Biomedical Engineering Reference
In-Depth Information
a
b
1
0.8
0.6
T = 3 K
T = 30 K
T = 300 K
no phonons
0.4
0.2
0
0
2
4
6
8
10
0
0.05
0.1
t [ns]
t [ns]
c
d
1
T = 3 K
T = 30 K
T = 300 K
no phonons
0.8
0.6
T = 3 K
T = 30 K
T = 300 K
no phonons
0.4
0.2
0
0
2
4
6
8
10
0
2
4
6
8
10
t [ns]
t [ns]
Fig. 9.30
Phonon impact on VIC process: time dependence of the exciton occupation at a few
temperatures compared to the evolution without carrier-phonon coupling for
D
E
=
4meV(
a
,
b
), 8.07 meV (
c
), and 13.36 meV (
d
). In (
b
), a short-time section of (
a
) is shown, with
the
red solid line
representing the total exciton occupation, the
magenta dotted line
corresponding
to the total occupation without phonons, and the
green dashed and blue dash-dotted lines
showing
the occupations of the two dots [
120
]
=
8nmfor
9.5.3
The Role of Phonons in the Vacuum-Induced
Coherence Effect
For a system of vertically stacked quantum dots, the amplitudes of the coupling
between single-exciton states due to both the Forster and the tunneling mechanism
are always negative, thus the darker eigenstate corresponds to the higher energy
eigenvalue. The lifetime of this state is strongly reduced due to coupling to lattice
vibrations which induce phonon-assisted excitation transfer from the higher to
the lower energy eigenstate. As a result, there is no dark or slowly decaying
eigenstate in which the exciton occupation could be trapped and thus the vacuum-
induced coherence effect is destroyed, unless special parameter choices are made.
In Fig.
9.30
, we show the impact of phonon dynamics on the process of spontaneous
buildup of coherence [
120
]. We keep the
mixing
angle
θ
(i.e., the ratio
V
/
Δ
)
2
√
V
2
as a parameter. As can be seen
in Fig.
9.30
a and c, phonon-related relaxation indeed strongly suppresses the effect
of exciton occupation trapping and induces a rapid decay of occupation. The role of
phonons in this process is clearly seen in Fig.
9.30
b, where we show the first 100 ps
of the evolution presented in Fig.
9.30
a. A very fast, compared to the purely radiative
case (Sect.
9.4.2
), phonon-assisted redistribution of occupations takes place, after
2
constant and use the energy splitting
E
=
Δ
+
