Our experimental program explores spinor Bose-Einstein condensates (BECs) of sodium atoms. Unique properties of the quantum fluid derive from its antiferromagnetic interactions, features that lead us to explore the rich frontier area between ultracold atoms and correlated electronic materials. Unlike its ferromagnetic cousin, rubidium-87, the sodium BEC in an optical trap possesses a nematic order parameter. A novel non-destructive imaging scheme is proposed to uncover the spatial dependence of this order, based upon detection of spin alignment rather than orientation. The spatial distribution of nematicity will be measured in the vicinity of a quantum phase transition mediated by the quadratic Zeeman Effect. The method will be used to examine both the dynamics of spatial fluctuations, including the nucleation of quantum half-vortices, as well as the structure of the equilibrium ground state. The antiferromagnetic interactions motivate us to experimentally realize and explore the limits to motional decoherence in a perfectly miscible two-component BEC. Finally, in a two dimensional antiferromagnetic BEC a Berezinskii-Kosterlitz-Thouless transition is predicted that is mediated by bosonic pairs of atoms with non-trivial spin (anti)-correlations.
Magnetism is intimately connected to spin. In a gas of atoms cooled to near absolute zero the spins of the individual atoms interact with one another to create ordered states - ferromagnetic if the magnetic moments are aligned with each other, or antiferromagnetic if the moments tend to oppose one another. In an antiferromagnet, the spins choose an axis in space and arrange themselves to point both positively and negatively along that axis, so that the total magnetic moment is zero. The energy difference between antiferromagnet and ferromagnet, if it were expressed as a temperature, is only a few billionths of a degree above absolute zero. Remarkably, we can experimentally distinguish between these two states, so the atoms are expressing their preference very strongly indeed. Our research will examine how an antiferromagnet reorders its axis of alignment in response to an external magnetic field. This is known as a phase transition, analogous to what happens to a liquid as the temperature increases to near its boiling point. In our gas, however, the transition is not mediated by thermal effects, but by quantum mechanics. Quantum phase transitions, as these are known, occur in many solid state materials, including superconductors, and our research can shed light on their properties. Apart from fundamental interest, they could lead to new devices that exploit the laws of quantum mechanics such as topological quantum computers.