Mobile impurities in a Bose-Einstein condensate form quasiparticles called polarons. Here, we show that two such polarons can bind to form a bound bipolaron state. Its emergence is caused by an induced nonlocal interaction mediated by density oscillations in the condensate, and we derive using field theory an effective Schrödinger equation describing this for an arbitrarily strong impurity-boson interaction. We furthermore compare with quantum Monte Carlo simulations finding remarkable agreement, which underlines the predictive power of the developed theory. It is found that bipolaron formation typically requires strong impurity interactions beyond the validity of more commonly used weak-coupling approaches that lead to local Yukawa-type interactions. We predict that the bipolarons are observable in present experiments, and we describe a procedure to probe their properties.

Landau's description of the excitations in a macroscopic system in terms of quasiparticles stands out as one of the highlights in quantum physics. It provides an accurate description of otherwise prohibitively complex many-body systems, and has led to the development of several key technologies. In this paper, we investigate theoretically the Landau effective interaction between quasiparticles, socalled Bose polarons, formed by impurity particles immersed in a Bose-Einstein condensate (BEC). In the limit of weak interactions between the impurities and the BEC, we derive rigorous results for the effective interaction. They show that it can be strong even for weak impurity-boson interaction, if the transferred momentum/energy between the quasiparticles is resonant with a sound mode in the BEC. We then develop a diagrammatic scheme to calculate the effective interaction for arbitrary coupling strengths, which recovers the correct weak coupling results. Using this, we show that the Landau effective interaction in general is significantly stronger than that between quasiparticles in a Fermi gas, mainly because a BEC is more compressible than a Fermi gas. The interaction is particularly large near the unitarity limit of the impurity-boson scattering, or when the quasiparticle momentum is close to the threshold for momentum relaxation in the BEC. Finally, we show how the Landau effective interaction leads to a sizeable shift of the quasiparticle energy with increasing impurity concentration, which should be detectable with present day experimental techniques.

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Ultracold Fermi atoms confined in optical lattices coupled to quantized modes of an optical cavity are an ideal scenario to engineer quantum simulators in the strongly interacting regime. The system has both short range and cavity induced long range interactions. We propose such a scheme to investigate the coexistence of superfluid pairing, density order and quantum domains having antiferromagnetic or density order in the Hubbard model in a high finesse optical cavity at T = 0. We demonstrate that those phases can be accessed by properly tuning the linear polarizer of an external pump beam via the cavity back-action effect, while modulating the system doping. This allows emulate the typical scenarios of analog strongly correlated electronic systems.Introduction. Coupling ultracold quantum gases to high-finesse optical cavities is a novel scenario to explore many-body phases in the full quantum regime by exploiting the controllability of light-matter interaction [1,2]. Major experimental breakthroughs have been achieved in the quantum limit of both light and matter. For instance, the Dicke phase transition has been observed in a Bose-Einstein condensate coupled to cavity modes [3]. Experimentally, it has been achieved the emergence and control of supersolid phases where the cavity backaction generates light-induced effective long-range interactions which compete with short-range interatomic interactions [4][5][6][7][8].On the theoretical side, recent studies have introduced settings where cavity fields generate gauge-fields [9, 10], artificial spin-orbit coupling [11], self-organized phases [12,13], topological phases [14,15], measurement induced entangled modes [16], induced magnetic and density order using measurement back action [17] and feedback control [18], dimerization [19], spin lattice systems [20] and quantum simulators based on global collective lightmatter interactions [21,22].