Coherent states for equally spaced, homogeneous waveguide arrays
- URL: http://arxiv.org/abs/2112.01673v1
- Date: Fri, 3 Dec 2021 01:49:03 GMT
- Title: Coherent states for equally spaced, homogeneous waveguide arrays
- Authors: Julio Guerrero and H\'ector M. Moya-Cessa
- Abstract summary: Coherent states for homogeneous waveguide arrays are defined in the infinite, semiinfinite and finite cases.
In the finite case, a construction in terms of coherent states on the circle is given.
This construction is shown to be a regularization of the infinite and semiinfinite cases.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Coherent states for equally spaced, homogeneous waveguide arrays are defined,
in the infinite, semiinfinite and finite cases, and resolutions of the identity
are constructed, using different methods. In the infinite case, which
corresponds to Euclidean coherent states, a resolution of the identity with
coherent states on the circle and involving a nonlocal inner product is
reviewed. In the semiinfinite case, which corresponds to London coherent
states, various construction are given (restricting to the circle with a
non-local scalar product, rescaling the coherent states, modifying them, or
using a non-tight frame). In the finite case, a construction in terms of
coherent states on the circle is given, and this construction is shown to be a
regularization of the infinite and semiinfinite cases.
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