相关论文: Non-Abelian Geometric Phases Carried by the Spin F…

Adiabatic $U(2)$ geometric phases are studied for arbitrary quantum systems with a three-dimensional Hilbert space. Necessary and sufficient conditions for the occurrence of the non-Abelian geometrical phases are obtained without actually…

Geometric phases, arising from cyclic evolutions in a curved parameter space, appear in a wealth of physical settings. Recently, and largely motivated by the need of an experimentally realistic definition for quantum computing applications,…

A non-Abelian geometric method is proposed for rotating of heavy hole spins in a singly positive charged quantum dot in Voigt geometry. The key ingredient is the delay-dependent non-Abelian geometric phase, which is produced by the…

The spinorial ball is an electronic manipulable device that we recently introduced to discuss the origin of spin-1/2 from rotations group representation, without relying on the quantum mechanics framework. Nevertheless, it is also a…

Far from being just a 2-level Quantum system the Qubit is a Unit Quaternion, also known as a Spinor. Therefore it follows that the Qubit is a 4-dimensional vector which traces a path on the surface of the unit 3-sphere. This is the meaning…

We use the theory of dynamical invariants to yield a simple derivation of noncyclic analogues of the Abelian and non-Abelian geometric phases. This derivation relies only on the principle of gauge invariance and elucidates the existing…

Using concepts of geometric orthogonality and linear independence, we logically deduce the form of the Pauli spin matrices and the relationships between the three spatially orthogonal basis sets of the spin-1/2 system. Rather than a…

The algebraic consistency of spin and isospin at the level of an unbroken SU(2) gauge theory suggests the existence of an additional angular momentum besides the spin and isospin and also produces a full quaternionic spinor operator. The…

Quantum mechanical phase factors can be related to dynamical effects or to the geometrical properties of a trajectory in a given space - either parameter space or Hilbert space. Here, we experimentally investigate a quantum mechanical phase…

Geometric phases are important in quantum physics and now central to fault tolerant quantum computation. For spin-1/2 and SU(2), the Bloch sphere $S^2$, together with a U(1) phase, provides a complete SU(2) description. We generalize to…

We calculate the geometric phase of a spin-1/2 system driven by a one and two mode quantum field subject to decoherence. Using the quantum jump approach, we show that the corrections to the phase in the no-jump trajectory are different when…

Phase spaces with nontrivial geometry appear in different approaches to quantum gravity and can also play a role in e.g. condensed matter physics. However, so far such phase spaces have only been considered for particles or strings. We…

The Bloch sphere is a familiar and useful geometrical picture of the dynamics of a single spin or two-level system's quantum evolution. The analogous geometrical picture for three-level systems is presented, with several applications. The…

A two-sphere ("Bloch" or "Poincare") is familiar for describing the dynamics of a spin-1/2 particle or light polarization. Analogous objects are derived for unitary groups larger than SU(2) through an iterative procedure that constructs…

We propose a generalized quantum geometric tenor to understand topological quantum phase transitions, which can be defined on the parameter space with the adiabatic evolution of a quantum many-body system. The generalized quantum geometric…

We naturally obtain the NOT and CNOT logic gates, which are key pieces of quantum computing algorithms, in the framework of the non-Abelian Chern-Simons-Higgs theory in two spatial dimensions. For that, we consider the anyonic quantum…

The state of quantum systems, their energetics, and their time evolution is modeled by abstract operators. How can one visualize such operators for coupled spin systems? A general approach is presented which consists of several shapes…

We have constructed the geometric phases emerging from the non-trivial topology of a space-dependent magnetic field, interacting with the spin magnetic moment of a neutral particle. Our basic tool is the local unitary transformation which…

It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries…

We introduce a self-consistent framework for the analysis of both Abelian and non-Abelian geometric phases associated with open quantum systems, undergoing cyclic adiabatic evolution. We derive a general expression for geometric phases,…