Picosecond control of quantum dot laser emission by coherent phonons

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by  Thomas Czerniuk

Picosecond control of quantum dot laser emission by coherent phonons
T. Czerniuk,1 D. Wigger,2,∗ A. V. Akimov,3 C. Schneider,4 M. Kamp,4
S. Ho¨fling,4 D. R. Yakovlev,1,5 T. Kuhn,2 D. E. Reiter,2 and M. Bayer1,5
1Experimentelle Physik 2, Technische Universita¨t Dortmund, 44221 Dortmund, Germany†
2Institut fu¨r Festko¨rpertheorie, Universita¨t Mu¨nster, 48149 Mu¨nster, Germany
3School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
4Technische Physik, Universita¨t Wu¨rzburg, 97074 Wu¨rzburg, Germany
5Ioffe Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia
Apicosecondacousticpulsecanbeusedtocontrolthelasingemissionfromsemiconductornanos-
7
tructures by shifting their electronic transitions. When the active medium, here an ensemble of
1
(In,Ga)Asquantumdots,isshifted intoorout ofresonance with thecavitymode, alarge enhance-
0
ment or suppression of the lasing emission can dynamically be achieved. Most interesting, even in
2
the case when gain medium and cavity mode are in resonance, we observe an enhancement of the

n lasing due to shaking by coherent phonons. In order to understand the interactions of the non-
a linearly coupled photon-exciton-phonon subsystems, we develop a semiclassical model and find an
J
excellent agreement between theory and experiment.

6
1
The enhanced light-matter-interaction of a semicon- excited QDs is shaken and guided into the cavity mode.

]
ductor nanostructure, which is placed in an optical res- Theseeffectsoccurondifferenttimescales,i.e.,theadia-
s
c onator, with the confined photonic field has paved the baticshiftisefficientforphononsofanyfrequency,while
i
t way to a largenumber of noveloptical phenomena, both the shaking effect requires frequencies comparable with
p
in the weak- [1, 2] and strong-coupling regime [3–5]. For the exciton lifetime in the lasing regime. This under-
o
the observation of any of these, the energy associated standing is essential to enhance the technology and ex-
.
s
with the resonantphotons needs to match the electronic ploit ultrafast control of lasing using coherent phonons.
c
i transition of the gain material. Usually this needs to be Sketches of the theory and the experiment are shown
s
y arranged during fabrication of the structure, since there in Figs. 1 (a) and 1 (b), respectively. Let us first focus
h are only limited tools to achieve resonance post-growth. on the lasing dynamics of the QD ensemble. We model
p Recently, a new approach to dynamically shift the elec- each QD as a two-level system consisting of the ground
[
tronictransitionofthe gainmaterialhasbeendeveloped state |Gi and the exciton state |Xi. Due to the differ-

2 [6],whichisproposedtobeusefulforthestudyofabroad ences in size, the corresponding transition energies ~ωi
v range of quantum phenomena [7]. This method is based are modeled by a Gaussian centered at ω with a full
QD
7 onultrafastmechanicalvibrations: abroadbandacoustic width at half maximum (FWHM) of ∆ . We assume
0 QD
pulsecontainingcoherentphononsuptoTHzfrequencies that the QDs are energetically closely spaced, such that
7
3 passes through the gain medium and changes dynami- we can use a continuous distribution n(ω). For each QD
0 callythe transitionenergies,resultinginastronglymod- mode ωi we employ a rate equation model to simulate
1. ifiedcouplingtotheopticalresonatormode. Theoriginal the pump dynamics. For the pumping we include an
0 experiment was performed on a microcavity laser with a additional energy level |Yi, which can be thought of as
7 quantum dot (QD) ensemble as the active medium, and a wetting layer state and which is populated from the
1 hasbeenextendedtonanostructureslikeopticallyactive ground state with a pump rate γ (|Gi → |Yi). The
p
:
v quantum wires [8], electronic transport devices [9], and excitation then relaxes in the exciton state via the re-
i optomechanical resonators [10, 11]. laxation rate γ (|Yi → |Xi). From the exciton state
X r
To fully explore the potential of this method, we de- spontaneousdecayintothegroundstateoccurs,whichis
r
a velopatheoreticalmodelofthe lasingdynamics inami- describedby the decayrateγd (|Xi→|Gi). EachQDis
crocavitylasersystem,whichconsistsofthreenonlinearly coupled to the cavity mode E with the frequency ωc via
coupled subsystems: excitons, photons, and phonons. thecouplingelementg inthe usualdipole,rotatingwave
Experimentsexploringseveralexcitationregimesandde- and slowly varying amplitude approximation.
tuningsbetweenQDensembleandmicrocavityresonator Initiallytheelectricfieldisgivenbywhitenoise. When
accompany the theory, from which we find good agree- theQDisinverted,apolarizationpω betweentheground
mentwithsimulations. Ourcombinedapproachallowsus state and the exciton builds up. The polarization is
tounderstandtheongoingdynamicsindetail. Inparticu- determined by the inversion and the detuning between
lar,weshowthatwecandistinguishbetweentwoeffects: each QD transition ωi and the cavity mode ωc, i.e., it
the first one is an adiabatic response of the lasing effi- is strongest, when the QD is resonant with the cavity
ciencyfollowingthetotalnumberofQDscouplingtothe ωi =ωc. Note that the polarization dephases due to the
resonator; the second one is a transient increase of the pump and decay. Further, there is an additional polar-
lasing output, when the initially off-resonantreservoirof ization dephasing contribution [12], which is accounted
2
(a) γ γ = 0.03 ps−1, γ = 0.5 ps−1, γ = 1 ps−1 and a laser
r |Y d r
strain |X cwoiuthpleinsgtacbolinsshteadntthoefogre=tic2a.l8mposd−e1l,sw[1h2i,ch13a]r.eTchonesliastseinngt
thresholdisdeterminedbyγ ,suchthatwetypicallylook
g γ γ d
d p atthepumprateincomparisontothiswithΓ=γp−γd.
p To modify the lasing properties, a coherent phonon
E
pulse is impinged on the QD ensemble. In experiment,
|G the phonons are generated by optical excitation of a
100nm aluminum film, which is deposited on the back-
Cavity QDs
(b)
m sideofthesample. Ontothealuminumfilmashort,high
Aluminu strainpulse DBR DBR E x citatio n epnaenrsgioenticfolallsoewripnuglsteheislfioghcutsaebds.oDrputeiotno,raapfeidwtphiecromseacloenxd-
long acoustic pulse of coherent phonons is launched and
Emission
subsequentlyinjectedintothe(100)-GaAssubstrate[14].
To prevent a strong scattering of the coherent phonons,
QDs the sample is placed into a cryostat and cooled down to
(c)
8K.Duringtheacousticpulse’spropagationthroughthe
0.5
100µm thick substrate, non-linear and dispersive crys-
) tal effects stretch the pulse and lead to the formation of
-310 0 100 phonons with frequencies of up to several hundred GHz
n ( 0.0 [15]. Figure 1 (c) shows the evolution of the strain η(t)
ai
Str attheQDlayer,whichwascalculatedusingthetransfer-
matrixandscatteringstatesmethod[16,17]. Twopulses
-0.5
can be distinguished: the first one is the incident pulse
1400 1500 coming from the substrate at t = 0 and the second one
0 500 1000 1500 is its reflection from the front surface of the sample. It
Time (ps) passes the QD layer at t ≈ 1.3ns according to twice the
transittimethroughthetopDBR.Notethatthereflected
FIG.1. (a)Sketchofthetheoreticalmodel. (b)Schemeofthe strain pulse has flipped its sign at the open surface.
experiment [6]. (c) Calculated strain profile η(t) at the QD
The strain field η(t) changes the transition energy of
layer, showing the incident pulse at t = 0 and the reflected
one at t≈1.3nsas close-ups in the insets. every QD via ~ωi →~ωi+Dη(t). In the simulations we
take D = −10 eV as the deformation potential coupling
constant [18] and define the instantaneous detuning of
for by the rate γ. Including the cavity loss by the rate the QD ensemble with respect to the cavity mode as
γ, the electric field dynamics is
l ∆(t)=~ω −[~ω +Dη(t)]. (2)
c QD
dE
dt =−γlE+igZ n(ω)pω(t)dω, (1) When passing the QD layer, the induced energy shift
results in a change in the emission intensity of the laser
where E(t) and pω(t) are in a frame rotating with the that is detected with a streak camera with a time reso-
cavityfrequency. Here,weseethatthe density,inversion lution of 25 ps. In the simulation we therefore integrate
andactualdetuning ofthe QDs viathe polarizationsare the electric field overa cosine-squaredtime window with
important for the strength of the electric field. a FWHM of 25 ps.
In the experiment, the same laser like in Ref. [6] is Simulationsandexperimentswereperformedforthree
studied. The microcavity resonator is made of two dis- different detunings between the QD ensemble and the
tributed Bragg reflectors (DBRs) sandwiching a GaAs cavity mode: a large positive and a negative detuning
cavity layer with a variable thickness, where optically and an almost resonant case. For each detuning, two
pumped (In,Ga)As QDs are placed. While the linewidth different pump rates denoted by P (experiment) and Γ
of the cavity mode is only 1.2meV, the broadening of (simulation) are studied, which are expressed in terms
the QD ensemble is 11meV, resulting in an inefficient of the respective lasing thresholds to provide compara-
coupling (see SOM). For the calculations we choose the ble situations in terms of physics. We note that slightly
parameters of the QD ensemble according to the exper- different excitation powers relative to the threshold had
imental setting and simulate N = 5 × 104 QDs. The to be used for best agreement. We assign this difference
cavity mode is set to the value from the experiment todifferentinput-outputcurvesmeasuredandcalculated
and its width is used to determine the cavity loss rate (cf. theSOM),whichwillbediscussedinmoredetailbe-
γ = 0.4 ps−1. For the lasing dynamics, we take the low. In the following, the upper panels (a) of eachfigure
l
parameters giving the best agreement with experiment show the experimentally measured normalized emission
3
10
nits)1.0 (a) 2.5 units)1.0 (a)
sity I(t)/I0 5 PL(arb. u00..051.325 Ene1r.g3y5 0(eV) 1.375 nsity I(t)/I0 12..50 PL(arb. 00..051.325 Ene1r.g3y5 0(eV) 1.375
n e 1.0
mission inte 105 P=1.11 Pth P=1.33 Pth (b) mission int 3.0 P=0.81 Pth P=1.06 Pth (b)
e
d e 10 ed
e z
aliz mali 2.0
m
5 r
r o
o N
N
1.0
0
Γ=1.48Γ Γ=1.61Γ
Γ=1.20Γ Γ=1.27Γ th th
th th
0 500 1000 1500
0 500 1000 1500
Time (ps)
Time (ps)
FIG. 3. Same as Fig. 2, but for a detuningof −17.8meV.
FIG.2. (a)Measurementand(b)simulationofthedynamics
of the lasing intensity under influence of the acoustic pulse
foradetuningof14.5meV.TheinsetshowstheQDensemble
(dashed) and the cavity mode (solid) spectra. ofthe peaks blurring somewhatthe measuredsignaland
also explain the slightly larger enhancement in theory
than in experiment. However, the good overall agree-
intensity, while in the lower panels (b) the theoretical ment underlines that the most important effects in the
simulations are displayed. complex laser dynamics are captured by the theoretical
First, we consider the case when the cavity mode is treatment.
positively detuned from the QD ensemble by 14.5meV, Another interesting aspect is that for higher pump in-
similar to the case in Ref. [6]. The dynamics of the las- tensity (red curve), the enhancement tends to become
ingintensityareshowninFig.2fortwopumpintensities smaller, which is clearly reproduced by theory. In the
slightly above the threshold. For both pump intensities, highlynonlinearregimecloseto thelasingthreshold,the
we see a strong amplification of the lasing in the experi- systemisverysensitivetocoherentphononsandthecon-
ment, when the incoming and reflected strain pulses hit trol of the emission is most efficient.
the QDensemble. This is wellreproducedby the theory, Withthisinmind,wenowlookatanegativelydetuned
which shows also two clear peaks at these times. The cavity mode with a detuning of ∆(0)= −17.8 meV. We
reason for the amplification is that negative parts (com- expectthe lasingdynamicsto bequite similar,sincealso
pression) of the strain pulse blueshift the QD ensemble, herethephononstunemoreQDsintoresonanceandthus
thereby shifting it towards the cavity. Also more details enhance the lasing, now for positive strain. Indeed, we
of the experiment can be reproduced by our model, e.g. seethatwehavetwolargeenhancements,onefromthein-
after the amplification there is a quenching followed by comingstrainpulsearoundt=0andoneatthereflected
smaller oscillations. pulsearoundt=1.3ns. However,therearedifferencesin
Takingacloserlook,weseedeviationsofthesimulated theresponseforthisdetuning. Theincomingstrainpulse
curve from the experimental data, e.g. the subsequent [Fig.1(c)]startswithastrongnegativepartcorrespond-
peaksfollowingthe twoleadingonesper pulsearerather ing to a blueshift of the QDs. For the redshifted QDs
distinct in theory but quite faint in experiment. These discussed previously (Fig. 2), this results in a strong en-
deviations may be explained by effects included in the hancement of the lasing, while here the blueshifted QDs
model in a simplified way or even neglected due to the (Fig. 3) are pushed even further away from the cavity.
complexity of the underlying physics. These are treat- Accordingly, the lasing in the first case starts with an
ment of carrier relaxation in the three-level model and enhancement, while the lasing for this case starts with a
neglecting possible multiexciton effects, acoustic wave quenching and only afterwards the output is enhanced.
damping and coupling to resonator modes such as the For the reflected pulse the sequence is inverted. More-
guided waves. These factors will lead to a broadening over, the total enhancement in the experiment with the
4
1.50
sity I(t)/I0 24 PL(arb. units)001...0501.325 Ene1r.g3y5 0(eV) 1.375 (a) on intensity I(t)/I0 1.25 PL(arb. units)001...0501.325 Ene1r.g3y5 0(eV) 1.375
en si
ssion int 0 P=1.07 Pth P=1.27 Pth (b) Emis 1.00 Γ=1.33Γth Γ=1.39Γth
mi 0 500 1000 1500
d e 2 Time(ps)
e
z
ali FIG. 5. Simulation of the laser emission for zero initial de-
m
tuning.
or 1
N
Γ=1.09Γ Γ=1.13Γ andthe transientshakingeffect. Thelatterisduetofast
0 th th
coherent phonons, which shift the QD transitions very
0 500 1000 1500 rapidly,suchthatthespectralholeintheQDpopulation
Time (ps) due to the lasing is subsequently blue- and redshifted
with respect to the cavity mode. In this way, highly
FIG. 4. Same as Fig. 2, but for a detuning of 1.5meV in the excited formerly off-resonant QDs can contribute to the
experiment and 3.0meV in the simulations.
lasing and the spectral hole is artificially broadened.
In the experiment the two mechanisms cannot be dis-
tinguished: bothcontribute. Togetsomeinsight,weuse
redshifted QDs is about three times higher, due to the
our theoretical model for the special case of zero detun-
fact that the absolute detuning is smaller. In addition,
ing,whenthemaximumoftheQDdistributionisalready
the maximum of negative strain in the incoming pulse is
in resonance with the cavity mode. Here, we would ex-
slightlyhigherthanitsequivalentofpositivestraininthe
pectthatthestrainpulsecanonlydetunetheQDensem-
reflected pulse. Thus, the negative part can compensate
ble, thus, the adiabatic contribution leads to quenching
a larger detuning.
only. However, in the simulations shown Fig. 5 we see
The final measurement was taken for an almost reso-
thatfor anypump rate abovethe lasingthreshold,a sig-
nantcaseof∆(0)=1.5meV,forwhich∆(0)=3meVis
nificant enhancement of the lasing emission is obtained
assumedin the theoreticalcurveinFig.4to achieverea-
at t ≈ 0.05 ns and at t ≈ 1.4 ns corresponding to the
sonableagreement. Inparticulartheobservedquenching
times,whenthefastoscillatorypartpassestheQDlayer.
requiresthis adjustment andit will be shownbelow that
Here, the dominant shaking effect does clearly overcome
inthecaseofanevensmallerdetuningonlyintensityen-
the adiabatic responseandwe conclude that the shaking
hancements remain. When the strain pulse hits the QD
effect is important to describe the laser dynamics.
ensemble, there is a strong enhancement, seen in both
experiment and theory. Then a long period of quench- Besides the detuning, another crucialinput parameter
ing follows, while afterwards sizable oscillations are ob- isthepumpintensity. Inexperiment,thelasingthreshold
served. Let us compare this to the profile of the strain is defined as the first kink, where the output exceeds the
pulse [cf. Fig. 1 (c)]. The first soliton-like peaks of the spontaneous emission. This threshold region is quite ex-
strain pulse around t = 0 shift the QD ensemble very tended until full lasing is reached [6]. In contrast, in our
rapidly into resonance followed by an oscillatory part, semiclassicalmodelthereisasteepset-inoflasingatthe
which on average increases the detuning. The second threshold and already small variations of the pump in-
regime is given for the more regular oscillations in the tensity close to the threshold modify the lasing response
strain pulse for times 200 ps < t < 1200 ps, where the significantly (see SOM). To include a broader threshold
QDs follow the shift adiabatically. The lasing emission region, one needs to go to a fully quantum mechanical
showninFig.4reflectstheseoscillations. Alsotheasym- model to account for spontaneous emission[13], which
metry in the incoming and reflected pulse is observed in is extremely challenging when also including phonons.
the simulations. Moreover there are lasing parameters like the relaxation
An open question is still the relative contribution of rate γr, which are not easily experimentally accessible
the two fundamentally different mechanisms mentioned andhaveasignificantimpactontheresponseinournon-
earlier-namelytheadiabaticmodulation,whencoherent nonlinear model.
phonons of any frequency overcome an initial detuning, In conclusions, we have shown theoretically and ex-
5
perimentallythatstraincanbe usedtocontrolthe light- andS.H¨ofling,“Anelectricallypumpedpolaritonlaser,”
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M. Bombeck,C. Schneider,S.H¨ofling,A.Forchel, D.R.
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A.V.A.acknowledgestheAlexandervonHumboldtFoun- Lett. 108, 226601 (2012).
dation. M.B.acknowledgespartialfinancialsupportfrom [10] T. Czerniuk, C. Bru¨ggemann, J. Tepper, S. Brodbeck,
the RussianMinistryofScienceandEducation(contract C. Schneider, M. Kamp, S. H¨ofling, B. A. Glavin, D. R.
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tiveoptomechanical resonators,” NatureComm. 5, 4038
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(2014).
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