Biomedical Engineering Reference
In-Depth Information
radiative surrounding [
61
]. In order to describe the dynamics of the QD system
simultaneously interacting with both, phonon and photon, environments we have
proposed a method [
62
] based on the equation of motion for the reduced density
matrix of the exciton subsystem,
ρ
, in the interaction picture,
ρ
(
˙
t
)=
L
ph
[
ρ
(
t
)] +
L
rad
[
ρ
(
t
)]
,
(9.17)
where the dissipators
L
ph
[
ρ
(
t
)]
and
L
rad
[
ρ
(
t
)]
are defined by formulas (
9.8
)
and (
9.15
), respectively.
The presented method allows us to strictly reproduce the limiting cases men-
tioned at the beginning of the subsection. Moreover, the results for coupled (
V
0)
QDs interacting with the phonon reservoir are reasonably close to those obtained by
the correlation expansion technique [
63
].
=
9.3
Phonon-Assisted Processes
In this section, we discuss phonon-induced transitions in a double-dot system. First,
we describe phonon-assisted relaxation and tunneling processes. Then we present
the theory of phonon-assisted excitation (Forster-like) transfer. Next, pure dephasing
effects are briefly discussed. Finally, we discuss the phonon-induced decay of
entanglement between the charge states in the two dots.
From the experimental point of view, dissipative carrier transfer in self-
assembled structures has been studied with optical spectroscopy methods
(time-integrated and time-resolved photoluminescence, and photoluminescence
excitation experiments) both in lateral double-dot systems [
4
,
40
,
64
] and in stacked
quantum dot molecules (QDMs) [
9
,
38
,
39
,
41
,
42
,
65
-
72
] and QD chains (both
stacked and lateral) [
73
,
74
]. Various mechanisms have been invoked to account
for the observed properties. In most cases, the kinetics is attributed to tunneling
[
38
-
40
,
42
,
65
,
70
-
73
]. In some other experiments [
9
,
66
,
69
], signatures of radiative
(Forster-like) transfer have been observed. Coulomb scattering [
41
] and thermally
activated processes [
68
,
72
] also seem to play an important role, at least in some
systems. In a recent experiment [
75
], the inelastic contribution was extracted from
the electron kinetics in a double dot placed in a photodiode structure in which the
splitting between the levels could be tuned. The resulting tunneling rate followed
the dependence on the energy detuning typical for a phonon-assisted process.
9.3.1
Phonon-Assisted Relaxation and Tunneling
In this section, we discuss phonon-assisted relaxation processes in a tunnel-coupled
QDM. We investigate the system of a QDM doped with a single electron [
76
]
as well as the QDM containing a single hole [
77
]. In both cases, we describe
