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Area of Science:

  • Condensed Matter Physics
  • Ultracold Atomic Systems
  • Quantum Mechanics

Background:

  • Recent experimental advances in ultracold atoms.
  • Non-Hermitian (NH) Hamiltonians describe systems with dissipation or gain.
  • Standard BCS theory applies to Hermitian systems.

Purpose of the Study:

  • Analyze a NH BCS Hamiltonian with complex-valued interactions from inelastic fermion scattering.
  • Develop a NH mean-field theory for fermionic superfluidity.
  • Investigate unconventional phase transitions in NH fermionic systems.

Main Methods:

  • Developed a non-Hermitian mean-field theory.
  • Derived a NH gap equation for order parameters.
  • Analyzed quasiparticle Hamiltonians exhibiting exceptional points, lines, and surfaces.

Main Results:

  • Found unconventional phase transitions unique to NH systems.
  • Observed reentrant superfluidity with increasing dissipation for weak interactions.
  • Demonstrated dissipation-enhanced superfluidity for strong interactions via BCS-BEC crossover and quantum Zeno effect.

Conclusions:

  • The study provides a theoretical framework for understanding fermionic superfluidity under inelastic collisions.
  • Highlights unique phenomena in NH systems, such as reentrant superfluidity and dissipation-enhanced gaps.
  • Lays groundwork for future experimental and theoretical investigations in NH quantum matter.