Biomedical Engineering Reference
In-Depth Information
a
b
1
0.1
0.01
0.004
0.001
0
-1
c
d
1
0.1
0.01
0.004
0.001
0
-1
0
0.2
0.4
0.6
0.8
-0.1
0
0.1
t
[ns]
w
[ps
-1
]
Fig. 9.16
(
a
),(
c
) The optical polarization as a function of time after an ultrafast excitation for
uncoupled dots
V
0 in the linear-response limit. (
b
),(
d
) The corresponding spectrum. (
a
),
(
b
): QDs interacting with a common reservoir in the Dicke limit; (
c
), (
d
): QDs radiating into
independent reservoirs. Here,
=
V
B
=
01 ps
−
1
h
are as shown in the figure (in
ps
−
1
). Line definitions in (
b
)and(
d
)arethesameasin(
a
)and(
c
).
Black lines
in (
a
)and(
c
)show
the envelope
Γ
=
0
.
and the values of
Δ
/
±
exp
(
−
Γ
t
/
2
)
. The vertical scale in (
b
)and(
d
)isthesame[
124
]
we show the linear optical response in the time and frequency domains for a fixed
value of the recombination rate. The imaginary part of the Fourier transform of the
polarization is proportional to the absorption spectrum.
For
, there is no noticeable difference between systems interacting with
common and separate reservoirs as well in the time domain (gray lines in Fig.
9.16
a
and c) as in the frequency one (gray lines in Fig.
9.16
b and d). In both cases the
emitted signal is dominated by optical beats due to the interference of fields emitted
from the two dots which is manifested in the absorption spectrum as a sum of
two Lorentzians centered around distant frequencies. This is not surprising since
systems with considerably different transition energies emit into disjoint frequency
ranges of the electromagnetic field and thus essentially interact with different photon
reservoirs.
The effects of different types of coupling to the electromagnetic environment
become essential with decreasing energy mismatch and are manifested by the
decrease of the frequency of the oscillations in the collective case (more detailed
discussion in [
124
]). This does not lead to a considerable difference in the time
domain (Fig.
9.16
a and c), but the effect is clearly seen in the frequency domain
(Fig.
9.16
b). It is clearly seen in Fig.
9.16
b that for a DQD interacting with photon
modes in the Dicke limit the absorption spectrum differs considerably from a sum
of two identical Lorentzians when the latter overlap.
Δ
h
Γ
