Many different schemes have been proposed to use
quantum dots for quantum information processing, either as single
photon
source or support of qubits through chrage or spin excitations. The
analogy
between quantum dots and their deltalike density of states and
artificial
atoms gives strong motivation to go towards this direction.
Selfassembled
quantum dots remain however condensed matted nanostrucutres inb strong
interction
with their environment. The coupling to phonons, and in particular to
the
quasi dispersionless optical phonons, and coherent phonon processes
leads
to very specific properties, as described below.
From weak coupling to strong coupling
The relaxation processes in semiconductor quantum dots have been
debated
for more than a decade now since the first prediction by Bockelmann and
Bastard
in 1990 of a quenching of the relaxation of carriers in
zerodimensional
nanostructures. In the first years that followed the relaxation
mechanisms
were discussed based on the idea of a phonon bottleneck. LO phonon
emission
is a very efficient relaxation mechanism in IIIV bulk semiconductors
or
quantum wells. It leads to relaxation times towards the band edge of no
more
than a few picoseconds. It was expected however that the discrete
nature
of the density of states in quantum dots would hamper relaxation by
emission
of one LO phonon if the carrier energy jump is not equal to the LO
phonon
energy (36 meV in GaAs). Several alternative mechanisms were proposed
to
explain the yet relatively fast observed relaxation times: multiphonon
emission
assisted by acoustic and/or optical phonon or Augertype relaxation
processes
at high carriers densities. In any case the interaction of the carriers
with
the LO phonon thermostat, in terms of phonon emission and Fermi golden
rule
application, was considered in a weak coupling regime.
Only recently Inoshita and Sakaki suggested that the Fröhlich
coupling
between a confined electron and the LO phonon bath should not be
considered
in a weak interaction picture where the electron wave function
"dissolves"
itself into the phonon continuum. Instead they inferred from the three
dimensional
confinement in quantum dots that the electron and the phonons are
strongly
coupled leading to the formation of a bipartite electronphonon
particle
in itself (polaron). Provided that the coupling strength is larger than
the
continuum width, the coupling leads to continuous Rabi oscillation of
the
electron, i.e. everlasting emission and absorption of one LO phonon.
The
interaction with the LO phonons can thus no longer be regarded as an
electron
leaving its state by irreversibly emitting a phonon through the Fermi
golden
rule. Another way to grasp the origin of this strong coupling is to
note
that the LO phonon continuum is almost monochromatic and that the
electron
will only see a particular linear combination of phonons. The coupling
can
thus be viewed as the coupling between one discrete electron state with
a
nearly single isolated phonon level, leading to Rabi oscillations of
the
electron. Very recently the polaronic nature of conduction states in
ndoped
InAs/GaAs selfassembled quantum dots has been evidenced experimentally
using
magnetospectroscopy in the far infrared of the sp transition.
Electron relaxation should thus be considered in this polaron picture,
i.e.
not in a separated electron/phonon space. In this picture, the polaron
is
a stable eigenstate of the Hamiltonian, the electron performing
everlasting
Rabi oscillation between the mixed states. Relaxation should therefore
not
occur. However due to the anharmonicity of the lattice forces, a LO
phonon
disintegrates in a very short time. In GaAs the LO phonon population
decays
with a 7 ps time constant at low temperature. In practice it is
therefore
expected that the finite lifetime the LO phonon causes the polaron
relaxation.
Because of the instability of its phonon component, the polaron
exhibits
a relaxation triggered by its onephonon part.
We present in what follows the first experimental evidence of the
polaron
relaxation in selfassembled InAs/GaAs quantum dots. To identify the
related
decay mechanism the polaron relaxation time is measured by pumpprobe
spectroscopy
around 20 µm wavelength as a function of the excited state energy
and
from 5 K to room temperature. The pump source is provided by the
freeelectron
laser CLIO (Centre Laser Infrarouge d'Orsay). We show that the measured
relaxation
times originate from the polaronic nature of the excited states. Our
experimental
data support that even at detuning from the phonon energy as large as
19
meV the relaxation occurs and is triggered by the spontaneous
disintegration
of the optical phonon component into two acoustic phonons.
A simple polaronic picture
Let us consider a simple description of the polaron states that
enlightens
the experiment. The interaction scheme is depicted in the left hand
side
of Figure 1. If one considers only the one LO phonon modes 0> and
1>,
containing zero and one phonon respectively and only the s> and
p>
electron levels, the strong coupling of the p zerophonon states and
the
s onephonon state forms two polarons +> and > . A simple
expression
for the polaron eigenstate is given by the coherent superposition
alphas>ƒ1>+betap>ƒ0>
with normalized complex weights a and b satisfying alpha
^{2}+beta
^{2}=1.
Far away
from the energy of the optical phonon, polaron type corrections on the
confined
s and p electron state energies are small. As seen in the right hand
side
of Figure 1, the theoretical correction on the sp intersublevel
electron
transition is only a few meV. It also means that the weight a of the
phonon
part in the +> state is small for the investigated sample. For this
reason
the +> is also labelled "p" since it is close to a pure electron
p>
state. In the same way, the > state is essential phononic and we
will
forget it for now on. The electron s ground state is nearly unchanged
by
the coupling and remains electronic in nature in first approximation.
We
will continue to label it "s".

(Left) Schematic polaronic structure of
selfassembled
InAs/GaAs selfassembled quantum dots originating from the strong
coupling
of confined electronic s and p states and the one LO phonon continuum.
(Right)
Energy of the polaron states as a function of the dot size. The
anticrossing
corresponds to a polaron with an electron and phonon component of equal
weight.
Mixing of the electronic pstate to the phonon mode depends on the p
state
energy as compared to the phonon resonance. The mixing is maximal at
the
anticrossing where the electron and phonon weight is equal. For the
investigated
ndoped quantum dots (vertical arrow), the p state is more electronic
than
phononic.

Pumpprobe spectroscopy
The wavelength of the free electron laser CLIO, tunable in a large
infrared
spectral window 3120 µm, is set at 22.7 µm near the low
energy
side maximum of the sp polaron transition in Figure 4. CLIO provides
high
power picosecond pulses suitable to saturate the transition . In a
nearly
normal [001] incidence configuration the pump and probe beams are
focused
onto the sample surface with a spot size around 300 µm and
spatially
separated thanks to the 20° angle between them. Figure 2 reports
the
variation of transmission as a function of the pumpprobe delay for
temperatures
spanning the 5 K – 300 K range. At zero delay, a clear saturation of
the
absorption is evidenced. The partial bleaching is followed by the
reconstruction
of the absorption verifying roughly an exponential decay with a T1 = 70
ps
time constant at 5 K. This decay is attributed to the relaxation of the
polaron
initially in the laser excited p state towards the s ground state. This
result
clearly shows that the polaron has a finite relaxation time and is not
a
stable entity. Note however that this relaxation time is one to two
orders
of magnitude longer than the relaxation time of electrons in quantum
wells
or bulk GaAs. We show that it is a consequence of the strong coupling
in
the nanostructure.

Transmission modulation of ndoped InAs/GaAs quantum dot absorption as
a
function of the pumpprobe delay. The wavelength of the freeelectron
laser
is set at 22.7 µm near the maximum of the "sp" transition
absorption

Relaxation mechanism
In order to analyze the mechanism at the origin of the relaxation, the
decay
time is measured as a function of the energy by tuning the
freeelectron
laser wavelength across the absorption resonance. Because of the
inhomogeneous
broadening of the sp transition, wavelength tuning amounts to probing
different
dots with different sp transition energies. As reported in the left
hand
side of Figure 3, the closer to the phonon resonance, the shorter the
decay
time. This dependence is qualitatively expected from the idea of a
polaron
relaxing with the disintegration of its phonon component. The closer to
the
phonon resonance, the larger the phonon weight in the polaron state and
the
quicker the relaxation occurs since the probability of the
disintegration
varies with a
^{2}. To support quantitatively this idea, the
polaron relaxation
time is calculated using the non perturbative treatment of Li et al.
and
reported as a full line in the plot. The agreement with the
experimental
data is obtained with only the coupling strength as a fitting parameter
(4.4
meV) and therefore the polaron decay is attributed to the
disintegration
of the phonon part, here into two acoustic LA phonons.
To further support this polaronic picture, the temperature dependence
of
the relaxation time (right hand side of Figure 3) is also compared to
the
model of Ref. . The striking feature is the still long decay time
measured
at room temperature (37 ps). But again this is not surprising. In the
simulation
the LO phonon lifetime at low temperature is 7 ps (i.e. the low
temperature
GaAs measured value). The phonon lifetime is slightly shorter at room
temperature. In bulk GaAs this value is down to 3.5 ps. Assuming
instead
a lifetime of 5 ps at 300 K (dotted line in the r. h. s. of Figure 7),
a
good agreement is again found with the experimental data. Note that 5
ps
is a sensible time since the involved phonons are related to InAs
quantum
dots and not to bulk GaAs.
There has been other detailed theoretical analysis of the polaron
relaxation
in InAs/GaAs selfassembled quantum dots, in particular using
microscopic
Hermitian approach and including the treatment of quantum dot molecules
and
extended to the excitonic polaron. In these cases it is predicted that
the
relaxation occurs only in a narrow window (± 8 meV) around the
phonon
resonance. Our experimental data are not compatible with this model
since
relaxation is observed even far away (~ 19 meV) from the phonon
resonance.
This discrepancy is very likely related to the phonon instability
mechanism
chosen in the microscopic model for the phonon disintegration, namely
disintegration
of a zone center LO phonon into one band edge LO phonon and one TA
acoustic
phonon. Considering instead a disintegration into two acoustic LA
phonons should enable theoretically the polaron
to relax at ~ 54 meV, the energy corresponding to our measurements.

(left) Measured decay
time
as a function of the probed transition energy. The decay time becomes
shorter
as it gets closer to the LO phonon energy. (right) The relative
temperature
"robustness" of the relaxation time is attributed to the only slight
decrease
of the LO phonon lifetime at room temperature (5 ps) as compared to its
value
at 5 K (7 ps) as shown by the agreement with the sensible theoretical
dotted
line. This line assumes a constant phonon lifetime of 7 ps up to 100 K
and
then a linearly decreasing lifetime down to 5 ps at 300 K. The other
two
thick lines correspond to a model where the phonon lifetime is constant
(7
ps, upper line) or follows the temperature dependence from 7 ps to 3 ps
at room temperature (lower
line).
