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Attractive one-dimensional fermions form composite bosons in the fermionic Tonks-Girardeau regime. This pairing mechanism leads to universal occupation numbers, mirroring Bose-Einstein condensate properties.

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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Many-body systems

Background:

  • Studying one-dimensional (1D) quantum systems provides insights into fundamental many-body physics.
  • The fermionic Tonks-Girardeau (FTG) regime describes strongly interacting 1D fermions, exhibiting unique properties.
  • Understanding attractive interactions is crucial for phenomena like fermion pairing and superfluidity.

Purpose of the Study:

  • Investigate the properties of attractive p-wave one-dimensional fermions in the FTG regime.
  • Analyze the off-diagonal properties and the one-body density matrix.
  • Explore the pairing mechanism and the formation of composite particles.

Main Methods:

  • Analytical derivation of eigenvalues for the one-body density matrix.
  • Analysis of occupation numbers of natural orbitals.
  • Comparison with the properties of ideal Bose gases and Bose-Einstein condensates.

Main Results:

  • Diagonal properties of the system are identical to those of an ideal Bose gas.
  • Universal occupation numbers of natural orbitals, independent of the external potential shape.
  • Occupation of natural orbitals occurs in pairs, signifying the formation of composite bosons from two attractive fermions.

Conclusions:

  • The formation of composite bosons explains the pairing mechanism in this system.
  • The system's density equals that of a Bose-Einstein condensate, highlighting emergent bosonic behavior.
  • Attractive interactions in 1D fermions can lead to universal pairing phenomena.