arXiv subjects
Publications and source records attributed to Erich J. Mueller.
We study the effects of surface tension between normal and superfluid regions of a trapped Fermi gas at unitarity. We find that surface tension causes notable distortions in the shape of large aspect ratio clouds. Including these distortions in our theories resolves many of the apparent discrepancies among different experiments and between theory and experiments.
We calculate the collective modes of a partially polarized Fermi gas trapped in a spherically symmetric harmonic potential. We show that the breathing mode frequency exhibits non-monotonic dependence on polarization in the entire BCS-BEC crossover region. Moreover, we find that the breathing mode can be used to distinguish between two commonly used unitary gas equations of state.
We present the theory of bosonic systems with multiple condensates, unifying disparate models which are found in the literature, and discuss how degeneracies, interactions, and symmetries conspire to give rise to this unusual behavior. We show that as degeneracies multiply, so do the types of fragmentation, eventually leading to strongly correlated states with no trace of condensation.
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.
We explore the Bose condensed phases of an atomic gas on the molecular side of a Feshbach resonance. In the absence of atom-molecule and molecule-molecule scattering, we show that the atomic condensate is either a saddle point of the free energy with energy always exceeding that of the molecular condensate, or has a negative compressibility (hence unstable to density fluctuations). Therefore no phase transition occurs between the atomic and molecular condensates. We also show that a repulsive molecule-molecule scattering can stabilize a sufficiently dense atomic condensate, leading to the possibility of a phase transition. We caution that 3-body processes may render this transition unobservable.
A sum rule approach is used to calculate the zero temperature oscillation frequencies of a two component trapped atomic Fermi gas in the BCS-Bose Einstein condensation crossover region. These sum rules are evaluated using a local density approximation which explicitly includes Feshbach molecules. Breathing modes show non-monotonic behavior as a function of the interaction strength, while quadrupole modes are insensitive to interactions for both spherically symmetric and axially symmetric traps. Quantitative agreement is found with experiments on atomic $^6Li$ system and with other theoretical approaches.
We explore the theory of electrons confined by one dimensional power law potentials. We calculate the density profile in the high density electron gas, the low density Wigner crystal, and the intermediate regime. We extract the momentum space wavefunction of the electron at the Fermi surface, which can be measured in experiments on tunneling between parallel wires. The onset of localization leads to a dramatic broadening of the momentum space wavefunction together with pronounced sharpening (in energy) of the tunneling spectrum.
We show how lasers may create fields which couple to neutral atoms in the same way that the electromagnetic fields couple to charged particles. These fields are needed for using neutral atoms as an analog quantum computer for simulating the properties of many-body systems of charged particles. They allow for seemingly paradoxical geometries, such as a ring where atoms continuously reduce their potential energy while moving in a closed path. We propose neutral atom experiments which probe quantum Hall effects and the interplay between magnetic fields and periodic potentials.
Closed form analytic expressions are derived for the density profile of a harmonically trapped noninteracting Fermi gas in $d$ dimensions. Shell structure effects are included to leading order in 1/N, where $N$ is the number of particles. These corrections to the local density approximation scale as $δn/n\sim N^{-α}$, where $α=(1+1/d)/2$.
We formulate a renormalization group (RG) for the interaction parameters of the general two-body problem and show how a limit cycle emerges in the RG flow if the interaction approaches an inverse square law. This limit cycle generates a scaling structure in the energy spectrum. Our demonstration is relevant to the Efimov problem in nuclear physics where similar scaling appears.
We explore the dielectric properties of spinor condensates. Gases with vector (nematic) order, such as spin-1 condensates with ferromagnetic (antiferromagnetic) interactions, display optical activity (birefringence). This optical activity/birefringence is respectively seen for light detuned from resonance by a frequency which is not too large compared with the fine/hyperfine structure. Careful tuning of the light frequency can isolate either of these two effects. These features can be used to image spin textures in clouds of spin 1 bosons, and to discern states showing different types of spin order.
Slowly rotating spin-1 Bose-Einstein condensates are studied through a variational approach based upon lowest Landau level calculus. The author finds that in a gas with ferromagnetic interactions, such as $^{87}$Rb, angular momentum is predominantly carried by clusters of two different types of skyrmion textures in the spin-vector order parameter. Conversely, in a gas with antiferromagnetic interactions, such as $^{23}$Na, angular momentum is carried by $π$-disclinations in the nematic order parameter which arises from spin fluctuations. For experimentally relevant parameters, the cores of these $π$-disclinations are ferromagnetic, and can be imaged with polarized light.
We analyze recent experiments at JILA which observe periodic formation of stripes in a rotating Bose condensate [Engels et al. Phys. Rev. Lett. {\bf 89}, 100403 (2002)], and explain this behavior as a consequence of kinetic energy driven evolution, where the vortices follows a quadrupolar flow. We demonstrate that the structure of vortex lattices in the lowest Landau level is a useful tool for understanding such complex phenomena, even when the system is not in the quantum Hall regime.
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.
We consider the condensate wavefunction 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.
We study the Bose-Einstein condensation phase transition in a weakly interacting gas through a perturbative analysis of finite systems. In both the grand canonical and the canonical ensembles, perturbation theory suffers from infrared divergences and cannot directly determine the transition temperature in the thermodynamic limit. However, in conjunction with finite size scaling, perturbation theory provides a powerful calculation tool. We implement it here to estimate a shift in the transition temperature in the canonical ensemble consistent with grand canonical calculations.
We study the mechanical stability of the weakly interacting Bose gas with attractive interactions, and construct a unified picture of the collapse valid from the low temperature condensed regime to the high temperature classical regime. As we show, the non-condensed particles play a crucial role in determining the region of stability, even providing a mechanism for collapse in the non-condensed cloud. Furthermore, we demonstrate that the mechanical instability prevents BCS-type ``pairing'' in the attractive Bose gas. We extend our results to describe domain formation in spinor condensates.
We study the mechanical stability of the weakly interacting Bose gas with attractive interactions, and construct a unified picture of the collapse valid from the low temperature condensed region to the high temperature classical regime. As we show, the non-condensed particles play a crucial role in determining the region of stability. We extend our results to describe domain formation in spinor condensates.