Universality in phase transitions for ultracold fermionic atoms
Abstract
We describe the gas of ultracold fermionic atoms by a functional integral for atom and molecule fields. The crossover from BoseEinstein condensation (BEC) to BCStype superfluidity shows universal features in terms of a concentration parameter for the ratio between scattering length and average interatomic distance. We discuss the relevance of the Yukawa coupling between atoms and molecules, establish an exact narrow resonance limit, and show that renormalized quantities are independent of the Yukawa coupling for the broad resonance and BCS and BEC limits. Within our functional integral formalism we compute the atom scattering in vacuum and the molecular binding energy. This connects the universal concentration parameter to the magnetic field of a given experiment. Beyond meanfield theory we include the fluctuations of the molecule field and the renormalization effects for the atommolecule coupling. We find excellent agreement with the observed fraction of bare molecules in {sup 6}Li and qualitative agreement with the condensate fraction in {sup 6}Li and {sup 40}K. In addition to the phase diagram and condensate fraction we compute the correlation length for molecules, the inmedium scattering length for molecules and atoms, and the sound velocity.
 Authors:
 Institut fuer Theoretische Physik, Philosophenweg 16, 69120 Heidelberg (Germany)
 Publication Date:
 OSTI Identifier:
 20786973
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.73.033615; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; BINDING ENERGY; BOSEEINSTEIN CONDENSATION; CORRELATIONS; COUPLING; FERMIONS; FLUCTUATIONS; INTERATOMIC DISTANCES; LITHIUM 6; MAGNETIC FIELDS; MEANFIELD THEORY; MOLECULES; PHASE DIAGRAMS; PHASE TRANSFORMATIONS; POTASSIUM 40; RENORMALIZATION; RESONANCE; SCATTERING; SCATTERING LENGTHS; SOUND WAVES; SUPERFLUIDITY; YUKAWA POTENTIAL
Citation Formats
Diehl, S., and Wetterich, C. Universality in phase transitions for ultracold fermionic atoms. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVA.73.0.
Diehl, S., & Wetterich, C. Universality in phase transitions for ultracold fermionic atoms. United States. doi:10.1103/PHYSREVA.73.0.
Diehl, S., and Wetterich, C. Wed .
"Universality in phase transitions for ultracold fermionic atoms". United States.
doi:10.1103/PHYSREVA.73.0.
@article{osti_20786973,
title = {Universality in phase transitions for ultracold fermionic atoms},
author = {Diehl, S. and Wetterich, C.},
abstractNote = {We describe the gas of ultracold fermionic atoms by a functional integral for atom and molecule fields. The crossover from BoseEinstein condensation (BEC) to BCStype superfluidity shows universal features in terms of a concentration parameter for the ratio between scattering length and average interatomic distance. We discuss the relevance of the Yukawa coupling between atoms and molecules, establish an exact narrow resonance limit, and show that renormalized quantities are independent of the Yukawa coupling for the broad resonance and BCS and BEC limits. Within our functional integral formalism we compute the atom scattering in vacuum and the molecular binding energy. This connects the universal concentration parameter to the magnetic field of a given experiment. Beyond meanfield theory we include the fluctuations of the molecule field and the renormalization effects for the atommolecule coupling. We find excellent agreement with the observed fraction of bare molecules in {sup 6}Li and qualitative agreement with the condensate fraction in {sup 6}Li and {sup 40}K. In addition to the phase diagram and condensate fraction we compute the correlation length for molecules, the inmedium scattering length for molecules and atoms, and the sound velocity.},
doi = {10.1103/PHYSREVA.73.0},
journal = {Physical Review. A},
number = 3,
volume = 73,
place = {United States},
year = {Wed Mar 15 00:00:00 EST 2006},
month = {Wed Mar 15 00:00:00 EST 2006}
}

A functional renormalizationgroup study for the BoseEinstein condensate (BEC)BCS crossover for ultracold gases of fermionic atoms is presented. We discuss the fixed point which is at the origin of universality for broad Feshbach resonances. All macroscopic quantities depend only on one relevant parameter, the concentration ak{sub F}, besides their dependence on the temperature in units of the Fermi energy. In particular, we compute the universal ratio between molecular and atomic scattering length in vacuum. We also present an estimate to which level of accuracy universality holds for gases of Li and K atoms.

Phase diagram of twodimensional fastrotating ultracold fermionic atoms near unitarity
By analyzing vortex lattices, reentrant Cooper pairing, and FuldeFerrellLarkinOvchinnikov (FFLO) states in a single theoretical framework, we explore how vortices and spin textures join to protect superconductivity against large magnetic fields. We use a rapidly rotating ultracold gas of fermionic atoms near unitarity as a model system amenable to experimental exploration and discover a hierarchy of spinpolarized and FFLO phases in which a metal or a band insulator of unpaired particles coexists with a spatially modulated superfluid hosting a vortex lattice. Quantum fluctuations can transform these phases into strongly correlated 'vortexliquid' metals and insulators, respectively. We argue that vortex latticesmore » 
Fluctuations in the formation time of ultracold dimers from fermionic atoms
We investigate the temporal fluctuations characteristic of the formation of molecular dimers from ultracold fermionic atoms via Raman photoassociation. The quantum fluctuations inherent to the initial atomic state result in large fluctuations in the passage time from atoms to molecules. Assuming degeneracy of kinetic energies of atoms in the strong coupling limit, we find that a heuristic classical stochastic model yields qualitative agreement with the full quantum treatment in the initial stages of the dynamics. We also show that in contrast to the association of atoms into dimers, the reverse process of dissociation from a condensate of bosonic dimers exhibitsmore » 
Measuring the OneParticle Excitations of Ultracold Fermionic Atoms by Stimulated Raman Spectroscopy
We propose a Raman spectroscopy technique which is able to probe the oneparticle Green function, the Fermi surface, and the quasiparticles of a gas of strongly interacting ultracold atoms. We give quantitative examples of experimentally accessible spectra. The efficiency of the method is validated by means of simulated images for the case of a usual Fermi liquid as well as for more exotic states: specific signatures of, e.g., a dwave pseudogap are clearly visible. 
Inhomogeneous spectral moment sum rules for the retarded Green function and selfenergy of strongly correlated electrons or ultracold fermionic atoms in optical lattices
Spectral moment sum rules are presented for the inhomogeneous manybody problem described by the fermionic FalicovKimball or Hubbard models. These local sum rules allow for arbitrary hoppings, site energies, and interactions. They can be employed to quantify the accuracy of numerical solutions to the inhomogeneous manybody problem such as strongly correlated multilayered devices, ultracold atoms in an optical lattice with a trap potential, strongly correlated systems that are disordered, or systems with nontrivial spatial ordering such as a chargedensity wave or a spindensity wave. We also show how the spectral moment sum rules determine the asymptotic behavior of the Greenmore »