A proposal for simulating the Dicke-Lattice model in a mechanics-controlled hybrid quantum system is studied here. Where an array of coupled mechanical resonators (MRs) homogeneously interact with a group of trapped Bose-Einstein condensates (BECs) through the gradient magnetic field induced by the oscillating resonators. Assisted by the classical dichromatic radio-wave (RW) fields, each subsystem with a pair of 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 an additional adjacent phonon-phonon hopping couplings. For this lattice model with the Z2 symmetry, its quantum phase transitions (QPTs) behavior can be controlled by this periodic phonon-phonon interaction in the momentum space. This investigation may be considered as a fresh attempt on manipulating the critical behavior of the collective spins through the external mechanics method.

Optomechanical system develops a significant breakthrough in quantum science area, especially it can further improve the precision and sensitivity of the measurement in quantum region. We here study a feasible optomechanical proposal in a hybrid quantum system, which can ensure a quantum sensor with a further enhanced sensitivity. With the joint assistance of microwave (MW) modifying and optical parametric amplification (OPA), the effective line width of this supermode is further reduced around the critical point, and it can therefore results in a resolvable spectrum to display a much weaker mechanical frequency shift, which is perhaps induced by a tiny mass or charged particles in this system. We also hope there might be some useful applications for this attempt in the area of quantum measurement.

We study a potential hybrid quantum system with a plasmonic nanocavity coupled to a vibrating mode of single molecule and another optical cavity mode. To explore some important and valuable applications in quantum physics, we discuss and estimate several different applications with respect to the plasmon-mediated quantum interface, the plasmon-assisted engineering of two-mode continuous-variable entanglement, and pursuing an indirect and ultrastrong molecule-photon cooperativity. In addition, governed by the relation of symmetry breaking and quantum phase transitions (QPTs), the single-molecule induced QPTs is also studied in this tripartite hybrid quantum system. This theoretical study can strongly support the potential applications of this hybrid system in the field of quantum information processing (QIP). It is believed that our investigation on molecule-plasmon-photon hybridization can not only open a new avenue towards quantum manipulations, but also provide a fresh and reliable platform to carry out many applications with high efficiencies.

We here study a hybrid quantum system of one solid-state electronic spin coupled to a mechanical resonator (MR) using the crystal strain, with the purpose of engineering the mesoscopic spin-phonon entangled cat state. The feature of this work to be mentioned is that it proposes a different and feasible method to achieve the entanglement, especially with the higher fidelity. This scheme mainly contains two steps, namely the coherent population trapping (CPT) initialization and large-detuning evolution (LDE). By taking all of the adverse decoherence factors into our considerations,the numerical simulations indicate that its fidelity can reach more than 0.995 (or 0.999)
when the spin-mechanical coupling strength is 10 (or 100) times larger than spin dephasing and mechanical resonator dissipation rate, respectively. Because of the cooperation of CPT and LDE, this proposal also exhibits a considerable robustness for engineering the entangled cat state, and which may be considered as a general attempt that may be suitable for different systems.