Abstract
We introduce a scheme by which flat bands with higher Chern number \vert C\vert>1|C|>1 can be designed in ultracold gases through a coherent manipulation of Bloch bands. Inspired by quantum-optics methods, our approach consists in creating a ``dark Bloch band" by coupling a set of source bands through resonant processes. Considering a \LambdaΛ system of three bands, the Chern number of the dark band is found to follow a simple sum rule in terms of the Chern numbers of the source bands: C_D\!=\!C_1+C_2-C_3CD=C1+C2−C3. Altogether, our dark-state scheme realizes a nearly flat Bloch band with predictable and tunable Chern number C_DCD. We illustrate our method based on a \LambdaΛ system, formed of the bands of the Harper-Hofstadter model, which leads to a nearly flat Chern band with C_D\!=\!2CD=2. We explore a realistic sequence to load atoms into the dark Chern band, as well as a probing scheme based on Hall drift measurements. Dark Chern bands offer a practical platform where exotic fractional quantum Hall states could be realized in ultracold gases.
Highlights
We proposed a realistic scheme by which flat bands with a predictable higher Chern number can be constructed through a coherent manipulation of Bloch bands
While this work focused on the simplest Λ configuration, more bands could be involved in the construction in view of building N -pod settings [80,81]; this strategy suggests a promising route to reach even higher Chern numbers |CD| 2
The dark Chern bands deriving from our scheme offer a platform where exotic fractional quantum Hall states could be explored with cold atoms, including generalized Moore-Read and Read-Rezayi states [24, 26], topological nematic states [23] and “genon” defects [23, 29, 82]
Summary
Designing Bloch bands with topological properties has become a central theme in the context of quantum-engineered systems [1,2,3]. While flat bands with Chern number |C| = 1 are reminiscent of the conventional Landau levels in the continuum [22], flat bands with higher Chern number |C|>1 can lead to exotic strongly-correlated states that are specific to lattice systems [23,24,25,26,27,28,29] Such flatband models remain unsuitable for cold-atom experiments, as they rely on the design of complicated multi-layered lattices or complex long-range hopping processes [21, 24, 25, 30,31,32,33,34,35]. While our results directly apply to cold-atom settings, our findings are general and could be relevant to light-induced topological phases in the solid state [41,42]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
