Geometric Phases forSU(3) Representations and Three Level Quantum Systems

1997 ◽  
Vol 253 (1) ◽  
pp. 55-82 ◽  
Author(s):  
G. Khanna ◽  
S. Mukhopadhyay ◽  
R. Simon ◽  
N. Mukunda
Keyword(s):  
Quantum Systems ◽  
Geometric Phases

scholarly journals Photonic implementation of Majorana-based Berry phases

2018 ◽  
Vol 4 (10) ◽  
pp. eaat6533 ◽  
Author(s):  
Jin-Shi Xu ◽  
Kai Sun ◽  
Jiannis K. Pachos ◽  
Yong-Jian Han ◽  
Chuan-Feng Li ◽  
...  
Keyword(s):  
Quantum Systems ◽  
Majorana Fermions ◽  
Topological Characteristic ◽  
Fundamental Physics ◽  
Geometric Phases ◽  
Physical Systems ◽  
All Optical ◽  
Topological Version ◽  
Berry Phases ◽  
Statistical Evolution

Geometric phases, generated by cyclic evolutions of quantum systems, offer an inspiring playground for advancing fundamental physics and technologies alike. The exotic statistics of anyons realized in physical systems can be interpreted as a topological version of geometric phases. However, non-Abelian statistics has not yet been demonstrated in the laboratory. Here, we use an all-optical quantum system that simulates the statistical evolution of Majorana fermions. As a result, we experimentally realize non-Abelian Berry phases with the topological characteristic that they are invariant under continuous deformations of their control parameters. We implement a universal set of Majorana-inspired gates by performing topological and nontopological evolutions and investigate their resilience against perturbative errors. Our photonic experiment, though not scalable, suggests the intriguing possibility of experimentally simulating Majorana statistics with scalable technologies.

scholarly journals BLOCH THEOREM FOR THE EVOLUTION OF STATES IN THE CYCLIC QUANTUM SYSTEMS AND THE UNIFICATION OF RESONANT GEOMETRIC PHASES

1997 ◽  
Vol 46 (2) ◽  
pp. 227
Author(s):  
LI BO-ZANG ◽  
ZHANG DE-GANG ◽  
WU JIAN-HUA ◽  
YAN FENG-LI
Keyword(s):  
Quantum Systems ◽  
Geometric Phases ◽  
Bloch Theorem

scholarly journals Ray space ‘Riccati’ evolution and geometric phases for N-level quantum systems

Pramana ◽  
2007 ◽  
Vol 69 (3) ◽  
pp. 317-327 ◽  
Author(s):  
S. Chaturvedi ◽  
E. Ercolessi ◽  
G. Marmo ◽  
G. Morandi ◽  
N. Mukunda ◽  
...  
Keyword(s):  
Quantum Systems ◽  
Geometric Phases ◽  
N Level

Experimental Detection of Geometric Phases I: Quantum Systems in Classical Environments

2003 ◽  
pp. 225-253 ◽  
Author(s):  
Arno Bohm ◽  
Ali Mostafazadeh ◽  
Hiroyasu Koizumi ◽  
Qian Niu ◽  
Joseph Zwanziger
Keyword(s):  
Quantum Systems ◽  
Geometric Phases ◽  
Experimental Detection

Experimental Detection of Geometric Phases II: Quantum Systems in Quantum Environments

2003 ◽  
pp. 255-275
Author(s):  
Arno Bohm ◽  
Ali Mostafazadeh ◽  
Hiroyasu Koizumi ◽  
Qian Niu ◽  
Joseph Zwanziger
Keyword(s):  
Quantum Systems ◽  
Geometric Phases ◽  
Experimental Detection
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