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arXiv:1601.01004 · Physical Review Letters

Dynamics of Interacting Fermions in Spin-Dependent Potentials

Andrew Koller, Michael L. Wall, Joshua Mundinger, Ana María Rey

Published Nov 4, 2016• 27 citations
arXivHTMLPDF

Abstract

Recent experiments with dilute trapped Fermi gases observed that weak interactions can drastically modify spin transport dynamics and give rise to robust collective effects including global demagnetization, macroscopic spin waves, spin segregation, and spin self-rephasing. In this Letter, we develop a framework for studying the dynamics of weakly interacting fermionic gases following a spin-dependent change of the trapping potential which illuminates the interplay between spin, motion, Fermi statistics, and interactions. The key idea is the projection of the state of the system onto a set of lattice spin models defined on the single-particle mode space. Collective phenomena, including the global spreading of quantum correlations in real space, arise as a consequence of the long-ranged character of the spin model couplings. This approach achieves good agreement with prior measurements and suggests a number of directions for future experiments.

DOI
10.1103/physrevlett.117.195302

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Recent experiments with dilute trapped Fermi gases observed that weak interactions can drastically modify spin transport dynamics and give rise to robust collective effects including global demagnetization, macroscopic spin waves, spin segregation, and spin self-rephasing. In this Letter, we develop a framework for studying the dynamics of weakly interacting fermionic gases following a spin-dependent change of the trapping potential which illuminates the interplay between spin, motion, Fermi statistics, and interactions. The key idea is the projection of the state of the system onto a set of lattice spin models defined on the single-particle mode space. Collective phenomena, including the global spreading of quantum correlations in real space, arise as a consequence of the long-ranged character of the spin model couplings. This approach achieves good agreement with prior measurements and suggests a number of directions for future experiments.
The interplay between spin and motional degrees of freedom in interacting electron systems has been a long-standing research topic in condensed matter physics. Interactions can modify the behavior of individual electrons and give rise to emergent collective phenomena such as superconductivity and colossal magnetoresistance. Theoretical understanding of non-equilibrium dynamics in interacting fermionic matter is limited, however, and many open questions remain. Ultracold atomic Fermi gases, with precisely controllable parameters, offer an outstanding opportunity to investigate the emergence of collective behavior in out-of-equilibrium settings. In this thesis we will describe how an optical lattice clock operated with neutral Fermionic atoms can be turned into a quantum simulator of charged particles in a strong magnetic field. We will then discuss the counterintuitive notion that weak interactions in a Fermi gas can lead to large scale collective behavior and global correlations. These ideas are being tested experimentally at JILA and the University of Toronto. We also investigate in detail the so-called spin model approximation which is used extensively throughout this thesis.
This thesis summarizes experimental work investigating strongly interacting Fermi gases in two and three dimensions. Radio-frequency spin manipulation is used to initialize and probe strongly interacting Fermi gases dynamically to measure relaxation to a steady-state. Time-resolved spectroscopy is used to discover the p-wave contacts by observing how correlations in the system develop after quenching the atoms into an interacting state. By combining quasi-steady state measurements with new contact relations, an attractive p-wave interaction energy as large as half the Fermi energy is inferred. Spin echo measurements of the magnetization dynamics are used to observe spin transport in two and three dimensions in the presence of strong interactions. The bare spin diffusivity is distinguished from the Leggett-Rice effect, in which demagnetization is slowed by precession of a spin current around the local magnetization. Observations of the demagnetization dynamics support the conjecture that a general quantum bound on spin transport is obeyed where the diffusivity D greater than or similar to ħ/m, where m is the particle mass.
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We study spin-1/2 fermions in spin-dependent potentials under the spin-model approximation, in which interatomic collisions that change the total occupation of single-particle modes are ignored. The spin-model approximation maps the interacting fermion problem to an ensemble of lattice spin models in energy space, where spin-spin interactions are long range and spin anisotropic. We consider a Ramsey-type sequence in which quantum degenerate, initially spin-polarized fermions are rotated to a spin superposition, and the differences in potential for the two spin states induce sss-wave interactions. Applied to such a setup, we show that the spin-model approximation qualitatively captures the collective spin dynamics for weak interactions compared to the harmonic-oscillator frequency, and often captures quantitative features at timescales much longer than would be expected from perturbation theory. We explore corrections to the spin model, and the relative importance of corrections for both collective spin and fidelity metrics when realistic anharmonic potential corrections are taken into account, demonstrating that anharmonicity can significantly improve the fidelity of the spin-model approximation. Additionally, we present numerical techniques that are useful for analysis of spin models on an energy lattice, including enacting a change of single-particle basis on a many-body state as an effective time evolution, and fitting of spatially inhomogeneous long-range interactions with exponentials. This latter technique is useful for constructing matrix product operators for use in density-matrix renormalization group analyses, and may have broader applicability within the tensor network community.