RESUMO
This study is started from a photon-magnon model with a competition effect of the level attraction and repulsion, its Hermiticity is mainly decided by a phase-dependent and asymmetric coupling factor, namelyφ = 0 for Hermitian andÏ=πfor non-Hermitian. Then an extensional study predicts the quantum critical behaviors using an Hermitian and even no-Hermitian photon-spins model with an additional second-order drive. The numerical results firstly indicate that this coupling phaseφcan function the protective effect on quantum phase transitions (QPTs), and the new tricritical points can not only be modulated by this nonlinear drive, but also be influenced by the dissipation and the collective decoherence. Secondly, this competition effect can also induce a reversal of the value of order parameters between the positive and negative. This study can also bring more important results of QPTs toward the issue of symmetry breaking and non-Hermiticity.
RESUMO
A proposal for simulating the Dicke-Lattice model in a mechanics-controlled hybrid quantum system is studied here. An array of coupled mechanical resonators (MRs) can homogeneously interact with a group of trapped Bose-Einstein condensates (BECs) via the gradient magnetic field induced by the oscillating resonators. Assisted by the classical dichromatic radio-wave fields, each subsystem with the BEC-MR interaction can mimic the Dicke type spin-phonon interaction, and the whole system is therefore extended to a lattice of Dicke models with the additional adjacent phonon-phonon hopping couplings. In view of this lattice model with theZ2symmetry, its quantum phase transitions behavior can be controlled by this periodic phonon-phonon interactions in the momentum space. This investigation may be considered as a fresh attempt on manipulating the critical behaviors of the collective spins through the external mechanical method.