Rotation of Quantum Impurities in the Presence of a Many-Body Environment

We develop a microscopic theory describing a quantum impurity whose rotational degree of freedom is coupled to a many-particle bath. We approach the problem by introducing the concept of an “angulon”—a quantum rotor dressed by a quantum field—and reveal its quasiparticle properties using a combination of variational and diagrammatic techniques. Our theory predicts renormalization of the impurity rotational structure, such as that observed in experiments with molecules in superfluid helium droplets, in terms of a rotational Lamb shift induced by the many-particle environment. Furthermore, we discover a rich many-body-induced fine structure, emerging in rotational spectra due to a redistribution of angular momentum within the quantum many-body system.

Figure 1

(a) The interaction of a quantum rotor with a quantum many-body system explicitly depends on the rotor angular coordinates, $(\widehat{\theta },\widehat{\varphi })$, in the laboratory frame. (b) The anisotropic rotor-boson interaction is defined in the rotor coordinate frame, ${\mathbf{r}}^{\prime }=(r^{\prime },{\mathrm{\Theta }}^{\prime },{\mathrm{\Phi }}^{\prime })$. (c) Representation of Eq. (4) in terms of Feynman diagrams.

Figure 2

(a) The angulon spectral function, $A_L(\tilde{E})$, as a function of the dimensionless density, $\tilde{n}=n(mB{)}^{-3/2}$, and energy $\tilde{E}=E/B$. The low- and high-density regimes can be realized with cold molecules trapped inside a BEC and superfluid helium droplets, respectively. The ground state, $0_{00}^{-}$, is stable; so is the state $1_{01}^{-}$ after it crosses the phonon threshold at zero energy, marked by the horizontal dashed line. Within the plotted range of $\tilde{n}$, the rest of the excited states have finite lifetimes. (b) Differential rotational Lamb shift for the lowest nonzero-$L$ states. (c) Zoom in illustrating the many-body-induced fine structure (MBIFS) of the first kind, $L_{L,0}\to \{L_{L,0}^{-},L_{L,0}^{+}\}$, and of the second kind, $L_{L,0}^{-}\to L_{L-1,1}^{-}$. (d) Spectroscopic signatures of the MBIFS for the $L=1$ state. The numbers indicate the corresponding values of $\ln [\tilde{n}]$. Sharp features in panels (a), (c), and (d) were artificially broadened for better visibility.