Relaxation of Phonons in the Lieb-Liniger Gas by Dynamical Refermionization

Area of Science:

• Quantum many-body physics
• Ultracold atomic gases
• Statistical mechanics

Background:

• Investigating quantum gases far from equilibrium is crucial for understanding fundamental physics.
• Recent experiments motivate the study of Lieb-Liniger gas dynamics.
• Phonons in the Lieb-Liniger gas are not exact eigenstates of the Hamiltonian.

Purpose of the Study:

• To investigate the relaxation dynamics of a Lieb-Liniger gas from a Gaussian out-of-equilibrium state.
• To characterize the stationary state and its phonon population distribution.
• To explore whether the stationary state is thermal or non-thermal due to integrability.

Main Methods:

• Utilizing the Bethe-ansatz mapping between Lieb-Liniger eigenstates and noninteracting Fermi gas eigenstates.
• Employing bosonization techniques to analyze the system.
• Calculating the phonon population distribution in the relaxed stationary state.

Main Results:

• The Lieb-Liniger gas relaxes to a stationary state that is not necessarily thermal.
• A complete characterization of the stationary state and its phonon population distribution is achieved.
• Results are applied to an excited coherent state, with comparisons to hard-core limit results.

Conclusions:

• Integrability prevents the system from reaching a thermal equilibrium state, leading to a unique stationary state.
• The study provides a detailed understanding of non-equilibrium dynamics in integrable quantum gases.
• The findings offer valuable insights for experimental control and interpretation of quantum gas systems.