Motruk Johannes, Na Ilyoun
Department of Physics, University of California, Berkeley, California 94720, USA.
Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
Phys Rev Lett. 2020 Dec 4;125(23):236401. doi: 10.1103/PhysRevLett.125.236401.
The realization of interacting topological states of matter such as fractional Chern insulators (FCIs) in cold atom systems has recently come within experimental reach due to the engineering of optical lattices with synthetic gauge fields providing the required topological band structures. However, detecting their occurrence might prove difficult since transport measurements akin to those in solid state systems are challenging to perform in cold atom setups and alternatives have to be found. We show that for a ν=1/2 FCI state realized in the lowest band of a Harper-Hofstadter model of interacting bosons confined by a harmonic trapping potential, the fractionally quantized Hall conductivity σ_{xy} can be accurately determined by the displacement of the atomic cloud under the action of a constant force which provides a suitable experimentally measurable signal for detecting the topological nature of the state. Using matrix-product state algorithms, we show that, in both cylinder and square geometries, the movement of the particle cloud in time under the application of a constant force field on top of the confining potential is proportional to σ_{xy} for an extended range of field strengths.
由于具有合成规范场的光学晶格工程提供了所需的拓扑能带结构，冷原子系统中诸如分数陈绝缘体（FCI）等相互作用拓扑物质态的实现最近已进入实验可及范围。然而，检测它们的出现可能很困难，因为类似于固态系统中的输运测量在冷原子装置中难以进行，必须找到替代方法。我们表明，对于在由谐波捕获势限制的相互作用玻色子的哈珀 - 霍夫施塔特模型的最低能带中实现的ν = 1/2 FCI态，分数量子化霍尔电导率σ_{xy}可以通过在恒定力作用下原子云的位移精确确定，该恒定力为检测该态的拓扑性质提供了合适的实验可测量信号。使用矩阵乘积态算法，我们表明，在圆柱和方形几何结构中，在限制势之上施加恒定力场时，粒子云随时间推移的移动对于广泛的场强范围与σ_{xy}成正比。
