Biomedical Engineering Reference
In-Depth Information
cos
2
|
Ψ
+
−
sin
2
|
Ψ
−
,
|
10
=
sin
2
|
Ψ
+
+
cos
2
|
Ψ
−
,
|
01
=
respectively, where the contribution from each eigenstate depends on the rate
between the coupling and energy mismatch (tan
θ
=
V
/
Δ
). For the negative
amplitude of coupling
V
the initial state
|
01
(exciton in the lower energy dot) has
a stronger overlap with the state
which has a partly superradiant character.
Therefore the contribution from the short-living state to the initial state
|
Ψ
−
is larger
than from the long-living state and the initial decay of occupation is stronger. On the
other hand, if the exciton is initially confined in the higher energy dot, then the initial
state
|
10
|
01
has a larger overlap with a partly subradiant state
|
Ψ
+
and quenching of
the occupation is slowed down compared to the previous case.
9.4.3
Optical Response to an Ultrafast Laser Excitation
In this section, we identify the signatures of collective coupling to electromagnetic
environment in the linear optical response to the laser excitation. We assume that the
DQD, prepared initially in the ground state
|
|
, is excited with an instantaneous
laser pulse which is spectrally broad enough in order not to discriminate between
the two dots in the structure. Due to a small (sub-wavelength) distance between
the dots, they cannot be resolved spatially, either. Therefore, the pulse induces
optical polarizations symmetrically and independently in both dots. In most optical
experiments, the measured quantity is proportional to the square modulus of the
polarization
P
00
00
(
)
, thus in order to determine the signatures of the superradiant
emission we will compare the evolution of polarization induced by the DQD system
interacting with common electromagnetic field in the Dicke limit with the response
of a hypothetical system consisting of two dots interacting with independent
reservoirs. In the first case, after the excitation the DQD evolves according to the
Lindblad equation discussed in the Sect.
9.2.2.4
. In the second case, the system
dynamics are also governed by the Master equation in the Markov approximation
(Lindblad) where the Lindblad dissipator is a sum of two elements referring to
different dots. For a more detailed discussion, see [
124
].
t
9.4.3.1
Uncoupled Quantum Dots
First, we will analyze the optical response induced by a systems of uncoupled
quantum dots (
V
0). In this case, the system evolution is determined by
the interplay of the energy mismatch
=
V
B
=
Δ
and the recombination rate
Γ
.InFig.
9.16
,
