Polarons and bipolarons in Rydberg-dressed extended Bose-Hubbard model

TL;DR

We address impurity dynamics in a one-dimensional extended Bose-Hubbard bath realized by ultracold lattice gases. Using density matrix renormalization group, we analyze a single impurity and a pair of impurities across superfluid (SF) and charge-density-wave (CDW) phases. A single impurity forms a polaron in SF and behaves as a particle in an effective ionic-Hubbard landscape in CDW, while two impurities can form a bound state (bipolaron) without explicit impurity–impurity coupling, with stability in both bath phases; hard-core impurities, however, do not bind. The results provide experimentally accessible signatures in density-density correlations and offer guidance for lattice polaron experiments in ultracold gases and connections to ionic-Hubbard physics.

Abstract

Impurities immersed in hard-core Bose gases offer exciting opportunities to explore polaron and bipolaron physics. We investigate the ground state properties of a single and a pair of impurities throughout the superfluid and insulating (charge density wave) phases of the bosonic environment. In the superfluid phase, the impurity exhibits polaron-like behavior, forming a dressed quasiparticle. In contrast, in the insulating phase, the impurity regains its particle-like character, moving through a potential landscape shaped by the charge density wave order. Moreover, we show that two impurities can form a bound state even in the absence of an explicit impurity-impurity coupling. We establish the stability of this bound state within both the superfluid and insulating phases. Our results offer valuable insights for ongoing lattice polaron experiments with ultracold gases.

Figures (9)

• Figure 1: Structure factor $S(q=\pi)$ of the bosonic medium as a function of the boson-boson interaction $V_{B}/t$. The insets display the characteristic one-body correlation functions $\langle\hat{b}^{\dagger}_{i}\hat{b}_{j}\rangle$ as a function of the distance $|i-j|$. Markers are associated with DMRG calculations, while dashed lines correspond to algebraic and exponential fits in the SF ($V_{B}/t=0$) and CDW ($V_{B}/t=4$) phases, respectively. We consider $L=80$ and $n_{B}=1/2$. Away from half-filling the bosonic bath remains in the superfluid phase.
• Figure 2: (a) Binding energy $E_{p}$ of a single impurity as a function of the density of the bath $n_{B}$ for $V_{B}/t = 0$. Markers are associated with DMRG calculations, whereas the dashed lines correspond to the mean-field prediction $E_{p}\approx U_{BI}n_{B}$. The gray line represents a guide for the eye for zero energy. (b)-(d) Binding energy $E_{p}$ of a single impurity as a function of the boson-boson interaction $V_{B}/t$ for $n_{B} = 0.25, 0.5$ and $0.75$, respectively. The grey dashed line indicates the value of $V_{B}/t$ at which the SF-CDW transition takes place. We consider $U_{BI}/t=-2$.
• Figure 3: Quasiparticle residue $Z$ as a function of the boson-impurity interaction $U_{BI}/t$. Panels (a), (b), (c), and (d) are associated with $V_{B}/t = 0,1,2$, and $6$, respectively. The red line in panels (c) and (d) corresponds to the overlap between the unmodulated and modulated single-particle ground states of the ionic Hubbard model.
• Figure 4: (a) Density-density boson-impurity correlation $\mathcal{C}_{BI}(r)$ at the same site $(r=0)$ as a function of the interaction $U_{BI}/t$ for several bosonic filling factors $n_{B}$ and fixed $V_{B}=0$. (b) $\mathcal{C}_{BI}(r)$ as a function of the relative distance $r$ for three different values of $n_{B}$ and $(V_{B}/t,U_{BI}/t)=(0,-10)$. (c) Sames as panel (b) but for $(V_{B}/t, U_{BI}/t)=(4,-10)$. (d)-(g) Development of the density-density boson-impurity correlations as the medium transitions from the superfluid to the charge density wave for $U_{BI}/t =-6$. Panels (d), (e), (f) and (g) are associated with $V_{B}/t = 0,1,2$, and $4$ respectively.
• Figure 5: Binding energy $E_{\mathrm{Bip}}$ of the two-impurity state as a function of the boson-impurity interaction $U_{BI}/t$ for several values of the bosonic filling $n_{B}$. Panels (a), (b), (c) and (d) consider $V_{B}/t= 0, 1, 3$ and $4$, respectively. The gray line represents a guide for the eye for zero energy.