Study of Intrinsic Localized Modes in Quantum Lattices

为研究固体中声子振动的本征局域模式，研制了太赫兹非线性四波混合谱仪。对TEA激光器激发的连续波FIR激光器、二氧化碳气体激光器激发的连续波FIR激光器、钛蓝宝石激光器等傅立叶光谱仪进行了改进、转换和升级。那些设备已经操作过了。从理论上考虑了上述激光器的时间分辨四波混频光谱，得出了FIR激光器的频率必须与钛蓝宝石激光器重复频率的n次谐波重合的结论。必须调整钛蓝宝石激光器的腔长以达到这些频率的一致。空腔长度的调整估计在100mm以内，这样的长度调整是可能的。在本研究中，由于出现了意想不到的同步问题以及钛激光器的激发激光器出现故障，我们未能充分开发出FIR和钛蓝宝石激光器同步的四波混频光谱仪。然而，我们一直期待着开发完成，并测量固体的四波混合光谱。从非线性本征局域模态的角度对固体介质的相变现象进行了深入的研究。基于三阶非线性的本征局域模式已经在反铁磁体和MEMS振荡器中被实验观察到。四种混频光谱的测量和边带共振结构的发现是这些研究的有力工具。在本研究中，我们推测边带谐振结构的起源是交叉非线性谐振频移总是大于自非线性谐振频移。我们还推测，相同的机制保持这种非线性局域模式的形状。我们已经证实了类似的边带结构出现在基于二阶非线性的本征局域模式中，这是固体晶格振动所期望的。少

A THz nonlinear four wave mixing spectrometer has been developed for studies of intrinsic localized modes of phonon vibration in solids. A FIR laser excited by a TEA laser, a CW FIR laser excited by a carbon dioxide gas laser, a titanium-sapphire laser, Fourier spectrometers have been modified, converted and upgraded. Those equipments have been operated.From theoretical consideration of the time-resolved four wave mixing spectroscopy using above lasers, it has been concluded that the frequency of the FIR laser has to be coincide with a n-th harmonics of a repetition frequency of the titanium-sapphire laser. A cavity length of the titanium sapphire laser must be adjusted to achieve the coincidence of those frequencies. The adjustment of the cavity length is estimated to be within 100mm, and the adjustment with such length will be possible. In this study, we haven't achieved a full development of the four-wave mixing spectrometer with synchronized FIR and titanium-sapphire lasers, partia … More lly because of this unexpected synchronizing problem and because of a failure of an excitation laser of the titanium laser. However, we have been expecting that the development will be completed and four-wave mixing spectra of solids will be measured. It is also expected that problems of phase transition phenomena of solids like dielectrics will be well studied from the point of view of the nonlinear intrinsic localized modes.Intrinsic localized modes based on a 3rd order nonlinearity have been experimentally observed in antiferromagnets and MEMS oscillators. Measurements of four wave-mixing spectra and discovery of sideband resonant structure are very powerful tools in those studies. In this study, we have speculated that the origin of the sideband resonant structure is the fact that the cross nonlinear resonant frequency shift is always larger than the auto nonlinear resonant frequency shift. We have also speculating that the same mechanism keeps the shape of such nonlinear localized modes. We have confirmed that similar sideband structure appears for the intrinsic localized modes based on a 2nd order nonlinearity, that is expected for lattice vibrations of solid lattices. Less