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arXiv:1005.2366 · Physical Review Letters

Competition between Pairing and Ferromagnetic Instabilities in Ultracold Fermi Gases near Feshbach Resonances

David Pekker, Mehrtash Babadi, Rajdeep Sensarma, Nikolaj Thomas Zinner, Lode Pollet, Martin W. Zwierlein, Eugene Demler

Published Feb 1, 2011• 141 citations
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Abstract

We study the quench dynamics of a two-component ultracold Fermi gas from the weak into the strong interaction regime, where the short time dynamics are governed by the exponential growth rate of unstable collective modes. We obtain an effective interaction that takes into account both Pauli blocking and the energy dependence of the scattering amplitude near a Feshbach resonance. Using this interaction we analyze the competing instabilities towards Stoner ferromagnetism and pairing.

DOI
10.1103/physrevlett.106.050402

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We study the quench dynamics of a two-component ultracold Fermi gas from the weak into the strong interaction regime, where the short time dynamics are governed by the exponential growth rate of unstable collective modes. We obtain an effective interaction that takes into account both Pauli blocking and the energy dependence of the scattering amplitude near a Feshbach resonance. Using this interaction we analyze the competing instabilities towards Stoner ferromagnetism and pairing.
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.
We describe the dynamics of two component non-interacting ultracold Fermions which are initially in thermal equilibrium and undergo a rapid quench to either the repulsive or attractive side of a Feshbach resonance. The short time dynamics is dominated by the exponentially growing collective modes. We study the Stoner instability and formation of ferromagnetic textures on the repulsive side, and the pairing instability towards BCS or FFLO-like states (determined by the population imbalance) on the attractive side. In each case, we evaluate the growth rate of unstable modes and predict the typical lengthscale of textures to be formed.
We study nonequilibrium dynamics of ultracold two-component Fermi gases in low-dimensional geometries after the interactions are quenched from a weakly interacting to a strongly interacting regime. We develop a TTT-matrix formalism that takes into account the interplay between Pauli blocking and tight confinement in low-dimensional geometries. We employ our formalism to study the formation of molecules in quasi-two-dimensional Fermi gases near Feshbach resonance and show that the rate at which molecules form depends strongly on the transverse confinement. Furthermore, Pauli blocking gives rise to a sizable correction to the binding energy of molecules.
We study the influence of population imbalance on the pairing, spin, and density instabilities of a two-component ideal Fermi gas after a sudden quench of interactions near a Feshbach resonance. Over a large region of parameters the pairing instability is dominated by finite-momentum pairing, suggesting the possibility of observing Fulde-Ferrell-Larkin-Ovchinnikov--like states in the unstable initial dynamics. Long-wavelength density instabilities are found on the Bardeen-Cooper-Schrieffer side of the resonance, and are interpreted as a precursor of the phase separation expected at equilibrium. On the Bose-Einstein-condensate side of the resonance, the pairing instability is present for scattering lengths larger than a critical value that is only weakly dependent on population imbalance and always smaller than the scattering length at which the Stoner-like spin instability occurs.
Recent advances in rapidly quenched ultracold atomic Fermi gases near a Feshbach resonance have brought about a number of interesting problems in the context of observing the long-sought Stoner ferromagnetic phase transition. The possibility of experimentally obtaining a ``quasirepulsive'' regime in the upper branch of the energy spectrum due to the rapid quench is currently being debated, and the Stoner transition has mainly been investigated theoretically by using perturbation theory or at high polarization due to the limited theoretical approaches in the strongly repulsive regime. In this work, we present a nonperturbative theoretical approach to the quasirepulsive upper branch of a Fermi gas near a broad Feshbach resonance, and we determine the finite-temperature phase diagram for the Stoner instability. Our results agree well with the known quantum Monte Carlo simulations at zero temperature, and we recover the known virial expansion prediction at high temperature for arbitrary interaction strengths. At resonance, we find that the Stoner transition temperature becomes of the order of the Fermi temperature, around which the molecule formation rate becomes vanishingly small. This suggests a feasible way to observe Stoner ferromagnetism in the nondegenerate temperature regime.
We exploit a time-resolved pump-probe spectroscopic technique to study the out-of-equilibrium dynamics of an ultracold two-component Fermi gas, selectively quenched to strong repulsion along the upper branch of a broad Feshbach resonance. For critical interactions, we find the rapid growth of short-range anticorrelations between repulsive fermions to initially overcome concurrent pairing processes. At longer evolution times, these two competing mechanisms appear to macroscopically coexist in a short-range correlated state of fermions and pairs, unforeseen thus far. Our work provides fundamental insights into the fate of a repulsive Fermi gas, and offers new perspectives towards the exploration of complex dynamical regimes of fermionic matter.