We use a nonperturbative renormalization group approach to develop a unified picture of the Bose polaron problem, where a mobile impurity is strongly interacting with a surrounding Bose-Einstein condensate (BEC). A detailed theoretical analysis of the phase diagram is presented and the polaron-to-molecule transition is discussed. For attractive polarons we argue that a description in terms of an effective Fr\"ohlich Hamiltonian with renormalized parameters is possible. Its strong-coupling regime is realized close to a Feshbach resonance, where we predict a sharp increase of the effective mass. Already for weaker interactions, before the polaron mass diverges, we predict a transition to a regime where states exist below the polaron energy and the attractive polaron is no longer the ground state. On the repulsive side of the Feshbach resonance we recover the repulsive polaron, which has a finite lifetime because it can decay into low-lying molecular states. We show for the entire range of couplings that the polaron energy has logarithmic corrections in comparison with predictions by the mean-field approach. We demonstrate that they are a consequence of the polaronic mass renormalization which is due to quantum fluctuations of correlated phonons in the polaron cloud.We use a nonperturbative renormalization group approach to develop a unified picture of the Bose polaron problem, where a mobile impurity is strongly interacting with a surrounding Bose-Einstein condensate (BEC). A detailed theoretical analysis of the phase diagram is presented and the polaron-to-molecule transition is discussed. For attractive polarons we argue that a description in terms of an effective Fr\"ohlich Hamiltonian with renormalized parameters is possible. Its strong-coupling regime is realized close to a Feshbach resonance, where we predict a sharp increase of the effective mass. Already for weaker interactions, before the polaron mass diverges, we predict a transition to a regime where states exist below the polaron energy and the attractive polaron is no longer the ground state. On the repulsive side of the Feshbach resonance we recover the repulsive polaron, which has a finite lifetime because it can decay into low-lying molecular states. We show for the entire range of couplings that the polaron energy has logarithmic corrections in comparison with predictions by the mean-field approach. We demonstrate that they are a consequence of the polaronic mass renormalization which is due to quantum fluctuations of correlated phonons in the polaron cloud.

arXiv:1704.02605Physical Review AJul 6, 2017100 citations

Bose polarons in the strongly interacting regime

Dhruv Kedar, Ming-Guang Hu, Michael J. Van de Graaff +3 more

Bulletin of the American Physical SocietyMar 17, 20160 citations

Strong-coupling polarons in one dimensional Bose condensates

Jonas Jager, Ryan Barnett, Michael Fleischhauer +1 more

Bulletin of the American Physical SocietyMay 30, 20190 citations

Mediated interaction between polarons in a one-dimensional Bose gas

Aleksandra Petković, Zoran Ristivojević

We study a weakly interacting one-dimensional Bose gas with two impurities coupled locally to the boson density. We derive analytical results for the induced interaction between the impurities at arbitrary positive coupling and separation $r$ . At $r\ensuremath{\lesssim}\ensuremath{\xi}$, where $\ensuremath{\xi}$ denotes the healing length of the Bose gas, the interaction is well described by the mean-field contribution. Its form changes as the coupling is increased, approaching a linear function of $r$ at short distances in the regime of strong coupling. The mean-field contribution decays exponentially at arbitrary coupling for $r\ensuremath{\gg}\ensuremath{\xi}$. At such long distances, however, the effect of quantum fluctuations becomes important, giving rise to a long-ranged quantum contribution to the induced interaction. At longest distances it behaves as $1/{r}^{3}$ , while at strong coupling we find an intermediate distance regime with a slower decay, $1/r$ . The quantum contribution in the crossover regime is also calculated. The induced interaction between impurities (i.e., polarons) is attractive and leads to the formation of their bound state, known as bipolaron. We discuss its binding energy.We study a weakly interacting one-dimensional Bose gas with two impurities coupled locally to the boson density. We derive analytical results for the induced interaction between the impurities at arbitrary positive coupling and separation $r$. At $r\ensuremath{\lesssim}\ensuremath{\xi}$, where $\ensuremath{\xi}$ denotes the healing length of the Bose gas, the interaction is well described by the mean-field contribution. Its form changes as the coupling is increased, approaching a linear function of $r$ at short distances in the regime of strong coupling. The mean-field contribution decays exponentially at arbitrary coupling for $r\ensuremath{\gg}\ensuremath{\xi}$. At such long distances, however, the effect of quantum fluctuations becomes important, giving rise to a long-ranged quantum contribution to the induced interaction. At longest distances it behaves as $1/{r}^{3}$, while at strong coupling we find an intermediate distance regime with a slower decay, $1/r$. The quantum contribution in the crossover regime is also calculated. The induced interaction between impurities (i.e., polarons) is attractive and leads to the formation of their bound state, known as bipolaron. We discuss its binding energy.

arXiv:2103.08772Physical Review AFeb 22, 202233 citations

Single-impurity polarons in hard-core lattice bosons at low and intermediate fillings

Chao Zhang

We investigate a single mobile impurity in a two-dimensional hard-core Bose--Hubbard bath at low and intermediate fillings and determine how polaronic dressing evolves with bath filling for impurity--bath couplings ranging from weak to strong and ultimately to the two-component hard-core limit. Using large-scale, sign-problem-free worm-algorithm quantum Monte Carlo simulations, we extract momentum-space quasiparticle properties from the impurity Green's function and resolve the accompanying real-space bath rearrangement from an imaginary-time-averaged impurity-centered correlator. We also vary the impurity hopping $t_{\rm imp}$ to assess how reduced mobility modifies dressing in the strong-coupling regime. For the fillings accessible at each coupling, the impurity remains a dressed quasiparticle whose ground-state energy, effective mass, and residue vary smoothly with filling $n_{\rm b}$ . In real space, increasing $n_{\rm b}$ strengthens the short-range depletion while shifting the dominant response toward the impurity. In the two-component hard-core limit $U_{\rm ib}/t_{\rm b}\!\to\!\infty$ , the large-distance recovery of the cumulative density deformation exhibits only weak filling dependence over the range considered here, whereas short-range core indicators continue to evolve. Our results quantitatively characterize strongly dressed polarons in a correlated, compressible lattice bath and resolve how filling and impurity mobility modify the near-core response and spatial extent of the dressing cloud.We investigate a single mobile impurity in a two-dimensional hard-core Bose--Hubbard bath at low and intermediate fillings and determine how polaronic dressing evolves with bath filling for impurity--bath couplings ranging from weak to strong and ultimately to the two-component hard-core limit. Using large-scale, sign-problem-free worm-algorithm quantum Monte Carlo simulations, we extract momentum-space quasiparticle properties from the impurity Green's function and resolve the accompanying real-space bath rearrangement from an imaginary-time-averaged impurity-centered correlator. We also vary the impurity hopping $t_{\rm imp}$ to assess how reduced mobility modifies dressing in the strong-coupling regime. For the fillings accessible at each coupling, the impurity remains a dressed quasiparticle whose ground-state energy, effective mass, and residue vary smoothly with filling $n_{\rm b}$. In real space, increasing $n_{\rm b}$ strengthens the short-range depletion while shifting the dominant response toward the impurity. In the two-component hard-core limit $U_{\rm ib}/t_{\rm b}\!\to\!\infty$, the large-distance recovery of the cumulative density deformation exhibits only weak filling dependence over the range considered here, whereas short-range core indicators continue to evolve. Our results quantitatively characterize strongly dressed polarons in a correlated, compressible lattice bath and resolve how filling and impurity mobility modify the near-core response and spatial extent of the dressing cloud.

arXiv:2608.13988Aug 14, 20260 citations

Polarons in a strongly interacting Bose-Fermi mixture

Cheng-Hsun Wu, Ibon Santiago, Jee Woo Park +3 more

APSJun 1, 20120 citations

r

. At $r\ensuremath{\lesssim}\ensuremath{\xi}$, where $\ensuremath{\xi}$ denotes the healing length of the Bose gas, the interaction is well described by the mean-field contribution. Its form changes as the coupling is increased, approaching a linear function of

r

at short distances in the regime of strong coupling. The mean-field contribution decays exponentially at arbitrary coupling for $r\ensuremath{\gg}\ensuremath{\xi}$. At such long distances, however, the effect of quantum fluctuations becomes important, giving rise to a long-ranged quantum contribution to the induced interaction. At longest distances it behaves as

1/{r}^{3}

, while at strong coupling we find an intermediate distance regime with a slower decay,

1/r

. The quantum contribution in the crossover regime is also calculated. The induced interaction between impurities (i.e., polarons) is attractive and leads to the formation of their bound state, known as bipolaron. We discuss its binding energy.

t_{\rm imp}

to assess how reduced mobility modifies dressing in the strong-coupling regime. For the fillings accessible at each coupling, the impurity remains a dressed quasiparticle whose ground-state energy, effective mass, and residue vary smoothly with filling

n_{\rm b}

. In real space, increasing

n_{\rm b}

strengthens the short-range depletion while shifting the dominant response toward the impurity. In the two-component hard-core limit

U_{\rm ib}/t_{\rm b}\!\to\!\infty

, the large-distance recovery of the cumulative density deformation exhibits only weak filling dependence over the range considered here, whereas short-range core indicators continue to evolve. Our results quantitatively characterize strongly dressed polarons in a correlated, compressible lattice bath and resolve how filling and impurity mobility modify the near-core response and spatial extent of the dressing cloud.