Wavepacket revivals

Under even more intense photoexcitation ( 10mJ/cm2), the coherent A g and Eg phonons of Bi and Sb exhibit a collapse-revival in their amplitudes (Fig. 2.10) [42,43], This phenomenon has a clear threshold in the pump density, which is common for the two phonon modes but depends on temperature and the crystal (Bi or Sb). At first glance, the amplitude collapse-revival appears to be analogous to the fractional revival in nuclear wavepackets in molecules [44,45]. However, the pump power dependence may be an indication of a polarization, not quantum, beating between different spatial components of the coherent response within the laser spot [46],... 

Anharmonic effects lead to a destruction of the initially localized wave-packet with the consequence that the transient signal is damped. However, there is the possibility for the wavepacket to regain its initial shape after long times resulting in so-called revivals [see, for example, Alber and Zoller (1991)]. The revival period Trev contains additional information about the shape of the potential. 

A typical space-time distribution of the spatial density of the inversion (the inversion per single QD) w x, t) =a[ A x, tf - B(x, <)p] is shown in Fig. lb. As follows from (5) the depicted space-time dynamics corresponds to the evolution of a Rabi wavepacket defined as a superposition of Rabi waves with continuous spectrum of h. Physical interpretation of the picture predicted to observe in the QD chain can be given on the base of the collapse-revivals concept [1]. 

After formation, the wavepacket travels outwards towards the classical turning point, where it becomes very narrow. Close to the turning point, such a wavepacket has an uncertainty product ArAp very close to the minimum allowed by Heisenberg s uncertainty principle (h/2). It then reverses direction and accelerates towards the core (or the nucleus, in the case of H), where it is dispersed. For a pure Coulomb potential, the classical period in a Kepler orbit with n 85 is about 93 ps. After a few periods, the wavepacket appears to disperse completely, although it can revive at later times. 

I.Sh. Averbukh and N.F. Perel man, Fractional Revivals Universality in the Long-Term Evolution of Quantum Wavepackets Beyond the Correspondence Principle Dynamics , Phys. Lett. A 139, 449 (1989). 

S. L Vetchinkin and V.V. Eryomin, The Structure of Wavepacket Fractional Revivals in a Morse-Like Anharmonic System , Chem. Phys. Lett. 222, 394... 

---