Optimizing superconductor transport properties through large-scale simulation

# Shaken Bosonic condensates

Optical control and manipulation of cold atoms has become an important topic in condensed matter. Widely employed are optical lattice shaking experiments which allow the introduction of artificial gauge fields, the design of topological bandstructures, and more general probing of quantum critical phenomena. Here we develop new numerical methods to simulate these periodically driven systems by implementing lattice shaking directly. As a result we avoid the usual assumptions associated with a simplified picture based on Floquet dynamics. A demonstrable success of our approach is that it yields quantitative agreement with experiment, including Kibble-Zurek scaling. Importantly, we argue that because their dynamics corresponds to an effective non-linear Schrödinger equation, these particular superfluid studies present a unique opportunity to address how general Floquet band engineering is affected by interactions. In particular, interactions cause instabilities at which the behavior of the system changes dramatically.

Animation of a superfluid in shaken optical lattice. Shaking an optical lattice (purple) along the x-axis with a sufficient peak-to- peak amplitude causes an ordinary Bose superfluid to undergo a phase transition to a finite-momentum superfluid. In this exotic phase the superfluid splits into domains with positive (red) or negative (cyan) momentum.

The movie shows the evolution of domains in a Bose condensate under near-resonant shaking. The frequency is fixed, and the shaking amplitude is linearly ramped as $s\left(t\right)={v}_{3}t$ (as defined in the text.). The interaction strength ratio is $g/{g}_{\mathrm{expt}}=1.0$. The thick red line references ${s}_{c}$, on a timescale of $s/{s}_{c}=0$ to $s/{s}_{c}\sim 4.5$.

The movie shows the evolution of domains in a Bose condensate under near-resonant shaking. The frequency is fixed, the shaking amplitude increases as the movie progresses. The interaction strength ratio is $g/{g}_{\mathrm{expt}}=0.1$. The four lines reference the four lines ${s}_{1}$, ${s}_{2}$ , ${s}_{3}$ , ${s}_{4}$ in the manuscript below. Here the timescale is from $s/{s}_{c}=0$ to $s/{s}_{c}\sim 12$.

The movie shows the evolution of domains in a Bose condensate under near-resonant shaking. The frequency is fixed, the shaking amplitude increases as the movie progresses. The interaction strength ratio is $g/{g}_{\mathrm{expt}}=1.0$. The timescale is from $s/{s}_{c}=0$ to $s/{s}_{c}\sim 12$ . The ramp rate for this and above is $\stackrel{˙}{s}={v}_{0}$.

Brandon M. Anderson, Logan W. Clark, Jennifer Crawford, Andreas Glatz, Igor S. Aronson, Peter Scherpelz, Lei Feng, Cheng Chin, K. Levin,
Floquet-Band Engineering of Shaken Bosonic Condensates,
arxiv:1612.06908 (2017).