Bose–Hubbard models with photon pairing in circuit-QED

Benjamín Villalonga Correa, Andreas Kurcz, Juan José García-Ripoll
2013 Journal of Physics B: Atomic, Molecular and Optical Physics  
In this work we study a family of bosonic lattice models that combine an on-site repulsion term with a nearest-neighbor pairing term, $\sum_{< i,j>} a^\dagger_i a^\dagger_j + \mathrm{H.c.}$ Like the original Bose-Hubbard model, the nearest-neighbor term is responsible for the mobility of bosons and it competes with the local interaction, inducing two-mode squeezing. However, unlike a trivial hopping, the counter-rotating terms form pairing cannot be studied with a simple mean-field theory and
more » ... -field theory and does not present a quantum phase transition in phase space. Instead, we show that there is a cross-over from a pure insulator to long-range correlations that start up as soon as the two-mode squeezing is switched on. We also show how this model can be naturally implemented using coupled microwave resonators and superconducting qubits.
doi:10.1088/0953-4075/46/22/224024 fatcat:tr6eqih4zvavhlhtscomgv7sqm