Study On The Superradiant Phase Transition And Its Criticality Manipulated By The Optomechanical Nonlinearity

The theory of collective interactions between light and matter and its applica-tions are hot topics in the fields of quantum optics and condensed matter physics.Among them,the Dicke model,which describes the interactions between a single-mode bosonic field and N two-level systems(e.g.,two-level atoms,spin system-s,qubits,etc.),shows many interesting physical phenomena,such as superradiant phase transition,quantum entanglement and quantum chaos,etc.In recent years,the experimental realization of the Dicke superradiant phase transition has stimulat-ed the exploration of their quantum critical effects,including the construction of a hybrid Dicke model based on the cavity optomechanical system.The related results have important applications in many fields,such as quantum computing and quantum information,quantum manipulation and high-precision measurement.Recent years,cavity optomechanics,exploring the nonlinear photon-phonon in-teraction via radiation pressure,has achieved tremendous advances,including the realization of cooling a macroscopic mechanical resonator to ground state,optome-chanically induced transparency,coherent state conversion between cavity and me-chanical modes,and the generation of squeezed light.Moreover,many interesting quantum effects have been predicted when the optomechanical coupling reaches the single-photon strong coupling regime(i.e.,optomechanical coupling surpasses sys-tem decays),such as photon blockade,spectrum of single-photon emission and s-cattering,and phonon induced high-order sidebands.However,it is challenging to realize a strong optomechanical coupling in current experimental setups,which caus-es the quantum manipulation based solely on cavity optomechanics shows some re-strictions.In addition,there are many issues that need to be addressed in the study of superradiant phase transitions of Dicke model.For example,the theory of super-radiant phase transitions based on cavity QED systems is still on debate,and there are still many theoretical and technical difficulties in characterizing quantum phase transition in lattice systems.To address the above issues,in chapter 2 and chapter 3of this paper,we present methods for enhancing the optomechanical nonlinearity and characterizing the superradiant phase transition of lattice systems,respectively,and in chapter 4,we propose a theoretical method to manipulate the superradiant phase transition and its related critical effects using optomechanical nonlinearities in hybrid quantum systems.This thesis mainly consists of three parts:First,we propose a scheme to reach the nonlinear quantum regime of an op-tomechanical system consisting of both linear and quadratic couplings.By applying a driving laser into mechanical mode effectively,the original quadratic optomechanical coupling is reduced to the radiation-pressure form,and this introduced optomechan-ical nonlinearity can be modulated by adjusting the frequency of the driving field.This controllable optomechanical nonlinearity can be enhanced into a strong cou-pling regime,even if the system is initially in the weak-coupling regime.Moreover,the system dissipation can be suppressed effectively,which allows the appearance of phonon sideband and photon blockade effects in the weak-coupling regime.This work offers a new approach to enhancing the optomechanical nonlinearity,which may inspire the exploration of the dual-coupling optomechanical system as well as its applications in modern quantum science.Second,we establish a connection between quantum phase transition and ener-gy band theory in an extended Dicke-Hubbard lattice,where the periodical critical curves modulated by wave number leads to rich equilibrium dynamics.Interestingly,the chiral-symmetry-protected flat band and the localization that it engenders,ex-clusively occurs in the normal phase and disappears in the superradiant phase.This originates from the quantum phase transition induced simultaneous breaking up of the on-site resonance and off-site chiral symmetry of the system,which prohibits the destructive interference for obtaining a flat band.This work offers a method to i-dentify different phases of the lattice via detecting the flat band or simply the related localization in a single cell.On the other hand,we proposed an effective method to manipulate flat band,which is vital for many potential applications in quantum sim-ulation of nondispersive states and diffractionless long-distance light propagation.Third,we propose a scheme to manipulate superradiant phase transitions and their critical effects using optomechanical nonlinearity in a hybrid quantum system.Specifically,we introduce the quadratic optomechanical coupling into a normal Dicke model,and study the effects of this optomechanical nonlinearity on the superradiant phase transition,quantum chaos,entanglement,and excited state quantum phase transition.We find that the superradiant phase transition and entanglement of this system is immune to A~2term.Both the phase transition and entropy have reversed trends when the A~2term is included.Furthermore,we extend the above ground-state quantum phase transition to an excited-state quantum phase transition.By calculating the density of states(DOS)and Peres lattice,we find that,when the auxiliary cavity mode is prepared in a coherent state,the excited-state phase transition can occur in the weak coupling case.In addition,we find that the introduced quadratic coupling effectively lowers the threshold of chaos,and allows the chaos threshold to be photon-number dependent.Considering the input field is prepared in different Fock states,the system transforms between integrable and chaotic,leading to the single-photon triggered chaos.