Because of variety of gaps in excitation energies, a Quantum Hall system can be treated as a quantum mechanics with finite number of degrees of freedom at the low temperature limit. Especially, a bilayer Quantum Hall system on a sphere has two ground states and they rotate under a spin 1 2 representation of SU(2) with suffering an external electric field. We suggest this system can be regarded ...

The renormalization-group method is used to analyze the low-temperature behaviour of a two-dimentional, spin-s quantum Heisenberg ferromagnet. A set of recursion equations is derived in an one-loop approximation. The lowtemperature asymptotics of the correlation length and the uniform susceptibility are obtained. For small spins (s = 1/2, 1) the results are essentialy different from those in th...

We study junctions between superconductors mediated by the edge states of a quantum-spin-Hall insulator. We show that such junctions exhibit a fractional Josephson effect, in which the current phase relation has a 4π rather than a 2π periodicity. This effect is a consequence of the conservation of fermion parity—the number of electron mod 2—in a superconducting junction and is closely related t...

We use the spin-polarized excitons in a single quantum dot to design optical controls for basic operations in quantum computing. We examine the ultrafast nonlinear optical processes required and use the coherent nonlinear optical responses to deduce if such processes are physically reasonable. The importance and construction of an entangled state of polarized exciton states in a single quantum ...

We present a model system in R3 for a spin-1 quantum entity. If the state of the model system corresponds to a ’|s| = 1’-state of a spin-1 quantum entity, it behaves as a joint system of two separated spin2 quantum entities. If it corresponds to a ’s = 0’-state of a spin-1 quantum entity, it behaves as the joint system of two spin2 quantum entities that are entangled by correlations of the seco...

The integration of InAs/GaAs quantum dots into nanophotonic cavities has led to impressive demonstrations of cavity quantum electrodynamics. However, these demonstrations are primarily based on two-level excitonic systems. Efforts to couple long-lived quantum dot electron spin states with a cavity are only now succeeding. Here we report a two-spin-cavity system, achieved by embedding an InAs qu...

We use spin-density-functional theory to study the spacing between conductance peaks and the ground-state spin of 2D model quantum dots with up to 200 electrons. Distributions for different ranges of electron number are obtained in both symmetric and asymmetric potentials. The even/odd effect is pronounced for small symmetric dots but vanishes for large asymmetric ones, suggesting substantially...

We report the development of a fast pulse polarimeter for the application to quantum non-demolition measurement of atomic spin (Spin QND). The developed system was tunable to the atomic resonance of ytterbium atom and has narrow laser linewidth suitable for spin QND. Using the developed polarimeter, we successfully demonstrated the measurement of the vacuum noise, with 10 to 10 photon number pe...

We present an approach to the solution of the collinear form of the single-particle equations of relativistic spin-density-functional theory. It is based on the use of appropriate boundary conditions for r→0,` and the identification of ‘‘spin-up’’ and ‘‘spin-down’’ solutions by a node quantum number. A comparison with previous results and a complete set of reference data for atomic ground state...

In this chapter, we review the experimental efforts that focus on the measurement of single-electron spins in two particular Si-based semiconductor nanostructure systems. First, we describe experiments in a real transistor structure (i.e., a submicrometer commercial Si field effect transistor) in which the source/drain channel is used to electrically detect the spin states of an adjacent single...