Biomedical Engineering Reference
In-Depth Information
the value of the intraband dipole moment in an inhomogeneous, strained structure is
not exactly known. Moreover, the carrier-phonon coupling constants in the relevant
energy (or wave vector) range are strongly geometry dependent. For instance, by
changing the localization widths to
l
e
=
l
h
=
4
.
0nmand
l
z
=
0
.
8 nm one gets a
65 ns
−
1
.
considerably increased value of
Γ
=
3
.
9.3.3
Pure Dephasing Effects
Apart from the real transitions (relaxation, phonon-assisted tunneling, and excitation
transfer, as described in the previous sections), carrier-phonon coupling can induce
pure dephasing of coherences between various states of a DQD system. These
include the decay of optical coherence and of spatial coherences between states
localized in different dots, to be discussed in this section, as well as the decay of
entanglement, described in Sect.
9.3.4
below.
For single QDs, the phonon response to the ultrafast (sub-picosecond) charge
distribution corresponding to the optically generated exciton leads to a partial decay
of optical coherence [
14
-
16
,
94
] due to a kind of “which path” information transfer
from the charge subsystem to the phonon reservoir [
53
]. In DQDs, additional effects
appear in the evolution of excitonic coherence due to the interference of phonon
packets emitted by the two dots as well as to the mutual impact of the wave packets
emitted by one dot on the other dot [
58
]. As a result, a very small feature appears in
the evolution of the modulus of the optical polarization at the time when the wave
packet emitted upon excitation of one dot crosses the other one. A more pronounced
effect, due to the energy shift resulting from a local compression, is visible in the
phase of the optical polarization [
58
].
In terms of its contribution to the excitonic line shape, the pure dephasing effect
dominates over real transitions in individual dots at low temperatures since the
excited levels are separated by a large energy distance. In double dots, however,
the situation is different: the doublet of states in the ground state sector requires
a treatment of both real transitions (off-diagonal carrier-phonon couplings) and
dephasing (diagonal couplings) on equal footing. Such a treatment was proposed
based on a generalization of the cumulant expansion to a multilevel system [
95
].
In the second order, virtual transitions to the nearby excited state contribute to the
broadening of the excitonic line via effective two-phonon processes [
96
]. The line
width, calculated in this way, is dominated either by real transitions or by virtual
transitions, depending on the separation between the levels, with the real transition
contribution playing a major role for the energy splitting of a few meV [
95
].
Another class of dephasing mechanisms results from phonon anharmonicity.
In an anharmonic system, a polaron (lattice deformation or polarization field)
surrounding the charge distribution confined in a QD serves as a scattering potential
for phonons [
97
,
98
]. Since the scattering depends on the position of the scatterer, the
lattice can extract the information on the presence of an electron and exciton in one
or the other dot in the DQD system, hence destroying the spatial coherences present
