GaAs microcavity exciton-polaritons
in a trap

solidistatuspss

physicaphys. stat. sol. (b) 245, No. 6, 1076– 1080 (2008) / DOI 10.1002/pssb.200777610b

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basic solid state physics

Na Young Kim*, 1, 2, Chih-Wei Lai1, 3, Shoko Utsunomiya3, Georgios Roumpos1, Michael Fraser1, Hui Deng1,
Tim Byrnes3, Patrik Recher1, Norio Kumada4, Toshimasa Fujisawa4, and Yoshihisa Yamamoto1, 3
1

Edward L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
Institute of Industrial Science, University of Tokyo, Komaba Meguro-ku, Tokyo 153-8505, Japan
3
National Institute of Informatics, Hitotsubashi Chiyoda-ku, Tokyo 101-8430, Japan
4
NTT Basic Research Laboratories, NTT Corporation, Atsugi, Kanagawa 243-0198, Japan
2

Received 10 September 2007, accepted 15 January 2008
Published online 22 February 2008
PACS 42.50.Pq, 42.65.– k, 71.35.Lk, 71.36.+ c*Corresponding author: e-mail nayoung@stanford.edu, Phone: +1-650-725-8336

We present a simple method to create an in-plane lateral potential in a semiconductor microcavity using a metal thinfilm. Two types of potential are produced: a circular apertureand a one-dimensional (1D) periodic grating pattern. The amplitude of the potential induced by a 24 nm – 6 nm Au/Ti film
is on the order of a few hundreds of µeV measured at 6 – 8 K.
Since the metal layer makes the electromagnetic fields to beclose to zero at the metal – semiconductor interface, the photon mode is confined more inside of the cavity. As a consequence, the effective cavity length is reduced under the metal

film, and the corresponding cavity resonance is blue-shifted.
Our experimental results are in a good agreementwith theoretical estimates. In addition, by applying a DC electric voltage to the metal film, we are able to modify the quantum well exciton mode due to the quantum confined Stark
effect, inducing a ∼1 meV potential at ∼20 kV/cm. Our
method produces a controllable in-plane spatial trap potential
for lower exciton-polaritons (LPs), which can be a building
block towards 1D arrays and 2D lattices of LP condensates.

© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction Coupling electromagnetic fields withmassive particles and manipulating their coupling strength
have been of great interest in solid-state systems [1]. Theinterests lie in the investigation of fundamental physicalquestions, for example coherence and decoherence properties of coupled systems, and in new designs of novel optoelectronic devices such as vertical-cavity surface emitting
lasers. Diverse shapes of optical microcavity structures
have been implemented in order to confine the electromagnetic fields [2]. A Fabry–Perot planar microcavity is acommon choice to incorporate a quantum well structure. It
is composed of a pair of distributed Bragg reflectors(DBRs) from alternating semiconductor layers of different
refractive indices. In such a structure, when cavity photon
fields and quantum well exciton modes are strongly coupled, new quasiparticles called microcavity excitonpolaritons emerge as a manifestation of a strong light–
matter interaction [3].

Microcavity exciton-polaritons have been regarded ascomposite bosons at the low density limit and a promisingsolid-state candidate to observe novel physical phenomena
such as Bose–Einstein condensation (BEC) and superfluidity. Microcavity exciton-polaritons are advantageous forthe study of the aforementioned phenomena at elevatedtemperatures because of their lighter mass arising fromtheir photonic component. These particles have two distinct energy branches: upper exciton-polaritons and lower
exciton-polaritons (LPs). Recently, evidence of BEC in
LPs has been reported in terms of ground-state population,
the thermal equilibrium to lattice, spontaneous long-range
spatial and increased temporal coherence properties [4–8].
Along with the search for solid-state BEC systems,
many efforts to produce further confinement potentials inplanar systems have been attempted because additional
confinement would help to determine the definite groundstate energy and to facilitate the control of light–matter in© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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Paperphys. stat. sol. (b) 245, No. 6 (2008)

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while the laser excitation power is kept below the quantum
degeneracy threshold.
3 Results and discussion Representative near-field
spectra of the periodic grating configuration and the hole
structure are presented in Fig. 2. We excite the sample sur(a)

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2 Experiments Our λ/2 cavity contains three-stack offour GaAs quanum wells (QWs) located at the central antinodes of the cavity. The Al0.15Ga0.85As/AlAs cavity isformed by a 16-layer top DBR and a 20-layer bottom DBR.
GaAs QWs (6.8 nm in width) are separated by 2.7 nm
AlAs barriers. We studied two samples with different substrates: the substrate of Sample 1 is semi-insulating,whereas that of Sample 2 is n-doped. A spatial inhomogeneity caused by a tapering in the layer thickness of the wafer allows us to tune the cavity resonance. The vacuum
Rabi splitting energy is around 15 meV. On the surface ofthe top DBR, a grating or a hole is patterned by electron
beam or photo-lithography, followed by a 24/6 nm Au/Ti
metal deposition and a lift-off (Fig. 1(a)). The grating pattern consists of repeated pair of a metal finger and a gap.
Various sizes of the finger and the gap are used from
1.4 µm to 7.2 µm, and hole diameters vary from 10 µm to
90 µm.
Figure 1(b) illustrates the schematic of our experimental setup. We measure time-integrated photoluminescence(PL) of LP emissions at 6–8 K as a response to a 3 ps
pulsed excitation at ∼60 deg by a Ti:sapphaire laser(∼776 nm for Sample 1 nm and ∼768 nm for Sample 2).
The excitation spot is focused on the sample surface whose
diameter is around 20–100 µm. The LP emission signals
are collected in the normal direction by a high numericalaperture (NA = 0.55) objective lens. We use a standardµ-PL setup to access near-field (coordinate space) or farfield (momentum space) imaging and spectroscopy with arepositionable lens behind the objective lens. The in-planepotential strength is obtained from the LP emission energy

Figure 1 (online colour at: www.pss-b.com) (a) (Top) Scanningelectron microscopy image of a one-dimensional grating pattern(pairs of a 1.4 µm metal finger and a 1.4 µm gap). (Bottom) Arrays of circular-aperture metal films. (b) A schematic of the nearfield and the far-field imaging and spectroscopy setup.

PL intensity (arb. units)LP energy shift (meV)

teractions. Influencing either the exciton mode energy or
the cavity photon mode energy can create local in-planepotentials. Strain shifts the exciton energy, inducing aharmonic trap potential as an example of the former [9, 10].
The photonic component can be modified by modulating
the cavity layer thickness in a mesa structure [11, 12]. Here
we present a relatively simple way to form an in-plane potential by patterning a metal grating for a one-dimensional
periodic potential and a circular aperture structure for a
trap in two dimensions (2D). Under the metal film, the effective cavity length is reduced. Therefore, the energy of
the cavity photon mode increases, while the exciton moderemains unchanged. In addition, applying an electric field
perpendicular to the quantum wells causes a quantum confined Stark shift on the excitonic component, leading to the
red-shift in the zero-momentum LP energy. This method
has several advantages: (1) the in-plane potentials are created non-invasively after the full growth of a whole microcavity structure so that the non-radiative lifetime of the
QW exitons is not increased; (2) the dimension of the inplane potentials can be easily sub-microns by current advanced lithographic techniques; (3) various geometries in
1D and 2D of local in-plane potentials can be readily fabricated to excplore many-body interaction effects among exciton-polaritons.

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Figure 2 (online colour at: www.pss-b.com) Two-dimensional
spatially-resolved near-field spectroscopy of (a) a 5.6 µm onedimensional grid and (b) a 10 µm diameter hole at P = 1 mW in
Sample 2. A color bar represents the lower-polariton (LP) photoluminescence (PL) intensity. The LP energy shift and its PL intensity in real space for (c) the 5.6 µm grid and (d) the 10 µm aperture at P = 1 mW. The LP energy shift represents the LP energy
shifted by the minimum LP energy in space (1.6092 eV for (c)and 1.6077 eV for (d)). The cross marks in (b) indicate measurement positons above the metal film. Together with two more spatial points in x-axis, the average of the LP energy through metal
films at four spatially symmetric positions provides the potential
difference between the metal and the bare surface.
© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimP h o to n fie ld a m p litu d e

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R e (re fra c tiv e in d e x )© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim(a)R e (re fra c tiv e in d e x )face at low laser pump power below quantum degenerate
threshold with a laser spot size of around 100 µm(Fig. 2(a)) and 20 µm (Fig. 2(b)). Figure 2 (a) and (b) are
captured with a 5.6 µm metal–5.6 µm gap device and a
10 µm circular aperture, respectively. The PL intensity in
Fig. 2(a) shows a clear spatial modulation, and its peak-topeak oscillation period is ∼10.4 µm, which agrees wellwith the grating periodicity 11.2 µm to within a 7% error.
Since the LP emission at 780 nm through the metal film ismasked and its PL transmittance is reduced, we measure
the PL intensity through the metal reduced to 17–24% ofthat above the bare surface. Thus, we lose ∼41–49% of thelight emissions each time they pass the metal film. We extract the peak wavelength and the PL intensity of individual spectrum at each position, plotting them along position(Fig. 2(c) and (d)). An anti-correlated trend between the PL
intensity and the LP energy is clearly observed. The LPemission energy from the metal film is blue-shifted by
400 µeV on the average for this particular device. For thecircular aperture, we measured the LP spectra at four symmetric spatial locations (marked with a cross symbol in
Fig. 2(d)) on the metal film away from the open apertureby ∼50–100 µm. In this way, we can take into account of
the spatial inhomogenous detuning paramter. The averageof these four LP spectra above the metal film would provide the LP energy at the center of the circular aperture in
the case the metal film is covered. Considering the reduced
transmittance through the metal film, we double the excitation laser power above the metal film, extracting the LPenergy difference (EMetal – Ebare) between the metal film andthe bare surface. EMetal is denoted as the LP energy above
the metal film and Ebare represents the LP energy measured
from the bare surface.
We compute the effect of a thin metal film on the LPenergy and intensity using the transfer matrix method [13].
On the bare surface, the anti-node of the resonant cavity
photon wavefunction sits at the air-semiconductor interface
and the cavity photon field extends to the air. On the other
hand, when the metal film is deposited on the DBR, thecavity photon field is attenuated through the metal layer,squeezing the cavity photon mode into the inner structure
and pinning the cavity photon field at the metalsemiconductor interface to close to zero. Figure 3 illustrates the effect of the 30 nm metal film on the opticalfields compared to the bare surface case. Consequently, theeffective cavity length is reduced under the metal film andits resonant photon energy and corresponding LP energy
increase (blue-shift). At zero detuning where the cavity
photon energy is resonant with the QW exciton energy,
the cavity photon mode energy is blue shifted by 400 µeV
and the LP energy shift is expected to be roughly halfsize, 200 µeV since the photonic component of the LP atzero detuning is 50%. Using the complex refractive indices of Au and Ti at 800 nm (nAu = 0.15 – 4.86i,
nTi = 3.03 – 3.65i), the attenuation constants for Au andTi are αAu = 2π Im (nAu)/λ ~ 0.039 nm–1, αTi = 2π Im (nTi)/λ~ 0.029 nm–1. In addition, we consider reflection between

N. Y. Kim et al.: GaAs microcavity exciton-polaritons in a trap

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Figure 3 (online colour at: www.pss-b.com) Computed electromagnetic field amplitudes for a standing wave at resonance (blue)
from the bare surface (a) and from the 26 – 4 nm Au/Ti metal
layer (b) along the growth direction in z-axis. z is the distancefrom the center of the cavity. The real parts of refractive indicesof materials are drawn in green. Only the region near the surface
is shown here.

interfaces. Overall the amplitude of emission through a
25 nm Au metal film at 778 nm would be reduced to ∼40%,
which corresponds well to the measured value.
Theoretical model further predicts that the amount of
the LP energy shift depends on the detuning (∆) at a given
metal thickness. The more negative ∆ is, namely, when the
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Figure 4 (online colour at: www.pss-b.com) LP energy shift
through the Au – Ti metal film deposited on the top surface ofSample 1 (EMetal) compared to the bare surface (Ebare) as a functionof the detuning parameter (∆). Sample 1 has a vacuum Rabi splitting energy 2g ~ 2 × 6.97 meV and Eexc ~ 1.59241 eV.
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QW exciton energy (Eexc) is much larger than the cavity
photon energy (Ecav), the more the LP energy shift is increased. Suppose the cavity photon energy shift to be δ induced by the metal film. The LP energy at k// = 0 throughthe metal film is written as
EMetal = 12 [ Ecav + δ + Eexc - (2 g ) 2 + ( Ecav + δ - Eexc ) 2 ] ,where 2g is the vacuum Rabi splitting. Inserting ∆ = Ecav –Eexc, the energy difference between the metal and the baresurface is derived as
EMetal - Ebare = 12 [δ - (2 g ) 2 + (∆ + δ ) 2 + (2 g ) 2 + ∆ 2 ] .

The computed LP energy shift (EMetal – Ebare) is plottedalong the detuning in red (Fig. 4) with g ∼ 6.97 meV,
Eexc ~ 1.59241 eV and δ ~ 0.4 meV. The values of 2g andEexc are obtained from the fitting results to the multiple dispersion curves obtained at various locations in Sample 1(not shown). Figure 4 summarizes the outcome of the the
LP energy shift values from experimental data with sample
1 as well as the theoretical estimates.
The presence of the metal film modifies the cavity photon mode. In addition, we can modify the QW excitonmode by applying a DC voltage to the metal film acrossthe wafer. The electric field perpendicular to the QW layer
causes a quantum confined Stark effect [12]. Under theelectric field, the energy difference between the ground1.6062

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state of the conduction band and that of the valence band isreduced. Therefore, the QW exciton energy is reduced (redshift). On the other hand, since an electron wavefunction in
the conduction band and a hole wavefunction in the valence band are separated in space, the overlap of the electron and the hole wavefunctions is reduced, making the dipole moment of excitons smaller and yielding a reduced
exciton binding energy. The coupling between the QW excitons and the cavity photons becomes weaker. The weakercoupling will cause the LP energy increased (blue shift).
We compute the LP energy shift using a variational approach for exciton wavefunctions which takes into accountthe aforementioned electric field effect [15]. We assume
that only heavy-hole excitons are relevant and we ignore
light-hole excitons. Using the values of the GaAs QW parameters at low temperature, we find that the overall LP
energy becomes red shifted.
We apply the DC voltage to the metal film of Sample 2
whose substrate is heavily n-doped. This maximum value(10 V) corresponds to ∼20 kV/cm across the 4.7 µm insulating layer thickness. Experimentally, we observe that thetrend of the LP energy shift is symmetric in both polaritiesof the DC electric field and the LP energy is systematicallydecreased by ∼1 meV at the maximum applied electricfield. For low electric fields, the measured LP energy shift
can be explained by the theoretical estimate very well.
However, we find that the LP energy in experiment ismuch more rapidly decreasing than that in theory. Investigation of this discrepancy will be left for future work.
4 Conclusion We show that a simple deposition of ametal thin-film on the top surface can modify both the cavity photon mode energy and QW exciton mode energy. In
the former, the metal film layer acts as a mirror to define a
reduced cavity length, causing the higher LP energy under
the film. This can create an effective local in-plane potential in the range of around hundreds of µeV. We also showthat the QW exciton mode energy can be controlled by theapplied DC electric field perpendicular to the QW layer,
yielding a ∼1 meV LP energy shift at ∼20 kV/cm. We envision that this method provides a simple but robust way to
produce a controllable spatial potential to trap microcavity
exciton-polaritons. We can extend readily this method todesign and fabricate various patterns of geometries in 1D
and 2D.

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Acknowledgements This work is supported by JST/
SORST, NTT and Special Coordination Funds for Promoting
Science and Technology in University of Tokyo.

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Electric Field (k V/ cm )Figure 5 (online colour at: www.pss-b.com) (a) LP energy shift
due to the DC electric field across the wafer whose substrate isheavily n-doped. We apply the voltage up to 10 V across a
4.7 µm wafer. (b) The experimental LP energy shift taken at
k// = 0 (circles) and the theoretical LP energy shift (red line).
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References[1] S. Haroche and D. Kleppner, Phys. Today 42, 24 (1989).
[2] K. J. Vahala, Nature 424, 839 (2003).
[3] C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa,Phys. Rev. Lett. 69, 3314 (1992).
[4] H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto,
Science 298, 199 (2002).
© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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[5] H. Deng, G. Weihs, D. Snoke, J. Bloch, and Y. Yamamoto,
Proc. Natl. Acad. Sci. 100, 15318 (2003).
[6] H. Deng, D. Press, S. Götzinger et al., Phys. Rev. Lett. 97,
409 (2006).
[7] J. Kasprzak, M. Richard, S. Kundermann, A. Baas,
P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H.
Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, Nature 443, 409(2006).
[8] H. Deng, G. S. Solomon, R. Hey, K. H. Ploog, and Y. Yamamoto, Phys. Rev. Lett. 99, 126403 (2007).
[9] R. B. Balili, D. W. Snoke, L. Pfeiffer, and K. West, Appl.
Phys. Lett. 88, 031110 (2006).

[10] R. B. Balili, D. W. Snoke, L. Pfeiffer, and K. West, Science
316, 1007 (2007).
[11] O. E. Daïf, A. Baas, T. Buillet, J.-P. Brantut, R. I. Kaitouni,
J. L. Staehli, F. Morier-Genoud, and B. Deveaud, Appl.
Phys. Lett. 88, 061105 (2006).
[12] R. Idrissi Kaitouni et al., Phys. Rev. B 74, 155311 (2006).
[13] P. Yeh, Optical waves in layered media (John Wiley andSons, Hoboken, NJ, 2005).
[14] D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard,
W. Wiegmann, T. H. Wood, and C. A. Burrus, Phys. Rev.
Lett. 53, 2173 (1984).
[15] P. Harrison, Quantum Wells, Wires and Dots (John Wileyand Sons, Hoboken, NJ, 2000).

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