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Journal of Experimental and Theoretical Physics

, Volume 113, Issue 4, pp 562–574 | Cite as

Dissipative tunneling in nanosystems

  • V. A. Benderskii
  • E. I. Kats
Atoms, Molecules, Optics

Abstract

A quantum dynamical problem has been analytically solved for a two-level system where localized states L 0 and R 0 are strongly coupled with reservoirs of local oscillations {L n } and {R n }. It is additionally assumed that the spectra of reservoirs are equidistant and the coupling constants are the same. It has been shown that the evolution of states L 0 and R 0 in recurrence cycles depends on three independent factors, which characterize exchange with the two-level system, exchange of L 0 with {L n } (R 0 with {R n }) and the phonon-induced decay of {L n } and {R n }. In addition to coherent oscillations with the frequency of the two-level system, Δ, and dissipative tunneling with a rate Δ2C 2 (where C is the matrix element of the coupling of L 0 and R 0 with L n and R n ), a new regime appears where L-R transitions are induced by the partial recovery of the populations of L 0 and R 0 in each recurrence cycle due to synchronous transitions from reservoirs. These transitions induce repeating changes in the populations of the states of the two-level system (Loschmidt echo). The number and width of the echo components increase with the cycle number. Evolution becomes irregular because of the mixing of the contributions from pulses of the neighboring cycles, when the cycle number k exceeds the critical value k c = π2 C 2. Unlike the populations, their cycle-average values remain regular at kk c. When Δ ≪ πC 2, the cycle-average populations oscillate with a frequency of ΔΩ/πC 2 irrespective of mixing. The frequency of oscillations of the populations of the states {L n } and {R n } is approximately nΩ(Δ/2πC 2)2, where Ω is the spacing between the neighboring levels of the reservoir and nΩ is the difference between the energies of the states L 0 and L n . The appearance of the mentioned low-frequency oscillations is due to the formation of collective states of the two-level system that are “dressed” by the reservoir. The predicted oscillations can be detected by femtosecond spectroscopy methods.

Keywords

Level System Cycle Number Neighboring Level Secular Equation Reservoir State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Institute of Problems of Chemical PhysicsRussian Academy of SciencesChernogolovka, Moscow oblastRussia
  2. 2.Landau Institute for Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow oblastRussia
  3. 3.Institut Laue-LangevinGrenobleFrance

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