Coherence and decoherence in the Harper-Hofstadter model

• URL: http://arxiv.org/abs/2012.02202v2
• Date: Wed, 24 Mar 2021 19:35:38 GMT
• Title: Coherence and decoherence in the Harper-Hofstadter model
• Authors: Qi-Yu Liang, Dimitris Trypogeorgos, Ana Vald\'es-Curiel, Junheng Tao, Mingshu Zhao, and Ian B. Spielman
• Abstract summary: We quantum-simulated the 2D Harper-Hofstadter lattice model in a highly elongated tube geometry using an atomic Bose-Einstein condensate. We show that noise in $Phi_rm L$ would readily decohere the interference present in trajectories encircling the tube. We quantitatively explain our observations by transforming the HH model into a collection of momentum-space Aubry-Andr'e models.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We quantum-simulated the 2D Harper-Hofstadter (HH) lattice model in a highly elongated tube geometry -- three sites in circumference -- using an atomic Bose-Einstein condensate. In addition to the usual transverse (out-of-plane) magnetic flux, piercing the surface of the tube, we threaded a longitudinal flux $\Phi_{\rm L}$ down the axis of the tube This geometry evokes an Aharonov-Bohm interferometer, where noise in $\Phi_{\rm L}$ would readily decohere the interference present in trajectories encircling the tube. We observe this behavior only when transverse flux is a rational fraction of the flux-quantum, and remarkably find that for irrational fractions the decoherence is absent. Furthermore, at rational values of transverse flux, we show that the time evolution averaged over the noisy longitudinal flux matches the time evolution at nearby irrational fluxes. Thus, the appealing intuitive picture of an Aharonov-Bohm interferometer is insufficient. Instead, we quantitatively explain our observations by transforming the HH model into a collection of momentum-space Aubry-Andr\'{e} models.

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