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Springer eBooks

Investigation of Wave Packet Dynamics Using the Presented Time-Domain Method

Rajendran Saravanan, Aniruddha Chakraborty

Published Jan 1, 2021• 0 citations
Publisher
DOI
10.1007/978-981-16-6654-4_3

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Feb 25, 1999•0 citations
We present a method to calculate exact dynamics of a wave-packet in a quantum two-state problem with Dirac delta coupling. The advantage of our method is that the calculations are done in the time domain. Hence inverting the solutions from other domains (Laplace or Fourier domain) do not intervene us from presenting the solution in the time domain. The initial wave packet is considered to be a Gaussian function. The wave propagation in the quantum state is governed by time-dependent Schr\odinger equation and the coupling is given by non-diagonal element in the matrix representation. We present the exact analytic forms of the wave function for both the states in the time domain.
We show that the time frequency analysis of the autocorrelation function is, in many ways, a more appropriate tool to resolve fractional revivals of a wave packet than the usual time domain analysis. This advantage is crucial in reconstructing the initial state of the wave packet when its coherent structure is short-lived and decays before it is fully revived. Our calculations are based on the model example of fractional revivals in a Rydberg wave packet of circular states. We end by providing an analytical investigation which fully agrees with our numerical observations on the utility of time-frequency analysis in the study of wave packet fractional revivals.
Currently, it is obvious [1] that nonstationary tasks of quantum mechanics in more degree differ from those of classical physics than stationary ones. Accordingly, time- domain quantum optics experiments are very important for deepening our knowledge of quantum dynamics. It appears that a single-photon wave (SPW-) packets [2] are the best objects of quantum optics for investigation of the quantum dynamics at macroscopic level. One of the fundamental problems herein is the comprehension of interactions of quantum fields (SPW4MIN and TPW-packets) with macroscopic media. In particular, this is immediately associated with development of our knowledge about the fundamental properties of the irreversibility and of detecting quantum fields. At present, our notion about interaction of quantum fields with a detector, is mainly based on the phenomenological approaches to the properties of the detector [3]. That is why more exact quantum models of macroscopic detectors must be investigated. One of the macroscopic objects, which can be interesting for these purposes is the resonant quantum (Two-,Three-level) medium with phase memory intensively studied in coherent optics. Unusual properties of quantum time-domain interference effects and of photon echoes initiated in resonant media by interactions with an SPW-packet, have been predicted in our works 4LB4-6]. In the present paper study of the quantum dynamics at interaction of the field with the medium we will carry out by investigation of the two photon echo properties. At that, we consider interaction of a three- level (TL-) medium with polarized two-photon wave packets for the purpose of eliciting new nonclassical polarization properties in quantum dynamics of the echo signals.