Erich Mueller -- Graduate Research

My graduate research was conducted with Gordon Baym, principally on issues involving Bose Condensed Alkali Gases.

My thesis involved several topics:

1. The role of weak interactions on the transition temperature of a dilute Bose gas: Bose-Einstein condensation is a rather unique phase transition in that it occurs in a non-interacting gas of particles. Untill very recently there was no agreement as to how interactions change this transition. Studying the role of interactions is very difficult because at the transition temperature long-wavelength critical fluctuations render perturbation theory infrared divergent. In this section of my thesis, I show how to control these divergences by applying finite size scaling concepts. This technique is then used to calculate the transition temperature of an interacting Bose gas.
2. Fragmentation: One of the most surprising recent discoveries in the field of Bose-Einstein condensation has been the existence of a class of Bose gas models whose ground states have multiple, or fragmented, condensates. By analyzing specific examples, I show that in the thermodynamic limit these systems possess a spontaneously broken (non-gauge) symmetry and in this same limit fragmentation disappears, making fragmentation a phenomena which only occurs in small, mesoscopic, systems. I show how to experimentally detect fragmentation, and discuss when such detection is impossible.
3. Decay of persistent currents: As demonstrated by experiments at MIT [Onofrio et al. Phys. Rev. Lett. 85, 2228 (2000)], a Bose condensate of alkali atoms is superfluid. Naively, this superfluidity implies that fluid flow around the circumference of a toroidal trap should be dissipationless. Thermal fluctuations correct this picture, and lead to the decay of currents. By extending Langer and Ambegaokar's pioneering work on similiar fluctuations in superconductors [Phys. Rev. B 1, 1054 (1970)] I calculate the rate of dissipation due to these thermal fluctuations, and propose an experiment to measure this decay.
4. Mechanical instabilities in clouds of attractive bosons: Under increased pressure a classical gas with attractive interactions will undergo a liquid-gas phase transition. In a trapped atomic system this transition manifests itself as a physical collapse of the atomic cloud, analogous to the gravitational collapse of clouds of interstellar gases. I construct a quantum mechanical theory to predict the temperatures and densities at which a gas of bosons will collapse. \nobreak This theory spans all temperature regimes, from the T=0 degenerate gas to the high temperature classical gas. Experiments at JILA are in the right parameter range to explore the quantum-classical crossover described by this theory. In this work I also analyze two other instabilities which can be described using similar tools: 1) the formation of domains in spinor condensates (cf. experiments by Miesner et al. [Phys. Rev. Lett. 82, 2228 (1999)]), and 2) a BCS-type pairing which was predicted to occur in the attractive Bose gas. Importantly, our analysis reveals that such gases become mechanically unstable before any pairing can occur.
5. Kinetic theory of partially condensed gases: I present a kinetic theory which allows one to both describe the coherent motion of a condensate coupled to a disipative cloud of non-condensed particles. This theory is applied to understanding the production of quasiparticles when the interactions within the atomic cloud are suddenly changed.
6. Polaritonic theory of slow light: I give two simple explanations of electromagnetically induced transparency, and its applications to slowing light. The first is a mean-field theory, and the second a Greens function approach.

Published versions of this work:

1. Erich J. Mueller, Gordon Baym, and Markus Holzmann, Finite-size scaling and the role of the thermodynamic ensemble in the transition temperature of a dilute Bose gas, Journal of Physics B: Atomic, Molecular and Optical Physics 34, 4561 (2001)
2. Erich J. Mueller and Gordon Baym, Finite-temperature collapse of a Bose gas with attractive interactions, Physical Review A 62, 053605 (2000).
3. Erich J. Mueller, Paul M. Goldbart, and Yuli Lyanda-Geller, Multiply connected Bose-Einstein-condensed alkali-metal gases: Current-carrying states and their decay, Physical Review A 57 R1505-8 (1998)

During my graduate career, I was supported financially by Canada's Natural Sciences and Engineering Research Council, by the University of Illinois, and by the NSF.