Liu Tang-Kun

Quantum wavefunctions and fluctuations of mesoscopic RLC circuit

The quantum wavefunctions and the corresponding energy levels of a RLC (Resistance-Inductance-Capacity) electric circuit are obtained by using canonical quantization method and unitary transformation from the classical equation of motion. The quantum fluctuations of charge and current in an arbitrary eigenstate of the system have also been given as well as the uncertainty relation. It is showed that even if at 0 K charge and current in the circuit exhibit quantum fluctuations, which originates from fluctuations of zero point vibrations of the system.

Sudden Death, Birth and Stable Entanglement in a Two-Qubit Heisenberg XY Spin Chain

1College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China 2Department of Physics, Huazhong University of Science and Technology, Wuhan 430074, China 3State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, China (Dated: August 31, 2008) Abstract Taking the decoherence effect due to population relaxation int account, we investigate the entanglement properties for two qubits in the Heisenberg XY interaction a nd subject to an external magnetic field. It is found that the phenomenon of entanglement sudden death (E SD) as well as sudden birth(ESB) appear during the evolution process for particular initial states . The influence of the external magnetic field and the spin environment on ESD and ESB are addressed in detail. I t is shown that the concurrence, a measure of entanglement, can be controlled by tuning the parameters of the spin chain, such as the anisotropic parameter, external magnetic field, and the coupling streng th with their environment. In particular, we find that a critical anisotropy constant exists, above which ESB vanishes while ESD appears. It is also notable that stable entanglement, which is independent of differen t initial states of the qubits, occurs even in the presence of decoherence.Taking the decoherence effect due to population relaxation into account, we investigate the entanglement properties for two qubits in the Heisenberg XY interaction and subject to an external magnetic field. It is found that the phenomenon of entanglement sudden death ( ESD) as well as sudden birth ( ESB) appear during the evolution process for particular initial states. The influence of the external magnetic field and the spin environment on ESD and ESB are addressed in detail. It is shown that the concurrence, a measure of entanglement, can be controlled by tuning the parameters of the spin chain, such as the anisotropic parameter, external magnetic field, and the coupling strength with their environment. In particular, we find that a critical anisotropy constant exists, above which ESB vanishes while ESD appears. It is also notable that stable entanglement, which is independent of different initial states of the qubits, occurs even in the presence of decoherence.

Master equation describing the diffusion process for a coherent state

The evolution of a pure coherent state into a chaotic state is described very well by a master equation, as is validated via an examination of the coherent states evolution during the diffusion process, fully utilizing the technique of integration within an ordered product (IWOP) of operators. The same equation also describes a limitation that maintains the coherence in a weak diffusion process, i.e., when the dissipation is very weak and the initial average photon number is large. This equation is dρ/ dt = −κ[a+aρ −a+ρa − aρa+ + ρaa+]. The physical difference between this diffusion equation and the better-known amplitude damping master equation is pointed out.

Entanglement evolution in an anisotropic two-qubit Heisenberg XYZ model with Dzyaloshinskii–Moriya interaction

This paper investigates the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of Dzyaloshinskii–Moriya interaction. The time evolution of the concurrence is studied for the initial pure entangled states cos θ |00 + sin θ |11 and cos |01 + sin |10 at zero temperature. The influences of Dzyaloshinskii–Moriya interaction D, anisotropic parameter Δ and environment coupling strength γ on entanglement evolution are analysed in detail. It is found that the effect of noisy environment obviously suppresses the entanglement evolution, and the Dzyaloshinskii–Moriya interaction D acts on the time evolution of entanglement only when the initial state is cos |01 + sin |10. Finally, a formula of steady state concurrence is obtained, and it is shown that the stable concurrence, which is independent of different initial states and Dzyaloshinskii–Moriya interaction D, depends on the anisotropic parameter Δ and the environment coupling strength γ.

Entanglement Dynamics of Two-Qubit System in Different Types of Noisy Channels

In this paper, we study entanglement dynamics of a two-qubit extended Werner-like state locally interacting with independent noisy channels, i.e., amplitude damping, phase damping, and depolarizing channels. We show that the purity of initial entangled state has direct impacts on the entanglement robustness in each noisy channel. That is, if the initial entangled state is prepared in mixed instead of pure form, the state may exhibit entanglement sudden death (ESD) and/or be decreased for the critical probability at which the entanglement disappear.

Entanglement in One-Dimensional Random XY Spin Chain with Dzyaloshinskii–Moriya Interaction

The impurities of exchange couplings, external magnetic fields and Dzyaloshinskii–Moriya (DM) interaction considered as Gaussian distribution, and the entanglement in one-dimensional random XY spin systems is investigated by the method of solving the different spin-spin correlation functions and the average magnetization per spin. The entanglement dynamics at central locations of ferromagnetic and antiferromagnetic chains have been studied by varying the three impurities and the strength of DM interaction. (i) For the ferromagnetic spin chain, the weak DM interaction can improve the amount of entanglement to a large value, and the impurities have the opposite effect on the entanglement below and above critical DM interaction. (ii) For the antiferromagnetic spin chain, DM interaction can enhance the entanglement to a steady value. Our results imply that DM interaction strength, the impurity and exchange couplings (or magnetic field) play competing roles in enhancing quantum entanglement.C. J. Shan, W. W. Cheng, T. K. Liu, Y. X. Huang, and H. Li College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China (Dated: August 27, 2008) Abstract The impurities of exchange couplings, external magnetic fie lds and Dzyaloshinskii–Moriya (DM) interaction considered as Gaussian distribution, the entanglem ent in one-dimensional random XY spin systems is investigated by the method of solving the different spinspin correlation functions and the average magnetization per spin. The entanglement dynamics at central l oc tions of ferromagnetic and antiferromagnetic chains have been studied by varying the three impurities and the strength of DM interaction. (i) For ferromagnetic spin chain, the weak DM interaction can improve the amount of entanglement to a large value, and the impurities have the opposite effect on the entanglem ent below and above critical DM interaction. (ii) For antiferromagnetic spin chain, DM interaction can e nhance the entanglement to a steady value. Our results imply that DM interaction strength, the impurity an d exchange couplings (or magnetic field) play competing roles in enhancing quantum entanglement.The impurities of exchange couplings, external magnetic fields and Dzyaloshinskii--Moriya (DM) interaction considered as Gaussian distribution, the entanglement in one-dimensional random

Entropy evolvement properties in a system of Schrödinger cat state light field interacting with two entangled atoms

XY

Entanglement Dynamics and Bell Violations of Two Atoms in Tavis–Cummings Model with Phase Decoherence

spin systems is investigated by the method of solving the different spin-spin correlation functions and the average magnetization per spin. The entanglement dynamics at central locations of ferromagnetic and antiferromagnetic chains have been studied by varying the three impurities and the strength of DM interaction. (i) For ferromagnetic spin chain, the weak DM interaction can improve the amount of entanglement to a large value, and the impurities have the opposite effect on the entanglement below and above critical DM interaction. (ii) For antiferromagnetic spin chain, DM interaction can enhance the entanglement to a steady value. Our results imply that DM interaction strength, the impurity and exchange couplings (or magnetic field) play competing roles in enhancing quantum entanglement.

Quantum dense coding using a peculiar tripartite entangled state

The field entropy can be regarded as a measurement of the degree of entanglement between the light field and the atoms of a system which is composed of two-level atoms initially in an entangled state interacting with the Schr?dinger cat state. The influences of the strength of light field and the phase angle between the two coherent states on the field entropy are discussed by using numerical calculations. The result shows that when the strength of light field is large enough the field entropy is not zero and the degrees of entanglement between the atoms and the three different states of the light fields are equal. When the strength of the light field is small, the degree of entanglement is maximum in a system of the two entangled atoms interacting with an odd coherent state; it is intermediate for a system of the two entangled atoms interacting with the Yurke?Stoler coherent state and it is minimum in a system of the two entangled atoms interacting with an even coherent state.

Entanglement properties in a system of a pairwise entangled state

X iv :0 80 8. 37 09 v1 [ qu an tph ] 27 A ug 2 00 8 Entanglement dynamics and Bell Violations of two atoms in Tavis-Cummings model with phase decoherence ∗ C. J. Shan†,1 W. W. Cheng, 1 T. K. Liu‡,1 D. J. Guo, 2 and Y. J. Xia2 1College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China 2Department of Physics, Qufu Normal University, Qufu 273165, China (Dated: August 27, 2008) Abstract Considering the dipole-dipole coupling intensity between two atoms and the field in the Fock state, the entanglement dynamics between two atoms that are initially entangled in the system of two two-level atoms coupled to a single mode cavity in the presence of phase decoh erence has been investigated. The two-atom entanglement appears with periodicity without considerin g phase decoherence, however, the phase decoherence causes the decay of entanglement between two atoms, with the increasing of the phase decoherence coefficient, the entanglement will quickly become a constan t v lue, which is affected by the two-atom initial state, Meanwhile the two-atom quantum state will forev er stay in the maximal entangled state when the initial state is proper even in the presence of phase decoher enc . On the other hand, the Bell violation and the entanglement does not satisfy the monotonous relation, a large Bell violation implies the presence of a large amount of entanglement under certain conditions, whi le a large Bell violation corresponding to a little amount of entanglement in certain situations. However, the violation of Bell-CHSH inequality can reach the maximal value if two atoms are in the maximal entangled st ate, or vice versa.Considering the dipole-dipole coupling intensity between two atoms and the field in the Fock state, the entanglement dynamics between two atoms that are initially entangled in the system of two two-level atoms coupled to a single mode cavity in the presence of phase decoherence has been investigated. The two-atom entanglement appears with periodicity without considering phase decoherence, however, the phase decoherence causes the decay of entanglement between two atoms, with the increasing of the phase decoherence coefficient, the entanglement will quickly become a constant value, which is affected by the two-atom initial state. Meanwhile the two-atom quantum state will forever stay in the maximal entangled state when the initial state is proper even in the presence of phase decoherence. On the other hand, the Bell violation and the entanglement do not satisfy the monotonous relation, a large Bell violation implies the presence of a large amount of entanglement under certain conditions, while a large Bell violation corresponds to a little amount of entanglement in certain situations. However, the violation of Bell-CHSH inequality can reach the maximal value if two atoms are in the maximal entangled state, or vice versa.