Anisotropic and non-additive interactions of a Rydberg impurity in a quantum bath

Abstract

We present a framework for treating anisotropic and non-additive impurity-bath interactions - features that are ubiquitous in realistic quantum impurity problems, but are often neglected in conventional approaches relying on additive, spherically symmetric pseudopotentials. To illustrate this, we focus on a Rydberg atom immersed in a Bose-Einstein condensate, where the internal-state degeneracy of the Rydberg impurity gives rise to configuration-dependent non-additive potentials. With increasing interaction strength, anisotropy-induced partial-wave mixing generates distinct polaron and molaron resonances, allowing for radially and angularly excited bound states to become accessible. This approach captures the anisotropy and non-additivity characteristic of a Rydberg impurity immersed in a quantum bath, and provides broad applicability to a host of quantum impurity problems beyond the Fröhlich paradigm.

Figures (5)

• Figure 1: Absorption spectrum of a $\ket{25p}$ Rydberg impurity in a BEC with density $\rho=2\times 10^{14} \,$cm$^3$, shown as a function of the electron-atom scattering length $a_s$ and detuning $\omega$. Representative features from different contributions—polarons (teal), dimer molarons (pink), and trimer molarons (purple)—are highlighted. (a) In the polaron regime the interaction is effectively spherical. (b,c) In the molecular regime, the electron localizes on specific bosons, forming a molecule and creating an anisotropic potential for additional bath atoms. As discussed in the main text, contributions to the absorption spectrum are truncated at the trimer level.
• Figure 2: Absorption spectra for a Rydberg impurity in $\ket{25p}$. The shifts from the bare resonances (vertical lines) to the observed peak positions, induced by many-body dressing, are indicated by arrows. (a) At density $\rho = 2 \times 10^{15}\,\mathrm{cm}^{-3}$ and scattering length $a_s = -0.1\,a_0$, trimer peaks exhibit smaller binding energies compared to dimers, deviating from additive dimer sums and highlighting non-additive effects. (b) At $\rho = 1 \times 10^{13}\,\mathrm{cm}^{-3}$ and $a_s = -0.028\,a_0$, the dimer branch crosses a resonance and consequently lies above the polaron branch, highlighting the non-additivity in the many-body dressing. Both panels employ a logarithmic intensity scale.
• Figure 3: a) Sketch of a Rydberg atom aligning in a magnetic field. b) Partial wave components of the anisotropic Rydberg p-state impurity potential in \ref{['Eq:Channel_H']}, highlighting its oscillations and centrifugal barriers. (c) The absorption spectrum of the Rydberg atom in $\ket{25p,m=0}$ within a BEC of density $\rho = 7 \times 10^{14}\,\mathrm{cm}^{-3}$ exhibits additive behavior in the molaron features: their energies are additive, and all states share the same many-body dressing, as reflected in the identical resonance structure. The dimer (pink) and trimer (purple) molarons are marked similar to \ref{['fig:Absorption_p_low_density']}. The role of anisotropy emerges only in the detailed form of the many-body dressing, which can be captured by the mean-field polaron energy with the effective scattering length (\ref{['Eq:p_pol_energy']}), shown as the teal line.
• Figure 4: Absorption spectra for a Rydberg $\ket{50s}$ state as a function of the electron–atom scattering length $a_s$. (a) Full calculation of the absorption $A(\omega)$ using the Loschmidt echo in \ref{['eq:S(t)']}. (b) Effect of truncating the cluster expansion in \ref{['eq:S_k_add']} at $k=2$, showing how limiting the sum alters the spectral features, especially close to unitarity.
• Figure 5: Potential energy surfaces of a Rydberg $p$-state and a ground state atom, split by a magnetic field.