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Non-Hermitian Absorption Spectroscopy.

Kai Li1, Yong Xu1,2

  • 1Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China.

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This study introduces a new spectroscopic method to measure complex energy spectra in non-Hermitian quantum systems. This technique overcomes challenges posed by boundary effects, making momentum-space band structures experimentally accessible.

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Area of Science:

  • Quantum physics
  • Atomic physics
  • Condensed matter physics

Background:

  • Non-Hermitian Hamiltonians are experimentally realized in cold atom systems.
  • Measuring complex energy spectra in momentum space for realistic systems with boundaries is an open challenge.
  • Non-Hermitian skin effects complicate the relationship between open-boundary and momentum-space energy spectra.

Purpose of the Study:

  • To develop an experimental method for measuring complex energy spectra in momentum space for non-Hermitian quantum systems.
  • To address the challenge of accessing momentum-space band structures in the presence of boundary effects and non-Hermitian skin effects.
  • To generalize radio-frequency spectroscopy for non-Hermitian systems.

Main Methods:

  • Generalization of radio-frequency spectroscopy.
  • Weakly coupling system energy levels to auxiliary energy levels.
  • Derivation of a formula relating auxiliary level decay to momentum-space energy spectra.

Main Results:

  • A method is derived to measure both real and imaginary parts of complex energy spectra.
  • Measurement outcomes are shown to be independent of boundary conditions in the thermodynamic limit.
  • The proposed non-Hermitian absorption spectroscopy protocol is demonstrated on the Hatano-Nelson model and non-Hermitian Weyl semimetals.

Conclusions:

  • The developed spectroscopic protocol experimentally measures complex energy spectra in momentum space for non-Hermitian systems.
  • The method provides strong evidence for the experimental accessibility of momentum-space band structures, even with boundary conditions.
  • The protocol is feasible and applicable to various non-Hermitian models.