Current Research

Here is a selection of the topics I have been working on in the last year.

Rotating Spin-1 Bose Clusters

Tin-Lun Ho and Erich J. Mueller, PRL 89, 050401 (2002): At very fast rotation speeds a harmonically trapped gas of Bosons can form a series of strongly correlated states analogous to those found in the fractional quantum Hall effect. We study these states in the case of spin-1 bosons, empirically finding a set of simple "Hunds rules" which allows us to predict the wavefunction as a function of angular momentum. We find a striking corelation between the angular momentum of a state and its spin. For example, the ground state with odd angular momentum always has an odd spin. We also find a tendency towards "fermionization," where the many-body bosonic wavefunction factors into the product of two fermionic wavefunctions, one describing the orbital structure and the other the spin structure. The resulting states have a "spin-liquid" structure. We propose a method for experimentally observing these features, by studying colections of small Bose clusters within an optical lattice.

Rotating Spin-1 Bose Clusters
	Tin-Lun Ho and Erich J. Mueller, PRL 89, 050401 (2002): At very fast rotation speeds a harmonically trapped gas of Bosons can form a series of strongly correlated states analogous to those found in the fractional quantum Hall effect. We study these states in the case of spin-1 bosons, empirically finding a set of simple "Hunds rules" which allows us to predict the wavefunction as a function of angular momentum. We find a striking corelation between the angular momentum of a state and its spin. For example, the ground state with odd angular momentum always has an odd spin. We also find a tendency towards "fermionization," where the many-body bosonic wavefunction factors into the product of two fermionic wavefunctions, one describing the orbital structure and the other the spin structure. The resulting states have a "spin-liquid" structure. We propose a method for experimentally observing these features, by studying colections of small Bose clusters within an optical lattice.

Vortex Lattices in two-component Bose gas

Erich J. Mueller, and Tin-Lun Ho PRL 88, 180403 (2002): We study the rotational properties of two component Bose-Einstein condensates. For sufficiently fast rotation, the ground state of consists of two interpenetrating vortex lattices. As one changes the interactions between the two components these lattices undergo several phase transitions, changing their geometry and relative position. We present a theory of the resulting phase diagram.

Swallowtails

Erich J. Mueller, cond-mat/0207677: I provide an understanding of mysterious swallow-tail loops which have been found in the mean field energy structure of bosons in optical lattices. I show that these loops are a generic feature of hysteresis and in the present case are due to superfluid persistent currents which exist because the condensate is able to screen out the lattice potential. I show that for certain parameters, there exists a formal equivalence between particles in a periodic potential and particles in a ring with an impurity potential, where such persistent currents are better understood. The decay of the currents due to quantum fluctuations are calculated.

Swallowtails
	Erich J. Mueller, cond-mat/0207677: I provide an understanding of mysterious swallow-tail loops which have been found in the mean field energy structure of bosons in optical lattices. I show that these loops are a generic feature of hysteresis and in the present case are due to superfluid persistent currents which exist because the condensate is able to screen out the lattice potential. I show that for certain parameters, there exists a formal equivalence between particles in a periodic potential and particles in a ring with an impurity potential, where such persistent currents are better understood. The decay of the currents due to quantum fluctuations are calculated.

Nonequilibrium vortex dynamics

Erich J. Mueller, and Tin-Lun Ho, in preparation: We study the motion of a vortex lattice when a quadrapolar deformation is applied to a condensate, as in recent experiments, cond-mat/020449. Our analytic theory reproduces all of the striking behaviour seen in the experiment: 1) a gradual change in the geometry of the vortex lattice, 2) the appearance of stripes, 3) an elogation of the condensate at an angle 45 degrees from the applied stress.

Nonequilibrium vortex dynamics
	Erich J. Mueller, and Tin-Lun Ho, in preparation: We study the motion of a vortex lattice when a quadrapolar deformation is applied to a condensate, as in recent experiments, cond-mat/020449. Our analytic theory reproduces all of the striking behaviour seen in the experiment: 1) a gradual change in the geometry of the vortex lattice, 2) the appearance of stripes, 3) an elogation of the condensate at an angle 45 degrees from the applied stress.

Vortex Interference

Erich J. Mueller, and Tin-Lun Ho, in preparation: We study the interference between condensates containing vortex lattices. Distinctive stripes and bubbles are seen. Some animations.

Vortex Interference
	Erich J. Mueller, and Tin-Lun Ho, in preparation: We study the interference between condensates containing vortex lattices. Distinctive stripes and bubbles are seen. Some animations.

Spin textures in rotating spin-1 Bose gas

Erich J. Mueller, and Tin-Lun Ho, in preparation: In a spin-1 gas, angular momentum is carried in spin textures. In the case of ferromagnetic interactions, where the order parameter is a vector, these textures are skyrmions, as depicted in the figure to the left. We find these skyrmions form a triangular lattice. For Antiferromagnetic interactions, the order parameter is a nematic, and angular momentum is carried by pi-disclinations. In the cores of these disclinations, the nematic order parameter vanishes, but the vector "ferromagnetic" order parameter is non-zero. We find that the disclinations form a square lattice, and the cores are antiferromagnetically aligned with respect to one another.
Erich J. Mueller, Iaccopo Carusoto, and Tin-Lun Ho, in preparation We show how gases with these spin texture exhibit birefringence, and discuss how this birefringence can be used to image the textures.