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This study experimentally validates theoretical predictions for the imaginary part of transmission time delay in non-unitary scattering systems. The findings show a carrier frequency shift in transmitted pulses, aligning with the imaginary component of the complex transmission time delay.

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Area of Science:

  • Quantum mechanics
  • Wave scattering theory
  • Microwave engineering

Background:

  • The scattering matrix (S) encodes system dynamics, relating incoming and outgoing waves.
  • Transmission time delay (τT) measures wave persistence, with its real part well-studied.
  • The imaginary part of τT in non-unitary systems lacks systematic experimental investigation.

Purpose of the Study:

  • To experimentally test theoretical predictions for the imaginary part of transmission time delay (Im[τT]).
  • To investigate Im[τT] in non-unitary scattering systems.
  • To explore the relationship between pulse carrier frequency shifts and Im[τT].

Main Methods:

  • Utilizing Gaussian time-domain pulses scattered from a two-port microwave graph.
  • Employing a system with well-isolated absorptive modes to ensure non-unitary behavior.
  • Performing frequency-domain measurements of the subunitary S matrix to independently determine Im[τT].

Main Results:

  • Observed a carrier frequency shift in scattered pulses.
  • Demonstrated agreement between the observed frequency shift and the independently determined Im[τT].
  • Validated theoretical predictions for Im[τT] in non-unitary scattering.

Conclusions:

  • The study experimentally confirms theoretical predictions for Im[τT] in non-unitary systems.
  • Results generalize and extend previous work on transmission time delay.
  • Establishes a method to predict pulse propagation in non-Hermitian systems.