Biomedical Engineering Reference
In-Depth Information
Fig. 9.28
Evolution of
entanglement of the initial
singlet state under the
influence of radiative
recombination without the
tunnel coupling (
V
1
0 K
50 K
100 K
0.8
0.6
0.4
0) at
various temperatures [
62
]
=
0.2
0
0
1
2
3
100
200
t
[ps]
Fig. 9.29
Evolution of
entanglement for
tunnel-coupled dots
(
V
1
0
1 eV
-1 eV
0.8
0.6
1meV,asshown)
compared to the uncoupled
case (
V
=
±
0.4
=
0) at
T
=
40 K [
62
]
0.2
0
0
1
2
3
100
200
t
[ps]
amplitude of the off-diagonal element of the density matrix between the states
|
01
and
|
10
, and is now equal to
C
[
ρ
(
t
)] =
2
|
01
|
ρ
(
t
)
|
10
|.
(9.37)
The evolution of the entanglement between the dots is shown in Fig.
9.28
.
At short (picosecond) time scales, phonon-induced dephasing leads to a drop of
concurrence, ending with a temperature-dependent plateau level, analogously to
what is seen in the right panel of Fig.
9.8
. In the absence of radiative recombination,
the entanglement would remain constant after this initial dephasing stage. However,
in the presence of carrier-photon coupling the exciton lifetime becomes finite,
which leads to an exponential population decay and, in consequence, to decay of
entanglement on the time scales
. The situation becomes much more com-
plicated, if the dots are coupled by a transfer-type interaction (that is,
V
∼
1
/
Γ
0). The
evolution in this case is shown in Fig.
9.29
. The interaction leads to the appearance
of a few new effects. The most striking feature are the oscillations of concurrence on
a picosecond timescale. Since the coupling is comparable to the energy mismatch,
the system performs rotations in the single-exciton subspace, coming close to the
separable states,
=
, every half-period. These oscillations are damped on
a time scale of tens of picoseconds, as the excitation is dissipatively transferred
to the lower-energy eigenstate of
H
DQD
by a process discussed in the previous
section. Depending on the sign of the interaction, this eigenstate (which can still
be entangled) can have either subradiant or superradiant character (for
V
|
01
or
|
10
>
0and
V
0, respectively). This property manifests itself on long timescales, leading to
the visible difference in the decay rates of entanglement for
V
<
=
1 meV and
V
=
−
1
meV (see right panel of Fig.
9.29
).
