Gareth Conduit
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My research in condensed matter physics concerns the properties of the materials that surround us in our everyday lives. Condensed matter physics focuses on how a large assembly of particles are affected by thermal energy and the interactions between particles. For example, as a kettle warms water it causes the constituent molecules to vibrate more and more vigorously. When a molecule's kinetic energy exceeds the attractive interaction between adjacent molecules the water boils, undergoing a liquid to vapor phase transition. This type of phenomenon is not unique to water; changing interactions between particles causes phase transitions in other many-body systems including ferromagnets and superconductors.

An important consideration when studying a condensed matter system is how the particles move relative to one another, particularly when on the verge of a phase transition. This can cause the system to display new cooperative behavior which can be markedly different from that of the separate constituent particles. Returning to the kettle, the water molecules' thermal energy causes them to move randomly, so the relative motion of any two molecules is on average independent. However, in systems near to a phase transition, with either short or long ranged interactions between particles, two distant particles will on average move together so as to become strongly correlated even though they are far apart. An everyday consequence of strong correlations is the formation of clouds. Since the widely separated water vapor molecules move together they can clump into regions of high density. When the high density regions are similar in size to the wavelength of light (many thousand times the average water vapor molecule separation), passing light is strongly scattered making the cloud appear white. A further increase in density causes water droplets to form which then leads to rain.

The collective behavior of particles discussed so far can be understood purely in terms of classical physics. However, intriguingly, this behavior finds a counterpart in the realm of quantum physics. Quantum mechanics introduces the concept of wave particle duality, meaning that every particle has a new effective length scale -- the de Broglie wavelength. When that length scale is less than the separation between adjacent particles their respective de Broglie wavelengths overlap so they become quantum degenerate, which dramatically alters the particles' behavior. One consequence is the Pauli exclusion principle that prevents electrons from occupying the same point in space therefore making materials solid.

Some interacting systems can be both strongly correlated and quantum degenerate. The coupling of quantum mechanics and strong correlations often leads to a rich range of new phenomena that are the subject of present-day research. The phenomena can be classed into two broad categories: Firstly, strong correlations can make widely used approximations invalid, so new theory must be developed to accurately describe the material. Secondly, the system could driven into a completely new phase of matter.

The traditional setting to explore many-body quantum phenomena has been electrons an a solid. The electrons interact with the long-range Coulomb force and are quantum degenerate at temperatures below ~30000°C, making this the prototypical condensed matter system. However, the complicated interplay between the electrons and the background lattice of atoms, and the extreme conditions demanded to observe novel phenomena creates additional obstacles when trying to study the fundamental phenomena. Instead, since a breakthrough in 1995, the possibility of using an gas of ultracold atoms has revolutionized many-body physics. An ultracold atomic gas provides unprecedented control over a many-body system. For example, an external magnetic field controls the relative energies of the orbiting electrons allowing the strength of atom-atom interactions to be varied. Atomic gases can now be used to address long-standing questions about the influence of strong correlations in the solid state.

Few-atom physics
with Yu Yang Fredrik Liu, and Thomas Whitehead.

Pairing of 3 trapped atoms
Two up spin atoms and one down spin atom in a trap. The solid red surface shows the strength of pairing and the excess up spin density by the blue net.

Recent developments with ultracold atomic gases have enabled single atom resolvability, with the Jochim group able to trap between two and ten fermionic atoms and address their quantum state. The few-atom system presents a unique opportunity of a system that can be solved exactly on a computer, but at the same time can be studied in experiment. Once the consequences of strong correlations have been properly understood in a few-atom system, it presents a nexus to understand intractable many-body physics.

To date the focus has been on equilibrium ground state properties with our work covering inhomogeneous superfluidity that could offer advantages to observe the elusive Fulde-Ferrel-Larkin-Ovchinnikov state, the itinerant ferromagnetic state first suggested by Stoner in 1939, and the exchange interactions behind both ferromagnetic and antiferromagnetic states. The suggestion on the emergence of the Fermi surface was followed up by the Jochim group's first observation of the Fermi surface in 2013. In the future the system offers the opportunity to provide a few-body standpoint into many-body problems, including a new opening to understand non-equilibrium physics.

Itinerant ferromagnetism in an ultracold atomic gas and the solid state
with Ben Simons, Andrew Green, and Lars Schonenberg.

Itinerant ferromagnet phases
The alignment of electron spins. Left: with weak interactions the gas forms a paramagnetic state. Right: with strong interactions the spins align as the gas forms a Stoner ferromagnet.

This project concerns an atomic gas containing two species of atoms, one species is taken to represent up-spin electrons in a solid and the second species to represent the down-spin electrons. Then, since the atomic species are set up with differing number densities and cannot interchange, the system has a fixed magnetic moment along one axis. If it becomes energetically favorable for the atomic gas to become ferromagnetic, the magnetic moment must form in-plane. This makes the system unique compared to ferromagnetic phenomenon in solid-state systems and has allowed new aspects of strongly correlated phases to be investigated [G.J. Conduit & B.D. Simons, Phys. Rev. A 79, 053606 (2009)].

Following on from this work, this phase has been explored for the first time by the Ketterle group at MIT [G.B. Jo et al., Science 325, 1521 (2009)]. I have performed a detailed critique of this experiment [G.J. Conduit & B.D. Simons, Phys. Rev. Lett 103, 200403 (2009)] and shown that its results cannot be understood within the framework of an itinerant ferromagnet at equilibrium, but is instead better described by a dynamic process with a condensed phase of topological defects undergoing mutual annihilation. A second possibility is highlighted in the followup work [G.J. Conduit & E. Altman, Phys. Rev. A 83, 043618 (2011)] that introduces a new formalism to expose how the interaction strength is renormalized by three-body atom loss.

Itinerant ferromagnet phase diagram
The phase diagram of a ferromagnet. At low temperature the system undergoes a first order phase transition, at high temperature a second order phase transition. The first order transition is preceeded by a spin spiral state.

Recently, in cooperation with the Ketterle group at MIT we have been exploring the possibilities for the next generation of the experiment, in which the goal is to eliminate the three-body loss. The proposal [G.J. Conduit & E. Altman, Phys. Rev. A 82, 043603 (2010)] is to start the gas in a spin spiral and then watch the ferromagnetic domains grow. This system, with its minimal three-body losses, should provide more clear signatures of the ferromagnetic transition that the original experimental setup. A two-dimensional [G.J. Conduit, Phys. Rev. A 82, 043604 (2010)] or mass imbalanced system [C.W. von Keyserlingk & G.J. Conduit, Phys. Rev. A 83, 053625 (2011)] could reduce competing many-body instabilities and at the same time also reveal distinctive signatures of ferromagnetism.

The generality of the formalism developed to describe ferromagnetism in an ultracold atom gas [G.J. Conduit & B.D. Simons, Phys. Rev. A 79, 053606 (2009)], enables it to be applied to also study novel behavior in the solid state system. The formalism predicts a new spatially varying ferromagnetic phase that should preempt the ferromagnetic phase transition in some materials [G.J. Conduit, A.G. Green & B.D. Simons, Phys. Rev. Lett. 103, 207201 (2009)]. To verify the robustness of our results we also developed a novel technique within the accurate ab initio Quantum Monte Carlo method which provided strong evidence for the formation of the phase. This phase has recently been observed in CeFePO [S. Lausberg et al., Phys. Rev. Lett. 109, 216402 (2012)].

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