Biomedical Engineering Reference
In-Depth Information
subspace, where an arbitrary state is a linear combination of localized states
|
10
and
|
01
,
|
Ψ
=
c
10
|
10
+
c
01
|
01
, with
c
10
and
c
01
being arbitrary complex numbers
2
2
such that
1. If a DQD system which is collectively coupled to its
radiative surrounding is in state
|
c
10
|
+
|
c
01
|
=
, then, according to the Fermi golden rule, the
probability that the system releases a photon is proportional to the square of the
modulus of the matrix element
|
Ψ
∼
H
rad
|
Ψ
=
(
g
k
λ
∼
(
c
01
)
2
2
2
P
00
,
λ
|
c
10
+
c
01
)
c
10
+
Γ
k
where
|
00
,
λ
denotes the state with no excitons and with one photon in the mode
k
is the spontaneous
decay rate for a single QD [Eq. (
9.16
)]. From the point of view of the resulting
transition probability two out of the states
λ
,
g
k
λ
is a coupling constant defined by Eq. (
9.7
), and
Γ
k
|
Ψ
are particularly interesting. These are
)
/
√
2, for which the transition proba
b
ility
reaches its maximum value, and the subradiant state
the superradiant state
|
+
=(
|
10
+
|
01
)
/
√
2, for
|−
=(
|
10
−|
01
which the probability of emitting a photon vanishes.
The states
are eigenstates of the carrier Hamiltonian (
9.3
) only if
the two dots form an energetically homogeneous atomic like system (
|
+
and
|−
0). In
this case, an exciton occupation of a DQD system prepared in the superradiant state
decays rapidly with a decay rate twice faster (2
Δ
=
) than when the electron-hole pair
is initially localized in one of the dots. If the DQD is in the subradiant state, then the
radiative decoherence does not affect the exciton residing in the system, i.e., the state
|−
Γ
becomes optically inactive (dark) with ab infinite lifetime. This specific property
of the subradiant states makes them useful for quantum information processing,
especially for noiseless encoding of quantum information [
25
]. The superradiant
state may be excited from the ground state by weak enough optical pulses which do
not allow to excite the higher biexciton state or in QD pairs with sufficiently large
biexcitonic shift. It is much more difficult to excite the subradiant state, but recently
preparation of this state in a pair of superconducting qubits in a cavity using local
qubit control in circuit quantum electrodynamics (QED) was presented [
117
]. The
above-mentioned effects are observed either for coupled (
V
=
0) and uncoupled
(
V
are eigenstates of the systems.
Although the collective effects have been known for many years and extensively
studied in atomic systems [
22
,
51
], the first experimental manifestation of these
phenomena in QD ensembles was presented in 2007 [
24
]. This is mostly because,
despite many features in common, there are still properties that differ considerably
for both types of structures. The main feature that distinguishes these two systems
and affects considerably their coupling to photon surrounding is the inhomogeneity
of transition energy
=
0) dots, since in both cases the states
|±
0 of the man-made QD systems. Below we investigate the
impact of the energy mismatch
Δ
=
and coupling between the dots on effects resulting
from collective interaction with electromagnetic field.
Δ
