distribution of time intervals between consecutively detected fluoresence photons.

Review Articles

Applications of laser cooled ions in a Penning trap [PDF]
R C Thompson Journal of Physics B: Atomic, Molecular and Optical Physics 42 154003 (2009)

This paper aims to describe in basic terms how the different types of ion traps work, giving some examples of their use. It then discusses some recent 'exotic' designs of ion traps and shows how they are optimized for particular experiments. Recent work at Imperial College London is used to illustrate some of the ideas introduced in this paper.

Spectroscopy and quantum optics with trapped ions [PDF]
R C Thompson Nathiagali Summer College, Pakistan (1999)

In these lecture notes, I describe the use of ion traps in experimental investigations of spectroscopy and quantum optics. Ion traps are well suited to this type of investigation because of the well-controlled conditions under which ions are held in traps and because they are well isolated from the environment. The notes start with an account of the way that ion traps work, concentrating on the radio-frequency or Paul trap. The techniques of laser cooling in ion traps are then discussed. Laser cooling is important because it allows new experiments to be performed which otherwise would not be possible. In particular, it allows one to work with single atomic particles and in some cases to cool them even to the ground state of the vibrational motion. The rest of the notes deal with various experimental studies undertaken in spectroscopy and quantum optics with trapped ions, including observations of quantum jumps; cavity quantum electrodynamics; non-classical states; quantum logic gates; the quantum Zeno effect; and frequency standards and fundamental constants. These notes do not attempt to give a full account of the theory of these phenomena, but rather to give an idea of the special characteristics of ion traps, of the very wide range of investigations that have been undertaken with them, and of the potential they hold for future investigations in spectroscopy, quantum optics and other areas of physics.

Fundamental physics with trapped ions [PDF]
G Zs K Horvath, R C Thompson and P L Knight Contemporary Physics 38 25 (1997)

Ion traps allow us to study single quantum systems, cooled to the lowest vibrational state of motion within confining electric and magnetic fields. In this article, we describe the working principles of ion traps and the methods used to cool the ions (principally laser cooling). We then discuss how these cold ions, held almost at rest in the trap, can be used to illuminate fundamental issues of quantum mechanics: quantum jumps, the quantum Zeno effect and the quantum statistics of photons scattered by the ions. Finally, we describe how several ions loaded in a trap are cooled into ordered crystals.

Spectroscopy of trapped ions
R C Thompson Advances in Atomic, Molecular and Optical Physics 31 63 (1993)

This article reviews recent progress in the use of trapped ions for spectroscopy, quantum optics and frequency standards. It does not attempt a detailed review of the use of ion traps for mass measurements or for the study of electrons, negative ions or molecular ions in traps. Even this limited area is a broad one to cover in a single review, so some topics have to be ommitted.

Spectroscopy and quantum optics of trapped ions
R C Thompson Comments on Atomic and Molecular Physics 29 349 (1992)

Ion traps offer many advantages for different types of experiments in spectroscopy and quantum optics as well as in other fields. In this paper the particular advantages of ion traps for this type of work are investigated. Several examples of their use are given, to show the wide range of application of traps and the remarkable progress which has been made with these devices.

Current Perspectives on the physics of trapped ions
R Blatt, P Gill and R C Thompson Journal of modern optics 39 193 (1992)

This paper presents a survey of recent work in the field of the physics of trapped ions, as an introduction to this Journal of Modern Optics special issue. The contrasting properties of trapped ion clouds and the single trapped ion are highlighted, together with their application to frequency standards and fundamental measurements.