Hydrodynamic modes in a trapped strongly interacting Fermi gas of atoms

Abstract

The zero-temperature properties of a dilute two-component Fermi gas in the BCS-BEC crossover are investigated. On the basis of a generalization of the variational Schwinger method, we construct approximate semi-analytical formulae for collective frequencies of the radial and the axial breathing modes of the Fermi gas under harmonic confinement in the framework of the hydrodynamic theory. It is shown that the method gives nearly exact solutions.

Quantized Superfluid Vortex Rings in the Unitary Fermi Gas

“…The qmc results of [52] suggest a value of α ≈ 1.14 [29] obtained by calculating the ground state energy difference |E(N ± 1, k) − E(N, 0)|, where N is even and hk is the momentum of the system with N ± 1 particles. In that calculation the Bertsch parameter was determined to be ξ = 0.42 (2), thus with an error of about 10% when compared to more recent qmc results [53] and experimental measurements ξ = 0.372 [44,54]. One can therefore infer that the error in the quasi-particle dispersion is much larger as it is a difference in energies.…”

“…which depends on the magnetic field B through the twobody scattering length a as described in [43,44] through the dimensionless interaction parameter x = 1/k F a. Dimensions are set in terms of the parameters of the free Fermi gas n = k 3 F /3π 2 , and ε F = h 2 k 2 F /2m. This reproduces the unitary equation of state with ξ = 0.370 and ζ = 0.901 (the contact), and the factor 3.0 = 9a/5a DD reproduces the dimer-dimer scattering length a DD ≈ 0.6a.…”

“…The etf approach that has been used to analyze the expansion [28] and [28,44] breathing mode frequencies of cold atomic gases in a trap, their surface oscillations [45], collisions of clouds of fermions [46], vortex generation [47], vortex pinning [48], and soliton dynamics [49]. The etf is equivalent to the quantum hydrodynamics approach at zero temperature, which has been used extensively by many authors for modelling the unitary Fermi gas during the last decade, but etf also includes the quantum pressure term typically neglected in a hydrodynamic approach.…”

BCS-BEC crossover of ultracold ions driven by density-dependent short-range interactions in a quantum plasma

“…Previous hydrodynamic theories of the BCS-BEC crossover mainly focused on neutral gas in an atomic system [30,32,62,71]. Our theoretical results for ion pairs in ultracold plasmas could be equivalently important as atom pairs for a BCS-BEC crossover.…”

“…The quantum hydrodynamic model is valid [5,37,64,66,68,70] for ω ep ≤ E F e , and the electron-ion collision relaxation time is greater than the electron plasma period, where ω ep is the electron plasma frequency, given as ω sp = 4πe 2 n 0 /m s . The applicability and validity of the quantum hydrodynamic model have been widely tested not only in quantum plasmas [5,34,37,[64][65][66][67][68]70], but also in the field of cold atomic systems [30,32,62,71].…”