Slow relaxation and sensitivity to disorder in trapped lattice fermions after a quench
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We consider a system of non-interacting fermions in one dimension subject to a single-particle potential consisting of (a) a strong optical lattice, (b) a harmonic trap, and (c) uncorrelated on-sited is order. After a quench, in which the center of the harmonic trap is displaced, we study the occupation function of the fermions and the time-evolution of experimental observables. Specifically, we present numerical and analytical results for the post-quench occupation function of the fermions,and analyse the time-evolution of the real-space density profile. Unsurprisingly for a non-interacting(and therefore integrable) system, the infinite-time limit of the density profile is non-thermal. However,due to Bragg-localization of the higher-energy single-particle states, the approach to even this non-thermal state is extremely slow. We quantify this statement, and show that it implies a sensitivity to disorder parametrically stronger than that expected from Anderson localization.
Schulz , M , Hooley , C A & Moessner , R 2016 , ' Slow relaxation and sensitivity to disorder in trapped lattice fermions after a quench ' Physical Review. A, Atomic, molecular, and optical physics , vol 94 , no. 6 , 063643 . DOI: 10.1103/PhysRevA.94.063643
Physical Review. A, Atomic, molecular, and optical physics
© 2016 American Physical Society. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at journals.aps.org/pra / https://doi.org/10.1103/PhysRevA.94.063643
M.S. acknowledges support from Engineering and Physical Sciences Research Council (EPSRC) (United Kingdom) via the CM-CDT program, Grant No. EP/L015110/1. C.A.H.’s work on this paper was performed in part at the Aspen Center for Physics, which is supported by NSF Grant No. PHY-1066293. He is grateful to them for their hospitality. He is also thankful for ongoing support from the EPSRC (United Kingdom) via the TOPNES program, Grant No. EP/I031014/1.
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