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Symmetries of phase space and optical states

Kappert, R (2013) Symmetries of phase space and optical states. Bachelor's Thesis, Mathematics.

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Coherent states are quantum mechanical states with properties close to the classical description. Before coherent states are considered there will be some theory about canonical transformations and Poisson brackets. Transformations that leave the Poisson bracket invariant are symplectic matrices and form for n dimensions the symplectic group Sp(2n;R). Sp(2,R) is isomorphic to SU(1,1), which has various representations. Coherent states can be created from the vacuum state by a displacement operator, which is in the super-Lie algebra of SU(1,1). Coherent states have minimal uncertainty and can be transformed to squeezed states. Squeezed states are states with one of its standard deviations smaller while the minimal uncertainty relation still holds. Squeezing can be done by the squeezing operator, which is in SU(1,1). Squeezed states can for example be used as qubit states or to amplify measurement signals without amplifying the noise.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 07:54
Last Modified: 15 Feb 2018 07:54

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