Biomedical Engineering Reference
In-Depth Information
Various types of coupling between the dots change the properties of the system
even further. Theoretical calculations show that for closely spaced dots, the tunnel
coupling, which is proportional to the wave function overlap, between the dots
should strongly affect their electronic structure [
27
-
29
] leading to a delocalization
of the low energy eigenstates of the DQD. Optical spectra of such structures indeed
show clear manifestations of electronic coupling [
10
,
30
-
33
]. The tunnel coupling
is analogous to chemical bonding between atoms and, therefore, turns the two dots
into one quantum system (also referred to as a quantum dot molecule). On the
other hand, the wave function overlap is not the only mechanism of interaction
between the QDs. In fact, for QD separations of about 10 nm, the energetically
lowest states in the absence of external fields correspond to spatially direct excitons
localized in individual QDs [
29
]. Such states are still bound by the Coulomb
interaction. While the static (“direct”) dipole coupling preserves the occupations
of the individual QDs, the Forster interaction via interband dipole moments [
34
,
35
]
(first introduced in the context of molecular systems [
36
,
37
]) enables the transfer
the exciton occupation between the dots. These dipole couplings are rather like
van der Waals forces between separate entities. Therefore the distance between
the dots is a crucial parameter, which can lead to a crossover between regimes
of distinguishable (Forster coupled) and indistinguishable (tunnel coupled) entities
occupying the DQD.
In a closed system, the (usually very weak) F orster interaction has considerable
effects only very close to resonance [
34
,
35
]. However, the carrier-phonon coupling
provides the necessary dissipation channel which enables excitation transfer driven
by the Forster interaction, even if the energy mismatch between the dots is much
larger than the interaction energy. Phonon-assisted excitation transfer between the
quantum states of a molecule was in fact observed in many experiments [
9
,
38
-
42
].
In closely stacked dots this excitation transfer process is mostly due to phonon-
assisted tunneling of charge carriers, but for larger separations the tunneling is
exponentially suppressed. Therefore, phonon-assisted transitions involving tunnel-
ing are very inefficient for a 10 nm separation even though a small energy splitting
matches the acoustic phonon energies [
42
]. In such cases, the transfer is most likely
to occur due to the Forster coupling.
In this chapter we present a review of a number of phenomena that appear in
DQD systems due to the exciton-phonon and exciton-photon interactions, and the
interplay between the two. In Sect.
9.2
we discuss the system under study, introduce
the full Hamiltonian, and outline the methods used to find the evolution of the
DQD system. Section
9.5
is devoted to phonon-assisted effects, such as phonon-
induced relaxation, phonon-induced partial pure dephasing, and phonon-induced
entanglement decay. In Sect.
9.4
the effects on the DQD subsystem resulting
from the interaction with the radiative environment are discussed. This includes
collective luminescence effects, the linear and nonlinear optical responses of DQD
ensambles, and vacuum-induced coherence. In Sect.
9.5
we focus on the role of the
interplay between the phonon and photon environments when discussing collective
luminescence, vacuum-induced coherence, and entanglement decay. Section
9.6
concludes the chapter.
