A massive redistribution of the polariton occupancy to two specific wave vectors is observed under conditions of continuous wave excitation of a semiconductor microcavity.

The “condensation” of the polaritons to the two specific states arises from stimulated scattering at final

state occupancies of order unity. The stimulation phenomena, arising due to the bosonic character of

the polariton quasiparticles, occur for conditions of resonant excitation of the lower polariton branch.

High energy nonresonant excitation, as in most previous work, instead leads to conventional lasing in

the vertical cavity structure

A. I. Tartakovskii

A. Imamoglu

A. Yariv

C. Weisbuch

D. M. Whittaker

F. Tassone

G. Khitrova

H. Cao

J. Bloch

J. J. Baumberg

J. S. Roberts

L. V. Keldysh

Le Si Dang

M. Emam-Ismail

M. Kira

M. S. Skolnick

P. G. Savvidis

P. Senellart

R. Huang

R. M. Stevenson

S. Pau

V. N. Astratov

English

Crossref

Physical Review Letters

Continuous Wave Observation of Massive Polariton Redistribution by Stimulated Scattering in Semiconductor Microcavities

Stevenson, R.M.

Astratov, V.N.

Skolnick, M.S.

Whittaker, D.M.

Emam-Ismail, M.

Tartakovskii, A.I.

Savvidis, P.G.

Baumberg, J.J.

Roberts, J.S.

White Rose Research Online

This is a repository copy of Continuous wave observation of massive polariton redistribution by stimulated scattering in semiconductor microcavities.White Rose Research Online URL for this paper:http://eprints.whiterose.ac.uk/1465/Article:Stevenson, R.M., Astratov, V.N., Skolnick, M.S. et al. (6 more authors) (2000) Continuous wave observation of massive polariton redistribution by stimulated scattering in semiconductor microcavities. Physical Review Letters, 85 (17). pp. 3680-3683. ISSN 0031-9007 https://doi.org/10.1103/PhysRevLett.85.3680eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. VOLUME 85, NUMBER 17 P H Y S I C A L R E V I E W L E T T E R S 23 OCTOBER 2000Continuous Wave Observation of Massive Polariton Redistribution by Stimulated Scatteringin Semiconductor MicrocavitiesR. M. Stevenson,1 V. N. Astratov,1 M. S. Skolnick,1 D. M. Whittaker,2 M. Emam-Ismail,1 A. I. Tartakovskii,3,1P. G. Savvidis,4 J. J. Baumberg,4 and J. S. Roberts51Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom2Toshiba Research Europe Ltd., Cambridge CB4 4WE, United Kingdom3Institute of Solid State Physics, RAS, 142432 Chernogolovka, Russia4Department of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, United Kingdom5Department of Electronic and Electrical Engineering, Sheffield S1 3JD, United Kingdom(Received 5 July 2000)A massive redistribution of the polariton occupancy to two specific wave vectors, zero and 3.9 3104 cm21, is observed under conditions of continuous wave excitation of a semiconductor microcavity.The “condensation” of the polaritons to the two specific states arises from stimulated scattering at finalstate occupancies of order unity. The stimulation phenomena, arising due to the bosonic character ofthe polariton quasiparticles, occur for conditions of resonant excitation of the lower polariton branch.High energy nonresonant excitation, as in most previous work, instead leads to conventional lasing inthe vertical cavity structure.PACS numbers: 71.36.+c, 03.75.Fi, 42.50.–pSemiconductor microcavities permit unprecedented con-trol of the properties of both light and matter in the solidstate and of their mutual interactions [1,2,3]. This controlhas resulted in a new field of exciton-polariton physics,with specific properties which can be tailored by structuredesign. Of particular interest for the present work, the po-lariton coupled modes are expected to exhibit bosonlikecharacter under excitation conditions where photoexcitedelectron-hole pairs retain strong excitonic character. Whenthe bosonic character is dominant, the polariton quasipar-ticles are expected to exhibit scattering stimulated by finalstate populations in excess of unity [4]. Such behaviorhas been much discussed in the literature. Some earlyclaims [5] of such “boser” behavior were either later with-drawn [5] or refuted [6]. Subsequently nonlinear behav-ior in cw luminescence experiments was attributed to finalstate stimulation [7]. However, the expected narrowing ofthe emission [8] above threshold, characteristic of macro-scopic final state population, was not observed [7], andindeed it has been suggested that the results could be ex-plained by nonlinear exciton-exciton scattering alone [9].Finally, we have recently reported a definitive observationof stimulated scattering of polaritons in ultrafast experi-ments: injection of a weak probe pulse into the final statewas shown to stimulate scattering from a resonantly ex-cited pump population [10,11]. Evidence for stimulationhas also been presented in a three beam experiment byHuang et al. [12].In the present work, we show that under appropriate cwexcitation conditions stimulated scattering processes aredominant in determining the energy and wave vector distri-bution of the polariton population. Such scattering leads tohighly nonthermal distributions, peaked at particular val-ues of wave vector. This result is surprising in view of pre-vious work under nonresonant excitation, where althoughnonlinear increases of the low k population with excitationwere observed [7,13,14], a smoothly varying distributionwith k was found. We show here that strong stimulationoccurs for resonant excitation close to the point of inflec-tion of the dispersion curve of the lower polariton branch.In contrast to the ultrafast case strong stimulation occurs inthe presence of the excitation beam alone [11]; the processis self-stimulated with carrier-carrier interactions sufficientto permit final state populations close to unity to build upand thus to initiate stimulation. Angle resolved lumines-cence experiments are employed to probe the microscopicbehavior. At low densities the population peaks close to theinjection wave vector, with clear evidence for a relaxationbottleneck [14]. With increasing excitation the distribu-tion shifts towards k  0, until above a low k density of106 cm22, corresponding to occupancies of order unity,an increase in the k  0 population by 2 orders of mag-nitude is found. At the same time a corresponding strongincrease in the population is found at a particular largewave vector, required to conserve energy and momentumin the scattering process. The observed phenomena have anumber of characteristics of a Bose-Einstein condensationto the k  0 polariton state.The experiments are carried out on a 3l2 microcav-ity grown by metalorganic vapor-phase epitaxy technique(MOVPE). Three In0.06Ga0.94As quantum wells are em-bedded at each of the two antinodes of the optical field.The vacuum Rabi splitting was 6 meV, with off reso-nance cavity and exciton linewidths of 0.5 and 1 meV,respectively. The measurements were carried out at a tem-perature of 5 K. Excitation was provided by a Ti:sapphirelaser focused to an 100 mm spot. The angles u of ex-citation and detection could be varied separately from nor-mal incidence to 35±, corresponding to in-plane k from 0to 4.2 3 104 cm21 k  vc sinu. Photoluminescence3680 0031-90070085(17)3680(4)$15.00 © 2000 The American Physical SocietyVOLUME 85, NUMBER 17 P H Y S I C A L R E V I E W L E T T E R S 23 OCTOBER 2000(PL) spectra were collected by a lens (collection angle61±) which focused the PL onto a fiber, with both lensand fiber mounted on the same rotating rail.A series of PL spectra collected at u  0 are presentedin Fig. 1(a) as a function of excitation intensity from2 Wcm2 to 2 3 103 Wcm2. Results are presented fora negative detuning of 4 meV between uncoupled cavityand exciton modes; very similar results are observed onresonance. The excitation angle is 15.5±, close to the pointof inflection of the E-k dispersion curve of the lowerpolariton branch, shown in Ref. [10] to be the angle atwhich energy and wave vector is conserved in a polariton-polariton scattering process to low and high wave vectors[see Fig. 2(b)]. At all powers the spectra are dominatedby PL from the lower polariton branch. Up to a thresholdof 6 3 102 Wcm2, the spectra increase linearly withpower and then show a very strong superlinear increase, asshown on the light output versus excitation intensity plotof Fig. 2(a). As in the ultrafast case [10], above thresholdthe PL peak is shifted to higher energy by 0.5 meV [15]and shows a marked narrowing from 0.5 meV to a widthof 0.2 meV, limited by the spectrometer resolution. Asdiscussed below [shown in Fig. 2(b)] the shift correspondsto renormalization of the whole dispersion curve to higherFIG. 1. (a) Photoluminescence spectra collected at u  0± forexcitation resonant with the lower polariton branch at 15.5±,as a function of excitation intensity from 2 Wcm2 to 2 3103 Wcm2. The laser is retuned to higher energy to main-tain resonance above the threshold. (b) PL spectra as a functionof excitation intensity for nonresonant excitation at 1.55 eV.energy. Consequently for all spectra above thresholdthe laser has been retuned slightly to higher energy [seeFig. 1(a)] to maximize the PL signal.To shed light on the microscopic behavior, PL spectrawere recorded as a function of detection angle, for variousexcitation intensities, shown in Fig. 3. Integrated intensi-ties of the PL peaks versus k are shown in Fig. 4(a). Atrelatively low powers (,2.2 3 102 Wcm2, below thresh-old), the PL signals are maximum close to the laser energyand decrease in intensity for both positive and negative an-gles away from 15.5±, as shown in Fig. 3(a). This is anexample of the polariton relaxation bottleneck observedfor nonresonant excitation [14]: The escape time of po-laritons from the cavity (1 psec) is much more rapidthan the relaxation to lower energy, likely to be domi-nated by acoustic phonon relaxation tac . 1029 sec atthese low powers ,107 polaritonscm2 [14,16]. Withincreasing power [6.4 3 102 Wcm2, Fig. 3(b) close tothreshold], the distribution shifts to lower wave vectors,with the emergence of a small maximum at k  0, asseen in Figs. 3(b), 3(c), and 4(a). The overall shift tosmaller k is consistent with the nonlinear increase of PLFIG. 2. (a) k  0 and 3.9 3 104 cm21 PL intensitiesversus excitation intensity. (b) Measured lower branch dis-persions below (2 3 102 Wcm2—open circles) and abovethreshold (2 3 103 Wcm2— filled squares), together withfitted upper and lower branch dispersions. (c) Photon fractionfor lower branch as a function of k.3681VOLUME 85, NUMBER 17 P H Y S I C A L R E V I E W L E T T E R S 23 OCTOBER 2000FIG. 3. PL spectra (a) below and (b) close to threshold, (c),(d), (e) above threshold as a function of detection angle. A verystrong change is observed between (a) at low power where thespectra are strongest close to the excitation energy, and (d), (e)where the spectra are dominated by peaks at zero and at 32±.The very strong features at 1.456 eV arise from the laser.intensity with power at k  0 observed previously [7,14]under nonresonant excitation and attributed [7,14] to po-lariton-exciton scattering [16] from the high k distributionto lower wave vector. For further increase of power, agiant increase of intensity at k  0 and thus a massive re-distribution of the polariton population to the k  0 stateoccurs. At the same time, a second strong PL signal atlarge k 3.9 3 104 cm21  31.8± is also observed andexhibits the same intensity variation as the k  0 signal[see Fig. 2(a)]. This “idler” signal [17] conserves energyE and k in a polariton-polariton scattering process fromthe injected laser E and k to companion states at k  0 at3.9 3 104 cm21, as indicated in Fig. 2(b).The above results enable the relative polariton densitiesnpol to be deduced as a function of k, since npol ~ IPLt,where t is the radiative lifetime of the polariton state,inversely proportional to its photon fraction, shown inFig. 2(c). The npolk variation thus deduced is shown inFig. 4(b). It is notable that at high intensity the populationsat k  0 and 3.9 3 104 cm21 are the same within a factorof 2, consistent with the two peaks arising from pairwiseFIG. 4. (a) Integrated intensities of PL peaks as a function of inplane k (angle), (b) as (a) but corrected for the photon fractionof the lower branch as a function of k [from Fig. 1(c)]. Bynormalizing to the measured power of the k  0 feature abovethreshold, the vertical axis is labeled in terms of state occupancy.scattering away from the resonantly created polaritons atk  2 3 104 cm21.We now place the k  0 densities of Fig. 4(b) on anabsolute occupancy scale. We have measured the outputpower of the beam around k  0, a value of 1.8 mWbeing found for an input laser power density of 2.3 3103 Wcm2 (180 mW actual power) [18]. The 1.8 mWsignal emitted from the 100 mm spot excited correspondsto the recombination of 9 3 1019 polaritonscm2sec,which given a k  0 lifetime of 1.7 3 10212 sec (at4 meV negative detuning), corresponds to a polaritondensity of 1.7 3 108 cm22. The density of states isgiven by dndk  k2p, and so over the width Dk2.6 3 103 cm21 of the near k  0 signal there areDk24p 5.4 3 105 available statescm2. Thus thestate occupancy near k  0 at the highest output powersis 310. From the relative densities of Fig. 4(b), we canthen deduce the occupancy of the k  0 states close tothreshold 6.4 3 102 Wcm2 to be 0.810.820.4. Although theerrors are significant, by at least a factor of 2, the mainconclusion is clear that the threshold for stimulation ofscattering to k  0 states (and the companion state at3.9 3 104 cm21) occurs at occupancies of order unity,consistent with bosonic final state stimulation [19].3682VOLUME 85, NUMBER 17 P H Y S I C A L R E V I E W L E T T E R S 23 OCTOBER 2000It is important to demonstrate that the microcavity re-mains in the strong coupling limit and that a bosonicdescription is appropriate. First, it should be noted thepolariton densities are small (,108 cm22 at the highestpowers), significantly below the density 5 3 1010 cm22where the Bose commutator of the correlated electron-holepairs in a similar structure has been calculated to fall to avalue of 0.8 [6]. Second, the k  0 PL peak above thresh-old increases in energy by only 0.5 meV, in strong con-trast to the behavior for excitation above the stop bandof the Bragg mirrors, where lasing occurs at 1.5 meVabove the energy of the lower polariton branch as shownin Fig. 1(b), corresponding closely to the energy of theuncoupled cavity mode, as expected in the weak couplinglimit. Threshold in Fig. 1(b) occurs for a PL output signal2 orders of magnitude greater than in Fig. 1(a), demon-strating the clear distinction in the mechanisms and in addi-tion the high efficiency of the bosonic stimulation process.Third, even well above threshold the polariton branch re-tains its characteristic dispersion, with a shift of the wholedispersion to higher energy with increasing power abovethreshold, shown in Fig. 2(b).Compared to nonresonant excitation where the high kpopulation is always dominant [14], for resonant excitationof the lower branch, sufficient k  0 population builds upto initiate stimulation. Similarly, in our resonant ultrafastexperiments, stimulation was strong only in the presenceof an additional probe beam [10,11] because only a smallfraction of the injection polaritons reached the k  0 statewithin the duration of the pump pulse.We now address the question of the physical significanceof the phenomena. The spectral narrowing above thresholdshows that, like a laser, the system possesses a macroscopiccoherence. Such a spontaneous appearance of coherenceindicates that the polariton system has undergone a phasetransition, consisting of the macroscopic occupation of asingle mode. Since polaritons are bosons, there is somejustification in describing this phase as a Bose-Einsteincondensate (BEC). Support for this description is providedby clear observation of stimulated scattering of other po-laritons into the macroscopically occupied mode, a char-acteristic property of a BEC. However, the system is farfrom thermal equilibrium, so although the initial buildup ofthe population comes from scattering down from the pumppopulation, the phase transition is not driven by cooling.In this sense, it differs from the ideal picture of a BEC,which has a well defined temperature and a chemical po-tential approaching zero.It is important to distinguish the behavior from that of anormal laser, which exhibits a macroscopic coherence, butonly in the photon field. In our microcavities, the coher-ence is in the polariton field, which is part photon, part ex-citon. The existence of an exciton component is significant,as it offers the possibility for interactions to occur, possiblyallowing the coherent state to be manipulated in ways notpossible for a laser. Our results show a strong resemblanceto a picture due to Keldysh of an idealized semiconductorlaser, operating in the low density limit. He describes theappearance of a coherent polariton mode, which he calls aBEC of polaritons, due to stimulated scattering as the popu-lation builds up in the bottleneck region [20].In conclusion, stimulated scattering of resonantly cre-ated polaritons has been reported under conditions of con-tinuous wave excitation. The state occupancy at thresholdis deduced to be of order unity, consistent with bosonic fi-nal state stimulation playing a key role in the phenomena.The strong increase of final state population correspondsto a “condensation” to a polariton mode with macroscopicoccupancy, the phenomena possessing a number of simi-larities to Bose-Einstein condensation.[1] C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa,Phys. Rev. Lett. 69, 3314 (1992).[2] M. S. Skolnick, T. A. Fisher, and D. M. Whittaker, Semi-cond. Sci. Technol. 13, 645 (1998).[3] G. Khitrova et al., Rev. Mod. Phys. 71, 1591 (1999).[4] A. Imamoglu, R. J. Ram, S. Pau, and Y. Yamomoto, Phys.Rev. A 53, 4250 (1996).[5] S. Pau et al., Phys. Rev. A 54, R1789 (1996); retracted inH. Cao et al., Phys. Rev. A 55, 4632 (1997).[6] M. Kira, E. Jahnke, S. W. Koch, J. D. Berger, D. V. Wick,T. R. Nelson, G. Khitrova, and H. M. Gibbs, Phys. Rev.Lett. 79, 5170 (1997).[7] P. Senellart and J. Bloch, Phys. Rev. Lett. 82, 1233 (1999).[8] Such narrowing was observed in II-VI microcavities by LeSi Dang et al., Phys. Rev. Lett. 81, 3920 (1998). Stimulatedscattering was suggested as one possible interpretation.[9] See Ref. [3], p. 1623.[10] P. G. Savvidis, J. J. Baumberg, R. M. Stevenson, M. S. Skol-nick, D. M. Whittaker, and J. S. Roberts, Phys. Rev. Lett.84, 1547 (2000).[11] Weak stimulation was seen in the ultrafast case without theprobe beam. It was only in the presence of the probe beamthat the stimulation was strong.[12] R. Huang, F. Tassone, and Y. Yamomoto, Phys. Rev. B 61,R7854 (2000).[13] J. Bloch and J. Y. Marzin, Phys. Rev. B 56, 2103 (1997).[14] A. I. Tartakovskii et al., Phys. Rev. B 62, R2283 (2000).[15] C. Ciuti et al. (unpublished) show theoretically that theshift arises from polariton-polariton interactions.[16] F. Tassone and Y. Yamomoto, Phys. Rev. B 59, 10 830(1999).[17] The term “idler” is taken from the field of optical paramet-ric oscillation (OPO); see, e.g., A. Yariv, Quantum Elec-tronics (Wiley, New York, 1988), p. 407.[18] We measure that 5% of the pump beam is absorbed inthe sample for resonant excitation, with 20% of this lightconverted into the signal around k  0.[19] In principle, stimulation could occur to other values ofkexc 6 Dk along the dispersion curve in E and k conserv-ing scattering processes. However, the 0, 3.9 3 104 cm21values for 2 3 104 cm21 excitation are probably favoredby the larger optical feedback for k  0 final states.[20] See L. V. Keldysh, in Bose-Einstein Condensation, editedby A. Griffin, D. W. Snoke, and S. Stringari (CambridgeUniversity Press, Cambridge, England, 1995), p. 256.3683

Continuous wave observation of massive polariton redistribution by stimulated scattering in semiconductor microcavities

A massive redistribution of the polariton occupancy to two specific wave vectors, zero and 3.9 x 104 cm-1, is observed under conditions of continuous wave excitation of a semiconductor microcavity. The “condensation” of the polaritons to the two specific states arises from stimulated scattering at final state occupancies of order unity. The stimulation phenomena, arising due to the bosonic character of the polariton quasiparticles, occur for conditions of resonant excitation of the lower polariton branch. High energy nonresonant excitation, as in most previous work, instead leads to conventional lasing in the vertical cavity structure

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Continuous wave observation of massive polariton redistribution by stimulated scattering in semiconductor microcavities

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