Study of Intrinsic Localized Modes in Quantum Lattices

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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