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Turn of Geometric Phase to Topological Phase in Gaussian Structured Light

Shokhmkar, Mahdi | 2020

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53456 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Bahrampour, Alireza; Bathaee, Marziehsadat
  7. Abstract:
  8. One of the challenging issues in quantum technologies is to be proper control of quantum systems. This plays an important role in a variety of physics fields such as quantum computation, simulation, information etc. Undesirable effects as well as presence of noises in real systems disturb the preferable quantum system evolution. Since a geometric phase (GP) caused from the Holonomy corresponding to a Hilbert space does not depend on the path parameter, it is independent of dynamical evolutions which can introduce control noises. Therefore, the GPs can be adequate candidates for implementing noise resistance quantum gates. Recently, [1] investigated a formalism in which the GP accumulated in a cyclic evolution of a spin system can be related to a topological property of projective Hilbert space provided the state of the system is anti-coherent and the evolution is a sequence of rotations in physical space. In this thesis we review both geometric and topological phases (TP) in physical systems by focusing on angular momentum systems. Then, we present how GP can be interpreted as TP. Meanwhile, we study the classical structured gaussian (SG) light in paraxial approximation and its related linear canonical transformations by virtue of mathematical formalisms of quantum mechanics used especially for describing a harmonic oscillator system. Then, we show the previously introduced discrete Holonomy in SG light can be seen as a topological phase. Finally, we show how one can translate this formalism to single photon SG
  9. Keywords:
  10. Geometric Phase ; Topological phase ; Structured Light ; Discrete Holonomy ; Gaussian Structured Light ; Quantum System

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