LONG-TERM EVOLUTION AND REVIVAL STRUCTURE OF RYDBERG WAVE-PACKETS

It is known that, after formation, a Rydberg wave packet undergoes a s eries of collapses and revivals within a time period called the reviva l time, t(rev), at the end of which it is close to its original shape. We study the behavior of Rydberg wave packets on time scales much gre ater than t(rev). We show that after a few revival cycles the wave pac ket ceases to reform at multiples of the revival time. Instead, a new series of collapses and revivals commences, culminating after a Lime p eriod t(sr) much greater than t(rev) with the formation of a wave pack et that more closely resembles the initial packet than does the full r evival at time t(rev). Furthermore, at times that are rational fractio ns of t(sr), the square of the autocorrelation function exhibits large peaks with periodicities that can be expressed as fractions of the re vival time t(rev). These periodicities indicate a new type of fraction al revival occurring for times much greater than t(rev). A theoretical explanation of these effects is outlined.