Here I first give a very broad description of the 3 main areas I work in, and then list some of the very recent and/or ongoing topics of my research group.

(i)Large-Scale Quantum Phenomena: In the traditional understanding of Quantum Mechanics, it is a theory of microscopic phenomena; phenomena at our scale are governed by Classical physics. Nevertheless we do have superfluids and superconductors in Nature, which show quantum effects not just at atomic scales but at scales of many metres- an explanation of these in terms of 'macroscopic quantum states' was originally proposed in a remarkable paper of F. London in 1938. In 1978 quantum tunneling between macroscopically different states, as well as 'Schrodinger's Cat' superpositions of them, were proposed by Leggett for superconductors (and seen experimentally in various labs in subsequent years). Similar macroscopic tunneling phenomena were proposed for domain walls in magnets (Stamp, 1992), and seen in later experiments in magnetic wires. Macroscopic coherence between 2 or more atomic BEC's has been seen in the last decade. One of the most challenging current problems is to create and understand large-scale quantum phenomena in systems other than superfluid/superconducting systems. In recent years this discussion has extended even to quantum cosmology and the early universe.

Perhaps the most exotic large-scale quantum phenomenon proposed involves the quantum 'entanglement' of many systems at the same time. The idea goes back to work by Einstein and Schrodinger in 1935, but received an important stimulus with the idea of 'quantum computation', discussed in many papers since the first proposal in 1980. The advent of quantum algorithms like the factorization algorithm, and of quantum error correction routines (both due to Shor in 1994-95) has led to a large effort to design and build quantum information processing systems. So far designs use either a combination of atomic and optical components (eg., ion traps, cavity QED devices), or solid-state components (either superconducting devices like SQUIDs, or components made from electronic spins). By far the most important problem blocking current progress is 'decoherence' (see below), which destroys the entanglement.

(ii)Quantum Magnetism & Strongly-Correlated Systems: The microscopic origin of magnetism is quantum-mechanical, but technological applications of magnetism use only the classical properties of magnetism -interference phenomena involving different spins do not enter into the workings of contemporary magnetic devices. Likewise spin waves and spin wave interactions can be described classically. Nevertheless some of the deepest and most challenging problems in condensed matter physics involve the behaviour of strongly-correlated spins. On the microsopic level important questions involve the relation between magnetism and the metal-insulator transition, as well as strongly-correlated states like those in high-Tc superconductors - in both these cases the spin degrees of freedom play an essential role. On a larger scale one is interested in coherent quantum structures like magnetic solitons, and in the different phases and kinds of magnetic order that can exist.

The order existing in spin systems is often much more subtle than that in most other systems, involving topological ordering in spin space, or non-local order parameters. In important cases we do not even know what kind of order parameter is involved, or even if there is one. Finally a central problem in many quantum magnetic systems is a proper description of the dynamics, whether this be by simple exchange and coupling to spin waves, or by more complex quantum relaxation or tunneling processes. Areas of most current interest in quantum magnetism include quantum magnetic phenomena in low-dimensional spins systems (particularly 2-dimensional), or in nanomagnetic systems; entanglement phenomena involving many different spins, the use of spin systems for quantum computation, and the physics of both quantum and classical spin glasses. The problem of magnetic dynamics is most acute in the last 2 examples.

(iii)Physics of Decoherence: All quantum systems have quantum phases associated with their motion; the wave-function of a set of N quantum systems incorporates a large number of "relative phases" describing any "entanglement" between them. However these phases are very delicate- even very weak uncontrolled interactions with the surroundings can destroy them, a process known as decoherence. This process is considered to be fundamental to the understanding of how classical physics 'emerges' from quantum dynamics - whether it also 'solves' the famous quantum measurement problem, or whether it can form a central feature of quantum cosmology, are very controversial questions. Perhaps the most important current theoretical problems that stand any chance of being confronted with experiment concern the mechanisms of decoherence in Nature.

In most cases decoherence mechanisms can be understood as an entanglement with the environment, and it turns out that very general models can be used to describe this. One model (due to Feynman & Vernon, and greatly extended by Caldeira and Leggett) treats the environment as a set of oscillators - this 'oscillator bath' well describes extended environmental modes like photons, electrons, phonons, magnons, gravitons, etc. Another model, due to Prokof'ev and Stamp, describes the environment as a set of discrete level systems, like 2-level systems or spins; this 'spin bath' describes localized modes like defects, dislocations, or paramagnetic and nuclear spins. Different modes are appropriate to different systems - it turns out that in almost all solids, oscillator baths cause most decoherence at high temperatures, but below a few Kelvin, spin baths completely dominate. Decoherence has been investigated in great detail in recent years in superconducting, magnetic, and some mesoscopic metallic systems, and in quantum optical systems. An understanding of decoherence and how to control it is essential to make any quantum information processing systems, which rely on entanglement between many different 'qubits'. This is currently the subject of a large theoretical and experimental effort in many different fields.

(B) Specific Projects (for references cited herein, see the publications section)

(i)Quantum Spin Glasses: Glasses are systems in which modes (often 2-level modes) have a very complex collective dynamics which is 'frustrated' by the interactions between them - this leads to a hierarchy of timescales in their dynamics. In 'quantum glasses' the dynamics is driven by tunneling. The archetypcal quantum spin glass is the LiHoxY1-xF4 system, where the long-range dipolar interactions between the Ho spins frustrate a simple dynamics. Recent work (Schechter and Stamp, 2005, 2006a), has shown how the nuclear spin bath in this system actually controls the dynamics - this is a special case of a more general result, that a spin bath environment can control dynamics around a quantum critical point. Future work will continue in this direction.

(ii)Dipolar and Structural Glasses: More than 99% of all solids in the real world actually show glassy behaviour at low T. The dynamics of such systems (which continues to change in character as one lowers T, no matter how low T ones goes to) is a major unsolved problem. Recent work (Schechter and Stamp, 2006b) has solved one question, which is why there is a glassy transition in spin glasses, but not in dipolar or structural glasses. Future work will concentrate on the dynamics of the strongly-coupled low T quantum glass.

(iii)Decoherence in Magnetic Qubit systems: Work over the last 10 years, principally by Prokof'ev and Stamp, showed that the quantum relaxational dynamics of interacting qubit systems was controlled by a combination of dipolar interactions between the qubits, plus coupling of the qubits to nuclear spins and phonons (and electrons of the system is conducting). Recent work (Stamp & Tupitsyn, 2004) described quantitatively how nuclear spins and phonons cause decoherence in magnetic qubits, and how dipolar interactions cause 'correlated decoherence' in the same (Morello, Stamp, & Tupitsyn, 2006). The latter work has led to a number of important experiments, including one in the UBC lab of WN Hardy. Future work here will focus on multi-qubit decoherence in magnetic molecule systems, and on the experiments currently being done.

(iv)Use of String Theory to understand Decoherence dynamics: There exist very interesting mappings between certain kinds of string theory and models describing decoherence in solid-state systems. One such model (the 'Schmid' model) was recently examined by us (Hasselfield et al, 2006), and another (the dissipative WAH model) is of some interest because of its relevance to important physical systems, and because its behaviour is rather controversial (Stamp & Chen, 2006). Further work on this may use Quantum Monte Carlo methods to look at the dynamics.

(v)Quantum Dynamics of Magnetic Solitons: Magnetic solitons, as was shown in 1992-98 by Stamp et al., can show macroscopic tunneling behaviour. More recently we have examined the theoretically fundamental problem of the dynamics of quantum vortices, and shown that (i) it can be calculated for magnetic vortices, where an experimental test should be possible; and (ii) that the equation of motion is non-local (Thompson & Stamp, 2006a, 2006b). Future work is concerned with the dynamics of magnetic domain walls in solid He-3, in a collaboration with DD Osheroff (Stanford).

(vi)Vortex Dynamics in superfluids: In superfluid He-4 one can examine a fairly direct way the quantum nucleation of vortices by tunneling, in experiments on ion dynamics at low T. A proper theory is still lacking of this rather fundamental process. Partial progress was made in the tunneling theory recently (Marchand, MSc thesis, 2006), and a full theory involving phonons in the vortex nucleation is now complete (Marchand & Stamp, in preparation).

(vii)Dynamics of "spin nets' of qubits: A crucial unsolved problem in both quantum magnetism and quantum information theory is the entangled dynamics of a set of qubits which interact with each other and with an environment (the latter causing decoherence). The first calculation of this for a spin system (Morello, Stamp, & Tupitsyn, 2006) showed the crucial role of 2-spin dipolar interactions and of 'correlated decoherence' caused by this (Tupitsyn, Stamp, & Morello, 2006b). Future work will extend the previous results in the quantum relaxation regime (Tupitsyn, Stamp, Prokof'ev, 2004; Tupitsyn & Stamp, 2004b) and the thermally activated regime (Tupitsyn & Stamp, 2004c), to cover multi-qubit dynsmics and multi-qubit decoherence processes. This will be applied to both spin systems and systems of superconducting qubits.

(viii)Quantum Dynamics of nanomagnetic molecules: The Prokof'ev-Stamp theory of quantum relaxation (1996,1998,2000), explains the dynamics of dipole interacting magnetic molecules which tunnel at low T in the presence of nuclear spins and phonons. It has now been tested in numerous experiments. The big challenge now is to understand decoherence for these systems, and to make predictions for their quantum dynamics in the regime of coherent behaviour. Preliminary work on this by Morello, Tupitsyn, & Stamp (2006a, 2006b) was described above. Current and future work is looking at dimer-coupled magnetic molecules, and on the dynamics of the related LiHoxY1-xF4 system (Schechter & Stamp, in preparation).

(ix)Dynamics of Quantum Walks: A new way of describing quantum information processing maps the system onto a 'quantum walk' of a particle on some mathematical graph. Recent work (Hines and Stamp, 2006a, 2006b), has given extensive results for how this mapping can be done once coupling to an environment (an oscillator or a spin bath) is included. Some rather striking results for spin bath environments (Prokof'ev & Stamp, 2006) show how non-intuitive some of the results can be. All of this work is an interesting new direction in the general theory of decoherence (Stamp, 2006). Current and future work is using this to investigate the very important problem of error correction in the presence of 'correlated errors'.