Number and phase uncertainties of the [ital q]-analog quantized field
- Department of Physics, State University of New York at Binghamton, Binghamton, New York 13902-6016 (United States)
The [ital q]-analog coherent states [vert bar][ital z][r angle][sub [ital q]] are used to identify some of the canonical physical properties of the single-mode [ital q]-analog quantized radiation field in the [vert bar][ital z][r angle][sub [ital q]] classical limit'' where [vert bar][ital z][vert bar] is large. In this quantum-optics-like limit, the fractional uncertainties of most physical quantities (momentum, position, amplitude, phase) which characterize the quantum field are shown to be [ital O](1), and only vanish as [ital O](1/[vert bar][ital z][vert bar]) when [ital q]=1. In contrast to this more-quantum-like behavior for [ital q][ne]1, the fractional uncertainties do still approach zero for the usual number operator, [ital N], and the [ital N]-Hamiltonian [ital H][sub [ital N]][equivalent to][h bar][omega]([ital N]+1/2) which describes a free [ital q]-boson gas. An empirical signature for [ital q]-boson counting statistics is that ([Delta][ital N])[sup 2]/[l angle][ital N][r angle][r arrow]0 as [vert bar][ital z][vert bar][r arrow][infinity]. Properties of the [ital q]-analog generalizations of the phase operators of Susskind and Glogower (SG) and of the phase operator [cflx ]gf[sub [ital q]] of Pegg and Barnett are investigated. In contrast to the manifest [ital q] deformed properties of SG operators for moderate [vert bar][ital z][vert bar][sup 2], the Hermitian'' phase operator [cflx ]gf[sub [ital q]] still exhibits almost normal classical behavior in the [vert bar][ital z][r angle][sub [ital q]] basis. In particular, the conventional number-phase uncertainty relation [Delta][ital N][Delta][cflx ]gf[sub [ital q]][ge]1/2 and approximate commutation relation [[ital N],[cflx ]gf[sub [ital q]]]=[ital i] are found to follow for the single-mode [ital q]-analog quantized field. So [ital N] and [cflx ]gf[sub [ital q]] are [ital almost] [ital canonically] [ital conjugate] operators in the [vert bar][ital z][r angle][sub [ital q]] classical limit.
- DOE Contract Number:
- FG02-86ER40291
- OSTI ID:
- 6589438
- Journal Information:
- Physical Review A; (United States), Journal Name: Physical Review A; (United States) Vol. 51:3; ISSN 1050-2947; ISSN PLRAAN
- Country of Publication:
- United States
- Language:
- English
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