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Previous Work
Our previous work falls into three main areas:
- Dynamics of laser cooled trapped ions
- Studies of the combined trap
- Studies of the quantum mechanics of single ions
To these three areas we are now adding quantum information processing with a single laser cooled trapped ion in a Penning trap.
Several general review articles have been written about aspects of spectroscopy, laser cooling and quantum optics with trapped ions over the last few years: Blatt et al (1992); Thompson (1993); Thompson et al (1994); Horvath et al (1997); Thompson (1998); Thompson (1999)
Dynamics of laser cooled trapped ions
When ions are held in an ion trap, they have characteristic oscillation frequencies which describe their motion in the trap. In the Penning trap these are the magnetron, axial and modified cyclotron frequencies. Studies of the variation of these frequencies with the parameters of the trap can give information about the trap itself (e.g. the value of the magnetic field and the physical dimensions of the trap) and about the ion cloud being held in the trap (e.g. its charge density).
The oscillation frequencies can be determined by driving the cloud close to a resonance and looking for effects on the cloud (e.g. the rate of fluorescence coming from the cloud). However, we developed a complementary technique which analyses the fluorescence coming from the cloud with no extra drive applied - this is therefore a passive rather than an active method, and the cloud is not perturbed by the measurement. We found that by analyzing the time intervals between successively detected photons we were able to see intervals characteristic of the various oscillation frequencies. We were thus able with this photon correlation technique to determine all the Penning trap oscillation frequencies together by taking a Fourier Transform of the time interval data. This work is described in Dholakia et al (1993). This was performed on trapped magnesium ions.
More recently, we have studied sympathetic cooling in the Penning trap. This occurs when two different species of ions are held in the trap at the same time. One of them is laser cooled (in this case the magnesium) and the other species is indirectly cooled by collisional interactions with the laser-cooled magnesium. We were able to demonstrate sympathetic cooling of various ions including molecular ions by driving their oscillation frequencies in the trap and monitoring the effect on the magnesium fluorescence when the drive was resonant with the different ion species. This is reported in van Eijkelenborg et al (1999).
One interesting variant of the photon correlation technique involves driving the ions close to a resonance in the trap and then monitoring the phase difference between the electrical drive signal and the driven motion of the ions. Again, this is done by recording a spectrum of time intervals, but this time between a fixed point on the drive oscillation and the time of arrival of the first detected photon. As one moves through the resonance frequency, the measured phase changes by p radians as expected. However, the interesting measurement is the frequency range over which this change occurs. Since this in effect is a forced simple harmonic oscillator, with the damping provided by the laser cooling, the width of the resonance tells us directly the rate of laser cooling for that oscillation mode. Thus this technique can be used to measure the rate of laser cooling for each type of motion in the trap. Our experimental work on this topic is described in van Eijkelenborg et al. The relevant theory for these measurements is given in Thompson and Papadimitriou (2000). Other work on the theoretical treatment of laser cooling in the Penning trap is reported in Horvath and Thompson (1999).
Studies of the Combined Trap
It is possible to combine the features of the Paul (RF) trap and the Penning trap. This gives a device called the combined trap. The usual electrodes are used, and both the RF field (used in the Paul trap) and the magnetic field (as in a Penning trap) are used together. The combined trap has a larger range of trapping parameters which give stable motion than in either trap alone. This arises because the magnetic field gives extra stability to the motion than comes from the RF field on its own. Our theoretical description of the combined trap and early experimental work (with magnesium ions) is given in Bate et al (1992). More complete experimental measurements of the combined trap using the photon correlation technique are described in Dholakia et al (1992).
We have also operated a novel combined trap which in which a linear rf trap has a magnetic field applied along its axis of symmetry - the linear combined trap. A variant of this type of trap with a tapered magnetic field is being employed in a novel QIP scheme which combines the benefits of trapped ion and NMR schemes. (Florian Mintert1 et al (2001))
Studies of the Quantum mechanics of Single Ions
One of the simplest but most striking demonstrations of the presence of a single ion in a trap is the observation of quantum jumps. This is the switching on and off of the fluorescence signal arising from the ion, which arises from the ion jumping between different internal energy levels. In our experiments in a Penning trap, this arises because the ground state of an ion (e.g. 24Mg+) is split into two Zeeman levels by an applied magnetic field. The laser cooling drives the ion from one of these levels into an excited state, and when the ion decays back to the same ground state Zeeman level we see a fluorescence photon. This cycle is repeated many times per second, resulting in a steady fluorescence signal (typically 20 000 counts per second). However, very rarely it is possible for the ion to decay to the other ground state Zeeman level. Once the ion is there, it cannot absorb any more laser light as the frequency now has the wrong value. Therefore the fluorescence signal turns off abruptly. Eventually the ion returns to the laser cooling cycle (in this case, due to a far off-resonant laser excitation) and then the signal returns. The result is a random telegraph signal, which switches on and off as the ion jumps between the two ground state levels. Our work on this system is described in Gisin et al (1993) together with the results of some simulations of the quantum mechanics of this system.
We have since made measurements of quantum jumps in different isotopes of magnesium. We have shown that the ratio of the fluorescence on times to off times is different for the different isotopes, as expected from theoretical considerations, as a result of the hyperfine interaction in the odd isotope. Furthermore, we have some evidence for a new type of quantum jump, which we call a nuclear quantum jump, where the nuclear spin projection changes rather than the electronic spin projection.
More recently, we have been building an experiment to study the Quantum Zeno Effect. This is a quantum mechanical effect related to our understanding of the theory of measurement in quantum mechanics. Put simply, if we drive a single quantum mechanical system coherently from one quantum mechanical state to another using a pulse of radiation (e.g. microwaves), we expect that with a pulse having a certain length the system will be known to have made the transition and will be found in the second state with high probability. However, quantum mechanics predicts that if we interrupt this process by making a measurement on the particle during the pulse, in effect asking it if it has made the transition or not, then the probability that it will have made the transition at the end of the pulse is reduced. In fact, the more interruptions are made, the less likely it will be that the transition is made. This bizarre result is called the quantum Zeno effect. It reflects the fact that in quantum mechanics measurement always has an effect on the system.
Our experiment has not yet been completed, but our progress on the experiment has been described in Thompson et al (1999) and a proposal for a modified version of the experiment is discussed by Plenio et al (1996).
A general discussion of quantum mechanical effects that can be studied in ion traps is given in Thompson (1992)