Coherence and decoherence in the Harper-Hofstadter model

Q.-Y Liang,I B Spielman,A Valdés-Curiel,J Tao,D Trypogeorgos,M Zhao

doi:10.1103/physrevresearch.3.023058

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.

Highlights

Understanding how and when closed quantum systems lose or retain coherence is a central intellectual and practical question for quantum technologies
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
In rare cases, such as collisional narrowing [2] or environment assisted tunneling [3], random processes can enhance coherence. We add to this list the quasiperiodic lattice described by the Harper-Hofstadter (HH) model [4,5] in a highly-elongated tube geometry—a 1D quasicrystal—by showing that the dynamics can be made immune to environmental noise

Summary

Discussion

The measured time dependence of the normalized variance, shown, is peaked at = 0 for all times but with variable amplitude In both cases, the numerical calculations [Fig. 4(c), and solid curve in Fig. 4(a)] are nearly indistinguishable from the data. The solid line results from the numerical simulation of the full model with RTF = 11.5 μm, with baseline shifted by the averaged value of the experimental data away from the peak.

Raman setup

Magnetic field and rf locks

Mean time evolution

Variance of the time evolution