Phonon bound state

T. J. Greytak, R. Woerner, J. Yan, and R. Benjamin. Experimental evidence for a two-phonon bound state in superfluid helium. Phys. Rev. Lett., 25 1547-1550 (1970). 

Light scattering from phonon bound states ... 

Frequencies of some phonons as measured by neutron scattering compared to Raman scattering frequencies of phonon bound states observed simultaneously in Raman scattering as well as the average of the Raman LO(L) frequency and the Raman bound state weighted by the Raman-... 

To illustrate the kind of useful information that can be obtained, we consider here in some detail one example—calculation of the optical phonon-phonon interactions in diamond. This will serve both to illustrate the power of the method and to shed some light into the phenomenon of two-phonon Raman anomaly in diamond. It was observed that the two-phonon Raman spectrum of diamond has an anomalous sharp peak (not seen for Si and Ge) at 2667 cm which is at an energy 3 cm higher than twice the optical phonon frequencies at r. Despite a number of theoretical works, the nature and origin of this peak is still a mystery. One particularly intriguing explanation was the two-phonon bound state theory by Cohen and Ruvalds. They proposed that a two-phonon bound state is formed... 

For the purpose of understanding the two-phonon bound state problem, we are interested in the k 0 phonons and their interactions. We, therefore, need to calculate x° X 1 XX X X" where A denotes the various optical modes. For example, °X X" gives the amplitude for the process... 

The parameters a and 3, however, only describe the direct four-phonon terms. To address the two-phonon bound state question, we have to consider other possible four-phonon diagrams of comparable... 

This work contributed in two major ways. First, the calculation shows that it is now possible for the first time to calculate from first principles phonon-phonon interaction parameters that are inaccessible from experiment. Second, since all the effective four-phonon terms (direct plus mediated processes up to are attractive for the k = 0 optical phonons in diamond, the formation of the two-phonon bound state is unlikely in this system. 

QUANTUM BREATHERS AND PHONON BOUND STATE IN THE FERROELECTRIC SYSTEM... 

Quantum Breathers and Phonon Bound State in the Ferroelectric System... 

Here, we present the data for two-phonon bound state (TPBS) or QB state in lithium tantalate system. It is pertinent to mention that in our recent work on another important nonlinear optieal material, sueh as split-ring-resonator (SRR) based meta-material, both K-G equation and nonlinear Sehrodinger equation (NLSE) show dark and bright solitons, and also dark and bright breathers. However, K-G equation in addition shows breather pulses, whereas NLSE does not show sueh pulses [64]. This work could also be relevant for an important nonlinear optieal material, sueh as lithium tantalate in the future directions of study, where K-G equation seems to show interesting behavior. 

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