| Quantum mechanics is developed and established in the field of microcosmic production.Compared with the classical physics which can only describe the motion of matter under macroscopic conditions,quantum mechanics is a fundamental change in the description of the motion forms and laws of matter.The advent of quantum mechanics has made modern physics an unprecedented success.Based on quantum mechanics,scientists have successfully explained the microscopic particle dynamics of atoms and molecules as well as the physical phenomena such as Einstein condensation at extremely low temperatures.Although the proposal of quantum mechanics has made brilliant achievements,it has been followed by fierce debates,among which the concepts of quantum entanglement,bell non-locality,and entropy uncertainty relationship,which were regarded as paradoxes at that time,which have attracted more and more attention and extensive research at this stage.Entanglement is a fundamental and wonderful feature of quantum mechanics and a special kind of quantum correlation,which embodies the non-locality of quantum states and leads to the violation of bell inequality.Moreover,it is widely used in quantum information,quantum computing,quantum cryptography,quantum teleportation,quantum coding and other fields.In addition,the uncertainty principle is one of the basic principles of quantum mechanics,which indicates the limitation of the precise measurement of two noncommutative observable measures at the same time,and is used to measure the uncertainty contained in the state of the physical system.People use various relations to describe the uncertainty principle,they are called the uncertainty relations.In recent years,the uncertainty of entropy plays an important role in quantum computing and quantum communication.When dealing with the Dicke model,people assume that it is composed of multiple atomic systems and use the H-P transformation method forresearch and analysis,but the number of atoms is required to be infinite.We find that the spin-coherent state variational method does not require this assumption,that there is no limit on the number of atoms.As we all know,quantum systems inevitably interact with the surrounding environment,resulting in quantum decoherence,which is not conducive to the completion of quantum information processing.Therefore,the study on the dynamic behavior of quantum systems can make better use of quantum resources.Based on the quantum system in which two particles are coupled with different environments,the dynamic behaviors such as entanglement,quantum correlation,bell-CHSH inequality and entropy uncertainty relation are discussed in this paper.The main research work is as follows:1.We study in the present paper the multiple stable-states of two different atoms in a single-mode quantum cavity by means of variational method.Eigenenergies and states are obtained analytically in the optic coherent state of cavity field.The ground state displays known Dicke phase transition from normal to superradiant phases at the critical value of atom-field coupling.Rich phase diagrams including the stable excited states are presented respectively for two atoms with different level spaces and atom-field couplings.By adjusting the ratios of two-atom couplings or level spaces one atom can be in the normally populated state while the other is in the inversely populated state.We also observe the stimulated radiation from the inversely populated state.Particularly the normal and stimulated radiations are interchangeable respectively for two atoms.Moreover the maximally entangled state is generated with two identical atoms.2.We in this paper study quantum correlations for two neutral spin-particles coupled with a single-mode optical cavity through the usual magnetic interaction.Two-spin entangled states for both antiparallel and parallel spin-polarizations are generated under the photon coherent-state assumption.Based on the quantum master equation we derive the time-dependent quantum correlation of Clauser-Horne-Shimony-Holt(CHSH)type explicitly in comparison with the well known entanglement measure concurrence.In the two-spin singlet state,which is recognized as one eigenstate of the system,the CHSH correlation and concurrence remain in their maximum values invariant with time and independent of the average photon-numbers either.The correlation varies periodically with time in the general entangled-states for the low average photon-numbers.When the photon number increases to a certain value the oscillation becomes random and the correlations are suppressed below the Bell bound indicating the decoherence of the entangled states.In the high photon-number limit the coherence revivals periodically such that the CHSH correlation approaches the upper bound value at particular time points associated with the cavity-field period.3.Based on a simple cavity-engineered architecture,we investigate in this paper the dynamics of quantum-memory assisted entropic uncertainty relation for two qubits initially prepared in a generic Werner state.The effects of cavity decay rate,qubit-cavity and cavity-cavity couplings on the uncertainty are revealed.It is found that the damped oscillation of uncertainty can be induced by the increase of two types of coupling strength mentioned above.We demonstrate that the maximum value of uncertainty depends on the purity of initial state,and the uncertainty can be increased or decreased,which is related to the threshold value of coupling strength between two cavities.In agreement with the recent observation,an asynchronous relation between uncertainty and mixedness is found during the initial time evolution.4.We investigate the dynamic creation of quantum correlation and entropic uncertainty relation(EUR)in a system of two non-interacting qubits,which are initially prepared in a classically correlated state and subject to the independent radiation in an isotropic or anisotropic photonic bandgap(PBG)crystal environment.It is shown that the detuning condition and environmental structure play a crucial role in controlling the emergence of geometric quantum discord(GQD)and one-norm GQD.In addition,the remarkable similarities and differences for quantum correlation in two PBGenvironments are also analyzed in detail.Finally,we explore the time evolution of EUR in our model under the influence of PBG environment and present some interesting results.5.We investigate in this paper measurement-induced disturbance(MID)and Negativity in a two-spin-qutrit model by considering the influence of the external magnetic field,nonlinear coupling parameter,the uniaxial field and temperature.It is shown that all of these parameters play a significant role in Negativity and MID.We make an explicit comparison between the Negativity and MID and disclose some interesting results.By the way,we find that Negativity is a better measure than MID to detect the sudden point in a finite temperature,which is obviously different from the previous findings. |
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