Generalized coherent states and the control of quantum systems

2005 ◽  
Vol 46 (12) ◽  
pp. 122106 ◽  
Author(s):  
Holger Teismann
Keyword(s):  
Coherent States ◽  
Quantum Systems ◽  
Generalized Coherent States ◽  
Control Of Quantum Systems

VECTOR COHERENT STATES AND NON-ABELIAN GAUGE STRUCTURES IN QUANTUM MECHANICS

1990 ◽  
Vol 05 (22) ◽  
pp. 4311-4331 ◽  
Author(s):  
G. GIAVARINI ◽  
E. ONOFRI
Keyword(s):  
Quantum Mechanics ◽  
Lie Group ◽  
Coherent States ◽  
Quantum Systems ◽  
Semisimple Lie Group ◽  
Abelian Gauge ◽  
Geometric Properties ◽  
Generalized Coherent States ◽  
Abelian Case ◽  
Vector Coherent States

We set the general formalism for calculating Berry's phase in quantum systems with Hamiltonian belonging to the algebra of a semisimple Lie group of any rank in the framework of generalized coherent states. Within this approach the geometric properties of Berry's connection are also studied, both in the Abelian and non-Abelian cases. In particular we call attention to the non-Abelian case where we make use of a vectorial generalization of coherent states. In this respect a thorough and self-contained exposition of the formalism of vector coherent states is given. The specific examples of the groups SU(3) and Sp(2) are worked out in detail.

scholarly journals Time and classical equations of motion from quantum entanglement via the Page and Wootters mechanism with generalized coherent states

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Caterina Foti ◽  
Alessandro Coppo ◽  
Giulio Barni ◽  
Alessandro Cuccoli ◽  
Paola Verrucchi
Keyword(s):  
Classical Limit ◽  
Coherent States ◽  
Equations Of Motion ◽  
Quantum Systems ◽  
Physical Systems ◽  
Quantum Time ◽  
First Case ◽  
Hamilton Equations ◽  
Generalized Coherent States ◽  
Evolving System

AbstractWe draw a picture of physical systems that allows us to recognize what “time” is by requiring consistency with the way that time enters the fundamental laws of Physics. Elements of the picture are two non-interacting and yet entangled quantum systems, one of which acting as a clock. The setting is based on the Page and Wootters mechanism, with tools from large-N quantum approaches. Starting from an overall quantum description, we first take the classical limit of the clock only, and then of the clock and the evolving system altogether; we thus derive the Schrödinger equation in the first case, and the Hamilton equations of motion in the second. This work shows that there is not a “quantum time”, possibly opposed to a “classical” one; there is only one time, and it is a manifestation of entanglement.

scholarly journals Multiparticle quantum plasmonics

Nanophotonics ◽  
2020 ◽  
Vol 9 (6) ◽  
pp. 1243-1269 ◽  
Author(s):  
Chenglong You ◽  
Apurv Chaitanya Nellikka ◽  
Israel De Leon ◽  
Omar S. Magaña-Loaiza
Keyword(s):  
Quantum Dynamics ◽  
Degrees Of Freedom ◽  
Single Photon ◽  
Quantum Systems ◽  
Many Body ◽  
Statistical Fluctuations ◽  
Quantum Plasmonics ◽  
Control Of Quantum Systems ◽  
Multiparticle Systems ◽  
Quantum Photonics

AbstractA single photon can be coupled to collective charge oscillations at the interfaces between metals and dielectrics forming a single surface plasmon. The electromagnetic near-fields induced by single surface plasmons offer new degrees of freedom to perform an exquisite control of complex quantum dynamics. Remarkably, the control of quantum systems represents one of the most significant challenges in the field of quantum photonics. Recently, there has been an enormous interest in using plasmonic systems to control multiphoton dynamics in complex photonic circuits. In this review, we discuss recent advances that unveil novel routes to control multiparticle quantum systems composed of multiple photons and plasmons. We describe important properties that characterize optical multiparticle systems such as their statistical quantum fluctuations and correlations. In this regard, we discuss the role that photon-plasmon interactions play in the manipulation of these fundamental properties for multiparticle systems. We also review recent works that show novel platforms to manipulate many-body light-matter interactions. In this spirit, the foundations that will allow nonexperts to understand new perspectives in multiparticle quantum plasmonics are described. First, we discuss the quantum statistical fluctuations of the electromagnetic field as well as the fundamentals of plasmonics and its quantum properties. This discussion is followed by a brief treatment of the dynamics that characterize complex multiparticle interactions. We apply these ideas to describe quantum interactions in photonic-plasmonic multiparticle quantum systems. We summarize the state-of-the-art in quantum devices that rely on plasmonic interactions. The review is concluded with our perspective on the future applications and challenges in this burgeoning field.

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