Metastable wave packet

In Figure 5.11d, we show the electron density up to 700 Bohr radii at t = 14.51 fs after the pump pulse. It consists of distinct wave fronts spreading out with virtually constant speed in other words, the metastable wave packet decays by ejecting electrons in isolated bursts. This peculiar behavior... 

Figure 5.11 Charge density after the XUV-pump pulse, at small (top row) and large (bottom row) radii. At each breathing cycle, the metastable wave packet, formed by a coherent superposition of doubly excited states, ejects a burst of electrons. The peak of the free electron density originating close to the nucleus results in a wave front, which propagates outward at almost constant speed, up to very large distances.

The panels in the first and last columns in Figure 5.11 correspond to two selected consecutive times at which a wave front originates close to the nucleus, 14.51 and 15.63 fs, while the central column corresponds to a time halfway between these two. In the upper row of Figure 5.11, we show the electron density within 15 Bohr radii from the nucleus its breathing motion is evident At f = 14.51 fs (a) the central part of the wave packet is at the peak of its contraction. At f = 15.09 fs (b) it reaches its maximal expansion. Finally, at f = 15.63 fs (c), it is contracted again. Thus, the relation between the breathing of the electron density at small radii and the ejection of isolated electron density bursts is more subtle than the obvious correspondence between their periodicities. Indeed, the instants at which the wave fronts are born in the vicinity of the nucleus correspond closely to the stages of maximum contraction of the localized part of the metastable wave packet. This evidence supports the idea that the collisional description of the autoionization dynamics of the doubly excited state of helium holds down to the least excited ones. 

We turn now to study the properties of the metastable state in more detail. We, therefore, concentrate on the long-time behavior, i.e., t > f0, and defer the discussion of the short-time dynamics to a later section. Figure 1.3 shows snapshots of the probability density of the evolving wave packet at different... 

It is clear that a core-hole represents a very interesting example of an unstable state in the continuum. It is, however, also rather complicated [150]. A simpler system with similar characteristics is a doubly excited state in few-body systems, as helium. Here, it is possible [151-153] to simulate the whole sequence of events that take place when the interaction with a short light pulse first creates a wave packet in the continuum, including doubly excited states, and the metastable components subsequently decay on a timescale that is comparable to the characteristic time evolution of the electronic wave packet itself. On the experimental side, techniques for such studies are emerging. Mauritsson et al. [154] studied recently the time evolution of a bound wave packet in He, created by an ultra-short (350 as) pulse and monitored by an IR probe pulse, and Gilbertson et al. [155] demonstrated that they could monitor and control helium autoionization. Below, we describe how a simulation of a possible pump-probe experiment, targeting resonance states in helium, can be made. 

The decay of the individual quasi-bound (metastable) resonance states follows an exponential law. The wave packet prepared by an ultrashort pulse can be represented as a (coherent) superposition of these states. The decay of the associated norm (i.e., population) follows a multi-exponential law with some superimposed oscillations due to quantum mechanical interference terms. The description given above is confirmed by experimental data. 

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