Waves and Excitations

Y. Ron Shen

The basic principles of four-wave mixing are reviewed. Emphasis is on the coupling between light waves and material excitational waves. Only cases where material excitations are excited by optical mixing of input waves are considered. The material excitations appear in the form of a dynamic grating that would coherently scatter the incoming radiation. Probing of the dynamic grating allows the deduction of information about the material excitations.

Nobuyuki Shukuno, Yuto Sano, Makoto Tsubota

We numerically study the dynamics of Faraday waves for Bose-Einstein condensates(BECs) trapped by anisotropic potentials using the three-dimensional Gross-Pitaevskii equation. In previous studies, Faraday waves were excited by periodic modulation of the interaction or potential; in contrast, this study systematically addresses the excitations of the two methods. When the interaction is modulated with a modulation frequency resonant with Faraday waves, the breathing mode along the tight confinement direction is excited, and the Faraday waves appear in the direction of weak confinement. A modulation frequency that is not resonant with Faraday waves does not excite Faraday waves. Thus, the dynamics depend on modulation frequencies. The behavior of the total energy and its decomposition characterize the dynamics. The excitation of Faraday waves depends on the anisotropy of the potentials as well; Faraday waves are excited only for elongated BECs. We compare the differences of the dynamics in modulation methods. There are no qualitative differences between the modulation of the interaction and potential. When the interaction and potential are simultaneously modulated, Faraday waves are excited but they do not necessarily work additively. To understand this phenomenon as a dynamical system, we choose a few dynamical variables and follow their trajectory in a phase space. The trajectory characteristics of Faraday waves and the breathing mode show that the methods of modulation are not very relevant; determining the target mode to excite is important.

Li-Zheng Lv, Peng Gao, Zhan-Ying Yang +1 more

Abstract We study the dynamics of rogue wave excitations and quasi-transitions in one-dimensional quantum droplets, whose homogeneous-density flat top provides an applicable background wave for nonlinear excitation. Using a quenching technique and a localized space modulation technique for the nonlinear effect coefficient, the rogue wave is excited on droplets. The excitation modes of rogue waves can be transitioned to dispersive shock waves or Kuznetsov–Ma breathers by regulating their modulation amplitude and width, and their maximal density and width can be regulated by modulation their amplitude. Meanwhile, two Gaussian modulations for droplets also bring the second-order rogue wave’s dynamics, whose maximal amplitude can approach 3.6 times that of the amplitude of droplets. Our results provide guidance for rogue wave excitation and transition on self-bound background waves and deepen our understanding of quantum droplets.