| dc.description.abstract |
<p>A trapped Fermi gas near a collisional resonance provides a unique laboratory for
testing many-body theories in a variety of fields. The ultracold Fermi gas produced
in our lab is comprised of the lowest two spin states of $^6$Li. At 834 G there is
a collisional or Feshbach resonance between the two spin states. The scattering length
between trapped atoms of opposing spins far exceeds the interparticle spacing of the
gas. On resonance, a strongly interacting, unitary, Fermi gas is created which exhibits
universal behavior. The unitary Fermi gas is a prototype for other exotic systems
in nature from nuclear matter to neutron stars and high temperature superconductors.</p>
<p>For magnetic fields less than 834 G the scattering length is positive, and pairs
Fermi atoms can form molecular dimers. These dimers, comprised of two fermions, are
bosons. At ultracold temperatures the molecular bosons populate the lowest energy
level and form a Bose Einstein Condensate (BEC). For magnetic fields greater than
834G the scattering length between fermions in opposing spin states is negative, like
Cooper pairs formed between electrons in a superconductor. The Bardeen, Cooper, and
Shriefer (BCS) theory was developed to describe the pairing effect in the context
of superconductors. In our experiment we produce an ultracold unitary gas. By tuning
the magnetic field to either side of the Feshbach resonance we can transform the gas
into a weakly interacting BEC or BCS superfluid. Therefore, the region near a Feshbach
resonance is called the BEC-BCS crossover.</p>
<p>This dissertation presents a precision measurement of the hydrodynamic sound velocity
in an ultracold Fermi gas near a Feshbach resonance. The sound velocity is measured
at various magnetic fields both above and below resonance. Moreover, we are able
compare our measurements to theoretical descriptions of hydrodynamic sound propagation.
Further, our measurement of sound velocity exactly reproduces the non-perturbative
case, eliminating the need to consider nonlinear effects. At resonance the sound
velocity exhibits universal scaling with the Fermi velocity to within 1.8\% over a
factor of 30 in density. In a near zero temperature unitary gas the average sound
velocity at the axial center was measured, $c(0)/v_F$ = 0.364(0.005), as well as the
universal constant, $\beta$ = -0.565(0.015). The measurement of sound velocity in
an ultracold gas throughout the BEC-BCS crossover provides further evidence of the
continuous connection between the physics of the BEC, unitary, and BCS systems.</p>
|
|
