Supersolid phases of Rydberg-excited bosons on a triangular lattice

Abstract

Recent experiments with ultracold Rydberg-excited atoms have shown that long-range interactions can give rise to spatially ordered structures. Observation of crystalline phases in a system with Rydberg atoms loaded into an optical lattice seems also within reach. Here we investigate a bosonic model on a triangular lattice suitable for description of such experiments. Numerical simulations based on bosonic dynamical mean-field theory reveal a rich phase diagram with different supersolid phases. Comparison with the results obtained for a square lattice geometry shows qualitatively similar results in a wide range of parameters, however, on a triangular lattice we do not observe the checkerboard supersolid. Moreover, unlike on a square lattice we did not find a phase transition from uniform superfluid to supersolid induced by increase of the hopping amplitude on a triangular lattice. Based on our results we propose an intuitive interpretation of the nature of different supersolid phases. We also propose parameters for the experimental realization.

Supersolid phases of ultracold bosons trapped in optical lattices dressed with Rydberg $p$-states

“…Furthermore, we do not find a change in the quality of the approximation upon variation of θ − θ 0 (see Appendix B). In previous calculations on Rydberg-excited gases in optical lattices, ground state phase diagrams computed within Gutzwiller mean-field theory with Hartree-decoupling were in qualitatively good agreement with results obtained by other methods [12,33]. We therefore expect the Gutzwiller-mean field theory to deliver qualitatively, and in some regimes also quantitatively accurate results.…”

“…The critical detuning ∆ 0 marks the transition point from the density wave regime to the vacuum state. For a given chemical potential µ and Rabi coupling Ω the critical value is analytically given by µ = −(∆ 0 + ∆ 2 0 + Ω 2 )/2 [12,13]. This results in our case in a critical detuning ∆ 0 /Ω = −0.75, which matches the value obtained in the numerical calculation.…”

“…Phase diagrams with similar regimes have been obtained in previous calculations for Rydberg-excited bosons with isotropic long-range interaction trapped in square and triangular optical lattices [12,33], though the emerging crystalline structures highly depend on the lattice and interaction geometries.…”

“…In order to establish a phase diagram, we define quantities which allow us to distinguish quantum phases more easily. Since we expect various crystalline orders to emerge, characterized by the spatial distribution of Rydberg-excited particles, we define the superlattice unit cell area through A SL = |a 1 ×a 2 | with the spanning vectors a 1 and a 2 [12,33]. This allows us to identify dense or sparse distributions of Rydbergexcited particles in the system (see FIG.…”

“…Since the length scale of the long-range interaction is typically larger than the lattice constant, novel quantum phases such as lattice supersolids -phases with simultaneously broken lattice translational and U (1) symmetry [7][8][9][10] -appear to be within reach. Although theoretical studies of interacting atomic lattice gases dressed with Rydberg s-states found parameter regimes for which supersolids should be experimentally observable [11][12][13], different obstacles have so far made the experimental realization of supersolids challenging. The lifetimes of these systems are limited through scattering processes and were shown to be much smaller than the typical single particle lifetime due to collective loss processes [4,14,15].…”