Detecting Fractional Chern Insulators in Optical Lattices through Quantized Displacement

Abstract

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 $\nu =1/2$ 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 ${\sigma }_{xy}$ 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 ${\sigma }_{xy}$ for an extended range of field strengths.

arXiv comment5 pages, 6 figures, plus supplementary material

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• Many-body Chern number from statistical correlations of randomized measurements
• Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles
• Measuring Arbitrary Physical Properties in Analog Quantum Simulation
• Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model
• Recent Developments in Fractional Chern Insulators
• Bosonic Pfaffian State in the Hofstadter-Bose-Hubbard Model
• Impedance responses and size-dependent resonances in topolectrical circuits via the method of images
• Measurable signatures of bosonic fractional Chern insulator states and their fractional excitations in a quantum-gas microscope
• Characterizing fractional topological phases of lattice bosons near the first Mott lobe
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• Uncover band topology via quantized drift in two-dimensional Bloch oscillations
• Optimal control for preparing fractional quantum Hall states in optical lattices
• Chiral Edge Excitations of $\nu =1/2$ Fractional Chern Insulators in the Bosonic Hofstadter Model