Phenomenological model of decaying Bose polarons

Cold atom experiments show that a mobile impurity particle immersed in a Bose-Einstein condensate forms a well-defined quasiparticle (Bose polaron) for weak to moderate impurity-boson interaction strengths, whereas a significant line broadening is consistently observed for strong interactions. Motivated by this, we introduce a phenomenological theory based on the assumption that the most relevant states are characterized by the impurity correlated with at most one boson, since they have the largest overlap with the uncorrelated states to which the most common experimental probes couple. These experimentally relevant states can however decay to lower energy states characterised by correlations involving multiple bosons, and we model this using a minimal variational wave function combined with a complex impurity-boson interaction strength. We first motivate this approach by comparing to a more elaborate theory that includes correlations with up to two bosons. Our phenomenological model is shown to recover the main results of two recent experiments probing both the spectral and the non-equilibrium properties of the Bose polaron. Our work offers an intuitive framework for analyzing experimental data and highlights the importance of understanding the complicated problem of the Bose polaron decay in a many-body setting.

💡 Research Summary

The paper addresses a long‑standing puzzle in the physics of Bose polarons: while weak‑to‑moderate impurity‑boson interactions produce a sharp quasiparticle peak, experiments consistently observe a broad spectral response and rapid loss of coherence for strong interactions. The authors propose that the experimentally relevant states are those in which the impurity is correlated with at most a single boson. These “one‑boson” states dominate the overlap with the non‑interacting impurity state that radio‑frequency (RF) and Ramsey probes couple to, but they are not eigenstates of the full many‑body Hamiltonian. Instead, they decay into lower‑energy many‑body states involving two or more bosons (e.g., trimers, tetramers).

To substantiate this conjecture, the authors first employ a variational ansatz that includes up to two Bogoliubov excitations (Eq. 2) and compute the impurity spectral function using a Krylov subspace method. The resulting spectrum exhibits two branches: a sharp low‑energy branch (ground‑state‑like) and a broad high‑energy branch. The high‑energy branch carries the majority of spectral weight and corresponds to the impurity dressed by a single boson; the low‑energy branch corresponds to a state dressed by two bosons. This analysis shows that the broad experimental peak is naturally associated with the one‑boson branch, which is a resonance that decays into the lower‑energy two‑boson branch.

Calculating the full decay rate microscopically would require inclusion of all three‑body and higher‑order loss channels, a task that quickly becomes intractable. The authors therefore introduce a phenomenological model that captures the essential physics with far fewer degrees of freedom. They replace the full two‑channel Hamiltonian by a single‑channel point‑like interaction (Eq. 3) and allow the interaction strength (g_I) to be complex. The imaginary part of (g_I) mimics the loss of probability amplitude from the one‑boson subspace into the omitted multi‑boson continuum. By fitting the real part to reproduce the known mean‑field and molecular limits, and by introducing two phenomenological parameters (\Gamma) (weak‑interaction damping) and (\gamma) (unitarity‑region damping), they obtain an analytic expression for the impurity propagator pole (Eqs. 4‑5).

Using realistic experimental parameters ((n^{1/3}a_B=0.005)), the model reproduces the broad spectral line observed in the Cambridge experiment (Ref.