Berman Gennady P., James Daniel F. V., Kamenev Dmitry I.
Theoretical Division and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545.
Chaos. 2001 Sep;11(3):449-463. doi: 10.1063/1.1383786.
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, em leader, mid R:deltamid R:<1; or by detuning the system from exact resonance, so that delta not equal 0. 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.
研究了简谐振子在单色波中基态的稳定性。该模型特别描述了线性离子阱中冷离子与两个频率相近的激光场相互作用的动力学。对“经典基态”——点(x = 0, p = 0)附近的稳定性进行了分析和数值研究。对于量子情况，基于准能量表示法开发了一种研究量子基态稳定性的方法。结果表明，通过增加共振数l（其中l = Ω/ω + δ，Ω和ω分别是波频率和振子频率，l = 1, 2, …，|δ| << 1），或者使系统偏离精确共振（即δ ≠ 0），可以显著提高基态的稳定性。在量子和经典两种情况下，针对模型的不同参数分析了大振幅波（存在混沌时）对基态稳定性的影响。(c) 2001美国物理研究所。
