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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.