Topological framework for directional amplification in driven-dissipative cavity arrays

Area of Science:

• Quantum optics
• Condensed matter physics
• Topological photonics

Background:

• Directional amplification selectively amplifies signals based on propagation direction, crucial for quantum information processing.
• Various physical implementations of directional amplifiers exist, but a unifying theoretical framework is lacking.

Purpose of the Study:

• To present a unifying topological framework for understanding non-reciprocity and directional amplification in driven-dissipative cavity arrays.
• To establish a direct correspondence between topological invariants and directional amplification regimes.

Main Methods:

• Development of a unifying framework based on topology.
• Analytical computation of the scattering matrix, gain, and reverse gain.
• Definition and computation of a topological invariant on the dynamic matrix spectrum.

Main Results:

• A one-to-one correspondence was found between a non-zero topological invariant and directional amplification.
• End-to-end gain grows exponentially with the number of cavities in directional amplification regimes.
• Explicit dependence of gain and reverse gain on the topological invariant was derived.

Conclusions:

• Topology provides a powerful tool for understanding and designing directional amplifiers.
• A topological phase diagram guides the design of both phase-preserving and phase-sensitive multimode directional amplifiers.
• This framework unifies diverse physical realizations of directional amplification.