Optical nanoscopy via quantum control

5.7 MB·

by  Timo Kaldewey

Optical nanoscopy via quantum control
One-sentence-summary:
A scheme for nanoscopic imaging of a coherent quantum mechanical system, a two-level atom, using a
far-field optical probe.
Timo Kaldewey,1,∗ Andreas V. Kuhlmann,1,† Sascha R. Valentin,2
Arne Ludwig,2 Andreas D. Wieck,2 and Richard J. Warburton1
1Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
2Lehrstuhl fu¨r Angewandte Festko¨rperphysik, Ruhr-Universita¨t Bochum, D-44780 Bochum, Germany
(Dated: January 9, 2017)
7
We present a scheme for nanoscopic imaging of a quantum mechanical two-level system using an
1
optical probe in the far-field. Existing super-resolution schemes require more than two-levels and
0
depend on an incoherent response to the lasers. Here, quantum control of the two states proceeds
2
viarapidadiabaticpassage. Weimplementthisschemeonanarrayofsemiconductorself-assembled

n quantumdots. Eachquantumdotresultsinabrightspotintheimagewithextentsdownto30nm
a (λ/31). Rapid adiabatic passage is established as a versatile tool in the super-resolution toolbox.
J

6
I. INTRODUCTION results [9]. In other words, Rabi oscillations do not rep-
] resent a simple on-off switch and are not well suited to
l
al The diffraction limit prevents a conventional opti- imaging. We propose instead that rapid adiabatic pas-
h cal microscope from imaging at the nano-scale. Sig- sage (RAP) is an excellent technique for imaging a TLS.
- nificantly however, diffraction-unlimited imaging of in- In RAP, the laser frequency is swept through the reso-
s
e dividual molecules is possible by creating an intensity- nance of the TLS during the pulse. RAP transfers the
m dependent molecular switch [1, 2]. For instance, molec- population from one state to the other but without the
. ular fluorescence can be turned on with green laser light oscillations at large pulse energies, Fig. 1(B). Applied
at (absorption of a green photon followed by relaxation), to an ideal TLS initially in state |0(cid:105), a weak RAP pulse
m and subsequently turned off with red laser light (stimu- leavesthesysteminstate|0(cid:105)whereasastrongRAPpulse
- lated depletion). Fluorescence is only allowed when the transfers the system to state |1(cid:105); and vice versa for the
d power of the red laser is below threshold: the red laser system initially in state |1(cid:105). The clear threshold of RAP
n acts as an on-off switch. This switching capability is on a TLS represents an ideal on-off switch with immedi-
o
translated into a microscopy scheme called STED (stim- ate applications in imaging.
c
[ ulatedemissiondepletionmicroscopy)througha“dough- Our scheme is shown in Fig. 1. The TLS is initially
nut” intensity profile of the red beam [3–6]. Practical in the ground state |0(cid:105). A pulse with positive chirp
1 considerations and not diffraction per se limit the re- and above-threshold pulse area is applied. This inverts
v
solving power of such an imaging scheme. A number the TLS provided it is located somewhere within the
6
4 of variants on this basic scheme exist [2, 7, 8]. However, diffraction-limited spot: it turns the system on. Subse-
6 all these schemes use more than two quantum states – quently, a pulse with negative chirp and above-threshold
1 the STED protocol for example uses at least four quan- pulse area is applied. This pulse inverts the system a
0 tum states (two separate vibronic transitions) – and all second time, leading to re-occupation of state |0(cid:105): it
1. the schemes exploit an incoherent response to the lasers. turnsthesystemoff. However,whenthefirstpulsehasa
0 Missingisaprotocolfordiffraction-unlimitedimagingof Gaussian intensity distribution (Fig. 1(C)) and the sec-
7 a coherent two-level system (TLS). ond pulse a doughnut intensity distribution (Fig. 1(D)),
1 The coherent response of a TLS to a pulse of resonant thesecondpulseisinactiveatthecenterofthedoughnut.
v: laserlightisaRabioscillation,arotationofthequantum Under these conditions, the system is left in the upper
i state around the Bloch sphere. For instance, the system “on” state |1(cid:105) only when it is located close to the center
X
is driven from its ground state |0(cid:105) to the excited state of the doughnut. The system is then left to decay by
r |1(cid:105) and then back to |0(cid:105) and so on, Fig. 1(B). In terms spontaneousemissionandthephotonisdetected. Inthis
a
of fluorescence, Rabi oscillations represent an off-on-off- way, a fluorescence bright spot results at the center of
on...behavior as a function of pulse area. If the TLS thedoughnut. Theresolutionintheimageisdetermined
is illuminated with a high intensity pulse with Gaussian by the spatial location at which the doughnut intensity
spatialprofilethenaseriesofringsintheopticalresponse crosses the RAP threshold, a “physics-based diffraction-
unlimited” resolution [2]. This imaging scheme can be
describedanalyticallyinaverysimpleway(Gaussianop-
tics for the two beams, the Landau-Zener formalism [11]
∗ [email protected] for RAP): Fig. 1(E) shows how a bright spot emerges at
† current address: IBM Research-Zurich, Sa¨umerstrasse 4, 8803 the doughnut center. The full model is described in the
Ru¨schlikon,Switzerland supplementary material [10].
2
A I(x,y) B
1.0
2nd pulse: doughnut 1
P
negative chirp (OFF)
n
x,y o
E I(x,y) ati 0.5
1st pulse: Gauss p
u
positive chirp (ON) cc
x,y O
z 0.0
0 2 4 6 8
Pulse Area (p)
C D E
ON pulse OFF pulse ON + OFF pulse
500 1.0 1.0
0.2
]
m 250
n
[

n
o 0 0.5 0.5
ti 0.1
si
o
P -250
-
y
-500 0.0 0.0 0.0
-500 -250 0 250 500 -500 -250 0 250 500 -500 -250 0 250 500
x-Position [nm]
FIG. 1. Concept of nanoscopic imaging of a quantum mechanical two-level system. (A) Temporal waveform and
spatialintensityprofileofthetwoopticalpulses: excitation(positivechirp,Gaussianprofile)andde-excitation(negativechirp,
doughnutprofile)pulse. (B)Responseofanidealtwo-levelsystemtoasinglelaserpulse. Thesystemisinitiallyintheground
state|0(cid:105);plottedistheoccupationoftheexcitedstate|1(cid:105),P ,asafunctionofpulsearea. Aresonant,unchirpedpulsedrivesa
1
Rabioscillation(dashedblackline). Achirpedpulse(greensolidline)transfersthesystemfromstate|0(cid:105)to|1(cid:105)forpulseareas
above π by means of rapid adiabatic passage. (C) - (E) Simulation of the imaging experiment: P as a function of sample
1
(x,y)-position. (C) Gauss-pulse only with I0 = 1I ; (D) doughnut-pulse only with I0 = 1I ; (E) Gauss-pulse I0 = 3I
G T D T G T
followed by doughnut-pulse I0 =205I resulting in a 15 times smaller spot size. Our model for the simulation is described in
D T
the supplementary material [10]. Here we used the following parameters: wavelength 940nm, refractive index solid immersion
lensn =2.13,beamdiameterbeforetheobjective∆X =2.0mm,focallengthf =3.7mm,detectionefficiencyβ =1,
SIL I,FWHM
chirp α =−α =3.24ps−2.
G D
EstablishinganimagingprotocolbasedonRAPstrikes tended emitter, with lateral extent ∼ 5 nm. Although a
us as important. First, it opens up a way to image on quantumdotmimicsarealatomithasamuchlargersize.
thenano-scalecoherentquantumopticalsystemssuchas Ourschemeopenstheperspectiveofimaginganelectron
cold atoms and trapped ions, also their solid-state coun- wave function with a far-field, optical microscope.
terparts, semiconductorquantumdotsand colorcenters.
Second, in a multi-level system, RAP avoids the exci-
tation of molecular vibrations (phonons in a solid-state
II. RESULTS
context). In STED microscopy, close to an eV of en-
ergy is dumped into the molecule per cycle, leading to
blinking and bleaching. This heating can be avoided in We use a single quantum dot to implement the RAP-
RAP (by choosing positive chirp for the |0(cid:105) → |1(cid:105) pro- based imaging scheme. At low temperature with reso-
cess, negative chirp for the |1(cid:105) → |0(cid:105) process [12, 13]). nant optical driving, an InGaAs quantum dot embedded
Third, the chirped laser pulses are spectrally broadband in GaAs mimics closely a two-level atom with radiative
yet the fluorescence is narrowband. This combination lifetime 800ps and emission wavelength 950nm [14–17].
allowsaninhomogeneousdistributionofemitters(distri- Here, state |0(cid:105) is the crystal ground state (empty quan-
butioninspaceorintime)tobeaddressedwiththesame tum dot), state |1(cid:105) is an electron-hole pair (the neutral
laser pulses. Any spectral fingerprint in the emitters is exciton, X0), the result of promoting the highest energy
retained by spectrally resolving the fluorescence, for in- valence electron across the fundamental gap to the low-
stance with a spectrometer and array detector. Finally, est energy conduction state, Fig. 2(A). There are two
our test system, a semiconductor quantum dot, is an ex- optically-allowedexcitonswithspin±1whichcanbecre-
ated with σ± polarisation (σ represents circular polari-
3
A Energy B Excitation: Detection: Spectral-Filtering:
)
z
LP LP H100
k
(
50
s
t
n 0
u
o 936 938 940
C Wavelength (nm)
LP LP
QD QD
C Pulse Area (p)
0 1 2 3 4 5 6 7 8 9 10 11
)
z
H200
k
(

al
n100
g
Si
F 0
R 0 0.71 1.42 2.13 2.84 3.56 4.27 4.98 5.69 6.40 7.11 7.82
Excitation Power ( µW)
FIG. 2. Rapid adiabatic passage on a single self-assembled quantum dot. (A) Energy level scheme of the quantum
dot (QD): |0(cid:105) represents the empty QD; |1(cid:105) the spin-up exciton, |1(cid:105)≡|↓⇑(cid:105). (↑ (↓) is a spin-up (spin-down) electron, ⇑ (⇓) a
spin-up(spin-down)hole)Thetransition|0(cid:105)↔|↓⇑(cid:105)isdrivenwithright-handedcircularlypolarisedlight(σ+). Thetwoexciton
states,|↓⇑(cid:105)and|↑⇓(cid:105),arecoupledviathefinestructurewhichleadstoaquantumbeat|↓⇑(cid:105)↔|↑⇓(cid:105). Oncreating|↓⇑(cid:105)withaσ+
polarisedpulseresultshenceinbothσ+-andσ−polarisedemission. Thebiexcitonstate,2X0,existsathigherenergiesbutisnot
populatedhere. (B)Polarisationcontrolinthedark-fieldmicroscope: theQDisexcitedwithσ+polarisedlight;σ−isdetected.
LPreferstoalinearpolariser,QWtoaquarter-waveplate. Thedetectedsignalisspectrallyfiltered. Thisincreasesthesignal
to background ratio. (C) Resonance fluorescence versus pulse area (and square root of averaged excitation power P ) on
avg
a single, empty quantum dot. Plotted is the detected emission from the |X0(cid:105) → |0(cid:105) transition following circularly polarised
excitationpulses(bluesquares). Theoriginallytransformlimitedpulses(τ =80fs)werepositivelychirped(φ =0.33ps2)toa
2
pulsedurationof4ps. ThedataarefittedtotheLandau-Zenerresult(redline)withA(1−exp(−c2τ(cid:112)τ4+φ2/φ ∗P )and
√ 2 2 avg
reveal c τ = 4.4±0.2µW−1/2 in agreement with independently estimated values from Rabi oscillations (4.4±0.4µW−1/2).
(cid:112)
The parameter c includes the dipole transition moment and when multiplied with τP gives the pulse area.
avg
sation), Fig. 2(A). We detect the spontaneous emission Zener result for a TLS. Only difficulties in rejecting the
(technically,the“resonancefluorescence”)astheexciton back-reflected laser pulse at large laser power limit the
decaystothegroundstate. Werejectback-reflectedlaser maximum pulse area to 11π.
lightwithapolarisation-baseddark-fieldconcept[17–20]: TheRAP-basedimagingproceedsbyimplementingthe
we excite with σ+ and detect with σ−, Fig. 2(B). (We two-pulse scheme, creating an image by sample scan-
note that the ±1 states are coupled together by some ning. We consider initially imaging a single quantum
symmetry breaking leading to a quantum beat [21] be- dot by collecting the resonance fluorescence only at
tween |+1(cid:105) and |−1(cid:105) with period ∼ 100 ps, Fig. 2(A). its X0 emission wavelength, Fig. 3(A)-(C). The Gauss-
This coupling allows us to detect the decay of excitons pulse alone (pulse area π) gives a Gaussian spatial re-
with both spins.) The chirped laser pulses are created sponse with mean full-width-at-half-maximum (FWHM)
from transform-limited pulses from a mode-locked laser 575nm, slightly larger than the confocal diffraction-
by introducing wavelength-dependent phase shifts. Un- limited spot size on account of the non-linear response
usually for quantum dot experiments [13, 22, 23], we use of RAP. Similarly, the response to the doughnut-pulse
the full bandwidth of a 100 fs laser pulse: this allows alone gives a doughnut-profile, with a width, as for the
us to address almost all the quantum dots in the sample Gauss-pulse, determined largely by diffraction. Apply-
with the same laser pulse despite the large inhomoge- ing both pulses sequentially breaks the diffraction limit:
neous broadening. Fig. 2(C) plots the resonance fluores- abrightspotemergeswithFWHM56nminthisparticu-
cence as a function of pulse area on a single quantum larexperiment. The signaland thesignal-to-background
dot following excitation with a single laser pulse. The ratio at the central bright spot are almost the same as
signal rises initially and is then roughly constant above for the Gauss-pulse alone. This is a significant point:
a pulse area of π. The signal follows closely the Landau- RAP-imagingsimplyconcentratestheavailablesignalto
4
A B C
120k
100k
25k
m] 100k
n1000 20k 80k
[ 80k

on 60k 15k 60k
ti
osi 500 40k 10k 40k
P
5k
y- 20k 20k
0
0 0 0
0 500 1000 0 500 1000 0 500 1000
x-Position [nm]
D E F
z)125k 125k 600
H 587nm 563nm
(100k 100k 500F
nal 75k 75k 400WH
Sig 50k 56nm 50k 60nm 300M
oX 25k 25k 200(nm
RF 0 0 100)
0
0 500 1000 0 500 1000 0 15 30 45 60 75
x-Position (nm) y-Position (nm) Doughnut Intensity (kW/cm²)
G H I
150k 60k 100k
] 50k
m
1000 75k
[n 100k 40k

n
o 30k 50k
ti
si 500 20k
o 50k
P 25k
- 10k
y
0 0 0 0
0 500 1000 0 500 1000 0 500 1000
x-Position [nm]
FIG.3. Imaginganensembleofquantumdots(QDs)withtheRAP-basedprotocol. (A)-(C)Resonancefluorescence
asafunctionofsampleposition. TheexcitationintensitiesarestatedinunitsofthethresholdintensityI =0.28kW/cm2. (A)
T
Gauss-pulseonly,intensityI0 =1.2I ;(B)doughnut-pulseonly,intensityI0 =1.2I ;(C)Gauss-pulseI0 =2.8I followedby
G T D T G T
doughnut-pulse I0 =205I =57kW/cm2. Shown is the signal in a spectral window (wavelength bandwidth 0.05 nm) around
D T
the X0 emission of one single QD. (D) and (E) show x and y line-cuts through the data in (A)-(C) in blue, orange and red,
respectively. SolidlinesareGaussianfitstotheblueandreddatapoints. (F)Extractedfull-width-at-half-maximum(FWHM)
of the central image of a single QD as a function of the doughnut-pulse intensity I . Thereby, I =1.2I blue triangles, and
D G T
I = 2.8I black squares. The smallest FWHM achieved here is 30nm. (G)-(I) Images, as (A)-(C), but adding the signal
G T
from four integration windows (each with a width in wavelength of 0.05nm) demonstrating the multiplexing capability of the
imaging scheme. The color scale in (I) is slightly over-saturated to increase the contrast for less bright QDs.
a smaller region in the image. tional diffraction limit, I is the dougnut intensity, and
D
The FWHM of the central image decreases with in- IT the off-on threshold intensity [10]. Here, we can
creasing doughnut-pulse intensity, Fig. 3(F). This is the anticipate ∆x(ID) based only on the characterization
signatureof“physics-baseddiffraction-unlimited”perfor- of the microscope performance (resonance fluorescence
mance: it is the control of the on-off switching which from Gauss beam at intensities well below saturation)
determines the resolution, not the diffraction-limited fo- and RAP characterization on the quantum dot. The
cusing of the laser beams. The FWHM ∆x follows result describes the experimentally determined FWHM
the same functional form as for STED microscopy [24], extremely well, Fig. 3(F).
(cid:112)
∆x(I ) = ∆xo/ 1+I /I where ∆xo is the conven- A key application of super-resolution microscopy is
D D T
5
to garner an image with detail which is obscured in a IV. MATERIALS AND METHODS
diffraction-limited microscopy. We demonstrate this by
imaging a region of the sample containing a number of The InGaAs quantum dots are embedded in a GaAs
quantum dots separated laterally by distances smaller n-i-p diode [25] and emit around 950 nm wavelength.
than or comparable to the diffraction limit of the mi- The heterostructure is grown by molecular beam epi-
croscope. An image with the Gauss-pulse alone, equiva- taxy. The collection efficiency is increased by incorpo-
lentlythedoughnut-pulsealone,showsstructurebutitis rating a semiconductor Bragg mirror below the quan-
difficulttodeterminethenumberandlocationofindivid- tum dots in the heterostructure growth and by placing
ual emitters, Fig. 3(G),(H). With the RAP-based imag- a solid immersion lens on the sample surface. Reso-
ing, thenumberandlocationofthepoint-likeemittersis nance fluorescence is distinguished from back-scattered
clearly visible, Fig. 3(I). The RAP-based imaging in the laser light by a polarisation-based dark-field microscope
present experiment is limited only by the technical diffi- [17, 20] and by spectrally-sensitive detection. The laser
culty of distinguishing the resonance fluorescence signal is a mode-locked Ti:sapphire laser and produces close-
from the reflected laser light at the highest doughnut- to-transform-limited pulses with a duration of ∼100fs.
pulse peak areas. The laser output is split into two beams, and two sepa-
ratepulse-shapersintroduceacontrolledamountofchirp
into the beams. One beam is delayed with respect to
the other and then each beam is coupled into an opti-
cal fiber. The two optical fibers transport the beams
to the two input ports of the microscope. Following
collimation in the microscope, one of the beams passes
III. DISCUSSION
through a 2π vortex phase plate. The two beams are
then combined at a beam-splitter. The microscope ob-
Working with a two-level emitter depends on distin- jective, sample and nano-positioners are held at 4.2 K in
guishing the resonance fluorescence of the emitter from aheliumbathcryostat. Onfocussing,thebeamwiththe
the laser light used to create it. Unlike fluorescence- phase-manipulatedwavefrontacquiresadoughnutinten-
based imaging there is a spectral overlap between signal sity profile. The doughnut maximum:minimum intensity
and source. The techniques used here (crossed polari- ratio>1000:1. Themicroscopeobjectivehasnumerical
sation and spectral analysis) can be supplemented with aperture 0.68 and operates close to the diffraction limit.
more effective spectral filtering for individual emitters Images are recorded by sample scanning.
or a collection of close-to-identical emitters (the source
is broadband, resonance fluorescence from an individual
emitter is narrowband). Time-gating the detector could ACKNOWLEDGMENTS
also be used to suppress the background laser signal: in
this experiment the pulses are gone in ∼ 50 ps yet the We acknowledge financial support from EU FP7 ITN
radiative lifetime is much larger, ∼ 800 ps. With these S3NANO,NCCRQSITandSNFproject200020 156637.
improvements we believe that the technique can become SRV,ALandADWacknowledgegratefullysupportfrom
a versatile one. BMBF Q.com-H 16KIS0109.
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7
V. SUPPLEMENTARY MATERIALS orthogonallypolarisedinordertosuppressreflectedlaser
lightinthedetectionchannel: thisisapolarisation-based
dark-fieldtechnique[17,20]. WithourRFmulti-purpose
A. The semiconductor sample
microscope, described in sec. VB2, CW excitation, and
a zirconia SIL on the sample surface, we reach a driving
1. The heterostructure
laser extinction ratio of 107:1 and a collection efficiency
of approximately 5 − 10%. The net result is that the
The InGaAs quantum dots (QDs) are embedded in a signal:background ratio is 250:1, e.g. Fig. S1(C). The X0
GaAs n-i-p diodegrown by molecular beam epitaxy [25].
transition is split into two, Fig. S1(C), as a consequence
ThelayerstructureisshowninFig.S1(A).Initially,asu-
ofthefinestructuresplitting,FSS(seeFig.1ofthemain
perlattice (18 periods of a 2nm GaAs, 2nm AlAs unit)
article). Thelinewidthsarearound2µeV,approximately
is grown on top of a GaAs wafer in order to smooth the
2.5 times larger than the transform limit [20]. Above
wafer surface. Following this, a distributed Bragg reflec-
saturation, the RF is more than 5MHz corresponding to
tor (DBR) consisting of 16 periods of 68.6nm GaAs and
a single photon flux of 25MHz. The detector, a silicon
81.4nm AlAs is grown in order to increase the photon
single photon avalanche diode (SPAD), has a quantum
collection efficiency from the top side. The back contact
efficiency of 20% at a wavelength of 950nm.
is provided by a layer of n-doped GaAs. An intrinsic
region, 30nm of GaAs, acts as tunnel barrier for the In-
GaAs QDs. The QDs are capped by 153nm GaAs. A
B. The experiment
subsequent barrier (a superlattice consisting of 46 peri-
odsofa3nmAlAs,1nmGaAsunit)hinderscurrentflow
Theimagingexperimentconsistsofalasersystemand
inthestrongverticalelectricfield. Thepenultimatelayer
a cryogenic optical microscope, Fig. S2. The laser is a
is p-doped GaAs forming the top contact of the diode.
tunable, mode-locked Ti:sapphire which creates close-
Compared to a Schottky diode structure the absorption
to-transform-limited pulses with a pulse duration of
of photons in the top gate is reduced. The final layer,
∼100fs. The pulse train is expanded with a beam ex-
44nmundopedGaAs, placesthep-dopedlayerarounda
pander and split into two. The individual pulse trains
node-positionofthestandingelectromagneticwave. The
are directed into compact pulse shaper units (PS1, PS2)
n- and p-doped layers are contacted independently. Se-
which introduce chirp by introducing a wavelength de-
lective etching of the capping allows contacting of the
pendent phase shift. Subsequently, one pulse is delayed
buried p-layer. Access to the n-layer is provided by wet
with respect to the other in a 300mm delay line, leading
etching of a mesa structure around the solid immersion
to a delay of up to 2ns, and then power and polarisation
lens (SIL). The n-contact is grounded; a voltage V is
g are controlled (neutral density filters for coarse power
applied to the p-contact.
control;ahalf-waveplate,polariser,half-waveplatecom-
bination for fine power control and control of the linear
polarisation axis). Finally, the two pulse trains are cou-
2. Quantum dot charging
pled into separate single-mode optical fibers.
The microscope consists of the “head” at room tem-
The sample is probed at liquid helium temperature, perature and an objective lens plus nano-positioners at
4.2K, in a bath cryostat. At these temperatures, there lowtemperature,Fig.S2. Thenano-positionersallowthe
is a pronounced Coulomb blockade: the number of elec- sample to be positioned at the focus of the microscope,
tronsinthequantumdotchangesstep-wiseasafunction andimagestoberecordedbysamplescanning. Thehead
of Vg [26–28]. Fig. S1(B) shows the photoluminescence converts one pulse train into a collimated beam with a
(PL)ofasingleQDasfunctionofVg. Thereareplateaus Gaussian intensity profile, the other into a collimated
withemissionfromtheneutralexciton,X0,fromtheneg- beam with a Gaussian intensity profile and azimuthal
atively charged trion (two-electron, one-hole complex), phase dependence. The two pulse trains are focused by
X1−,andfromtheX2−. ThereisalsoamuchweakerPL the objective onto the sample with close to diffraction-
signalfromthepositivelychargedtrion,X1+,atthemost limited performance, resulting in a Gauss-shaped focus
negative Vg. The X0 is used in the imaging experiments. and a doughnut-shaped focus. Resonance fluorescence is
WenotethattheVg-overlapoftheX0-X1− plateauisnot collectedbythesameobjectiveandcoupledinthemicro-
a feature once the QD is driven with resonant excitation scope head into a third fiber which transports the signal
[29]. to the detector, either a spectrometer-CCD camera sys-
tem or a SPAD.
3. Resonance fluorescence detection: CW excitation
1. Creation and characterization of chirped pulses
Resonance fluorescence (RF), the scattering induced
by resonant excitation, is shown in Fig. S1(C) on the A controlled chirp is introduced into the laser pulses
X0 transition. Thelaserexcitationandthedetectionare usingacompact,folded4f-pulseshaper[30],Fig.S3(B).
8
A B PL (Hz)
p-contact
V 937 X0 1323 60k
n-contact SIL g X1+ 50k
40k
p-contact m) 938 1322 30k
superlattice In n V)
capping layer As h ( 939 1320 me 20k
tunnel barrier Q gt (
D n y
n-doped backcontact s ele 940 1319 erg 10k
DBR Wav 941 X1- X2- 1318 En

superlattice 942 1316
0
wafer -0.25 0.00 0.25 0.50 0.75
Gate Voltage (V)
C D
800k
5M
Γ =2.2µeV Γ =2.3µeV
) )
z 600k 1 2 z
H H
4M
( (

al al
gn 400k gn 3M
Si Si
F F 2M
R R
200k
0 0
X X 1M
0 0
-20 -10 0 10 20 10p 100p 1n 10n
Detuning (µeV) Excitation Power (W)
FIG.S1. Resonance fluorescence on a single quantum dot (QD): CW excitation. (A)Theheterostructure: InGaAs
QDsinann-i-pdiodewithweakcavitystructure. Inthegrowthdirection: GaAswafer,GaAs/AlAssuperlattice(18periods),
distributed Bragg reflector (DBR) consisting of 16 GaAs/AlAs pairs, Si doped GaAs back contact, GaAs tunnel barrier,
InGaAs QDs, capping layer, blocking barrier consisting of AlAs/GaAs superlattice, C-doped GaAs as top contact. A ZrO
2
solidimmersionlens(SIL)isplacedonthesamplesurfacetoincreasethephotonextractionefficiency. (B)Photoluminescence
of a single QD, QD01, as a function of applied gate voltage and emission wavelength. The QD was excited non-resonantly at
830nmwithapowerof17µW. (C)ResonancefluorescencespectrumofQD01X0 withresonant,circularlypolarisedexcitation
of 27pW. The data (black circles) were fitted with a sum of two Lorentzian functions (green, individual functions shown in
red and blue). The individual linewidths are 2.2µeV and 2.3µeV. The photons were detected with a silicon single photon
avalanchediodewithanintegrationtimeof5ms. Thelaserfrequencywas319.77862THz(wavelength937.530nm). (D)Fitted
amplitudes of resonance fluorescence as a function of excitation power for the two X0 transitions.
Our scheme retains all the frequency components of the ment)resultsinapositivechirp[31]. Wedemonstratein
femto-second laser. Introducing chirp inevitably results Fig. S3(B) a stretching of the original, transform-limited
in an increased pulse duration. 130fspulsestoadurationofmorethan10ps,anincrease
by a factor of 100.
An unchirped pulse is directed onto a grating and its
The pulse duration is linked to the chirp. The elec-
firstorderdiffractionisthenfocusedbyacylindricallens
tric field of the unchirped pulse can be described with a
ontoamirror. Thelensandmirroraremountedtogether
Gaussian envelope in the time domain:
on a platform which can be moved with respect to the
grating with a micrometer linear stage, Fig. S3(B). This (cid:18)−t2 (cid:19)
allows a variation of the lens–grating separation while E(t)=E exp −iω t
0 2τ2 0
keeping the mirror in the focal plane of the lens. A √ 0
lens–gratingseparationlargerthanthefocallength(pos- ∆tI =2 ln2τ
0,FWHM 0
itive displacement) introduces a negative chirp, a sepa-
ration smaller than the focal length (negative displace- where ∆tI is the full-width-at-half-maximum
0,FWHM
9
doughnut input PS2 PS1
fibre output fibre
input
PPC output
λ/2 M
VPP FM
M
300mm
M M travel
Gauss input M
M
LP autocorrelator PPC
&
CAM FROG M M
detection
LP ND filter ND filter
L L
PS2 PS1
M
x beam M
y splitting v
M
z
M M
Sspect. λ/2 L PH L
croystat Mpulse M L PH L M
4.2 K analysis beam expander
SPAD/ pump tunable femtosecond
spectrometer laser laser M
FIG. S2. Scheme of the whole experiment. L lens, λ/2 half-wave plate, PH pin-hole, MS mini-spectrometer, PS pulse
shaper,NDneutraldensityfilter,PPCpower-polarisation-control,FROGfrequency-resolved-optical-gating,VPPvortexphase-
plate,LPlinearpolariser,SPADsinglephotonavalanchediode. Theautocorrelator-FROGcombinationisusedtocharacterise
the pulses before the microscope.
(FWHM)ofthepulseintensity. ∆tI =130fshere. new pulse duration τ is:
0,FWHM
Equivalently,theunchirpedpulsecanbedescribedinthe
(cid:115)
frequency domain: (cid:18)φ (cid:19)2
τ = τ2+ 2 (2a)
0 τ
E(ω)=E0τ2exp(cid:20)−τ202(ω−ω0)2(cid:21) (cid:118)(cid:117)(cid:117)(cid:16) 0 (cid:17)2 (cid:32) φ 4ln2 (cid:33)2
√ ∆tI =(cid:116) ∆tI + 2 . (2b)
2 ln2 FWHM 0,FWHM ∆tI
∆ωI = . 0,FWHM
0,FWHM τ
0 A key parameter for adiabatic passage is the sweep rate
α. It is related to φ by
The role of the pulse shaper is to add a phase for each 2
frequency component: d φ
ω(t)=α= 2 . (3)
dt τ4+φ2
φ 0 2
φ(ω)=φ +φ (ω−ω )+ 2(ω−ω )2. (1)
0 1 0 2 0 Weworkhereintheregimeφ2 (cid:29)τ02 suchthatτ (cid:39)φ0/τ0
and α(cid:39)1/φ .
2
Thelinearphasetermshiftstheentirepulseintimeandis Themeasuredpulsedurationasafunctionofdisplace-
irrelevanthere; thequadratictermrepresentsachirp. In mentisshowninFig.S3(B).Theresultscanbedescribed
practice, φ is directly proportional to the displacement perfectly with a quadratic phase dependence, eq. 1, al-
2
of the pulse shaper [32]. The link between φ and the lowing us to determine the sweep rate from eq. 3. Our
2
10
(a) (b)
chirped unchirped 1.0
pulse pulse
)
s
p
(
M 0.5
10
H
W )
²
F s
p
n, 0.0 (
o p
ati hir
r 5 C
mirror 2 u
D
-0.5
e
mirror 3 mirror 1 s
ul
P
0 -1.0
-10 -5 0 5 10
folding
blazed grating lens
mirror Lens-Grating Displacement (mm)
FIG. S3. Compact pulse shaper: concept and performance. (A) The incident beam is directed with mirrors 1 and 2
onto a blazed grating (1,800 lines/mm), diffracted and then focused by a cylindrical lens (focal length 150 mm) onto a mirror
placed in the focal plane of the lens. The lens and the folding mirror are mounted on a moving platform. A displacement (up
to ±10 mm) between grating and lens–mirror assembly introduces chirp. Note that the beam is reflected slightly upwards by
the mirror in the pulse shaper such that it overshoots mirror 1 on the return path. (B) Pulse duration ∆tI as a function
FWHM
of the lens–grating displacement. The pulse duration was measured with a FROG autocorrelator. The measured data points
(black circles) are fitted (blue solid line) using the result for quadratic phase, eq. 2b. The sweep rate α calculated from the
pulse duration is shown on the right axis.
pulse shaper is capable of generating φ up to a few ps2 operate at close to the diffraction limit at these wave-
2
with both signs. With a transform limited pulse dura- lengths.
tionof130fsandachirprange0ps2 to1ps2 wecanreach Reflected laser light is suppressed by exciting and de-
sweepratesfrom1ps−2 to80ps−2. Wenotethatthe8m tecting in orthogonal polarisations, either in a linear po-
longsinglemodefibersusedtotransportthelaserpulses larisation basis as in previous experiments [17, 20], or,
tothemicroscopeinourexperiment,Fig.S2,introducea as a new feature here, in a circular basis. We can make
positive chirp of 0.3±0.1ps2: this is compensated with this choice by choosing the angle of a quarter wave-plate
our pulse shaper. through which all beams pass, inserted as the final com-
ponentinthemicroscopehead. Theextinctionfactorfor
the reflected laser light depends strongly on the quality
2. Microscope design of the focal spot. On a bare piece of GaAs we typically
reach extinction ratios of 108:1; under a SIL on GaAs
withCWexcitationwereachedinthisexperiment107:1;
The microscope is based on a former version of an RF
and with excitation pulses, the single element aspheric
confocal microscope [17]. The “head”, Fig. S4, accepts
lens, and a SIL on GaAs the ratio decreases to 105:1.
two fiber inputs. In each input, the exact propagation
Theperformanceworsenswithpulsedexcitationbecause
axis is controlled (by rotating a laser window and a tilt
ofthespectralbandwidthofthelaserpulses: theaspheric
stage) and a linear polarisation state created (by a high
lens introduces a slight chromatic aberration.
qualitypolariser)afterthetwobeamsarecombinedbya
beam-splitter and sent to the objective at low tempera- The quality of the microscope’s focus is tested by
ture. One input passes through a 2π vortex phase-plate imaging a chrome grid with confocal detection in reflec-
(VPP). The VPP introduces a phase shift to the wave- tion. With femto-second laser pulses with center wave-
front: thephaseshiftisequaltothein-planeradialangle. length λ=940nm, we measured in this test experiment
On focusing, a doughnut intensity profile results. The ∆x=388±3nm which is close to the diffraction limit.
fiber output collects the back-scattered signal. A cam- Thequalityofthedoughnut-shapedfocusiscrucialfor
era provides an in situ image: it assists in positioning theimagingexperiment: alowqualityreducestheinten-
the sample surface with respect to the focus, and in co- sity of the central bright spot. We define quality here
aligning the three beams (two inputs, one output). The as the intensity ratio of the doughnut’s maximum to its
objectiveisasingleelementasphericlenswithnumerical minimum: it quantifies the relative residual intensity in
aperture NA = 0.68 which, with CW laser input, can the center, Fig. S5. Measured on a QD with left circu-
O