Biomedical Engineering Reference
In-Depth Information
a
b
0
1
occupation
n
10
n
01
0.8
-0.1
0.6
0.4
-0.2
0.2
0
-0.3
0
2
4
6
8
10
0
2
4
6
8
10
t
[ns]
t
[ns]
Fig. 9.13
Vacuum-induced coherence effect in a system of two identical QDs. (
a
) Exciton
occupation of the DQD system and occupations of the localized states
|
10
(
n
10
)and
|
01
(
n
01
).
(
b
) The off-diagonal density matrix element
ρ
10
[
120
]
01
,
with stable density matrix elements. Irrespective of the choice of the initial state,
the coherences are always equal
0,25, while the occupations of both dots are 0.25,
i.e., the total occupation of the system is reduced by half, compared to the initial
state. Thus, in a pair of closely spaced QDs, the existence of a nearby empty dot
strongly affects the evolution of the excitation of the other QD: The occupation of
a single dot decays exponentially while the presence of another dot leads to the
vacuum-induced coherence effect and population trapping.
In spite of rapid technological progress, “on demand” manufacturing of DQDs
consisting of two identical emitters is still not feasible. In Sect.
9.4.1
we have shown
that in the realistic case of nonzero energy mismatch, the collective character of the
sub- and superradiant states is lost, and the emission of light from both the sub- and
superradiant states takes place. Due to the lack of a stable state in which the system
might be trapped, the vacuum-induced coherence effect is destroyed and already
for the energy splitting of the order of
−
eV quenching of the exciton occupation
is observed (Fig.
9.14
). The coupling to photon reservoir maintains its collective
character until
t
μ
; therefore, the initial character of the exciton occupation
evolution does not differ considerably between identical and nonidentical dots and
in both cases the occupation of the initial state decreases while the number of
excitons confined in the initially empty dot increases, but later the population of
both dots starts to decay due to the emission from the subradiant state. For relatively
small energy mismatches it is clearly seen that after the emission from the short-
living state excitation is transferred to the subradiant state, the occupation of both
dots reaches the same number (due to equal, up to a sign, contributions of single-
exciton states to the subradiant state) and the following decay of both occupation
numbers is indistinguishable (Fig.
9.14
bandc).
The effect of vacuum-induced coherence is strongly affected by the coupling
(Forster or tunnel) between the single-exciton states. If the spatial separation of
the dots is small enough and the coupling exceeds the energy mismatch by far,
then the eigenstates of the carrier Hamiltonian (
9.30
)and(
9.31
) are relatively
close to the sub- and superradiant states, and thus a transition from a localized
single-exciton state to a nearly stable delocalized one is possible even for systems
∼
π
h
/
2
Δ
