Biomedical Engineering Reference
In-Depth Information
and excitation processes. A molecular resonance occurs at (
F
20 kV/cm),
resulting in a clear tunneling-induced anticrossing. Here, the applied field
F
Stark
shifts the spatially indirect exciton states by
±
±
Δ
S
, tuning them into resonance with
the direct states. For simplicity we have neglected QCSE effects which also shift
weakly the direct exciton states, being a nonessential element in our discussion. Lets
us consider now the case when the direct excitons are near resonant, thus strongly
coupled by
V
F
. In this case FRET splits considerably the direct exciton spectral lines
by
1248 meV. On the other hand, the tunneling
remains unchanged, since its anticrossing is dominated by
t
e
Δ
F
=
0
.
16 meV, Fig.
10.5
cfor
h
ω
V
F
.
A more detailed view of the FRET optical signature is seen in Fig.
10.6
,which
shows the level anticrossing map of the
1
10
X
exciton state. The splitting of the direct
state for
1248 meV appears as a plateau satellite far from the tunneling anti-
crossing, see Fig.
10.6
.However,for
F
ω
kV/cm, the satellite curvature
increases, following the (diabatic) spectral line of
1
01
X
. Interestingly, the FRET
mechanism competes strongly with electron tunneling, making the indirect exciton
to “light up,” by receiving some of the population of the direct state. Eventually the
FRET signature quenches at the anticrossing where electron tunneling dominates,
which demonstrates that tunneling is detrimental to FRET at low values of
F
.We
emphasize that a proper description of the dynamics of such system needs to take
into account the entire set of exciton states, since the direct coupling terms in the
Hamiltonian and the various higher order virtual processes make the decoupling of
direct and indirect exciton subspaces not possible. For completeness, we show in
the right column panel of Fig.
10.6
the results of our simulation when expanding
the Hamiltonian to include the biexciton manifold, expanding up to 14 the elements
of the excitonic basis; clearly there is no qualitative difference between the LACS
maps arising from the long time averaged dynamics. Figure
10.6
e, f compares the
populations for fixed values of the axial electric field,
F
(
−
35
,−
20
)
35 kV/cm.
The FRET satellite peak amplitude increases at stronger fields, suggesting that the
FRET signature strength can be controlled by electrical means.
In order to understand the changing behavior of the FRET satellite peak
amplitudes, we can truncate the Hamiltonian (
10.13
) such that its off-diagonal
matrix elements connect only the two direct excitons
=
−
70 and
−
1
10
X
0
01
X
|
,|
, and the vacuum,
0
00
X
|
state; the truncated Hamiltonian
H
D
is given by,
⎛
⎞
0
Ω
Ω
T
B
⎝
⎠
.
01
01
V
F
H
D
=
(10.16)
Ω
δ
T
10
10
Ω
B
V
F
δ
The level diagram corresponding to the Hamiltonian (
10.16
)isshownin
Fig.
10.7
a; Fig.
10.7
b shows the corresponding eigenvalue spectrum as function of
the direct state laser detuning,
10
10
10
01
δ
10
.For
Ω
B
Ω
T
=
Ω
and
δ
δ
01
, the spectrum
10
=
(
V
F
−
Ω
2
)
10
10
shows an anticrossing at
δ
10
=
−
V
F
and a level crossing at
δ
=
V
X
,
Ω
. As a consequence, if we tune the
V
F
2
V
F
with a relative separation
Δ
F
=
2
V
F
−
