Atom-Lignt Collective Dynamics And Quantum Phase Transition Inside The Micro-Cavity

Recent experimental and thereotical breakthrough of ultracold quantum gas has opened up a new avenue towards exploring quantum many-body physics.The experimental feasibility to engineer lattice geometry and the tunability of interaction strength make the ultracold atoms in optical lattices an excellent simulator of a vast kind of condensed matter phenomena.However,the experiments are mostly limited to short range collisional interactions,which hinders the further investigation of complex quantum phenomena originating from long-range interactions.Fortunately,the dynamical atom-photon coupling enhanced by an optical cavity offers a viable solution to overcome this drawback.Through exchanging photons with a radiation field,ultracold atoms loaded inside an optical cavity can establish an indirect long-range interaction.Another advantage of atom-cavity system is its capability to unprecedentedly highlight the dynamical property of photons,which contributes to possibilities of probing novel collective light-matter phases.Moreover,utilizing this setup,the research group of T.Essilinger has faithfully realized an infinite-range interaction between lattice bosons,and various quantum phases from competing short-and long-range interactions are observed.This progress paves a way to further understand atom-photon collective dynamics.The present thesis mainly investigates various collective dynamics of light and atoms inside a micro cavity,with special focus on quantum phase transitions of light and matter field.The main resuls are orgnized as follows:?1?We investigate the ground-and excited-state properties of a two-mode Dicke model.By varying the atom-photon coupling strength,the system exhbit rich phase diagrams,including the normal phase without collective excitations,the electric and magnetic superradiant phase,and electromagnetic superradiant phase.We analyze the symmetry and excitation spectrum of the system,and reveal a hidden continuous U?1?symmetry when the two atom-photon coupling strength are equal.If further increasing the coupling strength,the system enters the U?1?-broken electromagnetic superradiant regime,where a gapless excitation spectra?the Nambu-Goldstone mode?emerges.?2?We find that the interaction between single mode quantum light field and three-level particles support a unitary-invariant phase?.The relations between this phase and the system symmetry are revealed.The phase-dependent symmetries includesZ₂^E,Z₂^M,trivial U?1?,and nontrivial U?1?.The breaking of these symmetries respectively corresponds to four different phases:the electric superradiant phase,the magnetic superradiant phase,and the electromagnetic superraidant phase.A possible experimental implementation based on ultra-cold atoms is offered,which has a distinct advantage that the relative parameters can be tuned independently over a wide range.?3?By combining Rydberg atoms and cavity arrays together,we derive an extended-Jaynes-Cummings-Lattice model,which supports long-range interactions between dressed photons.A series of novel quantum phases induced by these long-range interactions are revealed.?4?To further understand the relation between lattice photons and Bose-Hubbard model,we proposed a new-type Dicke-lattice model.Since this model incorporates all of the counter-rotating terms in the interaction process,it applies to the whole parameter regions including ultra-strong coupling regime.Similar to the Bose-Hubbard model,the Dicke lattice model also support Mott-lobe ground-state structures and Mott-superfluid phase transitions.Interestingly,the Mott-lobe stroctures crucially depend on the atom number inside each cavity.?5?We study magnetic orders of fermions under cavity-assisted Raman couplings in a one-dimensional lattice at half filling.The cavity-enhanced atom-photon coupling introduces a dynamic long-range interaction between the fermions,which competes with the short-range on-site interaction and leads to a variety of magnetic orders.Adopting a numerical density-matrix-renormalization-group method,we investigate the various magnetic orders and map out the steady-state phase diagram.Interestingly,as all the phase transitions take place outside the superradiant regime,the magnetic orders are associated with cavity-_eld uctuations with a vanishing number of photons on the mean-field level.