Optical Gaussian States Carrying Orbital Angular Momentum

Within the framework of the tomographic probability representation, we introduce specific optical Gaussian states, which were recently proved to carry the orbital angular momentum. We obtain the symplectic and optical tomograms defining uniquely both quantum and classical states for the rotating Gaussian states of light. This approach needs to be developed and applied to the mentioned states due to the convenience of using in the state reconstructions and measurements. Having in mind this aim, we obtain the mean values and variances of the amplitude quadratures directly measurable in the homodyne optical-tomography experiments. Also we consider the time evolution of the rotating Gaussian states in terms of the tomograms and obtain the corresponding tomographic propagator.