Breakdown of Tan's Relation in Lossy One-Dimensional Bose Gases

Area of Science:

• Quantum physics
• Ultracold atomic gases
• Many-body systems

Background:

• In quantum gases with contact repulsion, atomic momentum distributions typically follow a 1/|p|^4 decay at high momenta.
• Tan's relation links this momentum tail's amplitude to the gas's energy derivative concerning interaction strength (scattering length).

Purpose of the Study:

• To investigate the breakdown of Tan's relation in one-dimensional Bose gases with contact repulsion.
• To identify and characterize peculiar stationary states that lead to this breakdown.

Main Methods:

• Analysis of stationary states in one-dimensional Bose gases with infinite conserved quantities.
• Examination of momentum distributions and rapidity distributions.
• Investigation of phenomena induced by atom losses in experimental settings.
• Exact calculations in asymptotic regimes of infinite and weak repulsion.

Main Results:

• Tan's relation is shown to break down for specific stationary states in the 1D Bose gas.
• These states possess a rapidity distribution that also decays as 1/|p|^4, adding to the standard Tan contact term in the momentum distribution.
• Atom losses, common in experiments, naturally generate these peculiar states through ghost singularities in the wave function.

Conclusions:

• The study reveals a breakdown of Tan's relation in 1D Bose gases, highlighting the role of specific stationary states.
• Atom losses are identified as a crucial experimental factor creating these states and modifying momentum distributions.
• The findings necessitate a re-evaluation of Tan's relation's applicability and interpretation in experimental ultracold atom systems, particularly in lower dimensions.