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Crossing the Boundaries: Gauge Dynamics at Strong Coupling

Exotic Superfluidity in Cold Atoms

Elena Gubankova

Published Jan 1, 2010• 0 citations
Publisher
DOI
10.1142/9789814304030_0039

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We investigate the mapping between magnetic susceptibility and entanglement in the metallic, insulating, conventional, and exotic polarized superfluid phases of one-dimensional fermionic lattice systems as described by the Hubbard model. Motivated by recent proposals for determining and quantifying entanglement via magnetic susceptibility measurements, we numerically study the intrinsic relationship between the two quantities at zero temperature. We find signatures of the metal-insulator transition and of the BCS-BEC crossover, but the most relevant result is that for conventional and exotic superfluids the mapping between magnetic susceptibility and entanglement is surprisingly simple: Directly proportional. This linear behavior is found to be universal for conventional superfluids and therefore could be exploited to quantify entanglement in current cold-atom and condensed-matter experiments.

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Abstract From flow without dissipation of energy to the formation of vortices when placed within a rotating container, the superfluid state of matter has proven to be a very interesting physical phenomenon. Here we present the key mechanisms behind superfluidity in fermionic systems and apply our understanding to one of the most exotic systems in the universe: the superfluid interior of a neutron star. The extreme conditions of neutron stars prevent us from directly probing the internal superfluid properties, however, we can experimentally realize conditions resembling the interior through the use of cold atoms prepared in a laboratory and simulated on a computer. Key insights can be gained by simulating the neutron star superfluid using another system with analogous properties: a cold atomic Fermi gas. Computational physicists are leveraging the power of supercomputers to simulate interacting atomic systems with unprecedented accuracy. In this paper we provide a pedagogical introduction to the physics, guiding the reader through the major conceptual steps to understand the relation between cold atoms, superfluids, and neutron stars. We stress the surprising similarity between these systems, which stems from universality, a fundamental notion in many-body physics. These topics are available in advanced textbooks, but introductory materials are harder to come by; this paper is intended to fill the gap for curious undergraduate and graduate students. We will show how cold atoms can help us make significant strides towards understanding the exotic physics found deep within the universe.
We investigate the mapping between magnetic susceptibility and entanglement in the metallic, insulating, conventional, and exotic polarized superfluid phases of one-dimensional fermionic lattice systems as described by the Hubbard model. Motivated by recent proposals for determining and quantifying entanglement via magnetic susceptibility measurements, we numerically study the intrinsic relationship between the two quantities at zero temperature. We find signatures of the metal-insulator transition and of the BCS-BEC crossover, but the most relevant result is that for conventional and exotic superfluids the mapping between magnetic susceptibility and entanglement is surprisingly simple: Directly proportional. This linear behavior is found to be universal for conventional superfluids and therefore could be exploited to quantify entanglement in current cold-atom and condensed-matter experiments.