Erich J. Mueller

Spin-imbalance in a one-dimensional Fermi gas

Superconductivity and magnetism generally do not coexist. Changing the relative number of up and down spin electrons disrupts the basic mechanism of superconductivity, where atoms of opposite momentum and spin form Cooper pairs. Nearly forty years ago Fulde and Ferrell and Larkin and Ovchinnikov (FFLO) proposed an exotic pairing mechanism in which magnetism is accommodated by the formation of pairs with finite momentum. Despite intense theoretical and experimental efforts, however, polarized superconductivity remains largely elusive. Unlike the three-dimensional (3D) case, theories predict that in one dimension (1D) a state with FFLO correlations occupies a major part of the phase diagram. Here we report experimental measurements of density profiles of a two-spin mixture of ultracold 6Li atoms trapped in an array of 1D tubes (a system analogous to electrons in 1D wires). At finite spin imbalance, the system phase separates with an inverted phase profile, as compared to the 3D case. In 1D, we find a partially polarized core surrounded by wings which, depending on the degree of polarization, are composed of either a completely paired or a fully polarized Fermi gas. Our work paves the way to direct observation and characterization of FFLO pairing.

Fragmentation of Bose-Einstein condensates

We present the theory of bosonic systems with multiple condensates, providing a unified description of various model systems that are found in the literature. We discuss how degeneracies, interactions, and symmetries conspire to give rise to this unusual behavior. We show that as degeneracies multiply, so do the varieties of fragmentation, eventually leading to strongly correlated states with no trace of condensation.

Two-component Bose-Einstein condensates with a large number of vortices

We consider the condensate wave function of a rapidly rotating two-component Bose gas with an equal number of particles in each component. If the interactions between like and unlike species are very similar (as occurs for two hyperfine states of (87)Rb or (23)Na) we find that the two components contain identical rectangular vortex lattices, where the unit cell has an aspect ratio of sqrt[3], and one lattice is displaced to the center of the unit cell of the other. Our results are based on an exact evaluation of the vortex lattice energy in the large angular momentum (or quantum Hall) regime.

High temperature expansion applied to fermions near Feshbach resonance.

We show that, apart from a difference in scale, all of the surprising recently observed properties of a degenerate Fermi gas near a Feshbach resonance persist in the high temperature Boltzmann regime. In this regime, the Feshbach resonance is unshifted. By sweeping across the resonance, a thermal distribution of bound states (molecules) can be reversibly generated. Throughout this process, the interaction energy is negative and continuous. We also show that this behavior must persist at lower temperatures unless there is a phase transition as the temperature is lowered. We rigorously demonstrate universal behavior near the resonance.

Artificial electromagnetism for neutral atoms: Escher staircase and Laughlin liquids

We present a method for creating fields that couple to neutral atoms in the same way that electromagnetic fields couple to charged particles. We show that this technique opens the door for a range of neutral atom experiments, including probing the interplay between periodic potentials and quantum Hall effects. Furthermore, we propose, and analyze, seemingly paradoxical geometries which can be engineered through these techniques. For example, we show how to create a ring of sites where an atom continuously reduces its potential energy by moving in a clockwise direction.

Detecting antiferromagnetism of atoms in an optical lattice via optical Bragg scattering

Antiferromagnetism of ultracold fermions in an optical lattice can be detected by Bragg diffraction of light, in analogy to the diffraction of neutrons from solid-state materials. A finite sublattice magnetization will lead to a Bragg peak from the ((1/2)(1/2)(1/2)) crystal plane with an intensity depending on details of the atomic states, the frequency and polarization of the probe beam, the direction and magnitude of the sublattice magnetization, and the finite optical density of the sample. Accounting for these effects we make quantitative predictions about the scattering intensity and find that with experimentally feasible parameters the signal can be readily measured with a CCD camera or a photodiode and used to detect antiferromagnetic order.

Exact parent Hamiltonian for the quantum Hall states in a lattice.

We study lattice models of charged particles in uniform magnetic fields. We show how longer range hopping can be engineered to produce a massively degenerate manifold of single-particle ground states with wave functions identical to those making up the lowest Landau level of continuum electrons in a magnetic field. We find that in the presence of local interactions, and at the appropriate filling factors, Laughlins fractional quantum Hall wave function is an exact many-body ground state of our lattice model. The hopping matrix elements in our model fall off as a Gaussian, and when the flux per plaquette is small compared to the fundamental flux quantum one only needs to include nearest and next-nearest neighbor hoppings. We suggest how to realize this model using atoms in optical lattices, and describe observable consequences of the resulting fractional quantum Hall physics.

Profiles of near-resonant population-imbalanced trapped Fermi gases

We investigate the density profiles of a partially polarized trapped Fermi gas in the BCS-BEC crossover region using mean field theory within the local density approximation. Within this approximation the gas is phase separated into concentric shells. We describe how the structure of these shells depends upon the polarization and the interaction strength. A comparison with experiments yields insight into the possibility of a polarized superfluid phase.

Optical-lattice Hamiltonians for relativistic quantum electrodynamics

We show how interpenetrating optical lattices containing Bose-Fermi mixtures can be constructed to emulate the thermodynamics of quantum electrodynamics (QED). We present models of neutral atoms on lattices in 1+1, 2+1, and 3+1 dimensions whose low-energy effective action reduces to that of photons coupled to Dirac fermions of the corresponding dimensionality. We give special attention to (2+1)-dimensional quantum electrodynamics (QED3) and discuss how two of its most interesting features, chiral symmetry breaking and Chern-Simons physics, could be observed experimentally.

Superfluidity and mean-field energy loops: Hysteretic behavior in Bose-Einstein condensates

We present a theory of hysteretic phenomena in Bose gases, using superfluidity in one dimensional rings and in optical lattices as primary examples. Through this study we are able to give a physical interpretation of swallowtail loops recently found by many authors in the mean-field energy structure of trapped atomic gases. These loops are a generic sign of hysteresis, and in the present context are an indication of superfluidity. We have also calculated the rate of decay of metastable current carrying states due to quantum fluctuations.