Interpolating coherent states for Heisenberg$ndash$Weyl and single-photon SU(1, 1) algebras
S. Sivakumar · Journal of Physics A Mathematical and General · 2002
New quantal states which interpolate between the coherent states of the Heisenberg–Weyl ( W 3 ) and SU (1, 1) algebras are introduced. The interpolating states are coherent states of a closed and symmetric algebra containing a parameter k which takes values from zero to one. The elements of the algebra are realized in terms of operator-valued functions of creation and annihilation operators. The realization is such that the operators become those of the W 3 algebra when k = 0 and of the SU (1, 1) algebra when k is unity. The overcompleteness of the interpolating coherent states is established by constructing suitable integration measures. Differential operator representations for the elements of the algebra are given along with the relevant spaces of entire functions. A nonsymmetric set of operators to realize the W 3 algebra is presented and the relevant coherent states are studied. Physical properties such as squeezing and photon statistics of the interpolating coherent states are investigated.