Wigner Functions and Spin Tomograms for Qubit States

We establish the relation of the spin tomogram to the Wigner function on a discrete phase space of qubits. We use the quantizers and dequantizers of the spin tomographic star-product scheme for qubits to derive the expression for the kernel connecting Wigner symbols on the discrete phase space with the tomographic symbols.     

Standard quantum mechanics featuring probabilities instead of wave functions

A new formulation of quantum mechanics (probability representation) is discussed. In this representation, a quantum state is described by a standard positive definite probability distribution (tomogram) rather than by a wave function. An unambiguous relation (analog of Radon transformation) between the density operator and a tomogram is constructed both for continuous coordinates and for spin variables. A novel feature of a state, tomographic entropy, is considered, and its connection with von Neumann entropy is discussed. A one-to-one map of quantum observables (Hermitian operators) on positive probability distributions is found.     

Probability-Representation Entropy for Spin-State Tomogram

The probability-representation entropy (tomographic entropy) of an arbitrary quantum state is introduced. Using the properties of the spin tomogram as the standard probability-distribution function, the tomographic entropy notion is discussed. The relation of tomographic entropy to Shannon entropy and von Neumann entropy is elucidated.     

Contextuality and the probability representation of quantum states

We consider the notions of contextuality and noncontextuality within the framework of the probability representation of quantum states. We present an example of qutrit states and violation of the noncontextuality inequalities using the spin tomogram and tomographic symbols of the observables.     

Bound entangled states of four qubits in the tomographic-probability representation

We discuss the entanglement phenomenon on the example of the Smolin state of four qubits. This state is known as the bound entangled state and its spin tomogram is found in an explicit form. We apply the qubit-portrait method for investigating the violation of the Bell inequalities, since this approach provides another tool to prove the entanglement properties of the four-qubit state under consideration.     

Dissipative Evolution of the Qubit State in the Tomographic-Probability Representation

We consider the evolution of qubit states for the Demkov problem in the presence of dephasing processes in the spin tomographic-probability representation. We present an explicit solution of the spin tomogram in terms of the ₁ F ₂ hypergeometric function. We calculate the tomographic Shannon and q entropies through the solution of the master equation in the form of tomographic-probability distribution of the qubit states obtained.     

NQR Spin Diffusion in an Inhomogeneous Internal Field

The theory of NQR spin diffusion is extended to the case of spin lattice relaxation and spin diffusion in an inhomogeneous field. Two coupled equations describing the mutual relaxation and the spin diffusion of the nuclear magnetization and dipolar energy were obtained by using the method of nonequilibrium state operator. The equations were solved for short and long times approximation corresponding to the direct and diffusion relaxation regimes.     

半导体中的自旋弛豫--从体材料到量子阱、量子线、量子点

本文对半导体中的自旋弛豫过程给出一个简要的回顾,介绍了半导体材料从体材料到量子阱、量子线、量子点不同维数的结构中各种自旋弛豫过程,主要关注了自旋去相位和相干控制。对于不同材料中的各种弛豫机制,关注的重点在于如何能够在实验上以一种可以控制的方式来改变可调参数从而达到控制自旋弛豫过程。这些参数主要有电场、磁场、温度、应变、有效g因子等等。本文的组织上,首先介绍研究前景,第1部分简要介绍了自旋弛豫的四种机制。第2部分按照维数的不同将半导体中自旋弛豫分为3个部分:体材料、量子阱、量子线、量子点,在每一部分中又基本上按照电子、空穴、激子的顺序进行了简要的总结:对于不同的载流子,考虑了自旋弛豫对可调参数的依赖关系。这些结果要么试图解释了已有的实验结果,要么从理论上给出预言从而给实验指明了方向,为室温下可以使用的自旋电子学器件设计提供了依据,为固态量子计算和量子信息处理铺平了道路。最后简单地给出展望。     

14N核四极共振自旋系统自旋-晶格弛豫时间的测量

¹⁴N核四极共振自旋系统的自旋-晶格弛豫是一种双指数弛豫。本文介绍了¹⁴N核四极共振自旋系统的自旋-晶格弛豫时间的3种测量方法,利用可变多面体方法对实验数据进行拟合,获得了¹⁴N核四极共振自旋系统的自旋-晶格弛豫时间T_1s和T₁₁,对有关文献中关于核四极共振弛豫时间的测量的3个观点提出了质疑。     

半导体中的自旋弛豫——从体材料到量子阱、量子线、量子点

本文对半导体中的自旋弛豫过程给出一个简要的回顾,介绍了半导体材料从体材料到量子阱、量子线、量子点不同维数的结构中各种自旋弛豫过程,主要关注了自旋去相位和相干控制。对于不同材料中的各种弛豫机制,关注的重点在于如何能够在实验上以一种可以控制的方式来改变可调参数从而达到控制自旋弛豫过程。这些参数主要有电场、磁场、温度、应变、有效g因子等等。本文的组织上,首先介绍研究前景,第1部分简要介绍了自旋弛豫的四种机制。第2部分按照维数的不同将半导体中自旋弛豫分为3个部分:体材料、量子阱、量子线、量子点,在每一部分中又基本上按照电子、空穴、激子的顺序进行了简要的总结:对于不同的载流子,考虑了自旋弛豫对可调参数的依赖关系。这些结果要么试图解释了已有的实验结果,要么从理论上给出预言从而给实验指明了方向,为室温下可以使用的自旋电子学器件设计提供了依据,为固态量子计算和量子信息处理铺平了道路。最后简单地给出展望。     

Spin diffusion of dipolar energy in NQR

The theory of spin diffusion was extended to the case of nuclear dipolar order in solids containing paramagnetic impurities and nuclei with spin I > 1/2 having nuclear quadrupole moment. We show that spin diffusion process of dipolar order takes place in solids containing paramagnetic impurities. At the start of relaxation process, the direct relaxation regime is realized with non-exponential time dependence. Then the relaxation regime will be changed to diffusion-limited one. Using obtained expressions for the spin lattice relaxation times for these two relaxation regimes, the diffusion coefficient of the dipolar order in nuclear quadrupole resonance can be estimated from experimental data.     

Tuning of the Electron Spin Relaxation Anisotropy via Optical Gating in GaAs/AlGaAs Quantum Wells

The carrier-density-dependent spin relaxation dynamics for modulation-doped GaAs/Al_(0.3)Ga_(0.7)As quantum weiis is studied using the time-resolved magneto-Kerr rotation measurements.The electron spin relaxation time and its in-plane anisotropy are studied as a function of the optically injected electron density.Moreover,the relative strength of the Rashba and the Dresselhaus spin-orbit coupling fields,and thus the observed spin relaxation time anisotropy,is further tuned by the additional excitation of a 532 nm continuous wave laser,demonstrating an effective spin relaxation manipulation via an optical gating method.     

Spin relaxation in single-layer and bilayer graphene

We investigate spin relaxation in graphene spin valves and observe strongly contrasting behavior for single-layer graphene (SLG) and bilayer graphene (BLG). In SLG, the spin lifetime (τ(s)) varies linearly with the momentum scattering time (τ(p)) as carrier concentration is varied, indicating the dominance of Elliot-Yafet (EY) spin relaxation at low temperatures. In BLG, τ(s) and τ(p) exhibit an inverse dependence, which indicates the dominance of Dyakonov-Perel spin relaxation at low temperatures. The different behavior is due to enhanced screening and/or reduced surface sensitivity of BLG, which greatly reduces the impurity-induced EY spin relaxation.     

Transient grating studies of phase and spin relaxations of excitons in GaAs single quantum wells

Exciton spin and phase relaxations at low temperatures in GaAs/AlGaAs single quantum wells were investigated by using transient grating technique. The technique allows us to obtain the exciton lifetime, spin relaxation, and phase relaxation in the same setup. In combination with a series of single quantum wells grown on the same substrate, the well width dependence of exciton spin relaxation was studied. The obtained spin relaxation results were analyzed with their phase relaxation times in a framework of MAS mechanism, and were in good agreement with the calculated results. Especially, the motional narrowing character of the exciton spin relaxation was well demonstrated.     

Spin relaxation and decoherence of holes in quantum dots

We investigate heavy-hole spin relaxation and decoherence in quantum dots in perpendicular magnetic fields. We show that at low temperatures the spin decoherence time is 2 times longer than the spin relaxation time. We find that the spin relaxation time for heavy holes can be comparable to or even longer than that for electrons in strongly two-dimensional quantum dots. We discuss the difference in the magnetic-field dependence of the spin relaxation rate due to Rashba or Dresselhaus spin-orbit coupling for systems with positive (i.e., GaAs quantum dots) or negative (i.e., InAs quantum dots) g factor.     

Ab initio GW calculations of the time and length of spin relaxation of excited electrons in metals with inclusion of the spin-orbit coupling

An ab initio method has been proposed for calculating the spin relaxation time of excited electrons in metals in the framework of the GW method with inclusion of the spin-orbit coupling. The time and length of spin relaxation in Al, Cu, Au, Nb, and Ta have been calculated. The concept of the spin-flip phase space has been introduced. It has been demonstrated that the ratio between the spin relaxation time and the lifetime of the excited electron is well explained within this concept. The time and length of spin relaxation in Nb appear to be considerably shorter than those in Al, Cu, and Au. These quantities in Ta are especially small in accordance with the strong spin-orbit coupling. A comparison of the results with the previous data on the time and length of spin relaxation due to the interaction with impurities and phonons shows that, at an excited electron energy of the order of 1 eV, the inelastic electron-electron scattering in the presence of spin-orbit coupling is a dominant mechanism of spin relaxation.