Scattering-induced quantum correlation in electronic waveguides with static magnetic impurities

Entanglement generation due to low-energy scattering of the transporting electrons in an electronic waveguide by a quantum dot magnetic impurity is theoretically investigated. The transverse confining potential of the waveguide is considered as a two-dimensional harmonic potential, and the interaction of the electron with the impurity is described by a zero-range pseudopotential modulated by an Ising or a Heisenberg spin interaction. Our calculation shows that the scattering process leads to creation of a considerable amount of entanglement in the state of the reflected and transmitted electrons. The situation is extended to the scattering of the electrons by two well-separated magnetic impurities localized on the nanowire axis. It is shown that the scattering process causes the magnetic impurities embedded in the nanowire to share their quantum information; subsequently, they can be entangled by spin interaction with the injected electron. The created entanglement between the impurities is calculated and discussed. It is shown that the exact three-dimensional problem can be approximated as a one-dimensional problem under certain circumstances. The approximate results are compared to exact calculations and discussed.     

Efficient entanglement concentration for quantum dot and optical microcavities systems

A recent paper (Chuan Wang in Phys Rev A 86:012323, 2012) discussed an entanglement concentration protocol (ECP) for partially entangled electrons using a quantum dot and microcavity coupled system. In his paper, each two-electron spin system in a partially entangled state can be concentrated with the assistance of an ancillary quantum dot and a single photon. In this paper, we will present an efficient ECP for such entangled electrons with the help of only one single photon. Compared with the protocol of Wang, the most significant advantage is that during the whole ECP, the single photon only needs to pass through one microcavity which will increase the total success probability if the cavity is imperfect. The whole protocol can be repeated to get a higher success probability. With the feasible technology, this protocol may be useful in current long-distance quantum communications.     

Post-Markovian dynamics of quantum correlations: entanglement versus discord

Dynamics of an open two-qubit system is investigated in the post-Markovian regime, where the environments have a short-term memory. Each qubit is coupled to separate environment which is held in its own temperature. The inter-qubit interaction is modeled by XY–Heisenberg model in the presence of spin–orbit interaction and inhomogeneous magnetic field. The dynamical behavior of entanglement and discord has been considered. The results show that quantum discord is more robust than quantum entanglement, during the evolution. Also the asymmetric feature of quantum discord can be monitored by introducing the asymmetries due to inhomogeneity of magnetic field and temperature difference between the reservoirs. By employing proper parameters of the model, it is possible to maintain nonvanishing quantum correlation at high degree of temperature. The results can provide a useful recipe for studying dynamical behavior of two-qubit systems such as trapped spin electrons in coupled quantum dots.     

Spin-Based Quantum Information Processing in Magnetic Quantum Dots

We define the qubit as a pair of singlet and triplet states of two electrons in a He-type quantum dot (QD) placed in a diluted magnetic semiconductor (DMS) medium. The molecular field is here essential as it removes the degeneracy of the triplet state and strongly enhances the Zeeman splitting. Methods of qubit rotation as well as two-qubit operations are suggested. The system of a QD in a DMS is described in a way which allows an analysis of the decoherence due to spin waves in the DMS subsystem.on leave from Institute of Physics, Odessa UniversityPresented at the 36th Symposium on Mathematical Physics, “Open Systems & Quantum Information”, Toruń, Poland, June 9–12, 2004.     

Effective Hamiltonian for the hybrid double quantum dot qubit

Quantum dot hybrid qubits formed from three electrons in double quantum dots represent a promising compromise between high speed and simple fabrication for solid state implementations of single-qubit and two-qubits quantum logic ports. We derive the Schrieffer–Wolff effective Hamiltonian that describes in a simple and intuitive way the qubit by combining a Hubbard-like model with a projector operator method. As a result, the Hubbard-like Hamiltonian is transformed in an equivalent expression in terms of the exchange coupling interactions between pairs of electrons. The effective Hamiltonian is exploited to derive the dynamical behavior of the system and its eigenstates on the Bloch sphere to generate qubits operation for quantum logic ports. A realistic implementation in silicon and the coupling of the qubit with a detector are discussed.     

Energy states of vertically aligned quantum dot array with nonparabolic effective mass

The electronic properties of a three-dimensional quantum dot array model formed by vertically aligned quantum dots are investigated numerically. The governing equation of the model is the Schrödinger equation which is incorporated with a nonparabolic effective mass approximation that depends on the energy and position. Several interior eigenvalues must be identified from a large-scale high-order matrix polynomial. In this paper, we propose numerical schemes that are capable of simulating the quantum dot array model with up to 12 quantum dots on a personal computer. The numerical experiments also lead to novel findings in the electronic properties of the quantum dot array model.     

Entanglement generation due to the Klein tunneling in a graphene sheet

Scattering of a ballistic electron by the quantum-dot spin qubits fixed in a graphene nanoribbon is investigated theoretically. Two simple cases are investigated in details: scattering from a static quantum dot and scattering from two static quantum dots located at a fixed distance from each other. For the first case, it is shown that the Klein tunneling in a graphene sheet leads to a final entangled state for the reflected and/or transmitted electrons. The amount of the generated entanglement through the scattering process is a function of the incident angle for the ballistic electrons. For the second case, it is shown that the created correlation between the quantum dots is a periodic function of their distance. For frontal incident electrons in both cases, there is not any reflection and the Klein tunneling effect leads to a final well-correlated state for the scattering system.     

Measurement-induced disturbance and negativity in mixed-spin XXZ model

In this paper, we investigate the quantum phase transition (QTP) and quantum correlation in the one-dimensional mixed-spin (1/2, 1) XXZ model with Dzyaloshinskii–Moriya (DM) interaction under an inhomogeneous magnetic field. By controlling the strength of DM interaction and inhomogeneous magnetic field, we can change the phase transition points. The results show that the DM interaction plays an important role in improving the quantum correlation, which can be gained at higher temperature by choosing the proper strength of DM interaction. Moreover, the homogeneous magnetic field cannot change the critical temperature $T_{c}$ alone, while the inhomogeneous magnetic parameter $b$ can suppress the effects of temperature on negativity. In addition, we make an explicit comparison between the negativity and measurement-induced disturbance (MID) for this model and discover that MID is more robust than thermal entanglement against temperature $T$ and may reveal more properties about quantum correlations of the system than entanglement. Furthermore, in some circumstances, the MID can detect the critical points of quantum phase transition while the negativity cannot.     

MATLAB-based program for optimization of quantum cascade laser active region parameters and calculation of output characteristics in magnetic field

A strong magnetic field applied along the growth direction of a quantum cascade laser (QCL) active region gives rise to a spectrum of discrete energy states, the Landau levels. By combining quantum engineering of a QCL with a static magnetic field, we can selectively inhibit/enhance non-radiative electron relaxation process between the relevant Landau levels of a triple quantum well and realize a tunable surface emitting device. An efficient numerical algorithm implementation is presented of optimization of GaAs/AlGaAs QCL region parameters and calculation of output properties in the magnetic field. Both theoretical analysis and MATLAB implementation are given for LO-phonon and interface roughness scattering mechanisms on the operation of QCL. At elevated temperatures, electrons in the relevant laser states absorb/emit more LO-phonons which results in reduction of the optical gain. The decrease in the optical gain is moderated by the occurrence of interface roughness scattering, which remains unchanged with increasing temperature. Using the calculated scattering rates as input data, rate equations can be solved and population inversion and the optical gain obtained. Incorporation of the interface roughness scattering mechanism into the model did not create new resonant peaks of the optical gain. However, it resulted in shifting the existing peaks positions and overall reduction of the optical gain.     

An atom�Cmolecule platform for quantum computing

We propose a combined atom–molecule system for quantum information processing in individual traps, such as provided by optical lattices. In this platform, different species of atoms—one atom carrying a qubit and the other enabling the interaction—are used to store and process quantum information via intermediate molecular states. We show how gates, initialization, and readout operations could be implemented using this approach. In particular, we describe in some detail the implementation of a two-qubit phase gate in which a pair of atoms is transferred into the ground rovibrational state of a polar molecule with a large dipole moment, thus allowing atoms transferred into molecules to interact via their dipole-dipole interaction. We also discuss how the reverse process could be used as a non-destructive readout tool of molecular qubit states. Finally, we generalize these ideas to use a decoherence-free subspace for qubit encoding to minimize the decoherence due to magnetic field fluctuations. In this case, qubits will be encoded into field-insensitive states of two identical atoms, while a third atom of a different species will be used to realize a phase gate.     

Numerical modeling of the InAs quantum dot with application of coordinate transformation and the finite difference method

In order to resolve the three dimensional Schrödinger equation, we report in this paper a method providing sufficient accuracy, stability and flexibility with respect to the size and shape of the quantum dot. This numerical method, already used in the two-dimensional case, is based on a suitable combination of coordinate transformation and the finite difference method. It provides an efficient and simple approach for the energy and wavefunction calculations of quantum nanostructures. The proposed method is used to investigate the electron and hole energy levels as well as their wave functions in InAs/GaAs strained and unstrained quantum dots with the aim to attain the 1.55 μm wavelength with realistic dot size. The optical transition energies and the oscillator strengths are also studied. The obtained results are in agreement with several previous works.     

Calculating modes of quantum wire and dot systems using a finite differencing technique

In this paper the Schrödinger equation of both a quantum wire and a quantum dot are solved using a finite difference approach. It is demonstrated that the method is valid for the simple case of an infinitely deep quantum wire, where the solutions obtained are within 0.25 meV of the analytical solutions. The method is then used to calculate the eigenenergies of a triangular wire with finite barriers. The eigenenergies of the more complex case of a pyramidal quantum dot were then calculated using this method. The method is compared to an eigenvalue method in terms of memory usage, time requirements and the numerical solutions. It is shown that this method has the advantages of being relatively fast, usable with any wire geometry and any potential profile. In addition, the demand on computer memory varies linearly with the size of the system under investigation.     

Fourth-order algorithms for solving local Schrödinger equations in a strong magnetic field

We describe an efficient numerical method for solving eigenvalue problems associated with the one-body Schrödinger equation or the Kohn-Sham equations in an arbitrarily strong uniform external magnetic field. The eigenvalue problem is solved in real space by using a fourth order, forward factorization of the evolution operator e−εH, which is significantly more efficient than conventional second-order algorithms. In particular, the magnetic field is solved exactly by the decomposition process. The algorithm is applicable to any external potential, in addition to the magnetic field. We envision its primary application in the area of electronic structure calculations of quantum dots.     

Numerical simulation on the dynamics of photoinduced cooperative phenomena in molecular crystals

We develop a new simulation method to study the dynamics of initial nucleation processes of photoinduced structural change of molecular crystals. In order to describe the nonadiabatic transition in each molecule, we employ a model of localized electrons coupled with a fully quantized phonon mode, and the time-dependent Schrödinger equation for the model is numerically solved. By applying a mean-field approximation in solving the Schrödinger equation, the calculation method is quite efficient on parallel computing systems. We show that coherently driven molecular distortion plays an important role in the successive conversion of electronic states which leads to photoinduced cooperative phenomena.     

Magnetotransport in a time-modulated double quantum point contact system

We report on a time-dependent Lippmann–Schwinger scattering theory that allows us to study the transport spectroscopy in a time-modulated double quantum point contact system in the presence of a perpendicular magnetic field. Magnetotransport properties involving inter-subband and inter-sideband transitions are tunable by adjusting the time-modulated split-gates and the applied magnetic field. The observed magnetic field induced Fano resonance feature may be useful for the application of quantum switching.     

Exact master equation and non-markovian decoherence for quantum dot quantum computing

In this article, we report the recent progress on decoherence dynamics of electrons in quantum dot quantum computing systems using the exact master equation we derived recently based on the Feynman–Vernon influence functional approach. The exact master equation is valid for general nanostructure systems coupled to multi-reservoirs with arbitrary spectral densities, temperatures and biases. We take the double quantum dot charge qubit system as a specific example, and discuss in details the decoherence dynamics of the charge qubit under coherence controls. The decoherence dynamics risen from the entanglement between the system and the environment is mainly non-Markovian. We further discuss the decoherence of the double-dot charge qubit induced by quantum point contact (QPC) measurement where the master equation is re-derived using the Keldysh non-equilibrium Green function technique due to the non-linear coupling between the charge qubit and the QPC. The non-Markovian decoherence dynamics in the measurement processes is extensively discussed as well.     

Thermal quantum correlation and entanglement in the Bose–Hubbard Hamiltonian

We study a two-qutrit system which is described by the Bose–Hubbard Hamiltonian with two external magnetic fields. The entanglement (through the negativity) and quantum correlation (through the geometric discord) between the qutrits are calculated as functions of the magnetic field (B), the temperature (T), the linear and nonlinear coupling constants among two spins (J and K). Then, we compare the effect of these parameters on entanglement and quantum correlation of this system. For some values of system parameters, we show that the negativity is zero while, the geometric discord is nonzero. Moreover, we investigate the effect of finite external magnetic fields direction on these measures. This study leads to some new and interesting results as well.     

Scheme for a spin-based quantum computer employing induction detection and imaging

A theoretical spin-based scheme for performing a variety of quantum computations is presented. It makes use of an array of multiple identical “computer” vectors of phosphorus-doped silicon where the nuclei serve as logical qubits and the electrons as working qubits. The spins are addressed by a combination of electron spin resonance and nuclear magnetic resonance techniques operating at a field of $\sim $ 3.3 T and cryogenic temperatures with an ultra-sensitive surface microresonator. Spin initialization is invoked by a combination of strong pre-polarization fields and laser pulses, which shortens the electrons’ $T_{1}$ . The set of universal quantum gates for this system includes an arbitrary rotation of single qubits and c-NOT operation in two qubits. The efficient parallel readout of all the spins in the system is performed by high sensitivity induction detection of the electron spin resonance signals with one-dimensional imaging. Details of the suggested scheme are provided, which show that it is scalable to a few hundreds of qubits.     

Dynamical Solution to the Quantum Measurement Problem, Causality, and Paradoxes of the Quantum Century

A history and drama of the development of quantum theory is outlined starting from the discovery of the Plank's constant exactly 100 years ago. It is shown that before the rise of quantum mechanics 75 years ago, the quantum theory had appeared first in the form of the statistics of quantum thermal noise and quantum spontaneous jumps which have never been explained by quantum mechanics. Moreover, the only reasonable probabilistic interpretation of quantum theory put forward by Max Born was in fact in irreconcilable contradiction with traditional mechanical reality and causality. This led to numerous quantum paradoxes; some of them, related to the great inventors of quantum theory such as Einstein and Schrödinger, are reconsidered in the paper. The development of quantum measurement theory, initiated by von Neumann, indicated a possibility for the resolution of this interpretational crisis by a divorce of the algebra of dynamical generators and a subalgebra of the actual observables. It is shown that within this approach quantum causality can be rehabilitated in the form of a superselection rule for compatibility of past observables with the potential future. This rule together with self-compatibility of measurements ensuring the consitency of histories is called the nondemolition principle. The application of these rules in the form of dynamical commutation relations leads to the derivation of the von Neumann projection postulate, as well as to more general reductions, instantaneous, spontaneous, and even continuous in time. This gives a quantum probabilistic solution in the form of dynamical filtering equations to the notorious measurement problem which was tackled unsuccessfully by many famous physicists starting from Schrödinger and Bohr. The simplest Markovian quantum stochastic model for time-continuous measurements involves a boundary-value problem in second quantization for input "offer" waves in one extra dimension, and a reduction of the algebra of "actual" observables to an Abelian subalgebra for the output waves.     

舰艇磁场磁偶极子阵列数学模型研究

为提高舰艇磁性防护能力,准确反映其磁场特性,舰艇测磁需要使用先进的测磁技术,这就可以用磁偶极子阵列模拟舰艇磁场源;文中根据舰艇测量面上的磁场数据建立了舰艇磁场换算的数学模型,给出一种运用实例评述测磁技术在舰艇磁性防护中的应用;实例结合点阵式大平面测磁法和磁荷模拟算法建立了测磁后舰艇磁场换算的数学模型,简单论述了该模型的数学原理、磁场函数计算方法及具体应用中有关参数的确定方法等,并对计算精度作了分析,仿真结果表明模型精度较高;测磁技术的应用在磁性防护中具有重要的实用价值。