Detecting Fractional Chern Insulators in Optical Lattices through Quantized Displacement

Area of Science:

• Quantum Matter
• Cold Atom Physics
• Topological Phases of Matter

Background:

• Engineering optical lattices with synthetic gauge fields enables the creation of topological band structures in cold atom systems.
• Realizing interacting topological states, such as fractional Chern insulators (FCIs), is now experimentally feasible.
• Traditional transport measurements for detecting topological states are difficult in cold atom experiments.

Purpose of the Study:

• To propose a novel, experimentally accessible method for detecting fractional Chern insulators (FCIs) in cold atom systems.
• To demonstrate that the fractionally quantized Hall conductivity (σxy) of a ν=1/2 FCI state can be measured via atomic cloud displacement.
• To establish a link between the dynamics of an atomic cloud under an external force and the topological properties of the system.

Main Methods:

• Utilizing matrix-product state (MPS) algorithms to simulate the behavior of interacting bosons in a Harper-Hofstadter model.
• Confining interacting bosons with a harmonic trapping potential within optical lattices.
• Applying a constant force field to the atomic cloud and analyzing its displacement over time.

Main Results:

• The displacement of the atomic cloud under a constant force is directly proportional to the fractionally quantized Hall conductivity (σxy) for a ν=1/2 FCI state.
• This proportionality holds true over an extended range of applied force strengths.
• The method is validated in both cylinder and square lattice geometries.

Conclusions:

• Atomic cloud displacement under a constant force provides a viable and experimentally measurable signal for detecting topological states like FCIs in cold atoms.
• This approach overcomes the limitations of traditional transport measurements in cold atom systems.
• The findings pave the way for experimental verification of fractional Chern insulators in engineered quantum matter.