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arXiv:cond-mat/0609290

Renormalized atomic interaction and quadrupole excitations of cold Fermi gas near Feshbach resonance

L.-W. Siu, T.T.S. Kuo, Boris A. Gelman

Published Sep 12, 2006• 0 citations
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Abstract

We present a model space particle-hole Green's function calculation for the quadrupole excitations of cold Fermi gas near Feshbach resonance using a simple model where atoms are confined in a harmonic oscillator potential. Both the Tamm-Dancoff and random phase approximations are employed. By summing up exactly the ladder diagrams between a pair of interacting atoms to all orders, we obtain a renormalized atomic interaction which has well defined and identical limits as the scattering length tends to $\pm \infty$. The experimentally observed abrupt rise in the excitation spectrum and its associated large decay width are satisfactorily reproduced by our calculation.

DOI
10.48550/arxiv.cond-mat/0609290

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We present a model space particle-hole Green's function calculation for the quadrupole excitations of cold Fermi gas near Feshbach resonance using a simple model where atoms are confined in a harmonic oscillator potential. Both the Tamm-Dancoff and random phase approximations are employed. By summing up exactly the ladder diagrams between a pair of interacting atoms to all orders, we obtain a renormalized atomic interaction which has well defined and identical limits as the scattering length tends to ±∞\pm \infty±∞. The experimentally observed abrupt rise in the excitation spectrum and its associated large decay width are satisfactorily reproduced by our calculation.
In this undergraduate thesis, we discuss the two-body quantum mechanical problem of two ultra- cold bosonic atoms at low energy limit, interacting through a square potential with and without an external confinement. The two-body s-wave scattering length is introduced in terms of the radial wavefunction. In free space with no confinement, the interaction-scattering length relation is calculated and compared in 3- and 1-dimensions; we show the recurring resonance regions where the scattering length diverges and the existence of dimer bound state with positively large scattering length. Lastly, in the case of a 3-dimensional isotropic harmonic confinement, again under the ultracold limit, we obtain the universal (s-state) energy spectrum of the two atoms in terms of the scattering length.
A sum rule approach is used to calculate the zero temperature oscillation frequencies of a two component trapped atomic Fermi gas in the Bardeen, Cooper, and Schrieffer--Bose Einstein condensation crossover region. These sum rules are evaluated using a local density approximation which explicitly includes Feshbach molecules. Breathing modes show nonmonotonic behavior as a function of the interaction strength, while quadrupole modes are insensitive to interactions for both spherically symmetric and axially symmetric traps. Quantitative agreement is found with experiments on atomic 6Li^{6}\mathrm{Li}6Li systems and with other theoretical approaches.
We present a calculation of the spectral functions and the associated rf response of ultracold fermionic atoms near a Feshbach resonance. The single-particle spectra are peaked at energies that can be modeled by a modified BCS dispersion. However, even at very low temperatures their width is comparable to their energy except for a small region around the dispersion minimum. The structure of the excitation spectrum of the unitary gas at infinite scattering length agrees with recent momentum-resolved rf spectra near the critical temperature. A detailed comparison is made with momentum integrated, locally resolved rf spectra of the unitary gas at arbitrary temperatures and shows very good agreement between theory and experiment. The pair size defined from the width of these spectra is found to coincide with that obtained from the leading gradient corrections to the effective-field theory of the superfluid.
A Feshbach resonance in the s-wave scattering length occurs if the energy of the two atoms in the incoming open channel is close to the energy of a bound state in a coupled closed channel. Starting from the microscopic Hamiltonian that describes this situation, we derive the effective atom–molecule theory for a Bose gas near a Feshbach resonance. In order to take into account all two-body processes, we have to dress the bare couplings of the atom–molecule model with ladder diagrams. This results in a quantum field theory that exactly reproduces the scattering amplitude of the atoms and the bound-state energy of the molecules. Since these properties are incorporated at the quantum level, the theory can be applied both above and below the critical temperature of the gas. Moreover, making use of the true interatomic potentials ensures that no divergences are encountered at any stage of the calculation. We also present the mean-field theory for the Bose–Einstein condensed phase of the gas.
The frequencies of the collective oscillations of a harmonically trapped Fermi gas interacting with large scattering lengths are calculated at zero temperature using hydrodynamic theory. Different regimes are considered, including the molecular Bose-Einstein condensate and the unitarity limit for collisions. We show that the frequency of the radial compressional mode in an elongated trap exhibits a pronounced non-monotonous dependence on the scattering length, reflecting the role of the interactions in the equation of state.