Long-lived phonons.

We have previously demonstrated that optical phonons and polaritons in simple compound semiconductors, e.g. , GaP, possess dephasing times in the picosecond and femtosecond time scales. ' In high-purity materials the source of the dephasing is dominated by three-particle anharmonic interactions. Others have demonstrated that longitudinal acoustic (LA) and transverse acoustic (TA) phonons decay with rates which vary with the inverse fifth power of the phonon frequency. The decay times of LA phonons can also be very short. In contrast to the short lifetimes of optical, LA, and some TA phonons, Orbach and Vredevoe have noted that if the lowest (in energy) TA phonon branch is dispersive, then the TA phonons cannot readily decay by three-particle interactions and simultaneously obey energy and (crystal) momentum conservation. As a consequence, these phonons should possess anomalously long lifetimes. At the time of Orbach and Vredevoe's paper, the existence of such long-lived phonons would have verified the simple, but critical, tenet that the phonon branches are in general dispersive and, in the absence of other scattering mechanisms, that the lowest-order phononphonon anharmonic interaction, plus energy and momentum conservation, govern phonon lifetimes. Although most of these tenets have since been verified by other means, none of these means have unambiguously measured the lifetime of long-lived phonons. Since long-lived phonons are a necessary ingredient in phonon bottlenecking and phonon breakdown, there has been much interest in attempts to demonstrate their existence. We now demonstrate that long-lived TA phonons which have been generated near the X-point of the Brillouin zone of GaP possess a lifetime of 66. 5+5 ns. We start with our recent observation' that in GaP a polariton (m. ) of frequency co =341 cm ' can decay into two LA phonons, each of coLA=172+26 cm ' (i.e., coL&=co /2), with equal, but oppositely signed, wave vectors. However, and more importantly here, we have also observed that a polariton with m =354 cm ' can decay into one LA phonon with coLA=236+16 cm ' and one TA phonon with AT&= 118+16cm '. These latter results should be compared to the phonon frequencies observed at the X-point through neutron scattering; namely, coLA(X) =249+4 cm ' and coTA( —X)= 107+3 cm Thus symbolically the dominant decay process for co =354 cm ' polaritons is