1,950 research outputs found
Squeezing: the ups and downs
We present an operator theoretic side of the story of squeezed states
regardless the order of squeezing. For low order, that is for displacement
(order 1) and squeeze (order 2) operators, we bring back to consciousness what
is know or rather what has to be known by making the exposition as exhaustive
as possible. For the order 2 (squeeze) we propose an interesting model of the
Segal-Bargmann type. For higher order the impossibility of squeezing in the
traditional sense is proved rigorously. Nevertheless what we offer is the
state-of-the-art concerning the topic.Comment: 21 pages; improved presentation; it has been published by Proceedings
of the Royal Society
Complex and real Hermite polynomials and related quantizations
It is known that the anti-Wick (or standard coherent state) quantization of
the complex plane produces both canonical commutation rule and quantum spectrum
of the harmonic oscillator (up to the addition of a constant). In the present
work, we show that these two issues are not necessarily coupled: there exists a
family of separable Hilbert spaces, including the usual Fock-Bargmann space,
and in each element in this family there exists an overcomplete set of
unit-norm states resolving the unity. With the exception of the Fock-Bargmann
case, they all produce non-canonical commutation relation whereas the quantum
spectrum of the harmonic oscillator remains the same up to the addition of a
constant. The statistical aspects of these non-equivalent coherent states
quantizations are investigated. We also explore the localization aspects in the
real line yielded by similar quantizations based on real Hermite polynomials.Comment: 15 pages, 6 figure
- …