相关论文: A generalized Pancharatnam geometric phase formula…
Geometric Phase in Quantum Mechanics is generally formulated entirely in terms of geometric structure of the Complex Hilbert Space. We will exploit this fact in case of mixed states for three level open systems undergoing depolarization…
We analyze the geometric aspects of unitary evolution of general states for a multilevel quantum system by exploiting the structure of coadjoint orbits in the unitary group Lie algebra. Using the same method in the case of SU(3) we study…
The adiabatic geometric phases for general three state systems are discussed. An explicit parameterization for space of states of these systems is given. The abelian and non-abelian connection one-forms or vector potentials that would…
A theoretical analysis of Pancharatnam and Berry phases is made for biphoton three-level systems, which are produced via frequency degenerate co-linear spontaneous parametric down conversion (SPDC). The general theory of Pancharatnam phases…
A generalised notion of geometric phase for pure states is proposed and its physical manifestations are shown. An appreciation of fact that the interference phenomenon also manifests in the average of an observable, allows us to define the…
Geometric phase has historically been defined using closed cycles of polarization states, often derived using differential geometry on the Poincare sphere. Using the recently-developed wave model of geometric phase, we show that it is…
Quantum mechanical methods for getting geometric phases for mixed states are analyzed. Parallel transport equations for pure states are generalized to mixed states by which dynamical phases are eliminated. The geometric phases of mixed…
We present the first scheme for producing and measuring an Abelian geometric phase shift in a three-level system where states are invariant under a non-Abelian group. In contrast to existing experiments and proposals for experiments, based…
Distinct from the dynamical phase, in a cyclic evolution, a system's state may acquire an additional component, a.k.a. geometric phase. The latter is a manifestation of a closed path in state space. Geometric phases underlie various…
We adopt a three-level bosonic model to investigate the quantum phase transition in an ultracold atom-molecule conversion system which includes one atomic mode and two molecular modes. Through thoroughly exploring the properties of energy…
Geometric phase, owing to its topological nature and properties of fault tolerance, plays an important role in devising real world applications in both classical and quantum domain. For classical systems, geometric phase has been observed…
An operator generalisation of the notion of geometric phase has been recently proposed purely based on physical grounds. Here we provide a mathematical foundation for its existence, while uncovering new geometrical structures in quantum…
When quantum mechanical qubits as elements of two dimensional complex Hilbert space are generalized to elements of even subalgebra of geometric algebra over three dimensional Euclidian space, geometrically formal complex plane becomes…
We consider various approaches to treat the phases of a qutrit. Although it is possible to represent qutrits in a convenient geometrical manner by resorting to a generalization of the Poincare sphere, we argue that the appropriate way of…
We present a new approach to quantum computation involving the geometric phase. In this approach, an entire computation is performed by adiabatically evolving a suitably chosen quantum system in a closed circuit in parameter space. The…
The phase structure of a two-fluid bosonic system is investigated. The proton-neutron interacting boson model (IBM-2) posesses a rich phase structure involving three control parameters and multiple order parameters. The surfaces of quantum…
Geometric phases are a universal concept that underpins numerous phenomena involving multi-component wave fields. These polarization-dependent phases are inherent in interference effects, spin-orbit interaction phenomena, and topological…
Since Pancharatnam's 1956 discovery of optical geometric phase, and Berry's 1984 discovery of geometric phase in quantum systems, researchers analyzing geometric phase have focused almost exclusively on algebraic approaches using the Jones…
We present a generalized Poincar\'e sphere (G sphere) and generalized Stokes parameters (G parameters), as a geometric representation, which unifies the descriptors of a variety of vector fields. Unlike the standard Poincar\'e sphere, the…
We provide explicit formulae for the noncyclic geometric phases or Pancharatnam phases of neutrino oscillations. Since Pancharatnam phase is a generalization of the Berry phase, our results generalize the previous findings for Berry phase…