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.     

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.     

Quantification of Quantum Entanglement in a Multiparticle System of Two-Level Atoms Interacting with a Squeezed Vacuum State of the Radiation Field

We quantify multiparticle quantum entanglement in a system of N two-level atoms interacting with a squeezed vacuum state of the electromagnetic field. We calculate the amount of quantum entanglement present among one hundred such two-level atoms and also show the variation of that entanglement with the radiation field parameter. We show the continuous variation of the amount of quantum entanglement as we continuously increase the number of atoms from N = 2 to N = 100. We also discuss that the multiparticle correlations among the N two-level atoms are made up of all possible bipartite correlations among the N atoms.     

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.     

Thermal Entanglement Properties in two Kinds of Two-qubit Spin Squeezing Model

Using the concurrence (C) criterion, we investigate the thermal entanglement properties in two-qubit spin squeezing model for two kinds of squeezing interaction: one-axis twisting model (OATM) and two-axis countertwisting model (TACM) with a transverse field. To the OATM, in the limit case of T→0, the ground state entanglement is initially increased from zero to the maximum value, then decreased in a period of time and suddenly disappeared finally with further enhancing the external magnetic field Ω. One interesting thing is that instead of decaying slowly to zero the entanglement is sudden disappeared with further enhancing Ω or μ (the spin squeezing interaction in X direction), and decreasing the parameter μ or Ω can obviously broaden the scope of entanglement exists. For the finite temperature case, a novelty point is the sudden birth phenomenon occured in the behaviors of entanglement, it is initially to be zero (persists for some time), with further improving Ω and μ the entanglement will be suddenly appeared, and the time interval (persists to be zero) before sudden birth is obviously prolonged with decreasing two parameters. The temperature range of entanglement exists can be extended evidently with increasing μ or Ω, and one can obtain entanglement at higher temperature through changing them. When to the TACM, the ground state entanglement is initially decreased from the maximum value and then suddenly disappeared with increasing Ω. While increasing γ the ground state entanglement is increased initially from zero to the maximum value and then sudden disappeared with further improving γ (the spin squeezing interaction in XY plane), proper tuing γ or Ω can prolong the lives of entanglement evidently. For the finite temperature case, the sudden birth phenomenon also occured in the the evoluted concurrence, the variation of parameters Ω and γ can reduce the time interval before sudden birth. The influence of the temperature T on thermal entanglement property is also investigated. The temperature range of entanglement existence can be extended evidently with increasing γ, one can obtain entanglement at higher temperature through changing parameters γ and Ω.     

Electron–positron pair production from vacuum in the field of high-intensity laser radiation

The works dealing with the theory of e⁺e^– pair production from vacuum under the action of highintensity laser radiation are reviewed. The following problems are discussed: pair production in a constant electric field E and time-variable homogeneous field E(t); the dependence of the number of produced pairs \({N_{{e^ + }{e^ - }}}\) on the shape of a laser pulse (dynamic Schwinger effect); and a realistic three-dimensional model of a focused laser pulse, which is based on exact solution of Maxwell’s equations and contains parameters such as focal spot radius R, diffraction length L, focusing parameter Δ, pulse duration τ, and pulse shape. This model is used to calculate \({N_{{e^ + }{e^ - }}}\) for both a single laser pulse (n = 1) and several (n ≥ 2) coherent pulses with a fixed total energy that simultaneously “collide” in a laser focus. It is shown that, at n ? 1, the number of pairs increases by several orders of magnitude as compared to the case of a single pulse. The screening of a laser field by the vapors that are generated in vacuum, its “depletion,” and the limiting fields to be achieved in laser experiments are considered. The relation between pair production, the problem of a quantum frequency-variable oscillator, and the theory of groups SU(1, 1) and SU(2) is discussed. The relativistic version of the imaginary time method is used in calculations. In terms of this version, a relativistic theory of tunneling is developed and the Keldysh theory is generalized to the case of ionization of relativistic bound systems, namely, atoms and ions. The ionization rate of a hydrogen-like ion with a charge 1 ≤ Z ≤ 92 is calculated as a function of laser radiation intensity (F and ellipticity ρ.     

Control of Quantum Echo and Bell State Swapping of Two Atomic Qubits in the Two-Mode Vacuum Field Environment

We investigate quantum echo control and Bell state swapping for two atomic qubits (TAQs) coupling to two-mode vacuum cavity field (TMVCF) environment via two-photon resonance. We discuss the effect of initial entanglement factor ?? and relative coupling strength R=g₁/g₂ on quantum state fidelity of TAQs, and analyze the relation between three kinds of quantum entanglement(C(ρ_a),C(ρ_f),S(ρ_a)) and quantum state fidelity, then reveal physical essence of quantum echo of TAQs. It is shown that in the identical coupling case R=1, periodic quantum echo of TAQs with π cycle is always produced, and the value of fidelity can be controlled by choosing appropriate ?? and atom-filed interaction time. In the non-identical coupling case R≠1, quantum echoes with periods of π, 2π and 4π can be formed respectively by adjusting R. The characteristics of quantum echo results from the non-Markovianity of TMVCF environment, and then we propose Bell state swapping scheme between TAQs and two-mode cavity field.     

Damping in the Interaction of a Field and Two Three-Level Atoms Through Quantized Caldirola–Kanai Hamiltonian

We investigate the damped interaction between two Λ-type three-level atoms and a quantized single-mode cavity field, for which the Hamiltonian of the field is rewritten in Caldirola–Kanai form. We obtain the wave functions for the case where the two atoms are initially prepared in arbitrary pure states and the field is initially prepared in the coherent state. We investigate numerically the influence of the damping parameter on the temporal behavior of the Mandel Q-parameter, linear entropy, and normal squeezing. We find the damping parameter and initial atomic states to play central roles in the nonclassical features and the degree of entanglement.     

Excitation of the Classical Electromagnetic Field in a Cavity Containing a Thin Slab with a Time-Dependent Conductivity

We derive an exact infinite set of coupled ordinary differential equations describing the evolution of the modes of the classical electromagnetic field inside an ideal cavity containing a thin slab with the time-dependent conductivity σ(t) and dielectric permittivity ε(t) for the dispersion-less media. We analyze this problem in connection with the attempts to simulate the so-called dynamical Casimir effect in three-dimensional electromagnetic cavities containing a thin semiconductor slab periodically illuminated by strong laser pulses. Therefore, we assume that functions σ(t) and δε(t) = ε(t) ? ε(0) are different from zero during short time intervals (pulses) only. Our main goal here is to find the conditions under which the initial nonzero classical field could be amplified after a single pulse (or a series of pulses). We obtain approximate solutions to the dynamical equations in the cases of “small” and “big” maximal values of the functions σ(t) and δε(t). We show that the single-mode approximation used in the previous studies can be justified in the case of “small” perturbations, but the initially excited field mode cannot be amplified in this case if the laser pulses generate free carriers inside the slab. The amplification could be possible, in principle, for extremely high maximum values of conductivity and the concentration of free carries (the model of an “almost ideal conductor”) created inside the slab under the crucial condition providing the negativity of the function δε(t). This result follows from a simple approximate analytical solution confirmed by exact numerical calculations. However, the evaluation shows that the necessary energy of laser pulses must be, probably, unrealistically high.     

Better Entanglement Witness for Genuine Multipartite Entanglement

In the short contribution, we consider inequalities of confirming genuine multipartite entanglement. We have a better entanglement witness for a particular mixed state to test genuine multipartite entanglement. Our physical situation is that we measure Pauli observables σ _x , σ _y , and σ _z per side. If the reduction factor is greater than 0.4, then we can confirm the measured quantum state is genuine multipartite entangled experimentally.     

Kraus Operator-Sum Solution to the Master Equation Describing the Single-Mode Cavity Driven by an Oscillating External Field in the Heat Reservoir

Exploiting the thermo entangled state approach, we successfully solve the master equation for describing the single-mode cavity driven by an oscillating external field in the heat reservoir and then get the analytical time-evolution rule for the density operator in the infinitive Kraus operator-sum representation. It is worth noting that the Kraus operator M _{l, m} is proved to be a trace-preserving quantum operation. As an application, the time-evolution for an initial coherent state ρ _|β〉 = |β〉〈β| in such an environment is investigated, which shows that the initial coherent state decays to a new mixed state as a result of thermal noise, however the coherence can still be reserved for amplitude damping.     

Monogamy Relations in Terms of Tsallis-Q Entropy in any Dimensional System

Monogamy of entanglement is a fundamental property of multipartite entangled states. In this article, due to the convexity of Trρ^q with respect to q when q ≥ 1, we give a monogamy-like relation in terms of Tsallis-q entanglement entropy of assistance (TqEEA) for pure states over an n- partite any dimensional system and monogamy-like relations in terms of Tsallis-q entanglement entropy (TqEE) for mixed states for any dimensional system, we also give a lower bound for the TqEE of a four-partite pure state. At last, we show that the generalized W-class states satisfy the polygamy relation in terms of TqEE when q = 2.     

Relation Between Stereographic Projection and Concurrence Measure in Bipartite Pure States

One-qubit pure states, living on the surface of Bloch sphere, can be mapped onto the usual complex plane by using stereographic projection. In this paper, after reviewing the entanglement of two-qubit pure state, it is shown that the quaternionic stereographic projection is related to concurrence measure. This is due to the fact that every two-qubit state, in ordinary complex field, corresponds to the one-qubit state in quaternionic skew field, called quaterbit. Like the one-qubit states in complex field, the stereographic projection maps every quaterbit onto a quaternion number whose complex and quaternionic parts are related to Schmidt and concurrence terms respectively. Rather, the same relation is established for three-qubit state under octonionic stereographic projection which means that if the state is bi-separable then, quaternionic and octonionic terms vanish. Finally, we generalize recent consequences to 2?N and 4?N dimensional Hilbert spaces (N ≥ 2) and show that, after stereographic projection, the quaternionic and octonionic terms are entanglement sensitive. These trends are easily confirmed by direct computation for general multi-particle W- and GHZ-states.     

Single-atom laser: Coherent and nonclassical effects in the regime of a strong atom-field correlation

Based on the approximation of strong correlations between an atom and an intracavity field, which implies the equal probabilities of finding the atom in the ground state and n photons in the field and of finding the atom in an excited state and n?1 photons in the field, it is shown that the conditional states of a field generated by a single-atom laser are described by the diagonal part of the generalized coherent Mittag-Leffler state. The quasi-distributions P and Q of the intracavity-field probability amplitude are found, and the boundedness of the Glauber function on a segment is shown. The possibility of inversionless lasing is demonstrated, and the absence of a lasing threshold is found for some region of parameters. The regimes of generation of the amplitude-squeezed states of the field are studied and the parameters of the system providing the maximum squeezing are determined. It is shown that the atom-field states are entangled at weak pump intensities.     

Entanglement in Mixed-Spin (1/2, 3/2) Heisenberg XXZ Model with Dzyaloshinskii-Moriya Interaction

In this paper, the entanglement in a mixed-spin (1/2, 3/2) Heisenberg XXZ model with Dzyaloshinskii-Moriya (DM) interaction in an inhomogeneous external magnetic field is studied. We not only calculate the ground-state entanglement but also investigate the behaviors of quantum phase transition following the changes of DM interaction and nonuniform magnetic field. More importantly, we note that the DM interaction improves the critical magnetic field B _c , the critical temperature T _c and broadens the region of entanglement.     

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.     

Uniform Entanglement Frames

We present several criteria for genuine multipartite entanglement from universal uncertainty relations based on majorization theory. Under non-negative Schur-concave functions, the vector-type uncertainty relation generates a family of infinitely many detectors to check genuine multipartite entanglement. We also introduce the concept of k-separable circles via geometric distance for probability vectors, which include at most (k?1)-separable states. The entanglement witness is also generalized to a universal entanglement witness which is able to detect the k-separable states more accurately.     

Nonergodic state of relaxation ferroelectric Cd<Subscript>2</Subscript>Nb<Subscript>2</Subscript>O<Subscript>7</Subscript> in a constant electric field

The temperature dependence of the residual polarization of the nonergodic relaxation state (NERS) obtained from the measurements of pyroelectric current during zero-field heating (ZFH) in the temperature interval from 10 to 295 K is investigated for the Cd₂Nb₂O₇ relaxation system in two cases: (1) after sample cooling in a constant electric field E (FC) from T = 295 K to a preset temperature, which is much lower than the “freezing” temperature of the relaxation state (T _f ≈ 182 K), field removal, and subsequent cooling in zero field (ZFC) to T = 10 K and (2) after ZFC from T = 295 K to the same temperature below T _f , application of the same field, and FC to T = 10 K. The behavior of the P _r ^FC (T) and P _r ^ZFC (T) dependences is analyzed. In the field E < 2 kV/cm, the P _r ^ZFC curves as functions of 1/T have a broad low-intensity peak in the region T ≈ T _f , which vanishes in stronger fields, when the P _r ^FC (1/T) curves intersect at T ≈ T _f and have no anomalies. The difference in the behavior of P _r ^ZFC (T) and P _r ^FC (T) indicates the difference in the nature of NERS formed during ZFC and FC of the system upon a transition through T _f . In the ZFC mode, NERS exhibits glasslike behavior; in the FC regime, features of the ferroelectric behavior even in the weak field. Analogous variations of P _r ^ZFC (T) and P _r ^FC (T) in a classical ferroelectric KDP are also given for comparison.     

Protecting Distribution Entanglement for Two-Qubit State Using Weak Measurement and Reversal

Protection of entanglement from disturbance of the environment is an essential task in quantum information processing. We investigate the effect of the weak measurement and reversal (WMR) on the protection of the entanglement for an arbitrarily entangled two-qubit pure state from these three typical quantum noisy channels, i.e., amplitude damping channel, phase damping channel and depolarizing quantum channel. Given the parameters of the Bell-like initial qubits’ state |ψ〉 = a|00〉 + d|11〉, it is found that the WMR operation indeed helps for protecting distributed entanglement from the above three noisy quantum channels. But for the Bell-like initial qubits’ state |?〉 = b|01〉 + c|10〉, the WMR operation only protects entanglement in the amplitude damping channel, not for the phase damping and depolarizing quantum channels. In addition, we discuss how the concurrence and the success probability behave with adjusting the weak or the reversal weak measurement strength.