Anisotropic Spin Cluster as a Qubit

We study an anisotropic spin cluster of 3 spin S=1/2 particles with antiferromagnetic exchange interaction with non-uniform coupling constants. A time-dependent magnetic field is applied to control the time evolution of the cluster. It is well known that for an odd number og sites a spin cluster qubit can be defined in terms of the ground state doublet. The universal one-qubit logic gate can be constructed from the time evolution operator of the non-autonomous many-body system, and the six basic one-qubit gates can be realized by adjusting the applied time-dependent magnetic field.     

Physical Realization of Quantum C-Not Gate

We investigate a Heisenberg spin cluster with two particles controlled by a time-dependent magnetic field. The system is controlled by tuning the amplitude, frequency, and interaction time of the three-step time-dependent magnetic field. Then we solve the time-dependent Schrodinger equation of the two-particle system, and obtain the time evolution operator. By the three-timestep interaction, the wavefunction evolves from the initial state to the final state, and the total evolution operator can be expressed as a product of the three evolution operators. By adjusting the physical parameters, the key two-qubit logic gate, the C-Not gate, can be realized physically.     

两粒子自旋系统量子纠缠的时间演化

研究了两个具有海森伯耦合的自旋为1/2的粒子在随时间变化的磁场中的运动情况.系统的哈密顿量具有SU（2）代数结构,运用代数动力学方法对此系统进行求解,得到了时间演化算子的严格解.基于严格解,求得两粒子体系随时间变化的波函数,从而计算得到两粒子体系的纠缠.对不同初始波函数,研究了系统纠缠随时间的变化情况.讨论了外场影响纠缠的条件. 关键词： 二粒子系统纠缠 代数动力学解法     

Single Qubit and Its Universal Logic Gate Made of a Heisenberg Spin Cluster with Five Particles

We investigate an anisotropic Heisenberg spin cluster with five particles controlled by a time-dependent magnetic field. With the algebraic dynamical method, we obtain the exact analytical solution to the time dependent Schr6dinger equation. Based on the analytical solution, it is shown that the system can be used as a universal single qubit logic gate controlled by the strength and frequency of the magnetic field, and the six special single qubit logic gates can be realized physically. We also discuss the anti-decoherence property of the qubit and its logic gates resulted from particle coupling effect and collectivity of the cluster.     

由各向异性海森伯自旋环链组成的量子位及其通用量子逻辑门

研究了各向异性耦合的三粒子海森伯自旋环链团簇在随时间变化的磁场中的运动.该系统的哈密顿量具有SU(2)代数结构.用代数动力学方法对此系统进行求解，得到了严格的解析解.基于严格解, 可以构造一位量子逻辑门.通过调节磁场强度和频率, 就可以控制该量子逻辑门, 实现一位量子逻辑门的任何操作. 关键词： 代数动力学 自旋环链团簇 一位量子逻辑门     

Observation of dark state polariton collapses and revivals

By time-dependent variation of a control field, both coherent and single-photon states of light are stored in, and retrieved from, a cold atomic gas. The efficiency of retrieval is studied as a function of the storage time in an applied magnetic field. A series of collapses and revivals is observed, in very good agreement with theoretical predictions. The observations are interpreted in terms of the time evolution of the collective excitation of atomic spin wave and light wave, known as the dark-state polariton.     

Entanglement creation and storage in two qubits coupling to an anisotropic Heisenberg spin chain

The time evolution of the entanglement of a pair of two spin qubits is investigated when the two qubits simultaneously couple to an environment of an anisotropic Heisenberg XXZ spin chain. The entanglement of the two spin qubits can be created and is a periodic function of the time if the magnetic field is greater than a critical value. If the two spin qubits are in the Bell state, the entanglement can be stored with relatively large value even when the magnetic field is large.     

Spin polarization effects and their time evolutions

The time evolution of the density corresponding to the polarization operator, originally constructed to commute with the Dirac Hamiltonian in the absence of an external electromagnetic field, is investigated in terms of the time-dependent Dirac equation taking the presence of an external electromagnetic field into account. It is found that this time evolution leads to ‘tensorial’ and ‘vectorial’ particle current densities and to the interaction of the spin density with the external electromagnetic field. As the time evolution of the spin density does not refer to a constant of motion (continuity condition) it only serves as auxiliary density. By taking the non-relativistic limit, it is shown that the polarization, spin and magnetization densities are independent of electric field effects and, in addition, no preferred directions can be defined.     

Localised spin modes of decorated magnetic clusters on a magnetic surface

A method for the calculation of the energies of spin modes of surface magnetic clusters on a magnetic surface, using broken translation symmetry in three dimensions (3D), is employed to determine the spin mode energies for a variety of planar clusters. The cluster is considered to be supported on a magnetically ordered substrate such that the localised spins of the cluster and the substrate interact via magnetic exchange. No electronic effects are considered. The analytical approach solves for the 3D evanescent crystal spin field in the bulk and the surface domains around the cluster. This spin field arises owing to the breakdown of magnetic translation symmetry caused by the surface cluster. The analytical approach can be applied to any cluster configuration, underlying the general character of the calculation. In particular, we consider here a 4-, 5-, and 9-atoms planar clusters supported on the surface of a ferromagnetic simple cubic lattice, the spin order being in the direction normal to surface boundary. The method is applied to calculate the spin mode energies of these planar clusters consisting of Gd atoms interacting via Anti-ferromagnetic exchange with an Fe(1 0 0) surface. These results are compared with the calculated energies of the spin modes of the free clusters, and also with those for the same planar clusters when the cluster-substrate exchange is considered hypothetically ferromagnetic.     

Berry phase in a nonisolated system

We investigate the effect of the environment on a Berry phase measurement involving a spin-half. We model the spin + environment using a biased spin-boson Hamiltonian with a time-dependent magnetic field. We find that, contrary to naive expectations, the Berry phase acquired by the spin can be observed, but only on time scales which are neither too short nor very long. However this Berry phase is not the same as for the isolated spin-half. It does not have a simple geometric interpretation in terms of the adiabatic evolution of either bare spin states or the dressed spin resonances. This result is crucial for proposed Berry phase measurements in superconducting nanocircuits.     

Long time evolution of a spin interacting with a spin bath in arbitrary magnetic field

We introduce a completely different method to calculate the evolution of a spin interacting with a sufficient large spin bath,especially suitable for treating the central spin model in a quantum dot(QD).With only an approximation on the envelope of central spin,the symmetry can be exploited to reduce a huge Hilbert space which cannot be calculated with computers to many small ones which can be solved exactly.This method can be used to calculate spin-bath evolution for a spin bath containing many(say,1000)spins,without a perturbative limit such as strong magnetic field condition,and works for long-time regime with sufficient accuracy.As the spin-bath evolution can be calculated for a wide range of time and magnetic field,an optimal dynamic of spin flip-flop can be found,and more sophisticated approaches to achieve extremely high polarization of nuclear spins in a QD could be developed.     

Coherent single electron spin control in a slanting Zeeman field

We consider a single electron in a 1D quantum dot with a static slanting Zeeman field. By combining the spin and orbital degrees of freedom of the electron, an effective quantum two-level (qubit) system is defined. This pseudospin can be coherently manipulated by the voltage applied to the gate electrodes, without the need for an external time-dependent magnetic field or spin-orbit coupling. Single-qubit rotations and the controlled-NOT operation can be realized. We estimated the relaxation (T1) and coherence (T2) times and the (tunable) quality factor. This scheme implies important experimental advantages for single electron spin control.     

Effects of impurity on fidelity of quantum state transfer via spin channels

By adopting the concept of fidelity, we investigated efficiency of quantum state transfer with the XX chain as the quantum channel. Different from the previous works, we concentrated on effects of spin and magnetic impurity on fidelity of quantum state transfer. Our results revealed that the spin impurity cannot prevent one from implementing perfect transfer of an arbitrary one-qubit pure state across the spin channel, however, the presence of magnetic impurity or both spin and magnetic impurities may destroy the otherwise perfect spin channels.     

Formal exact solution for the Heisenberg spin system in a time-dependent magnetic field and Aharonov-Anandan phase

We study the time evolution of the Heisenberg spin system in a time-dependent magnetic field. By a unitary transformation we obtain the formal exact solutions of the Schrödinger equation for this system. Based on the formal exact solutions, the Aharonov-Anandan phases are worked out.     

Time-evolution of electronic states in a Rashba anisotropic two-dimensional quantum dot

In this article we present the time evolution of the electronic spin and subbands states, of an electron in an anisotropic two dimensional Rashba quantum dot, to which a magnetic field of arbitrary strength is applied. We also explicitly include the confining (gate) effects as a two dimensional anisotropic harmonic oscillator. From the governing Hamiltonian we compute the time evolution of the initial state, leading to spin and subbands averages as functions of time. Our results indicate that the spin, on the average, precesses about the magnetic field, on an ellipse with intrinsic wobbling. The subbands populations, similar to the case of atom-photon interaction, follow the pattern of collapse–revivals.     

Full electrical control of the electron spin relaxation in GaAs quantum wells

The electron spin dynamics in (111)-oriented GaAs/AlGaAs quantum wells is studied by time-resolved photoluminescence spectroscopy. By applying an external electric field of 50 kV/cm a two-order of magnitude increase of the spin relaxation time can be observed reaching values larger than 30 ns; this is a consequence of the electric field tuning of the spin-orbit conduction band splitting which can almost vanish when the Rashba term compensates exactly the Dresselhaus one. The measurements under a transverse magnetic field demonstrate that the electron spin relaxation time for the three space directions can be tuned simultaneously with the applied electric field.     

A Realization of Yangian and Its Applications to the Bi-spin System in an External Magnetic Field

Yangian Y(sl(2)) is realized in the bi-spin system coupled with a time-dependent external magnetic field. It is shown that Y(sl(2)) generators can describe the transitions between the "spin triplet" and the "spin singlet" that evolve with time. Furthermore, new transition operators between the states with Berry phase factor and those between the states of nuclear magnetic resonance are presented.     

Heisenberg Model in a Rotating Magnetic Field

We study the Heisenberg model under the influence of a rotating magnetic field. By using a time-dependent unitary transformation, the time evolution operator for the Schrödinger equation is obtained, which involves no chronological product. The spin vectors (mean values of the spin operators) are obtained as explicit functions of time in the most general case. A series of cyclic solutions are presented. The nonadiabatic geometric phases of these cyclic solutions are calculated, and are expressed in terms of the solid angle subtended by the closed trace of the total spin vector, as well as in terms of those of the individual spins.     

Exactly-Analytical Approach for Neutrons in Magnetic Field and Berry's Phase Effect in Moving Translation Reference Frame

In connection with Bitter-Dubbers experiment, an exact solution for the quantum dynamics of neutrons in magnetic field which is harmonically inhomogeneous (helical) and changes harmonically with time is obtained by invoking a time-dependent transformation with spin space coupling. It predicts that a beam of neutrons with monotonous momentum will be split into two beams by the magnetic field. As its limiting case, the Berry's geometric phase in moving reference frame appears while the field is very strong.     

Damping-like effects in Heisenberg spin chain caused by the site-dependent bilinear interaction

We investigate a continuous Heisenberg spin chain equation which models the local magnetization in ferromagnet with time-and site-dependent inhomogeneous bilinear interaction and timedependent spin-transfer torque.By establishing the gauge equivalence between the spin chain equation and an integrable generalized nonlinear Schr?dinger equation,we present explicitly a novel nonautonomous magnetic soliton solution for the spin chain equation.The results display how the dynamics of the magnetic soliton can be controlled by the bilinear interaction and spin-polarized current.Especially,we find that the site-dependent bilinear interaction may break some conserved quantity,and give rise to damping-like effect in the spin evolution.