Emergence of Non-Abelian Magnetic Monopoles in a Quantum Impurity Problem

Recently, it was shown that molecules rotating in superfluid helium can be described in terms of the angulon quasiparticles [Phys. Rev. Lett. 118, 095301 (2017)]. Here, we demonstrate that in the experimentally realized regime the angulon can be seen as a point charge on a two-sphere interacting with a gauge field of a non-Abelian magnetic monopole. Unlike in several other settings, the gauge fields of the angulon problem emerge in the real coordinate space, as opposed to the momentum space or some effective parameter space. Furthermore, we find a topological transition associated with making the monopole Abelian, which takes place in the vicinity of the previously reported angulon instabilities. These results pave the way for studying topological phenomena in experiments on molecules trapped in superfluid helium nanodroplets, as well as on other realizations of orbital impurity problems.

Figure 1

Density plot of the angulon spectral function (the red curves), the charge of the $U(3)$ magnetic monopole, $g$ (the blue solid curve), and the amplitude of the $\pm 1$ component of the impurity wave function, $c_{\pm 1}$ (the black dashed curve) as a function of the dimensionless rotational constant, $\xi =\ln [B/u_0]$, for the $L=1$ state. The dimensionless bath density is set to ${\tilde{n}}_0=\ln [0.014]$. The vertical dashed line indicates the critical value, ${\xi }_c$, corresponding to the topological transition. See the text.

Figure 2

The monopole charge of the angulon $L=1$ state, $g$, as a function of the dimensionless rotational constant, $\xi =\ln [B/u_0]$, and the dimensionless density, ${\tilde{n}}_0=\ln [n_0(m{u}_0{)}^{-3/2}]$. Topological transition from the non-Abelian (NA) to the Abelian (A) monopole takes place in the angulon instability region ($I$). See the text.