We performed studies on microcavity polaritons trapped along the three dimensions of space, under resonant excitation on a confined lower polariton state. We observed various nonlinear behaviors as a function of the pump power, without any apparent loss of the strong-coupling. That may be understood as effects of Coulomb interaction. Indications of bistable behaviors in the system are observed and discussed

Baas, Augustin

Deveaud, Benoit

El Daïf, Ounsi

Morier-Genoud, Francois

Nardin, Gaël

Paraïso, Taofiq K.

Richard, Maxime

We performed studies on microcavity polaritons trapped along the three dimensions of space, under resonant excitation on a confined lower polariton state. We observed various nonlinear behaviors as a function of the pump power, without any apparent loss of the strong-coupling. That may be understood as effects of Coulomb interaction. Indications of bistable behaviors in the system are observed and discussed.LOE

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© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim p s scurrent topics in solid state physicscstatussolidiwww.pss-c.comphysicaEarly View publication on www.interscience.wiley.com (issue and page numbers not yet assigned;  citable using Digital Object Identifier – DOI)phys. stat. sol. (c), 1–4 (2008) / DOI 10.1002/pssc.200777618Resonant nonlinear studies oftrapped 0D-microcavity polaritonsGae¨l Nardin*, Ounsi El Daı¨f, Taoﬁq K. Paraı¨so, Augustin Baas, Maxime Richard,Francois Morier-Genoud, and Benoit DeveaudInstitut de Photonique et d’E´lectronique Quantiques, E´cole Polytechnique Fe´de´rale de Lausanne (EPFL), Station 3, 1015 Lausanne,SwitzerlandReceived 10 September 2007, accepted 3 December 2007Published online 18 February 2008PACS 71.20.Nr, 71.36.+c∗ Corresponding author: e-mail gael.nardin@epﬂ.ch, Phone: +41-21-693 54 49, Fax: +41-21-693 45 25We performed studies on microcavity polaritons trappedalong the three dimensions of space, under resonant ex-citation on a conﬁned lower polariton state. We observedvarious nonlinear behaviors as a function of the pumppower, without any apparent loss of the strong-coupling.That may be understood as effects of Coulomb interac-tion. Indications of bistable behaviors in the system areobserved and discussed.1 Introduction Most breakthroughs in semiconduc-tor physics and technology over the last thirty years origi-nated from quantum conﬁnement of elementary excitationsalong one, two, or three spatial dimensions [1] and from theimprovement of their coupling to the electromagnetic ﬁeld.Indeed, conﬁnement in semiconductor structures allowsdesign and shaping of their electrical and optical proper-ties, and the study of various effects, ranging from the Pur-cell effect [2] to full quantum conﬁnement. Such conﬁne-ment allows to control the emission properties of matter,and can be used for applications in many ﬁelds, rangingfrom optoelectronics to quantum information.Microcavity polaritons are 2D quasi-particles arisingfrom the strong-coupling between a quantum well excitonand a cavity photon. Thanks to their excitonic content, po-laritons can interact strongly, added to their peculiar dis-persion shape, this allowed to observe polariton paramet-ric scattering where two polaritons in an initial pump state(Ep,kp), scatter towards idler (Ei,ki) and signal (Es,ks)states, along the lower polariton (LP) dispersion curve [3,4]. This process is similar to the optical parametric oscil-lator (OPO). It has lead to the observation of several phe-nomena of interest as giant parametric ampliﬁcation [5] orcoherent control of polaritons [6] along with a varied phe-nomenology. For one given pump state, the allowed cou-ples of signals and idlers are described by 8-shaped lines inthe 2D reciprocal space, as was observed by [7]. One inter-esting pump state is at the so-called magic angle, for whichthe signal state corresponds to the bottom of the dispersion,that is the lower polariton ground state (E0,k = 0). Thissituation shows the smallest density threshold for paramet-ric conversion [3,4,8].2 Experimental facts2.1 Sample We fabricated a GaAs/AlAs 2D semi-conductor λ-microcavity with an embedded InGaAs quan-tum well, giving rise to a Rabi splitting of 3.5 meV. Wehave designed and realized 6 nm high mesas of 9 µm indiameter on the top of the spacer layer, which act as 0Dtraps for the photon mode. We previously demonstratedand characterized strong-coupling in 0 and 2 dimensionsfor the various mesa sizes [9]. The 0D structure shows avery high-Q factor of ∼ 21000, thanks to the fact that theconﬁning mesas have sizes smaller than the typical opticaldisorder in GaAs microcavities [10,11].In such a conﬁned structure, the dispersion curve showsdiscrete levels, delocalised in the reciprocal (k-)space, andthus with an angular broadening, as we have previouslyobserved [12,13]. This should favor parametric processes,due to the relaxation of the wave vector conservation con-dition.© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 2 G. Nardin et al.: Resonant nonlinear studies of trapped 0D-microcavity polaritons© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-c.comphysicap s sstatus solidi cIn the scope of the quest for parametric ampliﬁcation inour system, we present here studies under resonant excita-tion on a 0D trapped polariton state in a 9 µ-mesa. We per-formed detailed studies of the behavior of the photolumi-nescence (PL) emission of the ground state of the system,while increasing the density of created population, whichis linearly linked to the pump power.While the non-resonant excitation at high energy of thesystem creates free carriers contributing to the total densityof population and thus to the loss of the strong-couplingregime [12–14], resonant excitation of the system createsonly polaritons. In order to excite selectively a given eigen-state, one needs to be able to observe these states. As theyare deﬁned in the wave vectors’ basis, it is necessary toobserve the reciprocal space (accessible through angle re-solved imaging and excitation) of the sample in order to beable to select which state to populate.2.2 Experimental set-up Excitation of the sampleis performed with a continuous tunable TiSa laser, the exci-tation angle is  10◦, and the energy of the laser is 1486.3meV. By imaging the k-space of the sample on the slitof a spectrometer, we obtain angle resolved spectra, andthus image the k-space of the system. Fig. 1(a) shows thePL spectrum obtained in this conﬁguration for a 9 µm-diameter mesa, at zero detuning for the lower conﬁned po-lariton mode, while exciting non-resonantly (at high en-ergy) the system. One can see that the conﬁned states havelobes depending on the angle of detection. (These lobescorrespond to the quantum number m [13,15]) We there-fore chose the laser pumping angle so that it correspondsto a lobe on the image shown on Fig. 1(a), in order to,as much as possible, improve its coupling to the system.The energy chosen shows an available signal-idler coupleof states fulﬁlling the energy conservation with a precisionbetter than the linewidth: Eidler−Epump = 0.87 meV andEpump−Esignal = 0.90 meV, where the signal state is theLP ground conﬁned state. These values are smaller than thelinewidth of the conﬁned photon: 0.90−0.87 = 0.03 meV< 0.1 meV  γ0D, and thus of the conﬁned polariton.Figure 1 (a) Dispersion in photoluminescence under non-resonant excitation of the 9 µm-diameter mesa lower polaritonat zero detuning, the white signal at high energy is the 2D lowerpolariton (at the exciton’s energy). The pump state chosen and itspotential signal below are circled in red. (b) Resonant pumping.(c) Emission at the nonlinear threshold. Mentioned pump powerscorrespond to the experiment shown on Fig. 2.Figure 2 (a) PL intensity of the lower polariton ground conﬁnedlevel as a function of the laser power (color online). (b) Linewidthof the lower polariton ground conﬁned level (circles), and ﬁrstexcited level (crosses). (c) Energy shift of the lower polaritonground conﬁned level (circles) and ﬁrst excited level (crosses),the ratio of the largest shift over the Rabi splitting is given.3 Results Results obtained are shown on Fig. 2, threeregimes are distinguishable for the PL intensity evolution:linear, quadratic and then a saturation. We integrated thewhole angular extension of the 0D ground state. The sig-nal shown on Fig. 2(a) is thus directly proportional to thewhole population of this state. A quadratic ﬁt describeswell the evolution between 60 µW and 260 µW. We wereeasily able to trace the evolution of the linewidth and en-ergy of this state on Figs. 2(b) and (c). There is indeeda small increase of the linewidth due to density effects.There is also a slight blueshift of the resonance energy.This blueshift being small compared to the Rabi splitting(0.08 times the Rabi), we can fairly assume that the sys-tem stays in strong coupling regime during the ﬁrst tworegimes. We discuss below the high excitation power case.4 Signs of bistability? The ﬁrst linear regime isattributed to linear relaxation channels, while the quadraticregime shows the contribution, as in the 2D case, ofpolariton-polariton scattering, namely, parametric lumi-nescence [16]. We did not observe any luminescence at theEnergy (eV)1.4821.483(a) (b) (c)Angle (°)0 10101.4840 10100 1010Non-resonant Resonantpump power 76 WResonantpump power 280µWµ0.200.180.160.140.120.100.080.06Linewidth (meV)4003002001000Laser Power ?µW) First excited level Ground level0.250.200.150.100.050.00Peak energy (meV)4003002001000Laser power (µW) First excited level Ground level6543210PL Intensity (arb.u.)4003002001000Laser Power ?µW) Linear fit Quadratic fit(a)(b)(c)0.08Rabi0.02Rabiphys. stat. sol. (c) (2008) 3www.pss-c.com © 2008 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimContributedArticleidler state, but its intensity is expected to be extremely low[4,5]: it shows a very small photonic component (due toits positive detuning) and it has many relaxation and cou-pling channels possible with lower energy states or withthe 2D exciton. The following saturation is attributed tothe fact that the polariton mode blueshifts while the popu-lation increases, leading to a detuning with respect to theexcitation.Two phenomena can be considered for the blueshift ofthe polariton mode: the polariton-polariton interaction [8,16] and the bleaching of the strong coupling regime [17].It has been shown for the ﬁrst phenomenon by [18,19] andfor the second by [20] that both phenomena can lead tooptical bistability in the case of 2D polaritons. Indeed, wewere able to ﬁt the peculiar shapes of the ground state in-tensity evolution by a cubic polynomial expression, char-acteristic of bistability, by inverting the two axes of theplotted graphs. Fig. 3(a) shows again the evolution of theground mode luminescence intensity under increasing ex-citation power, more points have been taken at critical po-sitions such as apparent regime change. Fig. 3(b) shows thesame data as Fig. 3(a), but the pump power is plotted asa function of the emitted PL intensity. A cubic polynomialﬁts very well the measurements. In the following, we try todetermine which source of blueshift is dominating in oursystem, and if it can leads to bistability.Figure 3 Evolution of the ground state PL intensity of a 9 µmmesa, seen in two different ways: on one graph the PL intensityis shown as a function of the pump power, in the other graph it isthe pump power which is seen as a function of the PL intensity.4.1 Degenerate scattering Reference [19] showsthat bistability can be obtained through degenerate para-metric oscillations, and reference [18] provides an exper-imental evidence in the case of normal incidence excita-tion. Polaritons scatter coherently within the pumped state(where energy and phase-matching conditions are obvi-ously fulﬁlled) yielding a nonlinear dependence of the po-lariton ﬁeld with the pump power. Polaritons then relax lin-early through phonons towards the ground state. The evolu-tion of the ground state population is thus representative ofthe evolution of the pumped state population. In this case,the system shows a bistable behaviour for a positive de-tuning of the laser with respect to the pumped polaritonenergy. The results shown on Fig. 3 were performed withsuch a positive detuning, but didn’t show any hysteresis orinstability behavior. For various detunings, the evolutionof the PL intensity was never sharper than what is shownhere. We therefore ruled out the degenerate scattering as-sumption.4.2 Bleaching of the strong-coupling regimeReference [20] suggests another phenomena yielding abistable behavior in the dependence of a polariton popula-tion with respect to a pump intensity: the bleaching of thestrong coupling regime, while exciting resonantly a polari-ton state. The developed model uses the experimental pa-rameters of [21] (an AlGaAs/AlAs cavity with ﬁve embed-ded GaAs quantum wells). According to Ref. [20], bista-bility depends on a broadening factor directly related tothe linewidth of the exciton resonance. If the latter is toolarge, no bistability is observed, but simply a cubic behav-ior. We could not tune this parameter, as we worked on onesample showing a given linewidth, and could therefore notconclude on this point.Future samples with various exciton linewidths may al-low us to observe bistable behaviour and conﬁrm the as-sumption of the bleaching of the strong coupling.5 Balance and conclusions We performed var-ious studies looking for a massive redistribution of thepolariton population towards a single state, this wouldopen the way to parametric oscillation and ampliﬁcation.We observed quadratic regimes, indicating that polariton-polariton scattering takes place in the relaxation processestowards the ground conﬁned polariton states, but did notobserve any oscillation, most probably because the non-linear thresholds were too high, compared to the strong-to-weak coupling cross-over threshold. A solution to over-come this effect would be to increase the number of quan-tum wells within the cavity. This would yield an increaseof the strong-to-weak-coupling transition without affectingthe nonlinear thresholds.We have observed cubic dependances, indicating thatbistability, as described by [20], would be possible in ourmesa structures. In this case, the subsequent quantizationof the modes would allow to observe efﬁcient fast opticalswitching in future samples.Parametric effects in between conﬁned states and be-tween conﬁned and extended states can also be expected,© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-c.comphysicap s sstatus solidi cand may allow the observation of coherence transfer be-tween states or coherent effects [22]. The conception ofnew trap shapes, in particular coupled traps, would allowthe possibility of seeing such effects between polaritonstrapped in different mesas.As one can see, the fabrication of new sample struc-tures (in terms of composition or of trap shapes) will allowa wide range of phenomena to be observed, ranging frombasic effects to applications.Acknowledgements We thank Stefano Portolan and Da-vide Sarchi for rich discussions, and Jean-Philippe Brantut forexperimental support. We acknowledge ﬁnancial support fromthe Swiss National Centre for Competence in Research (NCCR)Quantum Photonics.References[1] D. Bimberg, M. Grundmann, and N.N. Ledentsov, Quan-tum Dot Heterostructures (Wiley, 1999).[2] E.M. Purcell, Phys. Rev. 69, 681 (1946).[3] P. G. Savvidis, J. J. Baumberg, R.M. Stevenson, M. S.Skolnick, D.M. Whittaker, and J. S. Roberts, Phys. Rev.Lett. 84(7), 1547–1550 (2000).[4] R.M. Stevenson, V.N. Astratov, M. S. Skolnick, D.M.Whittaker, M. Emam-Ismail, A. I. Tartakovskii, P. G. Sav-vidis, J. J. Baumberg, and J. S. Roberts, Phys. Rev. Lett.85(17), 3680–3683 (2000).[5] M. Saba, C. Ciuti, J. Bloch, V. Thierry-Mieg, R. Andr, L. S.Dang, S. Kundermann, A. Mura, G. Bongiovanni, J. L.Staehli, and B. Deveaud, Nature 414(Dec), 731 (2001).[6] S. Kundermann, M. Saba, C. Ciuti, T. Guillet, U. Oesterle,J. L. Staehli, and B. Deveaud, Phys. Rev. Lett. 91(10),107402 (2003).[7] W. Langbein, Phys. Rev. B 70(20), 205301 (2004).[8] C. Ciuti, P. Schwendimann, B. Deveaud, and A. Quat-tropani, Phys. Rev. B 62(8), R4825–R4828 (2000).[9] O. E. Daı¨f, A. Baas, T. Guillet, J. P. Brantut, R. I. Kaitouni,J. L. Staehli, F. Morier-Genoud, and B. Deveaud, Appl.Phys. Lett. 88(6), 061105 (2006).[10] D. Sanvitto, A. Daraei, A. Tahraoui, M. Hopkinson, P.W.Fry, D.M. Whittaker, and M. S. Skolnick, Appl. Phys. Lett.86(19), 191109 (2005).[11] O. E. Daı¨f, 0D Microcavity Polaritons. Trapping Light-matter Quasiparticles (Ph. D. Thesis, EPFL, Lausanne,2007).[12] A. Baas, O. E. Daı¨f, M. Richard, J. P. Brantut, G. Nardin,R. I. Kaitouni, T. Guillet, V. Savona, J. L. Staehli,F. Morier-Genoud, and B. Deveaud, phys. stat. sol. (b)243(10), 2311–2316 (2006).[13] R. I. Kaitouni, O. E. Daı¨f, A. Baas, M. Richard, T. Paraiso,P. Lugan, T. Guillet, F. Morier-Genoud, J. D. Ganire, J. L.Staehli, V. Savona, and B. Deveaud, Phys. Rev. B 74(15),155311 (2006).[14] O. E. Daı¨f, G. Nardin, T. K. Paraı¨so, A. Baas, M. Richard,F. Morier-Genoud, and B. Deveaud, submitted to Appl.Phys. Lett.[15] P. Lugan, D. Sarchi, and V. Savona, phys. stat. sol. (c) 3(7),2428–2431 (2006).[16] C. Ciuti, P. Schwendimann, and A. Quattropani, Semicond.Sci. Technol. 18(10), S279–S293 (2003).[17] R. Butte´, G. Delalleau, A. I. Tartakovskii, M. S. Skolnick,V.N. Astratov, J. J. Baumberg, G. Malpuech, A. Di Carlo,A. V. Kavokin, and J. S. Roberts, Phys. Rev. B 65(20),205310 (2002).[18] A. Baas, J. P. Karr, H. Eleuch, and E. Giacobino, Phys. Rev.A 69(2), 023809 (2004).[19] M. Wouters and I. Carusotto, Phys. Rev. B 75(7), 075332(2007).[20] A. Tredicucci, Y. Chen, V. Pellegrini, M. Bo¨rger, andF. Bassani, Phys. Rev. A 54(4), 3493–3498 (1996).[21] T. B. Norris, J. K. Rhee, D. S. Citrin, M. Nishioka, andY. Arakawa, Nuovo Cimento D 17(11-12), 1295–1303(1995).[22] S. Kundermann, T. Guillet, M. Saba, O. E. Daı¨f, J. L.Staehli, and B. Deveaud, phys. stat. sol. (a) 201(3), 381–388 (2004).4 G. Nardin et al.: Resonant nonlinear studies of trapped 0D-microcavity polaritons

Resonant nonlinear studies of trapped 0D-microcavity polaritons

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Resonant nonlinear studies of trapped 0D-microcavity polaritons

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