Medium-enhanced polaron repulsion in a dilute Bose mixture

TL;DR

This work reveals a medium-induced, leading-order repulsion between condensed bosonic impurities in a dilute Bose gas, arising from exchange of Bogoliubov modes and the dressing cloud, and shows that the sign and magnitude depend sensitively on whether the medium response is constrained by fixed density or fixed chemical potential. By combining a rigorous two-impurity variational approach with a diagrammatic analysis, the authors derive an explicit expression for the polaron–polaron interaction $F$ and identify a beyond-Bogoliubov correction $\Delta F$ from repeated mode exchanges, while showing Efimov-like three-body effects are subleading in the weak-coupling regime. They also clarify how the measured sign of polaron interactions in experiments across cold atoms and 2D semiconductors can be reconciled by the experimental protocol (degenerate vs thermal impurities, fixed $\mu$ vs fixed $n$). The results emphasize the importance of medium-response constraints in quasiparticle theories and provide a framework to interpret diverse experimental observations in quantum mixtures. Overall, the paper advances understanding of polaronic quasiparticles in Bose mixtures and has broad implications for quasiparticle theory in quantum many-body systems.

Abstract

We investigate the fundamental problem of a small density of bosonic impurities immersed in a dilute Bose gas at zero temperature. Using a rigorous perturbative expansion, we show that the presence of the surrounding medium enhances the repulsion between dressed bosonic impurities (polarons) in the regime of weak interactions. Crucially, this differs from prevailing theories based on Landau quasiparticles, which neglect the possibility of quantum degenerate impurities and predict an exchange-induced attraction. We furthermore show that the polaron-polaron interactions are strongly modified if the medium chemical potential rather than the density is held fixed, such that the medium-induced attraction between thermal impurities becomes twice the expected Landau effective interaction. Our work provides a possible explanation for the differing signs of the polaron-polaron interactions observed in experiments across cold atomic gases and two-dimensional semiconductors, and it has important implications for theories of quasiparticles and quantum mixtures in general.

Figures (5)

• Figure 1: Polaron interaction strength \ref{['eq:gpol1']} for degenerate impurities (solid) compared with the result \ref{['eq:gpol2']} for thermal impurities (dashed). From top to bottom, we have $a_{\downarrow\downarrow}/\xi=0.25,\,0.2,\,0.15$, and $0.1$, and for all lines $a_{\uparrow\uparrow}/\xi=0.1$.
• Figure 2: Leading-order diagrams for the polaron interactions. The first line depicts the direct interaction in (a) and its medium-enhanced corrections (b,c), whereas the diagrams in the second line are independent of the direct interactions. The black lines denote impurity propagators, while the blue solid and dotted lines are the Bogoliubov excitations and condensate lines of the majority particles, respectively. Squares correspond to the impurity-medium interaction $g_{\uparrow\downarrow}$, and the circles to the direct impurity interaction $g_{\downarrow\downarrow}$.
• Figure 3: (a) Hartree and (b) exchange interaction at order $a_{\uparrow\downarrow}^2$. When ${\bf p}_1 = {\bf p}_2$, as is the case for degenerate impurities, these processes coincide and do not contribute to the interaction $F$ in Eq. \ref{['eq:energycanonical']}.
• Figure S1: Leading-order diagrams for the polaron-polaron interactions, reproduced from the main text.
• Figure S2: Diagrams contributing to three-body scattering processes and Efimov physics.