Stability of the ground state of a harmonic oscillator in a monochromatic wave

The stability of the ground state of a harmonic oscillator in a monochromatic wave is studied. This model describes, in particular, the dynamics of a cold ion in a linear ion trap, interacting with two laser fields with close frequencies. The stability of the "classical ground state"-the vicinity of the point (x=0,p=0)-is analyzed analytically and numerically. For the quantum case, a method for studying a stability of the quantum ground state is developed, based on the quasienergy representation. It is demonstrated that stability of the ground state may be substantially improved by increasing the resonance number, l, where l=Omega/omega+delta, Omega and omega are, respectively, the wave frequency and the oscillator frequency, l=1,2,..., \ delta \ <1; or by detuning the system from exact resonance, so that delta not equal0. The influence of a large-amplitude wave (in the presence of chaos) on the stability of the ground state is analyzed for different parameters of the model in both the quantum and classical cases. (C) 2001 American Institute of Physics.