Inelastic Collision in Quantum Gases

Inelastic collisions in quantum gases occur when two particles interact and transition to a different internal state, often leading to the loss of particles from the trap. Unlike elastic collisions, which only exchange momentum while preserving the internal states, inelastic collisions change the quantum state of the system. Think of it like two cars that don’t just bump and continue driving, but instead merge into different vehicles altogether!

Ultracold Molecular Gases, Ultracold Chemistry and Loss

Ultracold polar molecules represent an exciting frontier in quantum physics, offering controllable long-range anisotropic interactions through their dipole moments. Their potential applications span quantum computation, quantum simulation, and the study of novel quantum phases.

However, a significant challenge in these systems is the prevalence of two-body losses from chemical reactions. Taking \(^{40}\text{K}{}^{87}\text{Rb}\) molecules as an example, the reaction \(2\text{KRb}\rightarrow \text{K}_2+\text{Rb}_2\) converts internal energy to kinetic energy, causing the product molecules to escape from the trap.

Loss Rate and Contacts

It can be shown that in thermal systems, the two-body loss rate of ultracold molecular gases is closely related to the contact, a thermodynamic quantity that characterizes the strength of short-range correlations in the system. The effect is especially interesting in single-component Fermi gases, where the dominant partial wave collision channel is $p$, which has non-trivial momentum dependence, thus leading to temperature dependence of the contact.

For weakly interacting gases, we’ve worked out complete equations of state and expressions of contact that work for arbitrary partial wave channels. We found something surprising: For s-wave Bose gases, the contact is just about two particles interacting, while for p-wave Fermi gases or higher partial wave systems, even at relatively high temperatures, one needs to account for three-body or higher-body effects.

Inelastic Quantum Boltzmann Equation and Thermalization

Analogous to the fact that a classic granular fluid with inelastic collision can be described by the generalized inelastic Boltzmann equation, the lossy quantum gas can also be effectively described by an inelastic quantum Boltzmann equation(IQBE), where the term describing the inelastic collision/loss can be derived from Lindblad master equation of open quantum systems.

By solving IQBE, we find that the loss effect in a single-component Fermi gas not only simply reduces the number of particles \(N\) in the system, but also modifies the decay behavior itself, making it distinguishable from traditional two-body losses: \(\frac{dN(t)}{dt}\propto -N(t)^\mathcal{N},\quad \mathcal{N}\neq 2.\)

Besides, intuitively, an inelastic collision/two-body loss drifts the system away from equilibrium. We show that this may not be true in single-component Fermi gases.

Reference

  1. Gao, X.-Y., Blume, D., and Yan, Y., Temperature-dependent contact of weakly interacting single-component Fermi gases and loss rate of degenerate polar molecules, Phys. Rev. Lett. 131, 043401 (2023)
  2. Gao, X.-Y., Blume, D., and Yan, Y., Exact Thermodynamics For Weakly Interacting Normal-Phase Quantum Gases: Equations of State For All Partial Waves, Phys. Rev. Res. 6, 033173 (2024)
  3. Gao, X.-Y., and Yan, Y., Fate of thermalization of ultracold fermions with two-body dissipation, to be published by Phys. Rev. Lett. (2025)