Excitonic bloch oscillations in a terahertz field

Physical Review B - Condensed Matter and Materials Physics

Volumn 59, Issue 8, 1999, Pages 5770-5783

  Dignam, M M ^a  

^a LAKEHEAD UNIVERSITY   (Canada)

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Indexed keywords

EID: 0001537675     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.59.5770     Document Type: Article

References (40)

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32. The fact that elements such as (Formula presented) do not depend on n is a consequence of two factors: (1) The full excitonic Hamiltonian (including static and terahertz fields) is invariant under simultaneous translation of the exciton center of mass by an integral number of superlattice periods d in the z direction and (2) there are equal numbers of electrons and holes in the system. As a result of this, one can also show that any four-operator expectation values of the form (Formula presented) are also independent of n.
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37. In the absence of the electron-hole Coulomb interaction, it is easy to show that the sum over m given by (Formula presented) Thus the expression for the intraband polarization yields the dc polarization as well as the terahertz polarization associated with each harmonic of the superlattice dispersion relations.
38. See, e.g., Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 3.
39. For the system considered, this corresponds to a dephasing time of 0.52 ps. This time has been chosen to be somewhat smaller than the experimentally estimated dephasing time of 1 ps in order to aid in the discussion of the basic physical effects.
40. It should be noted that one of the consequences of taking the central frequency to be different from the (Formula presented) WSL state frequency would be to introduce a relatively weak asymmetry between the absorption for the (Formula presented) and (Formula presented) WSL states when (Formula presented) For simplicity we have not presented such cases in this paper.