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arXiv:0807.0018 · Physical Review A

Spin collective modes of two-species Fermi liquids: He3 and atomic gases near the Feshbach resonance

Hari P. Dahal, S. Gaudio, J. D. Feldmann, Kevin S. Bedell

Published Sep 3, 2008• 3 citations
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Abstract

We present theoretical findings on the spin collective modes of a two-species Fermi liquid, prepared alternatively in a polarized equilibrium or a polarized nonequilibrium state. We explore the effects on these modes of a diverging $s$-wave scattering length, as occurs near a Feshbach resonance in a fermionic atomic gas. We compare these atomic gas modes with those of the conventional $^{3}\mathrm{He}$ system, and we find that they differ from the conventional systems, and that the gap and spin stiffness are tunable via the Feshbach resonance.

DOI
10.1103/physreva.78.035601

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We present theoretical findings on the spin collective modes of a two-species Fermi liquid, prepared alternatively in a polarized equilibrium or a polarized nonequilibrium state. We explore the effects on these modes of a diverging sss-wave scattering length, as occurs near a Feshbach resonance in a fermionic atomic gas. We compare these atomic gas modes with those of the conventional 3He^{3}\mathrm{He}3He system, and we find that they differ from the conventional systems, and that the gap and spin stiffness are tunable via the Feshbach resonance.
The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions that play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems, interactions are characterized by a single parameter, the sss-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.
The authors prepare a quasi-two-dimensional spin-polarized Fermi gas with orbital excitations and p-wave interactions enabled by a Feshbach resonance. Radio-frequency spectroscopy indicates sss-wave scattering symmetry in the plane, demonstrating how gapped orbital degrees of freedom can be used to control scattering symmetry in strongly confined ultracold gases.
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At the location of a magnetic-field Feshbach resonance, a mixture gas of fermionic atoms and dimers of fermionic atom pairs is investigated in the unitarity limit where the absolute value of the scattering length is much larger than the mean distance between atoms. The dynamic equilibrium of the mixture gases is characterized by the minimum of the Gibbs free energy. For the fermionic atoms and dimers with divergent scattering length, it is found that the fraction of the dimers based on a very simple theory agrees with the high fraction of zero-momentum molecules observed in a recent experiment (M. W. Zwierlein et al, Phys. Rev. Lett. 92, 120403 (2004)). The dimeric gas can be also used to interpret the frequency of the radial breathing mode observed in the experiment by J. Kinast et al (Phys. Rev. Lett. 92, 150402 (2004)).
Measuring the tunability of effective two-body interactions near Feshbach resonances is a powerful, experimental tool in systems of ultracold atoms. It has been used to explore a variety of intriguing phenomena in recent experiments. This chapter applies the method of collective mode instabilities to the concrete example of quenches of the non-interacting Fermi gas to the strongly interacting regime. Section 9.3 begins by discussing the relation between linear response and collective modes. It shows how to compute the pairing and the ferromagnetic responses using the equation of motion formalism. Section 9.4 demonstrates how to describe a Feshbach resonance using a pseudo-potential model. Section 9.5 applies the pseudo-potential model to compute the many-body T-matrix and thus obtain the pairing collective mode. Section 9.6 discusses how to incorporate the many-body T-matrix into the ferromagnetic susceptibility. Section 9.7 summarizes the results for the pairing versus Stoner competition in the context of the MIT experiments. Section 9.8 provides concluding remarks.
Due to Pauli blocking of intermediate states, the scattering matrix (or TTT matrix) of two fermionic atoms in a Fermi gas becomes different from that of two atoms in free space. This effect becomes particularly important near a Feshbach resonance, where the interaction in free space is very strong but becomes effectively suppressed in the medium. We calculate the in-medium TTT matrix in ladder approximation and study its effects on the properties of collective modes of a trapped gas in the normal-fluid phase. We introduce the in-medium interaction on both sides of the Boltzmann equation, namely, in the calculation of the mean field and in the calculation of the collision rate. This allows us to explain the observed upward shift of the frequency of the quadrupole mode in the collisionless regime. By including the mean field, we also improve considerably the agreement with the measured temperature dependence of frequency and damping rate of the scissors mode, whereas the use of the in-medium cross section deteriorates the description, in agreement with previous work.