Quantum recurrence and fractional dynamic localization in ac-driven perfect state transfer Hamiltonians
arXiv:1403.1976 · doi:10.1016/j.aop.2014.03.010
Abstract
Quantum recurrence and dynamic localization are investigated in a class of ac-driven tight-binding Hamiltonians, the Krawtchouk quantum chain, which in the undriven case provides a paradigmatic Hamiltonian model that realizes perfect quantum state transfer and mirror inversion. The equivalence between the the ac-driven single-particle Krawtchouk Hamiltonian and the non-interacting ac-driven bosonic junction Hamiltonian enables to determine in a closed form the quasi energy spectrum of and the conditions for exact wave packet reconstruction (dynamic localization). In particular, we show that quantum recurrence, which is predicted by the general quantum recurrence theorem, is {\it exact} for the Krawtchouk quantum chain in a dense range of the driving amplitude. Exact quantum recurrence provides perfect wave packet reconstruction at a frequency which is {\it fractional} than the driving frequency, a phenomenon that can be referred to as fractional dynamic localization.
arXiv comment4 figures, to appear in Annals of Physics
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