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Register a new userLife Cycle of Superfluid Vortices and Quantum Turbulence in the Unitary Fermi Gas
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Michael McNeil Forbes
Publication date
2014
fields
Physics
and research's language is
English
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The unitary Fermi gas (UFG) offers an unique opportunity to study quantum turbulence both experimentally and theoretically in a strongly interacting fermionic superfluid. It yields to accurate and controlled experiments, and admits the only dynamical microscopic description via time-dependent density functional theory (DFT) - apart from dilute bosonic gases - of the crossing and reconnection of superfluid vortex lines conjectured by Feynman in 1955 to be at the origin of quantum turbulence in superfluids at zero temperature. We demonstrate how various vortex configurations can be generated by using well established experimental techniques: laser stirring and phase imprinting. New imagining techniques demonstrated by the MIT group [Ku et al. arXiv:1402.7052] should be able to directly visualize these crossings and reconnections in greater detail than performed so far in liquid helium. We demonstrate the critical role played by the geometry of the trap in the formation and dynamics of a vortex in the UFG and how laser stirring and phase imprint can be used to create vortex tangles with clear signatures of the onset of quantum turbulence.
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Quantized vortices carry the angular momentum in rotating superfluids, and are key to the phenomenon of quantum turbulence. Advances in ultra-cold atom technology enable quantum turbulence to be studied in regimes with both experimental and theoretical control, unlike the original contexts of superfluid helium experiments. While much work has been performed with bosonic systems, detailed studies of fermionic quantum turbulence are nascent, despite wide applicability to other contexts such as rotating neutron stars. In this paper, we present the first large-scale study of quantum turbulence in rotating fermionic superfluids using an accurate orbital based time-dependent density functional theory (DFT) called the superfluid local density approximation (SLDA). We identify two different modes of turbulent decay in the dynamical equilibration of a rotating fermionic superfluid, and contrast these results with a computationally simpler orbital-free DFT, which we find can qualitatively reproduce these decay mechanisms if dissipation is explicitly included. These results demonstrate that one-body dissipation mechanisms intrinsic to fermionic superfluids play a key role differentiating fermionic from bosonic turbulence, but also suggest that simpler orbital-free theories may be corrected so that these more efficient techniques can be used to model extended physical systems such as neutron superfluids in neutron stars.
In a recent article, Yefsah et al. [Nature 499, 426 (2013)] report the observation of an unusual excitation in an elongated harmonically trapped unitary Fermi gas. After phase imprinting a domain wall, they observe oscillations almost an order of magnitude slower than predicted by any theory of domain walls which they interpret as a heavy soliton of inertial mass some 200 times larger than the free fermion mass or 50 times larger than expected for a domain wall. We present compelling evidence that this soliton is instead a quantized vortex ring by showing that the main aspects of the experiment can be naturally explained within the framework of time-dependent superfluid DFT.
We present a comparison between simulated dynamics of the unitary fermion gas using the superfluid local density approximation (SLDA) and a simplified bosonic model, the extended Thomas Fermi (ETF) with a unitary equation of state. Small amplitude fluctuations have similar dynamics in both theories for frequencies far below the pair breaking threshold and wave vectors much smaller than the Fermi momentum, and the low frequency linear responses match well for surprisingly large wave vectors, even up to the Fermi momentum. For non-linear dynamics such as vortex generation, the ETF provides a semi-quantitative description of SLDA dynamics as long as the fluctuations do not have significant power near the pair breaking threshold, otherwise the dynamics of the ETF cannot be trusted. Nonlinearities in the ETF tends to generate high-frequency fluctuations, and with no normal component to remove this energy from the superfluid, features like vortex lattices cannot relax and crystallize as they do in the SLDA. We present a heuristic diagnostic for validating the reliability of ETF dynamics by considering the approximate conservation of square of the gap: $int|Delta|^2$.
We discuss the unitary Fermi gas made of dilute and ultracold atoms with an infinite s-wave inter-atomic scattering length. First we introduce an efficient Thomas-Fermi-von Weizsacker density functional which describes accurately various static properties of the unitary Fermi gas trapped by an external potential. Then, the sound velocity and the collective frequencies of oscillations in a harmonic trap are derived from extended superfluid hydrodynamic equations which are the Euler-Lagrange equations of a Thomas-Fermi-von Weizsacker action functional. Finally, we show that this amazing Fermi gas supports supersonic and subsonic shock waves.
We present results from Monte Carlo calculations investigating the properties of the homogeneous, spin-balanced unitary Fermi gas in three dimensions. The temperature is varied across the superfluid transition allowing us to determine the temperature dependence of the chemical potential, the energy per particle and the contact density. Numerical artifacts due to finite volume and discretization are systematically studied, estimated, and reduced.
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