New generalized coherent states

We construct a new family of boson coherent states using a specially designed function which is a solution of a functional equation d epsilon(q, x)/dx = epsilon(q, qx) with 0 less than or equal to q less than or equal to 1 and epsilon(q, 0) = 1. We use this function in place of the usual exponential to generate new coherent states \q, z] from the vacuum, which are normalized and continuous in their label z. These states allow the resolution of unity, and a corresponding weight function is furnished by the exact solution of the associated Stieltjes moment problem. They also permit exact evaluation of matrix elements of an arbitrary polynomial given as a normally-ordered function of boson operators. We exemplify this by showing that the photon number statistics for these states is sub-Poissonian. For any q < 1 the states \q, z] are squeezed; we obtain and discuss their signal to quantum noise ratio. The function e( q, x) allows a natural generation of multiboson coherent states of arbitrary multiplicity, which is impossible for the usual coherent states. For q = 1 all the above results reduce to those for conventional coherent states. Finally, we establish a link with q-deformed bosons. (C) 1999 American Institute of Physics. [S0022-2488(99)01404-8].