One-Dimensional Bose Chemistry: Effects of Nonintegrability

Three-body collisions of ultracold identical Bose atoms under tight cylindrical confinement are analyzed. A Feshbach resonance in two-body collisions is described by a two-channel zero-range interaction. Elimination of the closed channel in the three-body problem reduces the interaction to a one-channel zero-range one with an energy-dependent strength. The related integrable Lieb-Liniger-McGuire (LLMG) model, with an energy-independent strength, forbids all chemical processes, such as three-atom association and diatom dissociation, as well as reflection in atom-diatom collisions. The resonant case is analyzed by a numerical solution of the Faddeev equations. The results demonstrate that as the internal symmetry of the LLMG model is lifted, reflection and chemical reactions become allowed and may be observed in experiments.

Figure 1

Probabilities of reflection (solid line) and dissociation (dashed line) in atom-diatom collisions vs the dimensionless collision energy ${ϵ}_2$ for $b=0$ and $u=0$. The scaled rate coefficient of 3B association $K_{3}m/\hslash$ vs the three-atom energy ${ϵ}_3$ is presented by the dot-dashed ($u=0$, $b=0$, $\theta =\pi /6$) and dot-dot-dot-dashed ($u=1.6$, $b=1$, $\theta =\pi /10$) lines.

Figure 2

The scaled rate coefficient $K_{3}m/\hslash$ vs $\theta$ for ${ϵ}_3=2.4$, $u=0$, $b=0$ (solid line), ${ϵ}_3=4.5$, $b=1$, $u=1.6$ (dashed line), and ${ϵ}_3=4.5$, $b=1$, $u=-2$ (dot-dashed line).

Figure 3

Probabilities of reflection (solid line) and dissociation (dashed line) in atom-diatom collisions vs the dimensionless detuning $b$ for ${ϵ}_2=3.6$. The scaled rate coefficient of 3B association $K_{3}m/\hslash$ is presented by the dot-dashed ($u=0$, ${ϵ}_3=2.4$, $\theta =\pi /6$) and dot-dot-dot-dashed ($u=1.6$, ${ϵ}_3=4.5$, $\theta =\pi /10$) lines.

Figure 4

Probabilities of reflection (solid line) and dissociation (dashed line) in atom-diatom collisions vs the dimensionless nonresonant interaction strength $u$ for ${ϵ}_2=3.6$ and $b=0$. The scaled rate coefficient of 3B association $K_{3}m/\hslash$ is presented by the dot-dashed ($b=0$, ${ϵ}_3=2.4$, $\theta =\pi /6$) and dot-dot-dot-dashed ($b=1$, ${ϵ}_3=4.5$, $\theta =\pi /10$) lines.