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Résumé |
The Bose-Hubbard (BH) model quantifies the quantum matter phases accessible to strongly correlated bosons confined in lattice potentials. In its elementary form the BH Hamiltonian is restricted to on-site interactions and a single lattice confined state. At sufficiently low temperatures, the transition from superfluid to Mott insulating phases is thus accurately quantified. Extending the BH model to additional degrees of freedom naturally provides a direct route to broaden the range of accessible quantum matter phases. In this presentation we introduce a new platform to experimentally emulate extended Bose-Hubbard models. In particular, we emphasise semiconductor excitons confined in electrostatic lattice potentials. By suitably tuning the lattice geometry we first probe experimentally a multi-orbital version of the BH model, i.e. the situation where excitons have access to a set of discrete (Wannier) states in every lattice site. In this regime, we show that a subtle competition between the on-site interaction strength and the energy separation between lattice confined states rules the buildup of Mott insulating phases [1]. We also evidence that electrostatic lattices can be designed to enter the regime the the BH Hamiltonian is extended to interactions between excitons confined in nearest neighbouring lattice sites. In this regime, we demonstrate that ordered insulating phases emerge at fractional lattice fillings, such as a checkerboard solid at half filling [2].
[1] C. Lagoin et al., Nat. Phys. 18, 149 (2022)
[2] C. Lagoin et al., Nature 609, 485 (2022)
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