Biomedical Engineering Reference
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where the parenthesis indicates an alternative route for the preceding transition.
However, in QDMs electron and hole tunneling expands the number of pathways
leading to biexcitons, which should involve indirect excitons as intermediate states.
For example,
00
00
X
01
01
X
10
01
X
11
02
X
02
02
X
11
11
X
01
01
X
10
10
X
→
→
→
→
(
)
→
(
)
,
(10.20)
which, among many other pathways, interferes with the FRET transition
0
01
X
1
10
X
.
On the other hand, biexciton recombination times are typically faster than monoex-
citon recombination times[
32
],
→
1
4
τ
X
0
, which might cause biexciton transition
spectral lines to broaden significatively in comparison. Moreover, binding Coulomb
interactions typically produce a red shift with respect to the monoexciton transition,
reducing their relative detuning from as low as 1.7 meV up to 3.5 meV [
39
]. For
these reasons biexciton resonances cannot be ruled out from the dynamics involving
monoexcitons as just given by the Hamiltonian in (
10.13
).
In optically driven QDMs the pumping of biexcitons,
2
20
X
,
0
02
X
and
1
11
X
, strongly
affects the time evolution of the monoexcitons, as the additional biexcitonic
manifold redistributes the monoexciton probability densities [
40
]. However, as
we have shown in the previous section, the monoexcitonic FRET satellite in the
molecular doublet spectral line is quite robust. The right panel of Fig.
10.6
shows
the results of simulations using the full Hamiltonian with 14 basis states, including
monoexciton and biexciton manifolds. The main biexcitonic effects appear as a
small attenuation of the central peak in Fig.
10.6
f, with the satellite peak keeping
its relative amplitude. Interestingly, our simulation shows that FRET signatures
manifest on biexcitonic complexes by themselves, such as the spatially indirect
biexcitons,
1
02
X
,
2
11
X
,
0
11
X
and
1
20
X
, as seen in Fig.
10.8
. These spatially indirect
states possess an effective dipole moment (due to their spatially direct component),
such that they would be connected by the FRET mechanism. Additionally, these
neutral biexcitons can be thought of being composed by a trion localized in one QD
together with a single charge (electron or hole) localized in the second QD.
Let's focus our attention on the biexciton manifold spawning the transition cas-
cade
1
01
X
τ
XX
0
0
11
X
, as shown in Fig.
10.8
c. Truncation of the full Hamiltonian
restricted to such states yields
2
11
X
↔
↔
⎛
⎞
Δ
S
Ω
T
Ω
B
⎝
⎠
.
11
02
H
XXI
=
Ω
δ
+
Δ
V
F
(10.21)
T
S
20
Ω
B
V
F
δ
11
+
Δ
S
A crucial symmetry of this Hamiltonian makes its eigenvalues invariant against
variations in the applied electric field
F
, since all three states possess the same
Stark shift
Δ
S
. This symmetry makes the eigenvalue problem of (
10.21
) formally
equivalent to that of (
10.16
); in this case FRET optical signatures appear as a bright
exciton spectral doublet with the satellite peak following the Stark shifted spectral
