In this paper, collective excitations in a homogeneous fermion-fermion mixture with different Fermi surfaces are studied. In the Fermi liquid phase, the zero-sound velocity is found to be larger than the largest Fermi velocity. With attractive interactions, the superfluid phase appears below a critical temperature, and the phase mode is the low-energy collective excitation. The velocity of the phase mode is significantly different from the zero-sound velocity. The difference between the two velocities may serve as a tool to detect the superfluid phase.
An effective interaction between fermions in a Bose-Fermi mixture is derived. It is induced by density fluctuations of the bosonic background. The contributions from states containing both one and two virtual phonons are taken into account self-consistently. The time dependence of the effective interaction has been removed by assuming that the velocity of the fermions at the Fermi surface is much larger than the sound velocity in the Bose gas. This assumption is more appropriate for the actual experimental situations than the usual approximation of neglecting retardation effects. The effective interaction turns out to be attractive and, as a consequence, can give rise to a superconducting phase in the Fermi component of the mixture. The fermions are considered in only one magnetic state, so that pairing can be effective only in odd-
l channels. It has been found that the onset of the superconducting phase can occur at temperatures
(>100nK) of the same order of magnitude as the Fermi temperature $(\ensuremath{\sim}300\mathrm{nK}),$ and the energy gap in the excitation spectrum is a small fraction $(\ensuremath{\sim}1%)$ of the Fermi energy.
We analytically investigate superfluid phase in two dimension at zero temperature for asymmetric Fermi gas. Analytic expressions for both gap and chemical potentials at mean-field level are obtained as a function of binding energy and population imbalance when mass of different types of fermions is equal. We identify regions corresponding to normal, Sarma phase for different polarization, or mass ratio and discuss topological phase diagram in the BCS-BEC crossover and find that energy gap and chemical potential behave differently in these topological quantum phase. We also obtain the low-frequency and long-wavelength collective excitation spectrum and find sound velocity has a maximum when two types of mass are equal.
A general analysis of Meissner effect and spin susceptibility of a uniform superconductor in an asymmetric two-component fermion system is presented in nonrelativistic field theory approach. We found that the pairing mechanism dominates the magnetization property of superconductivity and the asymmetry enhances the paramagnetism of the system. At the turning point from BCS to breached pairing superconductivity, the Meissner mass squared and spin susceptibility are divergent at zero temperature. In the breached pairing state induced by chemical potential difference and mass difference between the two kinds of fermions, the system goes from paramagnetism to diamagnetism, when the mass ratio of the two species increases.
We consider a superfluid state in a two-component gas of fermionic atoms with equal densities and unequal masses in the BCS limit. We develop a perturbation theory along the lines proposed by Gorkov and Melik-Barkhudarov and find that for a large difference in the masses of heavy
(M) and light
(m) atoms one has to take into account both the second-order and third-order contributions. The result for the critical temperature and order parameter is then quite different from the prediction of the simple BCS approach. Moreover, the small parameter of the theory turns out to be $({p}_{F}\ensuremath{\mid}a\ensuremath{\mid}∕\ensuremath{\hbar})\sqrt{M∕m}⪡1$, where
pF is the Fermi momentum and
a the scattering length. Thus, for a large mass ratio
M∕m the conventional perturbation theory requires significantly smaller Fermi momenta (densities) or scattering lengths than in the case of $M\ensuremath{\sim}m$, where the small parameter is ${p}_{F}\ensuremath{\mid}a\ensuremath{\mid}∕\ensuremath{\hbar}⪡1$. We show that three-body scattering resonances appearing at a large mass ratio due to the presence of three-body bound Efimov states do not influence the result, which in this sense becomes universal.
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
6Li. 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. \n 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. \n 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)/vF = 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.