Quantum State In Discrete Systems

Quantum state is a basic description of the nature of quantum system and shows many different phenomena from classical system.With the development of experimental technology,people have been able to implement the preparation,control and detection of quantum state in a variety of systems.For macroscopic quantum system,people have realized a lot of macroscopic quantum states,such as the superconductivity,superfluid,Bose-Einstein condensation and so on.For mesoscopic and microcosmic system,it has been prepared many kinds of artificial atoms and the corresponding coupled array.Therefore,the research for the character of the quantum state has important significance in the development quantum theory and practical application.Quantum information science is a cross discipline,which is the combination of quantum physics and information technology.It has played a good role to promote the basic science and technology.Quantum state is the carrier of quantum information.The application of quantum state properties,such as coherence,entanglement and the dynamics,etc,is the basis of quantum information science.Coupled array artificial atoms can be described by a discrete system.Compared with the continuous system,it is easier to analytically analyze and numerically simulate quantum state in a discrete system,therefore more feasible.On the other hand,quantum phase transition is a very important phenomenon in discrete quantum systems.Its essence is that the nature of the ground state change drastically when the parameters change near the critical point.Now quantum phase transition can be observed in a variety of system.The critical behaviors of both Hermitian and non-Hermitian systems show many interesting phenomena.Based on this,we studied the properties of quantum states in several discrete systems,which mainly include the following four parts:1.We present a scheme for transferring quantum state between atom and cavity field in Jaynes-Cummings model in the aid of spin-echo-like technique.It is based on the facts that the atom in a cavity can induce the generation of modified coherent states,which can be shown to be macroscopically distinguishable,and the anti-commutation relation between the Hamiltonian and the z-component Pauli matrix.We show that this scheme is applicable for a class of cavity field states.The application on two-cavity system provides an alternative scheme for preparation of non-local superpositions of quasi-classical light states.Numerical simulation shows that the proposed schemes are efficient.2.We study the dynamics of the Rabi Hamiltonian in the medium coupling regime with |g/?|~0.07,where g is atom-field coupling constant,? is the field frequency,for the quantum state with average photon number (?)~10~4.We map the original Hamiltonian to an effective one,which describes a tight-binding chain subjected to a staggered linear potential.It is shown that the photon probability distribution of a Gaussian-type state exhibits the amplitude modulated Bloch oscillation(BO),which is a superposition of two conventional BOs with a half-BO-period delay between them and is essentially another type of Bloch-Zener oscillation.The probability transition between the two BOs can be controlled and suppressed by the ratio g(?)/?,as well as in-phase resonant oscillating atomic frequency ?(t),leading to multiple zero-transition points.3.We show that a class of exactly solvable quantum Ising models,including transverse-field Ising model and anisotropic XY model,can be characterized as the loops in a two-dimensional auxiliary space.The transverse-field Ising model corresponds to a circle and the XY model corresponds to an ellipse,while other models yield a Cardioid,Limacon,Hypocycloid,and Lissajous curves,et al..It is shown that the variation of the ground state energy density,which is a function of the loop,experiences a non-analytical point when the winding number of the corresponding loop changes.The winding number can serve as a topological quantum number of the quantum phases in the extended quantum Ising model,which sheds some light upon the relation between quantum phase transition and the geometrical order parameter characterizing the phase diagram.4.We study the effect of PT-symmetric imaginary potentials embedded in the two arms of an Aharonov-Bohm interferometer on the transmission phase by finding an exact solution for a concrete tight-binding system.It is observed that the spectral singularity always occurs at k= ±?/2 for a wide range of fluxes and imaginary potentials.Critical behavior associated with the physics of the spectral singularity is also investigated.It is demonstrated that the quasi-spectral singularity corresponds to a transmission maximum and the transmission phase jumps abruptly by ? when the system is swept through this point.Moreover,We find that there exists a pulse-like phase lapse when the imaginary potential approaches the boundary value of the spectral singularity.These studies of basic properties of the quantum states will guide the relevant experiments and applications.