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1
Ghost Branch Photoluminescence From a Polariton Fluid Under Nonresonant Excitation
Maciej Pieczarka 1,*, Marcin Syperek 1, Łukasz Dusanowski 1, Jan Misiewicz 1, Fabian Langer 2,
Alfred Forchel 2, Martin Kamp 2,Christian Schneider 2, Sven Höfling 2,3, Alexey Kavokin 4,5,
Grzegorz Sęk 1
1 Laboratory for Optical Spectroscopy of Nanostructures, Department of Experimental Physics,
Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
2 Technische Physik, University of Würzburg and Wilhelm-Conrad-Röntgen-Research Center for
Complex Material Systems (RCCM), Am Hubland, D-97074 Würzburg, Germany
3 SUPA, School of Physics and Astronomy, University of St. Andrews, St. Andrews KY16 9SS,
United Kingdom
4 Spin Optics Laboratory, Saint Petersburg State University, 1, Ulianovskaya, 198504, St
Petersburg, Russia
5 Physics and Astronomy School, University of Southampton, Highfield, Southampton SO17 1BJ,
UK.
*corresponding author: maciej.pieczarka@pwr.edu.pl
PACS numbers: 71.36.+c, 67.10.-j, 71.35.Lk, 78.67.De
Abstract
An expanding polariton condensate is investigated under pulsed nonresonant excitation with a
small laser pump spot. Far above the condensation threshold we observe a pronounced increase in
the dispersion curvature with a subsequent linearization of the spectrum and strong luminescence
from a ghost branch orthogonally polarized with respect to the linearly polarized condensate
emission. The presence of the ghost branch has been confirmed in time-resolved measurements.
The dissipative and nonequilibrium effects in the photoluminescence of polariton condensates and
their excitations are discussed.
Exciton polaritons are composite bosons consisting of strongly coupled microcavity photons and
quantum well excitons. They are able to form a novel class of condensates (for recent reviews see,
e.g. [1], [2]). Despite their nonequilibrium and dissipative nature, where the polariton condensation
is governed by their amplified scattering and by the balance between the gain from the polariton
reservoir and the loss due to the escape of photons from the microcavity, they behave as
condensates of weakly interacting bosons. Collective phenomena like condensation [3], off
diagonal long range order [4], [5], topological excitations [6] or superfluid features in propagation
of polariton flows [7] have been demonstrated in such systems. A spectacular consequence of the
parametric scattering in polariton gases is appearance of non-parabolic scattering bands, including
normal branches (NBs) and ghost branches (GBs), the latter ones populated by the virtual off-
branch exciton-polaritons [7,8]. Excitations of polariton condensates are expected to be
2
characterized by linearized dispersions of the Bogoliubov-like spectra [9]. The fluid excitations at
low momenta are expected to behave as collective sound waves rather than single particles.
Recently, the linear dispersion NB and the GB of a resonantly pumped polariton condensate [10]
have been observed in a four-wave mixing experiment.
The experiment providing a direct access to the dispersion of excitations of spontaneously formed
condensates in polariton systems is photoluminescence (PL) under nonresonant excitation. The
nonresonant pumping can be realized either with a detuned laser or with the current
injection [11,12]. In the nonresonant pumping scheme, incoherent excitons are generated and relax,
subsequently feeding the reservoir and governing the dynamics of the system [13]. The relaxation
of created hot excitons involves multiple scattering processes, which destroy the coherence and
phase of the excitation, ensuring that these properties are not inherited by the condensate, in
contrast to the resonant excitation case. At the same time, the excessive noncondensed quasi-
particles build up an incoherent reservoir, causing additional decoherence [14] and forming a
repulsive potential [15], which shapes the condensate spatially and spectrally. This results in a high
sensitivity of polariton fluids to the size and profile of the optical pump beam. Moreover, it affects
significantly the excitation spectrum of the condensate [16]. Bogoliubov dispersions have been
reported in this excitation scheme, however, no fingerprints of the GB have been observed
yet [17], [18]. This fueled the debate on the possibility of observing the GB in nonresonant PL [19]
where the strong emission of the condensate occurs and that one being related to the NB can easily
mask the GB signal. The resonant experiment done by V. Kohnle et. al. in [10] is in stark contrast
to nonresonant pumping scheme, since the polariton condensate formation occurred in absence of
incoherent reservoir and the collective excitations were created by a resonant trigger pulse.
In this Letter, we report on the direct observation of a PL signal of the GB together with a
pronounced linearization of the dispersion of an expanding polariton condensate under nonresonant
excitation. We verify the observation via polarization- and time-resolved experiments, which
elucidate the origin of the observed features.
The investigated sample was a GaAs-based microcavity with embedded high-indium content
In0.3Ga0.7As quantum wells. The cavity consist of two Bragg mirrors (top and bottom) of alternating
GaAs and AlGaAs pairs of layers. The length of the cavity is equal to λ/2. The quality factor of the
cavity estimated from the reflectivity spectra taken far from the polariton anticrossing resonance
was around 1000. The system was in a strong coupling regime characterized by the normal mode
splitting of 7 meV. Experiments described in this letter were performed at negative photon-exciton
detunings of around -0.5 meV and -2 meV. Details on the experimental setup are given in the
supplementary material [20].
The non-linear properties of polariton condensates have been investigated using excitation power
dependent PL measurements both in real and momentum space. In our experiment the pumping
laser was focused to a diffraction limited Gaussian shape of about 2 µm in diameter. The PL
intensity as a function of the excitation power (average power measured outside of the cryostat) for
two linear and perpendicular polarization detections, co-linear and cross-linear to the polarization
axis of the polariton condensate, is shown in Fig. 1(a). The data is extracted from time-integrated
data, hence the values are averaged over many excitation pulses. At low excitation densities, the
3
lower polariton branch (LP) dispersion is formed as can be seen in Fig 1(b). With a further increase
of the excitation power, we observe a distinct nonlinear threshold in the intensity dependence on
pumping shown in Fig. 1(a), consistent with the formation of a flat dispersion characteristic of a
propagating polariton condensate [Fig. 1(c)] at the threshold. This kind of dispersion is predicted
[16] when exciting a polariton condensate by a small excitation spot. The condensation threshold
is also manifested by a decrease of the linewidth of the measured emission which drops down by a
factor of 5 at threshold, and by a blueshift of the emission peak of about 3 meV (not shown). The
energy shift of the propagating condensate created nonresonantly is composed of the kinetic energy
of polaritons, repulsive interactions within the condensate and a term coming from the interaction
of polaritons with pump-spot-induced reservoir of noncondensed quasi-particles [15,21]. Hence,
the condensate energy is shifted above the minimum of the bare cavity mode, while the strong
coupling is preserved.
The microcavity polaritons subject to a natural disorder potential which originates from the width
and composition fluctuations of the quantum wells and Bragg mirrors [22]. Much effort has been
directed to reduce the impact of disorder [21], by growing nearly perfect, defect-free cavities.
Nevertheless, even in the best quality samples the localization and scattering of polaritons by a
stationary disorder potential is inevitably present. We observe polariton trapping by the disorder
potential as one can see in Figure 2. Localization of polaritons in real space has been observed at
moderate pump densities in our experiment. Bright spots of the luminescence located outside the
pump area are visible in Fig. 2(a), in agreement with the flat parts of the polariton dispersion
observed in the reciprocal space [Fig. 2(c)] [24]. The most striking phenomena have occurred at
higher polariton densities. First, we observed an evident spreading of the polariton cloud to
distances much larger than the pump spot – Fig. 2(b). This can be interpreted in terms of ballistic
flow of the polariton condensate pumped above the percolation threshold in a 2D disorder potential.
Furthermore, well above the threshold a pronounced linearization of the polariton emission and a
clear evidence of the GB emission at the negative energies (below the condensate emission energy)
have been observed, as presented in Fig. 2(d). The GB becomes visible at pump densities around
20Pth at different detunings and at different spot positions at the sample surface. The buildup of the
GB luminescence could be attributed to the off-branch multiple-scattering processes in the
polariton gas [7]. However, the intensity of GB is strong and comparable to the NB and we detected
a change in the dispersion curvature, indicating a collective phenomenon of mixing the NB and
GB [10]. The linear spectrum and the appearance of the GB are fingerprints of collective
Bogoliubov-like excitations of a propagating polariton fluid. Similar features can be induced
resonantly in a propagating condensate in the supersonic regime in the presence of obstacles which
disturb the flow [23], [25]. Here, one can observe interference ripples in the real space image [Fig.
2(d)], which is a signature of nonradial propagation of scattered polariton waves [26]. These
patterns are stable for many minutes as they are observed in a time-integrated picture, thus the
interference phenomena have a major contribution to the final integrated signal, as confirmed by
the reproducibility of the features after many pulses. The disorder in our sample is believed to be
the source of excitations in the expanding polariton fluid, behaving as a static scattering landscape.
Additionally, one has to note a slight anisotropy of the emission intensity distribution over the
dispersion branches, which reflects a non-uniform disorder potential in the real space. The latter
4
shapes both the coherent flow of polaritons and the scattered waves. The specific spectra and
interference patterns are determined by the position of the excitation spot on the sample surface.
Let us now discuss the polarization characteristics of emitted photons. One important property of
polaritons is their spin fine structure inherited from excitons and photons. The optically active LPs
have the spin projection
1S
on the growth axis direction. Due to the anisotropic spin
interactions the minimization of the system energy favors the superposition of spin up and spin
down polaritons at the condensation threshold, resulting in a linear polarization buildup [27].
Moreover, in an isotropic medium this is a signature of a spontaneous symmetry breaking induced
by the condensation, and the vector polarization can be considered as an order parameter [28], [27].
In our experiment the nonlinear threshold is accompanied by a rapid increase of the degree of linear
polarization (DOLP) around
0k
, presented in Fig. 3(a) (where
/DOLP I I I I
;
,
I
are
the intensities detected in two orthogonal linear polarizations). The condensate forms at each point
in the real space with the same direction of linear polarization vector. We can observe a small
polarization asymmetry of the polariton ground state which is why the polarization vector of the
condensate is always pinned to one of the crystal axes [29,30]. For higher pumping levels we
observe depinning of the polarization vector, manifested in a decrease of the total DOLP with
respect to the pump power [31]. This data is extracted from the time-integrated measurements, so
the measured DOLP values are averaged over hundreds of time evolutions, resulting in the lower
value of the DOLP compared to each individual realization [31]. However, it allows the effect of
the abovementioned depinning in the pump power dependent measurements to be visible. Now,
considering the polarization properties of the NB and GB, one should expect the NB to be polarized
as the condensate and the GB signal to be orthogonal to it. This is due to the physical origin of the
two coupled branches of excitations. While the NB is populated due to the non-zero effective
temperature of the polariton gas, the GB is populated due to the depletion of the condensate by
polariton-polariton scattering similarly to the off-branch scattered states observed at resonant
pumping in [7]. According to the polarization selection rules [32], scattering of linearly polarized
polaritons produces polaritons having an orthogonal linear polarization, preferentially. Indeed, our
polarization-resolved measurements have shown the GB to be orthogonally polarized with respect
to the condensate polarization axis. The results are shown in Figures 3(b), where signal from
separate GB and NB as a function of polarization angle is shown, and 3(e), where we plot a DOLP
map created from a direct overlap of the two dispersions from Fig. 3(c) and (d) (after correction to
the small polarization splitting of the order of 0.1 meV) and calculating the polarization degree for
each pixel of the recorded data. A large area of a positive DOLP is observed for the NB, which
comes from the background created by the full time evolution of the signal after the pump pulse.
More importantly, very distinct inversed polarization of the GB is clearly visible in the DOLP map.
It is worth noting that while the optical nonlinearities of the cavity itself can generate an analogue
of complex quantum fluid phenomena in the paraxial geometry [33], however the large value of
DOLP and linear polarization inversion for GB is a direct evidence of the polariton-polariton
scattering responsible for the population of GB. Clearly, this cannot be an effect of the linear
polarization splitting in the cavity, which could rather give a rise to the buildup of the circular
polarization of emission [34].
5
All the data discussed above has been obtained in the time-integrated measurements. The main
drawback of this kind of approach in experiments with pulsed excitation is a loss of the information
about the complex dynamics of the system after each excitation pulse, in particular, it leads to the
time-averaging of the blueshift of the polariton dispersion branch. This has been addressed in
Ref. [10], where the authors have observed an overestimated speed of sound in the time-integrated
picture as well as an asymmetry between slopes of the NB and GB. One can observe a similar
asymmetry in our experiment, where the NB has a greater slope than the GB - see Figs. 3(c-d). In
order to rule out the artifacts in our dispersions which might arise due to the time integration, we
have performed the time-resolved scanning of the measured dispersion of a propagating polariton
condensate at the detuning of –2 meV, and we studied in detail the dynamics of the polariton
luminescence after the pump pulse.
Approximately 50 ps after the pump pulse arrival we have observed a simultaneous and distinct
appearance of the positive and negative branches in the photoluminescence. A snapshot at 66 ps
after the pulse arrival is shown in Fig. 4(a). Clearly, they are not artifacts of time integration. One
can notice that the NB and GB have now comparable slopes in this time-resolved picture. However,
the extracted propagation velocity is still somewhat larger than the speed of sound calculated from
the condensate blueshift from Fig. 4(a): the velocity taken from the slope of the time-resolved
experiment is
1.95 /
slope
v m ps
and is greater than the velocity of
1.45 /
blue
v m ps
calculated
from the blueshift at
0k
, according to definition
pol
U
cm
, where U is the blueshift
(corresponding to mean field energy) and mpol is the LP effective mass. Confronting these velocities
to the values obtained from time-integrated series of a less photonic condensate corresponding to
the detuning of -0.5 meV, presented in Fig. 4(b), one can see even larger difference in both values.
Here, however, one has to take into account the overestimation of the slopes in the time-integrated
picture. The 𝑣𝑠𝑙𝑜𝑝𝑒 corresponds to the polariton mean field energy of
U
3.8 meV , being four
times larger than the observed temporal blueshift. One of the reasons might be technical, namely
the response resolution of the streak camera equipped with a monochromator is 12 ps. However,
the GB signal lasts for much longer, at least for 50 ps which excludes the apparatus effect. It has
to be noted, that the used excitation scheme creates a condensate with a nontrivial spatial
distribution of wave vectors [15]. Our case is far from the steady state of a static condensate and in
this experimental configuration the pump pulse creates moving condensate, characterized by the
outward coherent flow and disorder scattering of the polaritonic waves. This is why the condensate
at zero wave vector is more likely to be created via scattering on multiple defect centers [35]
resulting in lower blueshift than for a static condensate. We can also speculate on the spatially
varying local Doppler shift of created excitations which might be responsible for the observed
distinct slopes, adding additionally the local condensate velocity to the slope of the dispersion.
This, however, recalls for a further theoretical analysis.
The observed emission of the condensate and the GB are present at the energy very close or even
above the energy of the cavity mode in our sample, giving rise to the question if these phenomena
occur still in the strong coupling regime. In the time-resolved spectrum right after the pump pulse
arrival, we observe a strong emission corresponding to the bare cavity mode at the time scale below
6
the temporal resolution of our setup as shown in Fig. 4(c). All the recorded dispersion features
including the linearized NB and the orthogonally polarized GB signal occur later in time, where
the weak coupling lasing has completely vanished. We conclude that these spectral features are
characteristics of a polariton condensate formed in the strong coupling regime. In fact, in the
time-resolved measurements we observe a transition from weak to strong coupling similar to the
one reported in Ref. [36]. We believe that we were able to observe very clearly the renormalization
of the NB and the buildup of the GB partly due to the relatively modest quality factor of our sample,
which was low enough to enable efficient extraction of photons outside the cavity and high enough
to preserve the conditions for the polariton condensate formation. Moreover, the intrinsic disorder
of the cavity enhanced the elastic scattering favorable for the condensate formation.
In conclusion, we report on the first observation of a polariton ghost branch in a photoluminescence
experiment under nonresonant excitation. Even though the system in our approach was far from
equilibrium and from the steady state regime, we have observed a distinct renormalization of the
polariton dispersion characterized by the Bogoliubov-like normal and ghost branches. The origin
of the observed dispersion branches has been identified based on the observed orthogonal linear
polarizations of the branches and on the time-resolved dispersions showing temporal symmetric
slopes for the normal and ghost branches of the polariton condensate excitations.
Acknowledgments
We would like to thank Iacopo Carusotto for critical reading of this manuscript and for valuable
discussions. The authors acknowledge the financial support from the bilateral project of Deutsche
Forschungsgemeinschaft (project named LIEPOLATE) and Polish Ministry of Science and Higher
Education (project No. DPN/N99/DFG/2010). The experiment is partially performed within the
NLTK infrastructure, Project No. POIG. 02.02.00-003/08-00. AK acknowledges the financial
support from the Russian Ministry of Education and Science (Contract No.11.G34.31.0067).
7
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Figure captions
Fig. 1. a) Power dependent intensity curve of two linear polarizations, co-linear to the condensate
axis (blue circles) and cross-linear to the condensate (orange circles). Time integrated dispersions
below-(a), and slightly above the threshold-(b). LP branch (white solid line), blueshifted (blue
dashed) and bare cavity mode (white dashed) dispersions are shown. The color scale is linear.
Measurements for detuning -0.5 meV.
Fig. 2. Localization of polaritons at moderate densities in the momentum (a) and real space (c).
High pumping conditions with onset of linear dispersions (b) and the extended polariton cloud (d).
Line description is the same as in Fig. 1. The pump spot location is indicated as “x” in (b) and (d).
The color scale is linear.
Fig. 3. (a) DOLP as a function of the pumping power. (b) Polarization of separate NB and GB
signal extracted from the PL map measurements. The values are normalized. Co-linear (c) and
cross-linear (d) detection with respect to the condensate polarization and corresponding DOLP map
(e) of dispersion at the detuning of -0.5 meV. The DOLP scale is in the inset of (e) [-0.6;0.6]. The
intensity color scale is linear in (c) and (d).
Fig. 4. (a) Dispersion snapshot at 66 ps of the time-resolved evolution of the polariton dispersion
at the detuning of -2 meV . Cavity mode and LP are shown by white dashed and white solid lines,
respectively. The violet dotted lines are guides to the eye to highlight the similar slopes of the linear
dispersion part. The color map scales are logarithmic. (b) Velocities extracted from the slope of
time integrated data (orange circles) and sound speed calculated from dispersion blueshift (green
circles). (c) Snapshot at the ultrashort times after the pulse arrival, presenting photon lasing in the
weak coupling regime. The color scale is logarithmic.
10
Fig. 1
110 100
0,01
1
100
10000
Intensity (a.u.)
Power (mW)
a)
b) c)
11
Fig. 2
12
Fig. 3
13
Fig. 4
