  Based on N different coherent states with equal weights and phase-space
rotation symmetry, we introduce N-headed incoherent superposition states
(NHICSSs) and N-headed coherent superposition states (NHCSSs). These N coherent
states are associated with N-order roots of the same complex number. We study
and compare properties of NHICSSs and NHCSSs, including average photon number,
Mandel Q parameter, quadrature squeezing, Fock matrix elements and Wigner
function. Among all these states, only 2HCSS (i.e., Schrodinger cat state)
presents quadrature-squeezing effect. Our theoretical results can be used as a
reference for researchers in this field.
