dorsal/arxiv
View SchemaBarut-Girardello coherent states for u(p,q) and sp(N,R) and their macroscopic superpositions
| Authors | D. A. Trifonov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9711066 |
| URL | https://arxiv.org/abs/quant-ph/9711066 |
| DOI | 10.1088/0305-4470/31/26/008 |
| Journal | J.Phys.A31:5673-5696,1998 |
Abstract
The Barut-Girardello coherent states (BG CS) representation is extended to the noncompact algebras u(p,q) and sp(N,R) in (reducible) quadratic boson realizations. The sp(N,R) BG CS take the form of multimode ordinary Schr\"odinger cat states. Macroscopic superpositions of 2^{n-1} sp(N,R) CS (2^n canonical CS, n=1,2,...) are pointed out which are overcomplete in the N-mode Hilbert space and the relation between the canonical CS and the u(p,q) BG-type CS representations is established. The sets of u(p,q) and sp(N,R) BG CS and their discrete superpositions contain many states studied in quantum optics (even and odd N-mode CS, pair CS) and provide an approach to quadrature squeezing, alternative to that of intelligent states. New subsets of weakly and strongly nonclassical states are pointed out and their statistical properties (first- and second-order squeezing, photon number distributions) are discussed. For specific values of the angle parameters and small amplitude of the canonical CS components these states approaches multimode Fock states with one, two or three bosons/photons. It is shown that eigenstates of a squared non-Hermitian operator A^2 (generalized cat states) can exhibit squeezing of the quadratures of A.
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"abstract": "The Barut-Girardello coherent states (BG CS) representation is extended to\nthe noncompact algebras u(p,q) and sp(N,R) in (reducible) quadratic boson\nrealizations. The sp(N,R) BG CS take the form of multimode ordinary\nSchr\\\"odinger cat states. Macroscopic superpositions of 2^{n-1} sp(N,R) CS (2^n\ncanonical CS, n=1,2,...) are pointed out which are overcomplete in the N-mode\nHilbert space and the relation between the canonical CS and the u(p,q) BG-type\nCS representations is established. The sets of u(p,q) and sp(N,R) BG CS and\ntheir discrete superpositions contain many states studied in quantum optics\n(even and odd N-mode CS, pair CS) and provide an approach to quadrature\nsqueezing, alternative to that of intelligent states. New subsets of weakly and\nstrongly nonclassical states are pointed out and their statistical properties\n(first- and second-order squeezing, photon number distributions) are discussed.\nFor specific values of the angle parameters and small amplitude of the\ncanonical CS components these states approaches multimode Fock states with one,\ntwo or three bosons/photons. It is shown that eigenstates of a squared\nnon-Hermitian operator A^2 (generalized cat states) can exhibit squeezing of\nthe quadratures of A.",
"arxiv_id": "quant-ph/9711066",
"authors": [
"D. A. Trifonov"
],
"categories": [
"quant-ph",
"nucl-th"
],
"doi": "10.1088/0305-4470/31/26/008",
"journal_ref": "J.Phys.A31:5673-5696,1998",
"title": "Barut-Girardello coherent states for u(p,q) and sp(N,R) and their macroscopic superpositions",
"url": "https://arxiv.org/abs/quant-ph/9711066"
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