Due to the scale invariance, the thermodynamic laws of strongly interacting limit unitary Fermi gas can be similar to those of non-interacting ideal gas. For example, the virial theorem between pressure and energy density of the ideal gas P = 2 E /3 V is still satisfied by the unitary Fermi gas. This paper analyses the sound velocity of unitary Fermi gases with the quasi-linear approximation. For comparison, the sound velocities for the ideal Boltzmann, Bose and Fermi gas are also given. Quite interestingly, the sound velocity formula for the ideal non-interacting gas is found to be satisfied by the unitary Fermi gas in different temperature regions.Due to the scale invariance, the thermodynamic laws of strongly interacting limit unitary Fermi gas can be similar to those of non-interacting ideal gas. For example, the virial theorem between pressure and energy density of the ideal gas P = 2 E /3 V is still satisfied by the unitary Fermi gas. This paper analyses the sound velocity of unitary Fermi gases with the quasi-linear approximation. For comparison, the sound velocities for the ideal Boltzmann, Bose and Fermi gas are also given. Quite interestingly, the sound velocity formula for the ideal non-interacting gas is found to be satisfied by the unitary Fermi gas in different temperature regions.

Chinese Physics BFeb 1, 20115 citations

Trapping effect on the sound velocity of a multilayer Fermi gas

P. Salas, Miguel A. Sol 'is

Bulletin of the American Physical SocietyMar 5, 20150 citations

Precision Measurement of the Sound Velocity in an Ultracold Fermi Gas Through the BEC-BCS Crossover

James A. Joseph

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. \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, $c(0)/v_F$ = 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.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. \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, $c(0)/v_F$ = 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.

Jan 1, 20102 citations

^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. \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)/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.