Motivated by recent experimental efforts to realize quantum phases of matter with cold atomic Rydberg gases, I will discuss the phase diagram and excitation spectrum of supersolids in a two dimensional bosonic system with soft-core interactions.
Previous works [1] showed an exceptional agreement between Monte Carlo simulations and a numerical mean-field approach.  I will present a variational analysis of the Gross-Pitaevskii equation with a non-local interaction term and show that we can quantitatively reproduce the superfluid-supersolid transition at finite interaction strength in agreement with Monte Carlo results.  We then test the validity of this mean-field analysis perturbing the ground state wave function and looking at the spectrum of the corresponding Bogoliubov equations.  This approach provides an intuitive physical insight to the low energy dynamics of the system and is validated through the comparison of our findings with recent Monte Carlo simulations [2].

References

[1] N. Henkel, F. Cinti, P. Jain, G. Pupillo, T. Pohl, Phys. Rev. Lett. 108, 265301 (2012)
[2] S. Saccani, S. Moroni, and M. Boninsegni, Phys. Rev. Lett. 108, 175301 (2012).