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.

Constructing physical systems with dynamical symmetry

2014 ◽  
Vol 92 (4) ◽  
pp. 335-340
Author(s):  
Yan Li ◽  
Fu-Lin Zhang ◽  
Rui-Juan Gu ◽  
Jing-Ling Chen ◽  
L.C. Kwek
Keyword(s):  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Dynamical Symmetry ◽  
Algebraic Method ◽  
Quantum Systems ◽  
Physical Systems ◽  
Generalized Systems ◽  
Dependent Mass ◽  
Position Dependent Mass

An approach to constructing quantum systems with dynamical symmetry is proposed. As examples, we construct generalized systems of the hydrogen atom and harmonic oscillator, which can be regarded as the systems with position-dependent mass. They have symmetries that are similar to the corresponding ones, and can be solved by using the algebraic method. We also exhibit an example of the method applied to the noncentral field.

scholarly journals Bargmann invariants, geometric phases and recursive parametrization with Majorana fermions

2021 ◽  
Vol 964 ◽  
pp. 115315
Author(s):  
Rohan Pramanick ◽  
Swarup Sangiri ◽  
Utpal Sarkar
Keyword(s):  
Majorana Fermions ◽  
Geometric Phases

QUANTUM DISCORD UNDER SYSTEM–ENVIRONMENT COUPLING: THE TWO-QUBIT CASE

2012 ◽  
Vol 27 (01n03) ◽  
pp. 1345054 ◽  
Author(s):  
JIN-SHI XU ◽  
CHUAN-FENG LI
Keyword(s):  
Quantum Discord ◽  
Open Quantum Systems ◽  
Short Review ◽  
Quantum Systems ◽  
External Control ◽  
Control Effect ◽  
Fundamental Physics ◽  
System Environment ◽  
Open Quantum ◽  
Distinct Property

Open quantum systems have attracted great attention, since inevitable coupling between quantum systems and their environment greatly affects the features of interest of these systems. Quantum discord, is a measure of the total nonclassical correlation in a quantum system that includes, but is not exclusive to, the distinct property of quantum entanglement. Quantum discord can exist in separated quantum states and plays an important role in many fundamental physics problems and practical quantum information tasks. There have been numerous investigations on quantum discord and its counterpart classical correlation. This short review focuses on highlighting the system–environment dynamics of two-qubit quantum discord and the influence of initial system–environment correlations on the dynamics of open quantum systems. The external control effect on the dynamics of open quantum systems are involved. Several related experimental works are discussed.

scholarly journals Experimentally Accessible Witnesses of Many-Body Localization

2019 ◽  
Vol 1 (1) ◽  
pp. 50-62 ◽  
Author(s):  
Marcel Goihl ◽  
Mathis Friesdorf ◽  
Albert H. Werner ◽  
Winton Brown ◽  
Jens Eisert
Keyword(s):  
Statistical Physics ◽  
Optical Lattices ◽  
Cold Atoms ◽  
Quantum Statistical Mechanics ◽  
Quantum Systems ◽  
Many Body ◽  
Physical Systems ◽  
Tensor Network ◽  
Distinct Features ◽  
Flight Measurements

The phenomenon of many-body localized (MBL) systems has attracted significant interest in recent years, for its intriguing implications from a perspective of both condensed-matter and statistical physics: they are insulators even at non-zero temperature and fail to thermalize, violating expectations from quantum statistical mechanics. What is more, recent seminal experimental developments with ultra-cold atoms in optical lattices constituting analog quantum simulators have pushed many-body localized systems into the realm of physical systems that can be measured with high accuracy. In this work, we introduce experimentally accessible witnesses that directly probe distinct features of MBL, distinguishing it from its Anderson counterpart. We insist on building our toolbox from techniques available in the laboratory, including on-site addressing, super-lattices, and time-of-flight measurements, identifying witnesses based on fluctuations, density–density correlators, densities, and entanglement. We build upon the theory of out of equilibrium quantum systems, in conjunction with tensor network and exact simulations, showing the effectiveness of the tools for realistic models.

All-optical polarimetric generation of mixed-state single-photon geometric phases

2016 ◽  
Vol 93 (1) ◽  
Author(s):  
D. Barberena ◽  
O. Ortíz ◽  
Y. Yugra ◽  
R. Caballero ◽  
F. De Zela
Keyword(s):  
Mixed State ◽  
Single Photon ◽  
Geometric Phases ◽  
All Optical

Do granular systems obey statistical mechanics? A review of recent work assessing the applicability of equilibrium theory to vibrationally excited granular media

2017 ◽  
Vol 31 (10) ◽  
pp. 1742010 ◽  
Author(s):  
C. R. K. Windows-Yule
Keyword(s):  
Granular Media ◽  
Mechanical Energy ◽  
Theoretical Models ◽  
Canonical System ◽  
Granular Systems ◽  
Vibrationally Excited ◽  
Fundamental Physics ◽  
Physical Systems ◽  
Classical Systems ◽  
Granular Physics

Driven granular media — assemblies of discrete, macroscopic elements exposed to a source of mechanical energy — represent inherently out-of-equilibrium systems. Although granular media are ubiquitous in both nature and industry, due to their dissipative nature and resultant complex behaviors they remain startlingly poorly understood as compared to classical, thermodynamic systems. Nonetheless, in recent years it has been observed that the behaviors of granular media can, under certain circumstances, closely resemble those of equilibrium systems. One of the most important contemporary questions in the field of granular physics is whether these similarities are merely superficial, or whether the parallels run deep enough that the behaviors of these nonequilibrium systems can in fact be successfully captured using analogs to existing theoretical models developed for classical systems. In this review, we draw together the findings of a variety of recent studies where this question has been addressed, comparing and contrasting the results and conclusions presented. We focus our attention on vibrated and vibrofluidized granular beds, which provide a canonical system representative of various equilibrium and nonequilibrium physical systems, and whose simple dynamics offer a valuable testing ground for exploring the fundamental physics of the granular state.

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 Emergence of PT-symmetry breaking in open quantum systems

2020 ◽  
Vol 9 (4) ◽  
Author(s):  
Julian Huber ◽  
Peter Kirton ◽  
Stefan Rotter ◽  
Peter Rabl
Keyword(s):  
Symmetry Breaking ◽  
Open Quantum Systems ◽  
Symmetry Transformation ◽  
Quantum Systems ◽  
Coupled Systems ◽  
Physical Systems ◽  
Open Quantum ◽  
Parity Symmetry ◽  
Classical Correspondence ◽  
Liouville Operators

The effect of \mathcal{PT}𝒫𝒯-symmetry breaking in coupled systems with balanced gain and loss has recently attracted considerable attention and has been demonstrated in various photonic, electrical and mechanical systems in the classical regime. However, it is still an unsolved problem how to generalize the concept of \mathcal{PT}𝒫𝒯 symmetry to the quantum domain, where the conventional definition in terms of non-Hermitian Hamiltonians is not applicable. Here we introduce a symmetry relation for Liouville operators that describe the dissipative evolution of arbitrary open quantum systems. Specifically, we show that the invariance of the Liouvillian under this symmetry transformation implies the existence of stationary states with preserved and broken parity symmetry. As the dimension of the Hilbert space grows, the transition between these two limiting phases becomes increasingly sharp and the classically expected \mathcal{PT}𝒫𝒯-symmetry breaking transition is recovered. This quantum-to-classical correspondence allows us to establish a common theoretical framework to identify and accurately describe \mathcal{PT}𝒫𝒯-symmetry breaking effects in a large variety of physical systems, operated both in the classical and quantum regimes.

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