Quantum Optics Measurement Scheme for Quantum Geometry and Topological Invariants

Area of Science:

• Condensed Matter Physics
• Quantum Optics
• Topological Materials

Background:

• Exploring topological properties of materials is crucial for understanding their electronic behavior.
• Quantum optical measurement schemes offer novel ways to probe material characteristics.

Purpose of the Study:

• To demonstrate a quantum optical measurement scheme for exploring geometrical and topological properties of condensed matter systems.
• To relate photon correlation functions to the hybrid light-matter state and extract material properties.

Main Methods:

• Utilizing a quantum optical measurement scheme based on heterodyne detection.
• Placing a 2D material in a cavity with environmental coupling and computing photon correlation functions.
• Relating measured quantum metric to topological phase and extracting spin Chern number.

Main Results:

• Developed a method to compute correlation functions of photons exiting a cavity containing a 2D material.
• Showed that different photon polarizations provide access to the quantum geometric tensor components.
• Enabled characterization of topological phase and extraction of spin Chern number in relevant systems.

Conclusions:

• The proposed quantum optical measurement scheme effectively probes geometrical and topological properties of condensed matter.
• This technique offers a pathway to experimentally determine topological invariants like the spin Chern number and Euler number.
• Applicable to systems such as twisted bilayer graphene at the magic angle.