The semiclassical evolution of wave packets

Arjendu K. Pattanayak

Robert G. Littlejohn

Mark Mallalieu, Carlos R. Stroud

A semiclassical propagator is applied to describe the dynamics of circular-orbit wave packets which are initially well localized in three dimensions. A sum over classical Kepler trajectories for the wave-packet autocorrelation function is obtained which is extremely accurate well past the classical regime of the evolution regime of the wave packet. The nonclassical nature of the wave-packet evolution at long times is associated with the interference between amplitudes from classical paths at different energies. The time scale of the wave-packet revivals is related to the shearing rate of the corresponding classical ensemble.

F. Nicacio, Alfredo Ozorio de Almeida, K. Dechoum +1 more

Mark Mallalieu, Carlos R. Stroud

A semiclassical approximation is derived from the autocorrelation function describing the excitation and detection of Rydberg wave packets by pairs of phase-locked laser pulses. The resulting expression is in terms of a sum over Kepler trajectories, and provides a direct explanation of the periodicity and spreading of the wave packet at short times when the evolution is classical. More surprisingly, this solution also provides an accurate description of the complex revival behavior of the wave packets, which is nonclassical. The phases of the wave packets, which are detected by the pulse-locking scheme, are also accurately given by analytical expressions derived from the semiclassical sum. The phase of the wave packets at short times have a simple interpretation as the phases of Bohr-Sommerfeld, and are related to Berry's phase. The semiclassical expression for the phases of the nonclassical revival wave packets is simpler than the corresponding quantal solution.

Markus Saltzer, Joachim Ankerhold

We study to what extent propagation of wave packets through potential barriers can be described semiclassically in real time. By analyzing the semiclassical approximation to the exact path-integral representation of the quantum-mechanical time evolution operator, we show that in the long-time sector it is dominated by quasiclassical fluctuations associated with caustics. Contrary to the description of tunneling in imaginary times, simple tunneling paths even for complex energies do not exist. Our findings lead to an extended semiclassical propagation scheme for wave-packet dynamics which is numerical efficient and accurately describes deep incoherent tunneling through static and externally driven barrier potentials.