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arXiv:2411.06275

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

G. A. Domínguez‐Castro, Luis Santos, Luis A. Peña Ardila

Published Nov 9, 2024• 0 citations
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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.

DOI
10.48550/arxiv.2411.06275

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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.
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.
Quasiparticles and their interactions are a key part of our understanding of quantum many-body systems. Quantum simulation experiments with cold atoms have in recent years advanced our understanding of isolated quasiparticles, but so far they have provided limited information regarding their interactions and possible bound states. Here, we show how exploring mobile impurities immersed in a Bose-Einstein condensate (BEC) in a two-dimensional lattice can address this problem. First, the spectral properties of individual impurities are examined, and in addition to the attractive and repulsive polarons known from continuum gases, we identify a new kind of quasiparticle stable for repulsive boson-impurity interactions. The spatial properties of polarons are calculated showing that there is an increased density of bosons at the site of the impurity both for repulsive and attractive interactions. We then derive an effective Schrödinger equation describing two polarons interacting via the exchange of density oscillations in the BEC, which takes into account strong impurity-boson two-body correlations. Using this, we show that the attractive nature of the effective interaction between two polarons combined with the two-dimensionality of the lattice leads to the formation of bound states - i.e. bipolarons. The wave functions of the bipolarons are examined showing that the ground state is symmetric under particle exchange and therefore relevant for bosonic impurities, whereas the first excited state is doubly degenerate and odd under particle exchange making it relevant for fermionic impurities. Our results show that quantum gas microscopy in optical lattices is a promising platform to explore the spatial properties of polarons as well as to finally observe the elusive bipolarons.
Bose polarons, quasiparticles composed of mobile impurities surrounded by cold Bose gas, can experience strong interactions mediated by the many-body environment and form bipolaron bound states. Here we present a detailed study of heavy polarons in a one-dimensional Bose gas by formulating a nonperturbative theory and complementing it with exact numerical simulations. We develop an analytic approach for weak boson-boson interactions and arbitrarily strong impurity-boson couplings. Our approach is based on a mean-field theory that accounts for deformations of the superfluid by the impurities and in this way minimizes quantum fluctuations. The mean-field equations are solved exactly in the Born-Oppenheimer approximation, leading to an analytic expression for the interaction potential of heavy polarons, which is found to be in excellent agreement with quantum Monte Carlo (QMC) results. In the strong coupling limit, the potential substantially deviates from the exponential form valid for weak coupling and has a linear shape at short distances. Taking into account the leading-order Born-Huang corrections, we calculate bipolaron binding energies for impurity-boson mass ratios as low as 3 and find excellent agreement with QMC results.
A mobile impurity particle immersed in a quantum degenerate gas leads to the formation of a quasiparticle, which can serve as a sensor for its environment. Here, we develop a unified wave function description of an impurity in a two-dimensional Bose-Hubbard model across the Mott-insulator to superfluid transition. Using a multi-mode variational ansatz based on the quantum Gutzwiller approach, we show that the impurity can form several kinds of polaronic and molecular states. In addition to their spectral properties, the wave function provides direct access to the microscopic structure of these states, and we demonstrate that strong correlations in the critical regime of the quantum phase transition give rise to several non-analytic features in the polaron properties. Increasing the impurity-boson interaction leads to transitions between polaron and molecular ground states, and the number of bosons in the impurity dressing cloud grows rapidly at the quantum critical point as the bath modes soften. We furthermore reveal qualitatively distinct non-equilibrium many-body dynamics after the injection of the impurity in the different phases of the Bose-Hubbard model. Our spectral, real space, and dynamical predictions describe complementary properties of polarons in a strongly correlated bosonic bath, which can be observed using current techniques with atoms in optical lattices.
Abstract Lattice polarons, quasiparticles arising from the interaction between an impurity and its surrounding bosonic environment confined to a lattice system, have emerged as a platform for generating complex few-body states, probing many-body phenomena, and addressing long-standing problems in physics. In this study, we employ a variational ansatz to investigate the quasiparticle and spectral properties of an impurity coupled to a condensate gas of hard-core bosons in a two-dimensional optical lattice. Our findings demonstrate that the polaron features can be tuned by adjusting the filling factor of the bath, revealing intriguing polaron characteristics in the strongly interacting regime. These results offer valuable insights for lattice polaron experiments with ultracold gases and can serve as a guide for new experiments in emergent quantum devices, such as moiré materials, where optical excitations can be described in terms of hard-core bosons.
We study the physics of a mobile impurity confined in a two-dimensional lattice, moving within a Bose-Hubbard bath at zero temperature. Exploiting the quantum Gutzwiller formalism, we develop a beyond-Fröhlich model of the bath-impurity interaction to describe the properties of the polaronic quasiparticle formed by the dressing of the impurity by quantum fluctuations of the bath. We find a stable and well-defined polaron throughout the entire phase diagram of the bath, except for the very low tunneling limit of the hard-core superfluid. The polaron properties are highly sensitive to the different universality classes of the quantum phase transition between the superfluid and Mott insulating phases, providing an unambiguous probe of correlations and collective modes in a quantum critical many-body environment.