Entanglement Teleportation via Two-Qubit Spin Squeezing Model

Entanglement teleportation via two spins coupled to each other by one axis twisting spin squeezing interaction is investigated. We mainly concentrate on the properties of the channel entanglement, the output entanglement and the teleportation fidelity. It shows that the output entanglement increases linearly with increasing the value of the input entanglement. With the increasing of T, the teleportated entanglement increases sharply from zero to a maximum value and then decreases slowly to zero when the temperature is improved to one threshold value of T _c , and the threshold value of T _c increases with the increasing of the input entanglement. When enlarging the external magnetic, F _a firstly decreases quickly to a minimum value as the critical magnetic field Ω _c is reached, then it increases abruptly to a maximum value and finally it will be a certain value. Besides, the critical external magnetic Ω _c increases when μ is larger. For Ω<Ω _c the value of the average fidelity increases with the increasing of μ, but for Ω>Ω _c the value of it decreases from a maximum value. The influence of T on the average fidelity is similar with μ.     

Dense Coding in a Two-Spin Squeezing Model with Intrinsic Decoherence

Quantum dense coding in a two-spin squeezing model under intrinsic decoherence with different initial states (Werner state and Bell state) is investigated. It shows that dense coding capacity χ oscillates with time and finally reaches different stable values. χ can be enhanced by decreasing the magnetic field Ω and the intrinsic decoherence γ or increasing the squeezing interaction μ, moreover, one can obtain a valid dense coding capacity (χ satisfies χ > 1) by modulating these parameters. The stable value of χ reveals that the decoherence cannot entirely destroy the dense coding capacity. In addition, decreasing Ω or increasing μ can not only enhance the stable value of χ but also impair the effects of decoherence. As the initial state is the Werner state, the purity r of initial state plays a key role in adjusting the value of dense coding capacity, χ can be significantly increased by improving the purity of initial state. For the initial state is Bell state, the large spin squeezing interaction compared with the magnetic field guarantees the optimal dense coding. One cannot always achieve a valid dense coding capacity for the Werner state, while for the Bell state, the dense coding capacity χ remains stuck at the range of greater than 1.     

Quantum Discord Behaviors in Two Qubits Spin Squeezing Model with Intrinsic Decoherence

By taking into account the intrinsic decoherence and the external magnetic field, quantum discord(QD) behaviors in two-qubit spin squeezing model are investigated in detail. It is found that the magnitude of quantum discord is strongly dependent on the initial states, the squeezing interaction μ, the magnetic field Ω and the purity r of initial states. With t → ∞, one can obtain the steady quantum discord (SQD) value, the environmental decoherence cannot entirely destroy the quantum correlation. Based on the analysis of the SQD, the conditions about the existence of SQD are obtained with different initial states. Varying the parameters μ, Ω and r not only can weaken the effects of decoherence but also can improve the magnitude of QD and SQD. The effects of the parameters μ and Ω on the QD and SQD display so different and complicated features that one cannot get an uniform law about them, while the values of QD and SQD are improved with increasing r. Properly tuning the parameters μ, Ω and r, one can obtain a larger value of QD or SQD.     

Various Quantum Correlations in Two-Qubit Two-Axis Spin Squeezing Model in Thermal Equilibrium under an External Magnetic Field

This paper investigates the influence of the spin squeezing parameter γ, the external magnetic field B and the temperature T on the concurrence (C), the quantum discord (QD), and the geometric quantum discord (GQD) in the two-qubit two-axis spin squeezing model in thermal equilibrium under an external magnetic field. The results show that the spin squeezing parameter γ has a positive effect on all three correlations. When the system is in the ground state, the external magnetic field B has a weakening effect on the three types of quantum correlations. Particularly, the spin squeezing parameter can be used to alleviate the destructive effect of the magnetic field on the geometric quantum discord. At a relatively high temperature, the externally applied magnetic field B helps enhance the quantum discord (QD). Further, the quantum discord is more robust than concurrence, and thus is more suitable for use as a quantum resource in information processing.     

Thermal Entanglement Between Atoms in the Four-Cavity Linear Chain Coupled by Single-Mode Fibers

Natural thermal entanglement between atoms of a linear arranged four coupled cavities system is studied. The results show that there is no thermal pairwise entanglement between atoms if atom-field interaction strength f or fiber-cavity coupling constant J equals to zero, both f and J can induce thermal pairwise entanglement in a certain range. Numerical simulations show that the nearest neighbor concurrence C_AB is always greater than alternate concurrence C_AC in the same condition. In addition, the effect of temperature T on the entanglement of alternate qubits is much stronger than the nearest neighbor qubits.     

<Emphasis Type="Italic">SU</Emphasis>(2) Non-Abelian Photon

In this paper, we have proposed S U(2) non-Abelian electromagnetism gauge theory. In the theory, photon has self-interaction and interaction between them, which can explain photon entanglement phenomenon in quantum information. Otherwise, we find there are three kinds photons γ ⁺, γ ^? and γ ⁰, they have electric charge + e _γ , ? e _γ and 0, respectively, these prediction are accordance with some experiment results.     

A Liouville-type Theorem for Schrödinger Operators

In this paper we prove a sufficient condition, in terms of the behavior of a ground state of a symmetric critical operator P ₁, such that a nonzero subsolution of a symmetric nonnegative operator P ₀ is a ground state. Particularly, if P _j : = ?Δ + V _j , for j = 0,1, are two nonnegative Schrödinger operators defined on \(\Omega\subseteq \mathbb{R}^d\) such that P ₁ is critical in Ω with a ground state φ, the function \(\psi\nleq 0\) is a subsolution of the equation P ₀ u = 0 in Ω and satisfies \(\psi_+\leq C\varphi\) in Ω, then P ₀ is critical in Ω and \(\psi\) is its ground state. In particular, \(\psi\) is (up to a multiplicative constant) the unique positive supersolution of the equation P ₀ u = 0 in Ω. Similar results hold for general symmetric operators, and also on Riemannian manifolds.     

Nonclassical Properties for Two Coupled N-Two-Level Atom and a Single Two-Level Atom Under an External Magnetic Field

We study the interaction between a single two-level atom and N two-level atoms under the effect of a uniform magnetic field. The exact solution is obtained and the expectation value of the time-dependent quantum operators calculated using the Block state (the generalized coherent state). We discuss numerically the atomic inversion where the phenomenon of collapse and revival is observed. The change in the value of the atomic angle plays a role in variance squeezing, where it is pronounced for ?? = π/3. Entropy squeezing is discussed and occurred in the first quadrature. The degree of entanglement through linear entropy is examined where the system shows partial entanglement and at a certain value of parameters displays nearly maximum entanglement.     

The Precision of Parameter Estimation for Dephasing Model Under Squeezed Reservoir

We study the precision of parameter estimation for dephasing model under squeezed environment. We analytically calculate the dephasing factor γ(t) and obtain the analytic quantum Fisher information (QFI) for the amplitude parameter α and the phase parameter ?. It is shown that the QFI for the amplitude parameter α is invariant in the whole process, while the QFI for the phase parameter ? strongly depends on the reservoir squeezing. It is shown that the QFI can be enhanced for appropriate squeeze parameters r and θ. Finally, we also investigate the effects of temperature on the QFI.     

Large polarization squeezing in non-degenerate parametric amplification of coherent radiation

Polarization squeezing is shown to occur in non-degenerate parametric amplification of coherent light and the degree of squeezing at interaction time T can be as large as 1 ? e^-2T. This gives 86.4% polarization squeezing for T = 1 and 98.2% for T = 2. One simple case when this occurs is on taking initially plane polarized light having equal amplitudes in the two modes that finally has equal intensities of two circular polarizations. This suggest the experimental settings of parameters to achieve this extent of polarization squeezing in coherent light.     

New omega vortex identification method

A new vortex identification criterion called W-method is proposed based on the ideas that vorticity overtakes deformation in vortex.The comparison with other vortex identification methods like Q-criterion and λ_2-method is conducted and the advantages of the new method can be summarized as follows:(1) the method is able to capture vortex well and very easy to perform;(2) the physical meaning of W is clear while the interpretations of iso-surface values of Q and λ_2 chosen to visualize vortices are obscure;(3)being different from Q and λ_2 iso-surface visualization which requires wildly various thresholds to capture the vortex structure properly, W is pretty universal and does not need much adjustment in different cases and the iso-surfaces of W=0.52 can always capture the vortices properly in all the cases at different time steps, which we investigated;(4) both strong and weak vortices can be captured well simultaneously while improper Q and λ_2 threshold may lead to strong vortex capture while weak vortices are lost or weak vortices are captured but strong vortices are smeared;(5) W=0.52 is a quantity to approximately define the vortex boundary. Note that, to calculate W, the length and velocity must be used in the non-dimensional form. From our direct numerical simulation, it is found that the vorticity direction is very different from the vortex rotation direction in general 3-D vortical flow,the Helmholtz velocity decomposition is reviewed and vorticity is proposed to be further decomposed to vortical vorticity and non-vortical vorticity.     

Method of determination of muon-catalyzed fusion parameters in H-T mixture

A method for measurement of the muon-catalyzed fusion (μCF) parameters in an H-T mixture is proposed. The kinetics of the μ-atomic and μ-molecular processes preceding the pt reaction in the ptμ molecule is described. Analytical expressions are obtained for the yields and time distributions of γ quanta and conversion muons formed in nuclear fusion reactions in ptμ molecules. It is shown that information on the desired parameters μCF can be found from the joint analysis of the time distributions of γ quanta and conversion muons to be obtained in experiments with the H-T mixture at three (or more) appreciably different atomic concentrations of tritium. The experiments with the H-T mixture at the meson facility PSI (Switzerland) were optimized to gain precise information about the desired μCF parameters.     

Quantum Entanglement and Correlation Lengths of a S-wave Superconductors in the Presence of a Weak Constant External Potential

By considering a s-wave Bardeen-Cooper-Schrieffer superconductor, as a many body system, subject to a weak constant external potential, U, using perturbed linearized Gorkov equations at zero temperature and calculating perturbed Green’s functions up to the first approximation, we obtain the two-particle space-spin density matrix of the system. Then, we investigate the effect of the potential on bipartite entanglement (via concurrence) of electron spins of a Cooper pair and also quantum discord in terms of the potential and the relative distance of electrons of a Cooper pair, r. At some fixed values of r, concurrence is zero and does not change until U increases and receives to a special value. Specially, quantum entanglement length and quantum correlation length (in which quantum discord becomes zero) with respect to the potential are derived. We result that by increasing the potential, these lengths are increased. At higher values of U, quantum correlation length is not very sensitive to changes in U. Finally, the relation between these lengths is given.     

Observational Data Fitting to Constrain Variable Modified Chaplygin Gas in the Background of Horava-Lifshitz Gravity

FRW universe in Horava-Lifshitz (HL) gravity model filled with a combination of dark matter and dark energy in the form of variable modified Chaplygin gas (VMCG) is considered. The permitted values of the VMCG parameters are determined by the recent astrophysical and cosmological observational data. Here we present the Hubble parameter in terms of the observable parameters Ω _{d m0}, Ω _{v m c g0}, H ₀, redshift z and other parameters like α, A, γ and n. From Stern data set (12 points), we have obtained the bounds of the arbitrary parameters by minimizing the χ ² test. The best-fit values of the parameters are obtained by 66 %, 90 % and 99 % confidence levels. Next due to joint analysis with BAO and CMB observations, we have also obtained the bounds of the parameters (A, γ) by fixing some other parameters α and n. The best fit value of distance modulus μ(z) is obtained for the VMCG model in HL gravity, and it is concluded that our model is perfectly consistent with the union2 sample data.     

Tripartite Entanglement in an Atom-Cavity-Optomechanical System

We investigate tripartite entanglement in an atom-cavity-optomechanical system consisting of a two-level atom coupled to a cavity with an oscillating mirror at one end. The maximally entangled state between the atom, the field and the oscillating mirror can be prepared in the ideal case. It is shown that the atomic coherent angle that is relatively small makes tripartite entanglement much stronger against dissipative effects in a finite time interval. The parameter k plays a very important role in the oscillating frequency of the tripartite entanglement. More importantly, the π-tangle decays more quickly with the increasing of spontaneous emission rate γ and mean photon number n.     

Entangled Two Two-Level Atom in the Presence of External Classical Fields

In this contribution, we investigate a TTLAs (two two-level atoms) in interaction with an electromagnetic field in presence of the external classical fields. The general solution of the time evolution operator is obtained and used to derive the density matrix operator. The temporal evolution of the atomic inversion, the degree of entanglement measured by the negativity, as well as the single atom entropy squeezing are discussed. We consider the atomic system at either the upper or Bell states, while the field in the coherent state. It has been shown that the coupling parameter g (the coupling of the external classical fields) gets more effective for the case in which the g is not equal to zero. Also for a strong coupling parameter g the superstructure phenomenon can be reported. The results shown that for increase the value of the classical external fields parameter leads to the entanglement between the atoms and the fields gets stronger. Also it has shown that for specific value of the classical external fields the system never reaches the pure state except during the revival periods.     

The quest for <Emphasis Type="Italic">μ</Emphasis> → <Emphasis Type="Italic">e</Emphasis><Emphasis Type="Italic">γ</Emphasis>: present and future

The quest for μ → eγ is one of the most important endeavors to search for New Physics beyond the Standard Model. In this talk I will review the current status of the experimental searches by the MEG Collaboration at PSI. I will also present a study of the experimental limiting factors that will define the ultimate performances, and hence the sensitivity, in the search for μ → eγ with continuous muon beams of extremely high rate (one or even two orders of magnitude larger than the present beams), whose construction is under consideration for the next decade.     

Generation and Preparation of the Sustained Optimal Entropy Squeezing State of a Motional Atom Inside Vacuum Cavity

Considering two two-level atoms initially in Bell state, we send one atom into a vacuum cavity while leaving the other outside, and consider the motion of atom inside the cavity. Using quantum information entropy squeezing theory, the time evolution of the entropy squeezing factor of atom inside the cavity is discussed for two cases, i.e., before and after performing rotation operations and measuring atom outside, the influences of the field mode structure and atomic motions on the atomic entropy squeezing are evaluated. It is shown that atom inside the cavity has no entropy squeezing phenomenon before operating atom outside the cavity. However, the optimal entropy squeezing phenomenon of period T = 2π/p emerges and constant entropy squeezing phenomenon can occur by adjusting rotation operation to R(π/4), and setting the field mode structure parameter 0 < p < 50. In particular, if choosing p > 50, a sustained optimal entropy squeezing state (SOESS) can be generated. We also present the schematic circuit diagram of preparation of SOESS. Our proposal provides a possible way for the initial decoherent state recovering into sustained maximal coherent superposition state of single atom in the quantum noise environment.     

Entanglement of an <Emphasis Type="Italic">su</Emphasis>(1, 1) Quantum System Interacting with a Single Two-Level Atom in the Presence of Damping Terms

We discuss the effect of damping on a quantum system specifically described by the su(1, 1) Lie algebra and interacting with a two-level atom in the presence of external classical su(1, 1) terms. We obtain the numerical solution of the associated differential equations and discuss in detail several statistical aspects, atomic inversion, squeezing phenomena, and negativity. In addition, we analyze the effect of the decay parameter and the external classical su(1, 1) terms on the population inversion and purity. Finally, we examine the entropy squeezing and the degree of entanglement for some values of the damping and detuning parameters.     

String order and degenerate entanglement spectrum of S = 1 / 2 and S = 1 Heisenberg bond-alternating chains

Generalized string orders and entanglement spectrum of S = 1/2 and S = 1 Heisenberg bond-alternating chains have been investigated by the infinite time-evolving block decimation (iTEBD) method. Generalized string order parameters with appropriate θ are capable of distinguishing all the topological phases. Central charges c ? 1 and critical exponents β ?1/12 indicate all the topological QPTs belong to the Gaussian universality class. Interestingly, odd- and even-fold degeneracies of the entanglement spectrum are observed. Even-fold (doubly) degenerate entanglement spectra and the typical two-fold degenerate lowest-lying level are found to exist in both the spin-1/2 dimer and the S = 1 Haldane phases. However, odd-fold degenerate entanglement spectra with three-fold degenerate lowest-lying level are observed in both the S = 1 dimer and the S = 2 Haldane phase. The degeneracy of the lowest-lying entanglement spectrum level, which can be understood by entanglement spectra in the dimer limit (J ₁ = 0), is adopted to estimate the lowest boundary of the bipartite entanglement. The entanglement spectrum and the generalized string orders are valuable for uncovering the underlying features of these symmetry-protect topological (SPT) states. Similar entanglement spectrum shows that the S = 1 (S = 2) Haldane phase is essentially the same as the S = 1/2 (S = 1) dimer phase.