Confinement-induced unatomic trimer states in mass-imbalanced systems

As resonantly interacting trimers of the type AAB are progressively squeezed from $D=3$ to $D=2$, unatomic states emerge. We calculated the contacts from the high-momentum tail of the single-particle densities. The sharp increase in the contacts serves as a signature of the transition between the Efimov and unatomic regimes, characterized by the emergence of continuous scale invariance when the system reaches a critical dimension ${D}_{c}$. This continuous scale invariance starts to dominate the behavior of the system at the dimension $\overline{D}<{D}_{c}$, below which the trimers' momentum-distribution tails exhibit a power-law behavior signaling the unatomic regime. To illustrate our findings, we studied compounds with the forms $^{7}\mathrm{Li}\text{\ensuremath{-}}^{23}\mathrm{Na}_{2}$, $^{7}\mathrm{Li}\text{\ensuremath{-}}^{87}\mathrm{Rb}_{2}$, and $^{7}\mathrm{Li}\text{\ensuremath{-}}^{133}\mathrm{Cs}_{2}$. The increase in the trimers' mass imbalance reduces the interval between ${D}_{c}$ and $\overline{D}$. The emergence of unatomic states can be experimentally verified by observing the two-body contact parameter, which is a quantity directly related to the thermodynamic properties of the gas.