Generation and control of electronic hybrid entanglement via a two-dimensional Rashba anisotropic nanodot

In the present article we report the dynamics of electronic spin–subbands, as well as subband–subband, hybrid entanglements in a two-dimensional anisotropic quantum dot. The dot is under the influence of Rashba effect and an external magnetic field. To study the hybrid entanglements, we partition the system into two categories in which either spatial degrees of freedom, subbands, entangle with the spin or the subbands become entangled amongst themselves. For the first case we calculate the von Neumann entropy, while for the latter the negativity is calculated. Our calculations show that for both cases information is periodically distributed between the corresponding subspaces. Effects of Rashba parameter and magnetic field on the characteristics of such oscillatory behavior are also discussed. For spin–subband entanglement the oscillations include dips, surrounded by plateaus of maximal entanglement. The subband–subband entanglement shows vanishingly small plateaus. The duration of plateaus is controlled by Rashba coupling and the external field.     

Von Neumann entropy in a Rashba-Dresselhaus nanodot; dynamical electronic spin-orbit entanglement

The main purpose of the present article is to report the characteristics of von Neumann entropy, thereby, the electronic hybrid entanglement, in the heterojunction of two semiconductors, with due attention to the Rashba and Dresselhaus spin-orbit interactions. To this end, we cast the von Neumann entropy in terms of spin polarization and compute its time evolution; with a vast span of applications. It is assumed that gate potentials are applied to the heterojunction, providing a two dimensional parabolic confining potential (forming an isotropic nanodot at the junction), as well as means of controlling the spin-orbit couplings. The spin degeneracy is also removed, even at electronic zero momentum, by the presence of an external magnetic field which, in turn, leads to the appearance of Landau states. We then proceed by computing the time evolution of the corresponding von Neumann entropy from a separable (spin-polarized) initial state. The von Neumann entropy, as we show, indicates that electronic hybrid entanglement does occur between spin and two-dimensional Landau levels. Our results also show that von Neumann entropy, as well as the degree of spin-orbit entanglement, periodically collapses and revives. The characteristics of such behavior; period, amplitude, etc., are shown to be determined from the controllable external agents. Moreover, it is demonstrated that the phenomenon of collapse-revivals’ in the behavior of von Neumann entropy, equivalently, electronic hybrid entanglement, is accompanied by plateaus (of great importance in quantum computation schemes) whose durations are, again, controlled by the external elements. Along these lines, we also make a comparison between effects of the two spin-orbit couplings on the entanglement (von Neumann entropy) characteristics. The finer details of the electronic hybrid entanglement, which may be easily verified through spin polarization measurements, are also accreted and discussed. The novel results of the present article, with potent applications in the field of quantum information processing, provide a deeper understanding of the electronic von Neumann entropy and hybrid entanglement that occurs in two-dimensional nanodots.     

Dynamical entanglement for Fermi coupled stretching and bending modes

The dynamical entanglement for Fermi coupled C--H stretch and bend vibrations in molecule CHD₃ is studied in terms of two negativities and the reduced von Neumann entropy, where initial states are taken to be direct products of photon-added coherent states on each mode. It is demonstrated that the negativity defined by the sum of negative eigenvalues of the partial transpose of density matrices is positively correlated with the von Neumann entropy. The entanglement difference between photon-added coherent states and usual coherent states is discussed as well.     

Effect of external magnetic field on thermal entanglement of spin-subband states in a Rashba nanowire

In this study the authors use the negativity to study the entanglement of electronic spin and thermally induced subband states inside a quasi-one-dimensional Rashba nanowire (of width in the order of 100 nm), to which a perpendicular uniform magnetic field is applied. To be clearer, it is assumed that the nanowire is held at a temperature T, so that all subband excitations, with definite probabilities, are present. The partially transposed density matrix is shown to be block-diagonal whose eigenvalues are readily obtained. It is shown that at least one of the eigenvalues is always negative, so that the system of electronic spin and subbands inside a Rashba nanowire is never separable. Moreover, it is shown that the negativity, at certain temperatures, exhibits maxima. The temperatures at which the entanglement is maximal strongly depend on the magnetic field. The authors further present graphs of negativity, as functions of temperature, for different magnetic fields, indicating how this agent may be used to control the spin-subband entanglement.     

Scaling of entanglement entropy for spin chain with Dzyaloshinskii-Moriya interaction

This paper investigates the entanglement in an XX-type spin chain with Dzyaloshinskii-Moriya interaction under an external magnetic field.The von Neumann entropy of entanglement between two blocks for the ground state of the system is evaluated.It analyses and discusses the scaling behaviour of the entanglement entropy.     

依赖强度耦合双模Jaynes-Cummings 模型的纠缠和场熵演化

应用von Neumann熵研究了依赖强度耦合双模Jaynes-Cummings模型中原子与光场的纠缠度。给出了两模初始场均处于相干态和双模压缩真空态两种情况下熵演化的数值结果。讨论了初始场强度对原子―场纠缠度的影响。发现在强场条件下，原子与光场基本稳定在最大纠缠态但伴随着周期性的脉冲式解纠缠。     

Structure formation of entanglement entropy in a system of two superconducting qubits coupled with an LC-resonator

This paper investigates theoretically the evolutions of the entanglement entropy of a system of two coupled-charge-qubits interacting with an LC-resonator.It is found that when the initial states of the two qubits are prepared in a given superposition excited state,the evolution of the von Neumann entropy of the system depends significantly on the coupling strength between the two Josephson charge qubits.With the variation of the coupling strength,the evolution of the entanglement entropy of the system forms some structures,especially the periodically bistable properties,which are the first discovered for such a system to our knowledge.It is found that the relative entropy entanglement of the system is also sensitive to the variation of the coupling strength between the two charge qubits,some novel ’collective oscillations’ of the relative entropy are found for the system.     

Bipartite entanglement within the framework of real and ideal lasers

We study the nonlocal correlations and quantum entanglement for two deformed bosonic fields of arbitrary deformation parameters, q ₁ and q ₂, prepared in an entanglement of deformed coherent states. As a measure of entanglement, we use the von Neumann entropy and investigate its behavior for different strength regimes of the optical fields. We find that the photon number can enhance the von Neumann entropy, and the deformation parameters can restrain the system entanglement.     

Λ型三能级原子与数态单模光场互作用系统的纠缠特性

通过计算场的量子力学熵讨论了Λ型三能级原子与数态单模光场互作用系统的纠缠和退纠缠时间演化规律.结果表明，系统的纠缠呈现周期性，最大纠缠度依赖于原子初态、初始场光 子数及场失谐量与耦合系数之比.一周期内出现最大纠缠和退纠缠的次数与初始场光子数无 关.近简并下能级初始相对位相影响场熵演化，而激发态和基态之间的初始相对位相对场熵 演化无影响.     

Entanglement and nonclassicality evolution of the atom in a squeezed vacuum

As an important parameter, von Neumann entropy has been used to characterize the entanglement between atom and light field. We discussed the entanglement and nonclassicality evolution of an atom in a squeezed vacuum—a typical nonclassical field, and compare it with that of the coherent state. It shows that the atom-field entanglement in squeezed vacuum is much stronger and stabler than that in coherent state, whereas the nonclassicality of the light field depends on its initial status. This investigation is trying to find a new insight into the relation between entanglement of atom-field system and nonclassicality of light fields. The result shows that the entanglement between the atom and the field can be maintained well in the squeezed vacuum and this implies better control of atom and photon mutually.     

两格点两电子Hubbard-Holstein模型极化子的量子纠缠特性

本文利用相干态正交化展开方法, 对两格点两电子Hubbard-Holstein极化子模型的能谱以及动力学特性进行了精确求解. 讨论了耦合强度g、平均声子数n以及电子 初态对纠缠演化特性及系统冯诺依曼熵的影响. 数值计算结果表明: 1)纠缠度随时间的演化呈现出良好的周期性, 当其他的参数固定时, 演化周期随耦合强度g增大逐渐减小, 与平均声子数n无关; 2)系统冯诺依曼熵同电子状态占有率表现出严格的同步演化特性; (3) 在弱耦合强度和低平均声子数下, 初始电子态c_2↑⁺ c_2↓⁺|O>_e或c_1↑⁺ c_1↓⁺ |O>_e较c_1↑⁺c_2↓⁺—c_1↓⁺ c_2↑⁺具有更大的最大冯诺依曼熵, 并随耦合强度增大、平均声子数的增加而逐渐接近.     

Dynamical correlations of negativity and entropy for pure and mixed states in two coupled quartic oscillators

Various measures of entanglement have triggered considerable interest in the relationship between entanglement measures and other well-known quantities. As a demonstration, the dynamical correlation of negativity and entropy is studied in two coupled quartic oscillators for initial pure and mixed states that are respectively taken to be the products and mixed density matrices of coherent states and squeezed states on each oscillator. The correlation with energy is also considered. It is shown that for the initial pure states with a small magnitude, two negativities are positively correlated with the von Neumann entropy while they are anti-correlated with the energy of each oscillator in the weak coupling regime. For mixed states with a small magnitude the two negativities and the mutual entropy exhibit dominantly positive correlation, whereas those three quantities are dominantly anti-correlated with the sum of energies of two oscillators in the case of weak interactions. Such correlation behaviors in the mixed state with small magnitudes are most striking at the same step in maximal and minimal values and in oscillation. The differences in entropies and negativities between coherent states and squeezed states are discussed. These are useful for quantum entanglement and quantum information processing.     

Entanglement dynamics in Coriolis coupled rovibrational states of formaldehyde

The entanglement dynamics of two vibrational modes of a polyatomic molecule coupled by Coriolis interaction to overall molecular rotation is studied in terms of two negativities, N(t) and N_s(t), respectively, defined by the minimum of the eigenvalues and by the sum of the negative eigenvalues of the partial transpose of a density matrix. Various initial states are the products of Dicke states and the products of coherent states of vibrations and rotations. Formaldehyde is taken as an example, and the von Neumann entropy s(t) is simulated for the comparison with both negativities. It is shown that negativity N_s(t) is positively correlated with entropy s(t), and the correlated behavior between negativity N(t) and entropy s(t) strongly depends on initial states. However, these three indicators of entanglement display a dominantly positive correlation for the coherent states with small or large parameters. In addition, for the latter state two quantities N(t) and s(t) are nearly unchanged for a long time. This time can be further increased by the increasing of vibrational quantum number so that molecular information processing and quantum computing is allowed. These results are useful in quantum information theory.     

Quantum Entanglement and Normal-to-Local Transition in Molecule H2

Quantum entanglement of two stretches in molecule H2S is investigated for various initial states in terms of the reduced-density yon Neumann entropy and the mean entropy defined by average over time. It is shown that the maximal and the mean entropies of an initial state with local-mode character are smaller than those with normal-mode character, and the mean entropy displays a maximum near the position of the normal-to-local transition.     

Entanglement Dynamics in a Model Tripartite Quantum System

A Λ-type atom interacting with two radiation fields exhibits electromagnetically induced transparency and other nonclassical effects that appear in the entanglement dynamics of the atomic subsystem and in appropriate field observables. Both EIT and field-atom entanglement are important for quantum information processing. We investigate the roles played by specific initial field states, detuning parameters, field nonlinearities and intensity-dependent field-atom couplings on EIT and the entanglement between subsystems. Departure from coherence of the initial field states produces significant effects. We investigate these aspects in a model that exhibits the salient features of entangled tripartite systems. For initial photon-added coherent states, collapses and revivals of the atomic subsystem von Neumann entropy appear as the intensity parameter varies over a narrow range of values. These features could be useful in enabling entanglement.     

Entanglement property in matrix product spin systems

We study the entanglement property in matrix product spin-ring systems systemically by von Neumann entropy. We find that: (i) the Hilbert space dimension of one spin determines the upper limit of the maximal value of the entanglement entropy of one spin, while for multiparticle entanglement entropy, the upper limit of the maximal value depends on the dimension of the representation matrices. Based on the theory, we can realize the maximum of the entanglement entropy of any spin block by choosing the appropriate control parameter values. (ii) When the entanglement entropy of one spin takes its maximal value, the entanglement entropy of an asymptotically large spin block, i.e. the renormalization group fixed point, is not likely to take its maximal value, and so only the entanglement entropy Sn of a spin block that varies with size n can fully characterize the spin-ring entanglement feature. Finally, we give the entanglement dynamics, i.e. the Hamiltonian of the matrix product system.     

Spin–momenta entanglement in moving frames: Properties of von Neumann entropy

The fact that spin–momentum of massive particles become entangled (disentangled) as seen by moving observers, is used to investigate the properties of von Neumann entropy, as a measure of spin–momentum entanglement. To do so, we partition the total Hilbert space into momentum and spin subspaces so that the entanglement occurs between total spin states and total momenta of two spin- $\frac{1}{2}$ particles. Assuming that the occurrence of spin–momentum states is determined by Gaussian probability distributions, we show that the degree of entanglement ascends for small rapidities, reaches a maximum and diminishes at high rapidity. We further report how the characteristics of this behaviour vary as the widths of distributions change. In particular, a separable state, resulting from equal distribution widths, indeed becomes entangled in moving frames.     

利用信息流方法优化多激发自旋链中的量子态传输

研究了量子态在一条均匀耦合的反铁磁自旋链中传输时, 信道中自旋激发数变化对其传输性质的影响. 利用信息流方法分析输出端粒子的算符演化动力学, 获得了量子态传输的平均保真度与信道自旋初态之间的关系. 结果表明, 平均保真度的大小只依赖于信道中自旋激发数的奇偶性. 通过比较在奇偶激发信道中获得的最大平均保真度, 构建了优化信道来提升量子态在自旋链中的传输质量. 进一步分析了纠缠在激发信道中的传输情况, 发现纠缠的传输质量不仅和信道中自旋激发的具体个数有关, 还取决于激发自旋的初始排列. 特别地, 当信道中自旋无激发或全部激发时, 纠缠传输的大小和持续时间都优于其他的激发信道. 上述研究结果有助于在实际系统中搭建适合量子态和纠缠传输的量子信道.     

Entanglement in the supermolecular dimer [Mn4]2

This paper investigates the entanglement in the supermolecular dimer [Mn4]2 consisting of a pair of single molecular magnets with antiferromagnetic exchange-coupllng J. The conventional yon Neumann entropy as a function of the exchange-coupling is calculated explicitly for all eigenstates with the quantum number range from M = M1 ＋ M2 = -9 to 0. It is shown that the yon Neumann entropy is not a monotonic function of the coupling strength. However, it is significant that the entropy of entanglement has the maximum values and the minimum values for most eigenstates, which is extremely useful in the quantum computing. It also presents the time-evolution of entanglement from various initial states. The results are useful in the design of devices based on the entanglement of two molecular magnets.     

Dynamics of photon–photon entanglement in a bimodal nonlinear nanocavity

The photon–photon entanglement dynamics in a bimodal nanocavity, filled with a centrosymmetric nonlinear medium, is studied. In the present study, we have included the first and third order susceptibilities, giving rise to linear and the Kerr-type couplings. With no restrictions placed on the relative strength of these effects, we prove that the corresponding Hamiltonian is block-diagonal, each with ever-growing dimensions. We then show that, depending upon the initial total photon number, one needs to diagonalize a specific low-dimensional block, leading to the time evolution operator. Consequently, the time-evolution of the von Neumann entropy, as a measure of entanglement, is determined. From an analysis of the von Neumann entropy, we show that the entanglement exhibits oscillations, with plateaus, whose characteristics (period, duration, … ) strongly depend upon the strength of third order susceptibility. Moreover, it is shown that the entanglement is enhanced as the linear coupling is increased. The effect of detuning between photon's frequencies is also discussed.