Symmetries of the squeezed Kerr oscillator

Abstract The algebraic structure of the squeezed Kerr oscillator sp(2,R)~su(1,1) is described. It is shown that the Kerr oscillator has a novel and hitherto unknown symmetry su(2) which occurs for integer values of the ratio η=Δ/K of detuning Δ to the Kerr coefficient K. The effect of quadratic, cubic and quartic squeezing of the Kerr oscillator is discussed. The results are of importance for the generation and stabilization of states useful for quantum computing.