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Coherent dynamics of a single Mn-doped
quantum dot revealed by four-wave mixing
spectroscopy
Jacek Kasprzak,∗,†Daniel Wigger,‡Thilo Hahn,¶Tomasz Jakubczyk,†,§
Łukasz Zinkiewicz,§Paweł Machnikowski,‡Tilmann Kuhn,¶
Jean-François Motte,†and Wojciech Pacuski§
†Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
‡Department of Theoretical Physics, Wrocław University of Science and Technology,
50-370 Wrocław, Poland
¶Institut of Solid State Theory, University of Münster, 48149 Münster, Germany
§Institute of Experimental Physics, Faculty of Physics, University of Warsaw,
02-093 Warszawa, Poland
E-mail: jacek.kasprzak@neel.cnrs.fr
Abstract
For future quantum technologies the combination of a long quantum state lifetime
and an efficient interface with external optical excitation are required. In solids, the
former is for example achieved by individual spins, while the latter is found in semi-
conducting artificial atoms combined with modern photonic structures. One possible
combination of the two aspects is reached by doping a single quantum dot, providing
a strong excitonic dipole, with a magnetic ion, that incorporates a characteristic spin
texture. Here, we perform four-wave mixing spectroscopy to study the system’s quan-
tum coherence properties. We characterize the optical properties of the undoped CdTe
1
arXiv:2201.00792v1 [cond-mat.mes-hall] 3 Jan 2022
quantum dot and find a strong photon echo formation which demonstrates a signifi-
cant inhomogeneous spectral broadening. Incorporating the Mn2+ ion introduces its
spin-5/2 texture to the optical spectra via the exchange interaction, manifesting as six
individual spectral lines in the coherent response. The random flips of the Mn-spin
result in a special type of spectral wandering between the six transition energies, which
is fundamentally different from the quasi-continuous spectral wandering that results in
the Gaussian inhomogeneous broadening. Here, the discrete spin-ensemble manifests
in additional dephasing and oscillation dynamics.
Introduction
The incorporation of individual quantum systems into solid-state platforms,1–6 their coherent
control, and interfacing them with external degrees of freedom7–10 is a key for implementation
of quantum technologies. One of such promising platforms are semiconductor quantum
dots (QDs),11 which owing to constant progress in the epitaxial growth12,13 and chemical
synthesis,14 have now reached a tremendous structural quality.15 In parallel, processing of
this material has been driven virtually to perfection permitting advanced engineering of
the light-matter coupling with photonic structures.9As a result, QDs in photonic micro-
structures serve as compact sources of single photons for quantum cryptography.16
Conversely, optical or electrical control of single quantum states confined to a QD is
challenging, nonetheless intensely pursued in fundamental research.17–20 Over the last decade,
a major progress has been achieved in measuring21–23 and controlling24–26 the coherence
of optical transitions attributed to the bound electron-hole pair, forming a QD exciton.
This was achieved by performing coherent ultrafast nonlinear spectroscopy,27 in particular
four-wave mixing (FWM) on photonic devices hosting InGaAs QDs. However, the exciton
radiative lifetime T1lies typically in the nanosecond range, thus setting the upper bound for
its coherence time T2≤2T1. Although an exciton represents an efficient interface between
light and matter, its short T2limits its usage as a qubit. Hence, a promising perspective
2
in this field is the search for efficient coupling schemes between an exciton and quantum
systems exhibiting significantly longer T2, for example dark exciton states28,29 or individual
spins.30–33 Besides employing QDs charged by a single electron34 or hole,35 the latter can
be achieved by doping QDs with single magnetic ions, like manganese (Mn), which is part
of the emerging research area of solotronics, i.e., the field of optoelectronics associated with
single dopants.36,37
To bring the benefits of quantum optics and related tools to solotronics, one first needs
to introduce the dopant ion into the QD38–40 and enclose it within a photonic structure to
enhance the light-matter coupling.41,42 Recently, this requirement was fulfilled by molecu-
lar beam epitaxy (MBE) of the II-VI semiconductor CdTe, nowadays offering QD systems
hosting various magnetic ions37,43,44 and reliable fabrication of optical microcavities.45 Nev-
ertheless, the progress in coherent spectroscopy of single excitons in CdTe QDs has been
laborious,22,42 due to the restricted availability of femtosecond laser sources emitting in the
visible range.
In the present work, we perform FWM spectroscopy of single exciton in CdTe QDs em-
bedded in a microcavity. We first employ a non-magnetic dot, to demonstrate its quantum
character by performing the Rabi rotation measurements.46,47 Next, we determine the ex-
citon’s population and coherence dynamics. In the latter case, we reveal the formation of
a photon echo,21 phonon-induced dephasing (PID), 48,49 and coherence beating owing to the
fine-structure splitting (FSS) of the exciton.50,51 Finally, we focus on a QD doped with an
individual Mn2+ ion, which in the II-VI material CdTe acts as an isoelectronic impurity. We
show that the exciton-Mn2+ exchange interaction introduces an additional ensemble char-
acteristic in the time-averaged experiments. In this specific situation, the impact of the
Mn2+-spin with total spin quantum number S= 5/2results in the appearance of six differ-
ent transition energies associated with the six possible orientations of the Mn spin. It has
been shown that due to this characteristic spectral features the Mn spin can be initialized,
read out and controlled52,53 and protocols have been suggested for a selective switching of
3
the spin state.54–56 This report is thus an initial step on the spectroscopic quest towards fully
fledged coherent quantum control of possible spin-photon interfaces.30
Sample and Experiment
0
1
1.6 1.8 2 2.2
(a)
(b)
x4 DBR pairs
CdZnMgTe 70 nm
CdZnMgTe 60 nm
CdZnMgTe 60 nm
CdZnMgTe 120 nm
QDs CdTe:Mn
Mn spin
1 nm
CdZnMgTe 800 nm
x10 DBR pairs
SIL
Solid
Immersion
Lens
CdZnMgTe 70 nm
60 nm
Quantum
Dot
CdZnMgTe
emission
reflectivity
energy Ecav (eV)
Figure 1: Microcavity sample. (a) Schematic picture of the sample structure including top
and bottom distributed Bragg reflectors (DBRs), the Mn-doped quantum dot (QD) layer
(highlighted on the right), and a solid immersion lens (SIL) to improve focusing of the laser
light and the collection efficiency. (b) Reflectivity spectrum of the microcavity.
4
To perform FWM experiments of a single Mn-doped QD, we specifically conceive the
microcavity sample schematically depicted in Fig. 1(a). We have previously shown that in a
standard microcavity, the light-matter interaction is enhanced through the intra-cavity field
amplification,24 whilst preserving spectral matching with the excitation via femtosecond
laser pulses. The asymmetric cavity design permits to reflect almost the entire optical
response toward the detection path. With this methodology, we increase the FWM collection
efficiency by several orders of magnitude with respect to planar samples. Inspired by that
performance-boost, we here go beyond the previously used half-cavity design.42 We develop
full monolithic cavities, choosing the quaternary alloy CdZnMgTe as building material. After
having deposited a buffer on the GaAs substrate, a bottom distributed Bragg reflector (DBR)
is grown by alternating Mg content between 10% and 50%. After the completion of 10 layer-
pairs for the bottom DBR, we proceed by the formation of the λcavity. At the calculated
field antinode we flush a CdTe QD layer and nominally set the Mn concentration to 0.1%
to allow a diluted doping including incorporation of single Mn2+ ions into the QDs. Then,
4 layer-pairs for the upper DBR are deposited, completing the growth, which increases the
light-matter coupling compared to sample studied in Ref.42 . To further improve the in-
coupling of the optical excitation and the out-coupling of the optical signals, we attach a
solid immersion lens (SIL) made of zirconium oxide on the sample surface. This half-ball lens
with a 500 µm diameter allows to perform optical microscopy up to approximately 50 µm
away from its axis without introducing significant geometrical aberration. The SIL increases
the numerical aperture (NA) of the beam in the semiconductor material by reducing the
refraction when crossing the sample surface. It further decreases the spherical diffraction
resulting from the excitation fields passing through the semiconductor-air interface; at the
same time it reduces the total internal reflection of the emitted FWM signal on the way
back.
Monitoring micro-photoluminescence (µPL) at T= 7 K between energies EX= 1.85 eV
(λX= 670 nm) and 1.80 eV (690 nm), we observe the recombinations of individual excitons
5
localized at the interface fluctuations, forming weakly-confined QDs, similarly as in GaAs
structures.21,57 In the white light reflectance in Fig. 1(b) we identify the cavity mode centered
between Ecav = 1.85 eV (λcav = 670 nm) and 1.81 eV (685 nm) depending on the investigated
position on the sample with a full-width at half maximum (FWHM) of 12.5 nm, yielding the
quality factor of Q= ∆Ecav/Ecav ≈55.
Undoped quantum dot
time t
coherence
scan
(a)
(b)
t = 0t = −τ12 t = τ12
123
time t
t = 0t = −τ23
123
occupation
scan
photon
echo
FWM signal
FWM signal
Figure 2: Schematic picture of the performed FWM experiments. (a) Coherence scan by
varying τ12 resulting in the photon echo formation. (b) Occupation scan by varying τ23
exhibiting a typical exponential decay.
0
5
10
15
20
25
30
0 5 10 15 20 25 30
(a)
0
1
2
3
4
5
6
0 1 2 3 4 5 6
(b)
position y(µm)
position x(µm)
0 1
integr. PL intens.
position y′(µm)
position x′(µm)
0 1
integr. FWM ampl.
Figure 3: Spatial mapping of the PL in (a) and the FWM in (b). The scans reveal QDs with
excitons that are efficiently coupling to the optical excitation. Note, that the detected areas
on the sample are not aligned.
6
To perform FWM microscopy we use a laser pulse train centered around λ= 680 nm
at the repetition rate of 76 MHz, generated by an optical parametric oscillator (Inspire 50
by Radiantis) pumped by a femtosecond Ti:Sapphire oscillator (Tsunami-Femto by Spectra-
Physics). To induce FWM, we generate three beams E1,2,3, with respective inter-pulse delays
τ12 and τ23 as schematically shown in Fig. 2, introduced by a pair of mechanical delay
stages. The beams pass through acousto-optic modulators where they undergo distinct
shifts Ω1,2,3of the carrier frequency. Using a microscope objective (Olympus, NA=0.6), the
beams are focused reaching a diffraction limited spot on the surface of the sample. The
sample is placed in a helium-flow cryostat operating at T= 7 K. By raster scanning the
position of the objective, we can construct hyperspectral images of the optical signals.24,58
Fig. 3 shows exemplary scans of the PL and the FWM signal in (a) and (b), respectively,
where the maps were accumulated for a range of transition energies. A pulse shaper is
used to correct the temporal chirp, mainly stemming from the thick optics in the acousto-
optic modulators and the objective, to attain transform-limited pulses of around 150 fs
duration. The reflected light from the sample is collected by the same objective and directed
into an imaging spectrometer with a CCD camera at its output. The FWM response,
which in the lowest (third) order is proportional to E∗
1E2E3, propagates shifted by the radio-
frequency ΩFWM = Ω3+ Ω2−Ω1, which is around 80 MHz. Its amplitude and phase are thus
obtained via optical heterodyning the reflected light at ΩFWM. Additionally, a reference beam
ERis employed to perform spectral interferometry. More details about the experimental
setup can be found in Refs.24,59 . As explained below, by inspecting FWM temporal and
delay dynamics, we obtain full information regarding the system’s inhomogeneous σand
homogeneous γ= 2¯h/T2dephasing, as well as its population decay.
For our FWM investigations, we select those optical transitions that dominate in PL and
that are spectrally located at the center of the cavity mode. In Fig. 4(a) we present a typical
spectral interference (blue) heterodyned at ΩFWM originating from a undoped CdTe QD
together with the laser pulse spectrum (green). The retrieved FWM amplitude and phase
7
−1
0
1
0
1
(a)
0
1
1801 1802 1803 1804
0
1
(b)
FWM interf. (arb. u.)
reference spectrum
norm. FWM ampl.
FWM phase (π)
photon energy (meV)
Figure 4: FWM spectroscopy of a QD exciton. (a) Spectrum of the reference pulse in green
and a typical spectral heterodyne interferogram in blue. (b) FWM amplitude spectrum in
dark red and the FWM phase in pale red.
are presented in Fig. 4(b) as dark and pale red line, respectively. While the FWM amplitude
exhibits a typical peak structure, the respective phase shows a jump of approximately π.57
It is worth to note that QDs generating FWM are rather isolated with typical distances of
several µm, as exemplified by the FWM hyperspectral mapping presented in Fig. 3(b).
To first characterize the enhanced light-matter coupling, we measure how the FWM
amplitude depends on the applied laser pulse intensities. We thus fix the excitation powers
of E2and E3to P2=P3= 0.25 µW and vary E1’s power P1. In Fig. 5 we plot the spectrally
integrated FWM amplitude as a function of √P1, which is proportional to the pulse area
θ1=Rdt E1(t)/¯h, where E1is the electric field amplitude of the first pulse at the QD location
multiplied by the transition dipole matrix element. As the measured FWM amplitude (blue
dots) is proportional to the microscopic coherence of the exciton state,25,47 the signal is
proportional to |sin(θ1−θ0)|(blue line), i.e., a Rabi rotation is detected with a maximum
corresponding to θ1−θ0=π/2at P1= 0.55 µW. The offset θ0might stem from imperfect
reflection of the photonic structure and internal absorption. With respect to our previous
8
0
1
0 0.2 0.4 0.6 0.8 1 1.2 1.4
π/2π/2
norm. FWM ampl.
√P1(√nW)
Q= 55
Q= 90
Figure 5: Rabi rotations. FWM amplitude as a function of the applied peak field amplitude
of the first laser pulse √P1while P2,3are fixed. Measurement as dark dots and fits with
|sin(θ1−θ0)|as pale lines for the cavity quality factors Q= 55 (blue) and Q= 90 (yellow).
experiments performed on a half-cavity structure42 with Q≈20, a π/2pulse area is here
attained for an around 6 times weaker impinging laser power. Such an enhanced coupling
between the external excitation and the QD exciton is due to the moderately larger Q-
factor of the microcavity and thus a larger effective Ejfor the same external Pj. To further
demonstrate the correspondence between the cavity Q-factor and the powers required to
reach a π/2pulse, we measure the FWM’s intensity dependence on a similar microcavity
sample, that is fabricated from 12 (6) stacked DBR-pairs at the bottom (top). As a result
its Q-factor reaches 90. From the measured Rabi flopping (yellow points and line) we deduce
that the pulse area of π/2corresponds to P1= 0.12 µW. We note however that a further
increase of Qdoes not necessarily lead to a better light-matter coupling. This is due to
spectral filtering of the incoming excitation pulses and a respective increase of their temporal
duration inside the cavity.25 An optimal light-matter coupling is achieved when the spectral
widths of the cavity mode and of the driving pulses are matched.
9
0
10
20
30
40
50
60
0 10 20 30 40 50 60 0 10 20 30 40 50 60
delay τ12 (ps)
time t(ps)
τ12=31ps
(a)
exp.
time t(ps)
0
1
norm. FWM ampl.
photon echo
(b)
fit
Figure 6: Photon echo formation. FWM dynamics as a function of time tafter the third
pulse and the delay τ12. (a) Measurement and (b) fit with Eq. (1). The green points in (a)
show the measurement at τ12 = 31 ps.
We now shift the investigation to the temporal domain. A typical pulse sequence of
the experiment is presented in Fig. 2, where the signal is generated after the arrival of all
three pulses E1,2,3. In inhomogeneously broadened systems, the FWM signal for τ12 >0
(see Fig. 2(a)) forms a photon echo.21 Even though the echo formation is commonly known
for ensembles of emitters, it can also be generated for individual transitions. Here, the
photon echo arises due to the exciton’s stochastic spectral wandering in time, accumulating
into an effective inhomogeneous broadening of width σin the time-averaged heterodyne
experiment.22,23,51,60 To illustrate that, in Fig. 6(a) we show the measured time-resolved
FWM amplitude as a function of the time after the third pulse tand the delay τ12, while
fixing τ23 = 0. We observe that with increasing delay τ12 the maximum of the signal shifts in
time talong the diagonal τ12 =t(dashed line). We see that for τ12 >20 ps, the echo is fully
developed, i.e., the FWM signal takes the form of a Gaussian transient. This is exemplarily
shown by the time-resolved FWM amplitude measured at τ12 = 31 ps (green dots). By
fitting the entire FWM dynamics with
S(t, τ12)∼exp −t+τ12
T2exp −(t−τ12)2
2T2
σ(1)
as shown in Fig. 6(b) we directly retrieve the homogeneous dephasing time T2= (36.5±
10
0.2) ps and the inhomogeneous dephasing time Tσ= (9.25 ±0.05) ps. These times directly
correspond to spectral broadenings of γ= 2¯h/T2≈(36.1±0.2) µeV and σ= 2¯h/Tσ≈
(142 ±1) µeV.23,61
0
1
0 0.2 0.4 0.6 0.8 1 1.2
(a)
0
1
0 20 40 60 80
(b)
0
1
−10123
norm. FWM ampl.
delay τ23 (ns)
exp.
sim.
norm. FWM ampl.
delay τ12 (ps)
FWM ampl.
τ12 (ps)
Figure 7: FWM dynamics of the QD exciton. (a) Coherence dynamics as a function of the
delay τ12 exhibiting dephasing and FSS-induced beats. The inset shows the PID on a few
ps time scale. (b) Population dynamics as a function of the delay τ23 exhibiting a single
exponential decay.
To have a closer look at the coherence dynamics of the exciton, we measure the time-
integrated FWM signal as a function of τ12, depicted in Fig. 7 (a) as dark red dots. The
signal shows the expected behavior after time integrating the photon echo in Eq. (1) (Fig. 6)
over t, which consists of an exponential decay that dominates for large delays (τ12 Tσ) and
an increasing contribution during the development of the full echo for τ12 < Tσ. In addition
we find a modulation of the signal stemming from the FFS of the two linearly polarized
excitons in the QD. As the linearly polarized E1,2,3are misaligned from the anisotropy axes
of the QD, both excitons are excited and the corresponding coherences contribute to the
11
final FWM signal.22,23,62 With the model described in Ref.62 we can fit the measured data
and retrieve the pale red line with a FFS of δFFS = ¯h2π/Tδ= (82 ±5) µeV and a light
polarization angle of α= (25 ±1)◦with respect to one of the QD excitons. An exemplary
FWM spectrum exhibiting a large FFS can be found the Supporting Information Fig. S1.
We note that the exciton-biexciton transition is not covered by E1,2,3and therefore does not
influence the dynamics.62 Examples of neutral exciton-biexciton complexes with both bound
and unbound character, typical for weakly-confined QDs,63 are readily identified in FWM
on the same sample, as shown for a bound example in the Supporting Information Fig. S2.
In the inset of Fig. 7(a) the FWM dynamics are shown for a delay timescale of a few
picoseconds. After the signal’s rise from negative delays, it reaches a maximum around
τ12 = 0. After that it drops within less than 2 ps to approximately 0.5 of its maximum
value. This fast decay is recognized as PID, due to the optical excitation with pulses that
are siginificantly shorter than the polaron formation process.48,49 The FWM dynamics are
reproduced by the depicted simulation (pale red line) in the well established independent
boson model.48,64 In this model the exciton-phonons coupling is described by additional
dynamics of the exciton coherence, in the form of the PID function ˜pPID. The full FWM
dynamics are therefore given by
pFWM(t, τ12)∼˜pPID (t, τ12)S(t, τ12),(2)
where S(t, τ12)is the homogeneous and inhomogeneous dephasing contribution from Eq. (1).
For optical pulses that are much shorter than the considered phonon periods, the PID dy-
12
namics can be calculated analytically in the limit of ultrafast pulses via65
˜pPID (t, τ12)
= exp
gq
ωq
2h2 cos(ωqt)−3 + eiωqτ12 (2 −eiωqτ12 )
−Nq
eiωqτ12 (2 −eiωqt)−1
2i,(3)
with the thermal occupation of the phonon modes Nq={exp[¯hωq/(kBT)] −1}−1. For
simplicity we here assume a spherical exciton wave function for which the coupling constant
can be written as
gq=qD
p2ρ¯hV ωq
e−1
2q2a2,(4)
with the normalization volume V. For the material parameters we use the mass density
of ρ= 5870kg/m3, an effective deformation potential strength of D= 9 eV,66 and assume
an isotropic phonon dispersion ωq=cq with the longitudinal acoustic sound velocity c=
3.2nm/ps.67 We find the best agreement with the measured FWM dynamics for an exciton
localization length of a= 2 nm.
To complete the study of the undoped QD, in Fig. 7(b) we present the exciton occupation
dynamics, which are measured by the τ23-dependence of the FWM amplitude while fixing
τ12 = 0 (red dots). An exponential decay (pale red line) is observed with a decay time of
T1= (200 ±25) ps. This decay is attributed to the radiative recombination of the bright
exciton states. The decay of the dark exciton typically happens on a much longer timescale
of a few tens of ns68 and is therefore not resolved here. The collection of the QD parameters
ascertained by the FWM study is gathered in Table 1.
13
Table 1: Parameters characterizing the optical properties of the QD exciton retrieved by
FWM spectroscopy.
homogeneous broadening γ= (36.1±0.2) µeV
inhomogeneous broadening σ= (142 ±1) µeV
bright exciton lifetime T1= (200 ±25) ps
fine-structure splitting δFSS = (82 ±5) µeV
light-matter coupling θ=π/2@P= 0.55 µW
Mn-doped quantum dot
After this characterization of the excitonic properties, we come to the QD containing a single
Mn2+ ion. Such a QD is recognized by measuring a PL spectrum as presented in Fig. 8(a).
The insertion of an individual Mn2+ ion into a QD, within the volume of the exciton’s wave
function, is confirmed by detecting the comb of six separate spectral lines,38,69 as shown in
the PL spectrum in Fig. 8(a), which is characteristic for a sufficiently symmetric QD when
the exciton-Mn exchange interaction dominates over the anisotropic electron-hole exchange
interaction, i.e., when the splitting of the lines due to the exciton-Mn interaction is larger
than the fine-structure splitting.70 The exciton transition is sensitive to the spin state of
the magnetic ion: The exchange interaction between the QD exciton and the ion leads to
spin-dependent spectral shifts with respect to the undoped QD exciton in the range of a
few meV. The electron-Mn exchange interaction furthermore leads to spin flips resulting in a
coupling between bright and dark excitons which, however, typically becomes effective only
at high magnetic fields.38,71 Without an additional magnetic field, the Mn spin projection Sz
freely jumps between its possible realizations, namely ±5
2,±3
2, and ±1
2. In a time averaged
measurement, this results in the development of six spectral components.
The FWM spectral interferogram and the resulting FWM amplitude are shown in Fig. 8(b)
and (c), respectively. Here, we also recover six spectral lines with their amplitudes increasing
for smaller transition energies. Interestingly, fluctuations of such a single spin generate a pe-
culiar type of inhomogenous broadening acting on the exciton. A typical Mn spin-flip time
in a CdTe QD is on the order of several µs,38,69,72 which is much longer than the measured
14
0
1
(a)
Sz=±5
2±3
2±1
2
∓1
2∓3
2∓5
2
0
(b)
0
1
1835 1836 1837 1838 1839 1840
(c)
norm. PL intens.
FWM interf.norm. FWM ampl.
photon energy (meV)
sim.
exp.
Figure 8: Spectral characterization of a Mn-doped QD. (a) PL spectrum exhibiting the
six spectral lines induced by the Mn dopant. (b) FWM spectral interferogram. (c) FWM
amplitude spectrum with the measurement in dark and the simulation in pale violet.
exciton lifetime of 200 ps. During the integration time of 10 ms, the exciton performs a
few thousand spectral jumps. Because the spin-flip time is much longer than the exciton
lifetime, the corresponding random jumps of the transitions energy can be interpreted as a
discrete ensemble. In Fig. 9 we examine how the FWM signal behaves as a function of the
delay τ12. In Fig. 9(a) we show examples of the measured FWM spectra for three different
delays τ12 increasing from bottom to top as labeled in the plot. We already see that the
overall amplitude of the signal strongly decreases with larger delays. In Fig. 9(b) we show
the integrated FWM amplitude as a function of τ12 as violet dots, which confirms the rapid
drop of the system’s coherence. The significant decoherence within the first 2 ps is already
known from the undoped QD and it stems from the PID in Fig. 7(b, inset). After the PID,
15
0
1
0123456
(b)
1835 1836 1837 1838 1839 1840
0
1
0
1
0
τ12 = 0.2 ps
τ12 = 1 ps
τ12 = 2 ps
(a)
0.2
0.3
345
(a)
norm. FWM ampl.
delay τ12 (ps)
exp.
sim.
norm. FWM ampl.
photon energy (meV)
Figure 9: Coherence dynamics of a Mn-doped QD. (a) Evolution of the FWM spectrum with
increasing delay τ12 from bottom to top. (b) Integrated FWM amplitude as a function of
the delay τ12 with the experiment as dark violet dots and the simulation as pale violet line.
i.e., for τ12 >1.5ps only long-time dephasings (homogeneous and inhomogeneous) reduce
the signal. In the simulation depicted as pale violet line, we take the impact of the Mn ion
into account by calculating an ensemble (ens) average of the six transition energies ¯h∆ωn
via
pens
FWM(t, τ12) =
6
X
n=1
p(n)
FWM(t, τ12)e−i∆ωn(t−τ12),(5)
where each FWM contribution p(n)
FWM(t, τ12)can be individually weighted. These weights of
the six contributions are chosen such that the simulated spectral distribution (pale violet line)
in Fig. 8(c) agrees with the measured one (dark line). In the resulting coherence dynamics
in Fig. 9(b) the discrete equidistant ensemble results in a slight beating of the FWM signal.
16
This oscillation is highlighted by the inset, which is a zoom-in on the black rectangle. The
effect is similar to the FSS beat observed from the undoped dot in Fig. 7(a). However, here
it stems from all possible frequency differences in the six-state ensemble.
Conclusions
In this work, we have studied the coherence properties of an exciton confined to a CdTe QD
by FWM spectroscopy. The creation and detection of this nonlinear optical signal, scaling
with the third power of the investigated dipole moment of the quantum system, required the
incorporation into a low-Q DBR cavity. To finally reach the required efficiency for the light-
matter coupling we additionally applied a solid immersion lens on the sample surface. With
this setup we were able to detect photon echo dynamics, which allowed us to determine the
homogeneous and inhomogeneous dephasing of the QD exciton. We further measured beats
of the signal, revealing the fine-structure splitting of the linearly polarized excitons, and
their population lifetime. Considering a QD hosting a single Mn-dopant we performed the
first FWM spectroscopy study of the characteristic six-lined spectral structure. We showed
that this unique shape of transition energies, stemming from random fluctuations between
the Mn-spin states, results in additional dephasing dynamics and a signal beating in the
ensemble average.
As the Mn spin-orientation can be controlled by an external magnetic field, forthcoming
magneto-FWM micro-spectroscopy experiments will allow to further monitor the impact of
the observed discrete inhomogeneous broadening onto the exciton coherence dynamics. It will
furthermore allow to study the coherence dynamics associated with the exchange-induced
coupling between bright and dark excitons giving rise to the characteristic anticrossings
in the magneto-PL of Mn-doped QDs.38 This progress will reveal the system’s potential
for a coherent ultrafast spin-photon interface. In particular 2D FWM spectroscopy will
unveil internal coherent interactions in the coupled exciton-Mn2+ system. It is possible to
17
shift the Mn-doped QD emission energies below 1770 meV (wavelengths above 700 nm),
see PL spectrum in Fig. S3 of the Supporting Information. Further work regarding the
growth will optimize the sample performance at this spectral range, enabling implementation
of the resonant spectroscopy employing standard Ti:Sapphire femtosecond laser sources.
At this point, we can combine more sophisticated and innovative photonic nanostructures,
currently emerging for the CdTe-platform,73 with QDs that can already contain a variety
of different magnetic impurities.37,43 These technological and spectroscopic advances open
exciting prospects for coherent nonlinear spectroscopy of hybrid exciton-spin systems in
semiconductor nanostructures.
Acknowledgement
This work was partially supported by the Polish National Science Centre (NCN) under deci-
sion DEC-2015/18/E/ST3/00559. Tomasz Jakubczyk acknowledges support from the Polish
National Agency for Academic Exchange (NAWA) under Polish Returns 2019 programme
(Grant No. PPN/PPO/2019/1/00045/U/0001). Daniel Wigger thanks NAWA for financial
support within the ULAM program (Grant No. PPN/ULM/2019/1/00064).
Supporting Information Available
Supporting Information contains:
– Exemplary FWM spectra showing individual excitons with a large fine-structure splitting.
– Two-dimensional FWM spectrum showing the exciton-biexciton complex.
– Photoluminescence spectrum of a Mn-doped QD emitting around 1710 meV.
18
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27
Coherent dynamics of a single Mn-doped
quantum dot revealed by four-wave mixing
spectroscopy
(Supporting Information)
Jacek Kasprzak,∗,†Daniel Wigger,‡Thilo Hahn,¶Tomasz Jakubczyk,†,§
Łukasz Zinkiewicz,§Paweł Machnikowski,‡Tilmann Kuhn,¶
Jean-François Motte,†and Wojciech Pacuski§
†Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
‡Department of Theoretical Physics, Wrocław University of Science and Technology,
50-370 Wrocław, Poland
¶Institut of Solid State Theory, University of Münster, 48149 Münster, Germany
§Institute of Experimental Physics, Faculty of Physics, University of Warsaw,
02-093 Warszawa, Poland
E-mail: jacek.kasprzak@neel.cnrs.fr
arXiv:2201.00792v1 [cond-mat.mes-hall] 3 Jan 2022
0
1
1837 1837.5 1838 1838.5 1839
δFSS
norm. FWM ampl.
Energy E(meV)
Figure S1: Four-wave mixing spectrum of an un-doped quantum dot showing a fine-structure
splitting of δFSS ≈0.2meV.
−1
0
1
2
3
4
5
1750 1755 1760 1765
1750
1755
1760
1765
1750 1755 1760 1765
delay τ12 (ps)
energy E(meV)
(a)
BX
X
energy Eτ(meV)
energy E(meV)
0.01
0.1
1
norm. FWM ampl.
BX+X X
BX
(b)
Figure S2: (a) Delay scan of an un-doped quantum dot showing an exciton (X) biexciton
(BX) complex. The BX clearly appears for τ12 <0. (b) Corresponding 2D spectrum demon-
strating the coherent coupling between X and BX by the off-diagonal spectral peak. The
biexciton binding energy (BBE) is δBBE ≈12 meV.
0
1
1709 1710 1711 1712 1713 1714 1715 1716 1717
Mn + biexciton
Mn + exciton
norm. FWM ampl.
Energy E(meV)
Figure S3: Photoluminescence spectrum of a Mn-doped quantum dot showing the exciton
and biexciton manifolds at around 1715 meV and 1710 meV, respectively.
1
