Direct Transfer of Light’s Orbital Angular Momentum onto a NonresonantlyExcited Polariton Superfluid

Min-Sik Kwon,1,2,§ Byoung Yong Oh,1,§ Su-Hyun Gong,1,2,4 Je-Hyung Kim,1,2,‡ Hang Kyu Kang,3

Sooseok Kang,3 Jin Dong Song,3 Hyoungsoon Choi,1,2,† and Yong-Hoon Cho1,2,*1Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141, Republic of Korea2KI for the NanoCentury, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141, Republic of Korea

3Center for Opto-Electronic Convergence Systems, Korea Institute of Science and Technology (KIST), Seoul, 02792, Republic of Korea4Department of Physics, Korea University, 45 Anam-ro, Seongbuk-gu, Seoul, 02841, Republic of Korea

(Received 7 August 2017; revised manuscript received 29 November 2018; published 31 January 2019)

Recently, exciton polaritons in a semiconductor microcavity were found to condense into a coherentground state much like a Bose-Einstein condensate and a superfluid. They have become a unique testbedfor generating and manipulating quantum vortices in a driven-dissipative superfluid. Here, we generate anexciton-polariton condensate with a nonresonant Laguerre-Gaussian optical beam and verify the directtransfer of light’s orbital angular momentum to an exciton-polariton quantum fluid. Quantized vortices arefound in spite of the large energy relaxation involved in nonresonant pumping. We identified phasesingularity, density distribution, and energy eigenstates for the vortex states. Our observations confirm thatnonresonant optical Laguerre-Gaussian beam can be used to manipulate chirality, topological charge, andstability of the nonequilibrium quantum fluid. These vortices are quite robust, only sensitive to the orbitalangular momentum of light and not other parameters such as energy, intensity, size, or shape of the pumpbeam. Therefore, optical information can be transferred between the photon and exciton-polariton with easeand the technique is potentially useful to form the controllable network of multiple topological chargeseven in the presence of spectral randomness in a solid state system.

DOI: 10.1103/PhysRevLett.122.045302

A quantum vortex, initially discovered in superconduc-tors [1–3], superfluid helium [4–6], and cold atoms [7,8]is a topological defect that has rotational superflow withquantized phase winding. Because of the topologicalstability, it has potential applications in data storage andtransfer [9–11]. Fundamentally, a quantum vortex is asignature of phase coherence in a superconductor or asuperfluid carrying either a quantized magnetic flux ora quantized angular momentum, respectively. Studying thequantized vortex in exciton-polaritons has advantages overother superfluid systems due to its photonic componentthat can be controlled optically and easily visualized[12–16]. A microcavity exciton polariton has a finitelifetime and decays by leaking photons out of the cavitymaking the system inherently nonequilibrium [17–20]. Theleaking photons carry the density, momentum, energy, spin,and phase information of the polaritons. One can character-ize the nonequilibrium dynamics of the polariton fluid bycharacterizing the photoluminescence [21–23].Creating vortices in an exciton-polariton superfluid, how-

ever, has been technically challenging and a focus of recentresearch. As a result, numerous methods for vortex creationhave been developed, some of which include triggeredoptical parametric oscillation (TOPO), pumping with reso-nant Laguerre-Gauss (LG) beams [21,24], shaping or geo-metrically engineering the excitation beams with both

resonant and nonresonant pump methods [25–28]. Two ofthemost effectivemethods of controlled vortex creation havebeen utilizing TOPO for resonant pumping [21] or creatingchiral lenses for nonresonant pumping [25]. The downsideof TOPO is that it requires one of the beams to be preciselytuned to exact energy and momentum [29,30]. Nonresonantchiral lenses are free from these constraints [25]. They suffer,however, from a different type of fine-tuning. The nonreso-nant pumping method relies on the exciton reservoir formedaround the pump beam region as a source of polaritons,which condenses through stimulated scattering. The reser-voir also serves as a local potential barrier for polaritons dueto energy shift caused by strong repulsive interactionsbetween thermal reservoir excitons and condensed polar-itons. Thus, the amount of circular flow cannot be easilycontrolled as the potential landscape is sensitive to the size,shape, and intensity of the beam.In this Letter, we demonstrate that, for the first time,

quantized vortices can be injected with a high degree ofcontrol by simply transferring orbital angular momentum(OAM) of a single pump beam on to a polariton superfluid.There are two remarkable features in our result. One is thatthe number of vortices of the same sign, or at least anunequal number of vortices and antivortices resulting inthe net vortices of the same sign, is controllable. Thesecond remarkable feature is that, to achieve this, one does

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not need to have the pump beam on resonance withthe polaritons, exploring excited states of coherent polar-iton fluid combined with energy relaxation in an out-of-equilibrium system.Current theoretical models, such as the generalized

Gross-Pitaevskii equation, mainly describe dynamics ofa coherent polariton condensate in the lower polaritonbranch (LPB) based on mean field theory [31]. This modelis coupled with the rate equation of exciton reservoirdensity, which has considered pumping and loss of polar-itons with stimulated scattering in the LPB. In nonresonantpumping, hot electron-hole plasma with higher energyexperiences energy relaxation by phonon emission downto exciton reservoir states. The exact energy relaxationprocess, especially related to a system excited with OAM,has not been extensively looked into and hence not wellunderstood. Through the experiment of this Letter, how-ever, we show that OAM of the nonresonant pump beamcan be transferred down to polariton condensates. As wewill discuss below, this method of vortex generation issignificantly robust against a change in energy, intensity,shape, and size of the pump beam, and a very simple way ofcontrolling quantum vortices is now possible.In our experiment, the sample consisted of GaAs

quantum wells and a distributed Bragg reflector structureforming a microcavity. A Ti:sapphire pulse laser with anenergy of 1.73 eV (716 nm, center wavelength) was shonenonresonantly onto the semiconductor microcavity samplein a cryostat at 6 K [Fig. 1(a)]. The LG beam was generatedfrom a diffractive optic component. Interference of polar-itons was measured with a modified Mach-Zehnder (MZ)interferometer [14,32,33] integrated with a Fourier opticsimaging setup [34,35].Figure 1(b) shows the spatial intensity distribution

[Fig. 1(b), left] and interference [Fig. 1(b), right] of theLG pump beam with total orbital angular momentumnumber, l ¼ þ1 and about 30 μm diameter size reflectedfrom the sample. Density and interference of fluorescenceare shown in Figs. 1(c) and 1(d) for below and abovethreshold pump power (Pth ∼ 2.5 mW) of polariton con-densation, respectively. Above the threshold power, threenoticeable effects occurred. First, the spatial correlationregion with coherence expanded in the area of polaritonsfrom 70 to 570 μm2 [Fig. 1(d)]. Below the threshold, asmall region of the interference pattern with no anomalyexhibited short range correlation, stemming from thecorrelation length of the polaritons’ thermal de Brogliewavelength. Above the threshold, the thermal de Brogliewavelength of the polaritons becomes comparable to theiraverage separation [17]. Once a polariton condensate isformed, the interference pattern grows as the region ofcoherence expands [Fig. 1(d)].Second, there is a fork shape dislocation in the inter-

ference pattern [Fig. 1(d)]. The polariton condensate canbuild a quantized circulation that carries a phase winding.

The singularity at the center of a 2π phase winding appearsas a branch cut in the interference pattern that we observe inFig. 1(d). In other words, a single quantum vortex isgenerated when the system is excited by a pump with OAMof l ¼ þ1.The energy-momentum dispersion relation also goes

through an abrupt change as can be seen in Figs. 2(a),2(b). Quadratic dispersion of polaritons suddenly collap-ses into the ground state (1.59 eV) and the first excitedstate associated with the vortex above the threshold. Thechange in dispersion marks a clear transition into thecondensate.Spatially resolved photoluminescence (PL) reveals a

significant feature of this dispersion [Figs. 2(e), 2(f)].Below the threshold, polaritons are mostly concentratedaround the region excited by the pump beam at all energies.Once the polaritons form a condensate, the ground state andthe excited state shown in the figure are discretely separatedin energy. The excited state polaritons are collected aroundthe pump beam spot and forms vortices. The concentratedpolaritons in this region also serve as a potential landscapeand trapped condensates are formed inside the ring as theground state. In effect, one gets a multistate superfluidunique to a driven-dissipative system. The density distri-butions of the multiple states are overlapped in real spacedensity image. Thus, a consequence of the multistatecondensation is that the vortex core appears to be filleddue to the ground state near the center of the ring.

FIG. 1. Creation of a vortex by nonresonant transfer of OAM(phase winding). (a) Schematic configuration of a vortex opticallypumped with OAM in real space. (b) Spatial distribution of theintensity (left) and spatial interference (right, Mach-Zehnderinterferogram) of the LG laser beam with 2π phase winding(l ¼ þ1). (c),(d) Creation of a single quantized vortex withnonresonant LG beam of l ¼ þ1. Spatial density of polaritonsbelow the threshold in (c) and a single polariton vortex (whitecircles) above the threshold pump power in (d). Interference“fork” image indicating the presence of the single vortex in (d) isa magnified image extracted by Fourier filtering for clarity. Scalebars, 10 μm (white).

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A comparison with the polariton dispersion [Figs. 2(c),2(d)] under a nonresonant ring-shaped pump beam withoutOAM (l ¼ 0) shows the roles this confining potential andOAM injection play in the energy distribution. From thel ¼ 0 pump beam experiment, it is evident that the discreteenergy states are due to the confinement induced by thering-shaped reservoir forming a barrier potential. Theground state with zero momentum is more dominant thanthe excited state. However, in the nonresonant LG pumping(ring-shaped beam with OAM), the population of theexcited state with higher momentum increases due to therotational flow of polaritons, i.e., the quantized vortex[Figs. 2(a)–2(d)].To test if the vortex generated in the polariton super-

fluid is indeed the result of angular momentum transferfrom the incident nonresonant laser pump, the compari-son between the phase winding direction of a laser beamand the resulting vortex was made by utilizing amodified MZ interferometer. In Fig. 3, the MZ interfer-ence patterns are shown for both polariton emission[Figs. 3(b) and 3(f)] and the corresponding pump beam[Figs. 3(d) and 3(h)]. One can clearly see the phasewinding direction of a vortex matching that of theincident laser. This supports that the controlled chiralityof the vortex is not the result of the spontaneousbreaking of rotational symmetry. In other words, theorbital angular momentum of an incident laser is trans-ferred to the polariton superfluid and vortex chirality canbe controlled deterministically.We repeated the measurement with different angular

momentum values with the pump power fixed at 1.6 times

the threshold power (Fig. 4). Figures 4(a), 4(d), 4(g)indicate spatial polariton density distibution. In order togenerate the ring-shaped beam with zero OAM, the incidentGaussian pump beam propagated through chromium diskblocking mask on glass sheet [36]. When a ring-shapedbeam with zero OAM (l ¼ 0, zero phase winding) wasinjected, no phase singularity was observed. The diffusive

FIG. 2. Angle-resolved PL and real space-resolved PL of polariton condensates (a),(b) Measured energy-momentum dispersion of thelower polariton branch below and above the condensation threshold under the nonresonant LG pump (l ¼ þ1). White dotted curve,yellow dotted curve, and flat green dotted line represent the lower and upper polariton branch, cavity photon, and exciton dispersion,respectively, obtained through fitting the LPB. (b) The ground and the first excited states of a single vortex in polariton fluid above thecondensation threshold. (c),(d) Measured energy-momentum dispersion of LPB below and above the condensation threshold under thenonresonant ring pump (l ¼ 0). (d) The ground and the first excited states of polariton condensate above the condensation threshold.(e),(f) Measured spatially resolved PL below and above the condensation threshold under the nonresonant LG pump (l ¼ þ1).(f) Trapped polaritons (ground state) and vortex (excited state) above the condensation threshold in polariton fluid.

FIG. 3. Polariton vortex chirality vs LG laser beam’s chirality(a)–(d) The incident pump beam has the OAM, l ¼ þ1. (a)Interference image and (b) extracted phase image of the polaritonvortex shows a counterclockwise phase winding (l ¼ þ1). (c)Interference image and (d) phase image of the pump beam withthe counterclockwise phase winding. (e)–(h) The same set ofimages as (a)–(d) with the incident pump beam having l ¼ −1OAM. Insets of (a) and (e) were extracted by Fourier filtering thedotted box regions. Scale bars are 10 μm. Curved arrows indicatephase winding directions (chirality) of a single vortex.

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flow pattern can be obtained from the spatial phasedistribution [Fig. 4(c)]. The phase map is extracted fromthe spatial MZ interference [Figs. 4(b), 4(e), 4(h)]. Phasegradient in the radial direction is clearly present as a resultof polariton flow due to density gradient along the radiusboth inside and outside the ring. The polaritons wereaccumulated around the center of the ring without rota-tional flow (phase winding).With an OAM of l ¼ þ1 incident beam, in addition to

the radial phase gradient (radial polariton flow), a 2πazimuthal phase winding is present around the center ofthe ring [Fig. 4(f)]. When the total OAM of the incidentlaser was doubled to l ¼ þ2, two phase singularities wereseen in the emission [Fig. 4(i)]. Two single quantizedvortices were generated, consistent with the nature of asuperfluid. This indicates that the magnitude of the injectedbeam’s OAM is also preserved.These nonresonantly transferred angular momenta are

quite robust in maintaining OAM of polariton vorticeseven as the pumping intensity is changed. At highintensity, polariton-polariton and polariton-reservoir inter-actions increase inside the region of pumping beamdiameter [37]. Figure 5 is the phase map extracted fromthe MZ interferences. Figures 5(a)–5(d) show the phase

map of polariton condensates (l ¼ 0) generated from thering-shaped (l ¼ 0) excitation beam. There is no vortexup to about 10 times the threshold pump power. From this,we can infer that the interplay between sample inhomo-geneity and polariton flow in optically induced potentialare negligible in the pumped region of the sample.For the LG pump beam with the winding number

l ¼ þ1, shown in Figs. 5(e)–5(h), a single vortex appearedabove the threshold [Fig. 5(e)] and was stably maintainedin the center of the LG pump area up to a pump power of∼10 Pth [Figs. 5(f), 5(g)]. As shown in Fig. 5(h), muchabove the 10 Pth pump density, the phase around the singlevortex is blurred, indicating that the phase fluctuations arepresent around the vortex, which could eventually becomeunstable [Fig. 5(h). for details, see Ref. [38] ].Similarly, when the total OAM of the laser was increased

tol ¼ þ2, twovorticeswere stable even up to a pumppowerof 2 Pth [Figs. 5(i) and 5(j)]. Around 2 Pth, an additionalvortex appeared in the pumped region [Fig. 5(k)]. Theadditional formation of the vortex at high pump power islikely a result of hydrodynamic polariton flow [24] orinstability of nonequilibrium polariton condensate [41]based on polariton-polariton and polariton-reservoir inter-action in an optically induced potential landscape [42].As pump power increases very high up to about 30 Pth,

many polaritons can flow radially into the center due torepulsion from the largely populated exciton reservoir locatedalong the pumping region through energy relaxation [40](Fig. S6 in the Supplemental Material [38]). Overlapping ofpolariton wave functions can build coherence in the center.The vortices generated by LG beam pumping can interactwith the trapped polaritons at high pump power.

FIG. 4. Pump beam’s OAM dependence of the polariton vortexcount. OAM of the pump beam is tuned from l ¼ 0 to l ¼ þ2.(a),(d),(g) Polariton spatial density distributions. (b),(e),(h) Spa-tial MZ interference of polariton condensates. (a)–(c) A ring-shaped beam without OAM (l ¼ 0) was used. (a) Image of apolariton for l ¼ 0. In (c) Phase gradient is developed radiallywith no winding, showing no vortex. (d)–(f) The incident ringbeam has the OAM of l ¼ þ1. (d) Image of a polariton emissionat l ¼ þ1. (f) A corresponding 2π phase winding is visible.(g)–(i) The same set of images as (d)–(f) with the difference beingthe OAM having l ¼ þ2. Two vortices are observed. All of theseexperiments were carried out at 1.6 Pth. The white scale bars are10 μm. Green and blue circles indicate position of vortices.Arrows indicate chirality of the vortices.

FIG. 5. Stability of polariton vortices against the pumpingpower. Phase map images of the polariton condensates generatedby nonresonant pumping with (a)–(d) l ¼ 0, (e)–(h) l ¼ þ1, and(i)–(l) l ¼ þ2 are shown for various pumping powers. (a)–(d)Polariton condensate (l ¼ 0) with increasing pump power up to10.0 Pth shows no clear vortex. (e)–(h) A single vortex (l ¼ þ1)is stable up to pump power of 10.0 Pth. (i)–(l) Two l ¼ þ1vortices are stable up to 2.2 Pth with l ¼ þ2 LG pump beam.Scale bars, 10 μm.

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The robustness of the vortices was also checked againstthe change in pump beam radius. The vortices positionedand maintained their OAM inside the pumping area up to a30% increase of the beam radius (for details, see Ref. [38]).Even the presence of asymmetry in the intensity of the ring-shaped vortex beam did not affect the vortex formation (fordetails, see the Supplemental Material [38]). All of theseshow that our method of vortex formation by transferringOAM of the nonresonant pump beam is quite robust.How the orbital angular momentum is transferred in

this nonresonant pumping technique remains unknown.Coincidentally, the excited free carriers at 1.73 eV are140 meV above the polariton ground state of 1.59 eVwhich is almost exactly 4 times the longitudinal optical(LO) phonon energy of 36 meV in GaAs. To rule out thepossibility of some unidentified angular momentum pre-serving parametric scattering mediated with the LO pho-non, we swept our pump laser energy from 1.70 to 1.77 eV.Vortices were found when the energy of the pump beam isnot an exact integer multiple of the LO phonon energy,suggesting that parametric scattering by LO phonons isunlikely to be responsible for the vortex formation.What could be happening is a somewhat subtler process.

As mentioned earlier, the l ¼ 0 ring-shaped pump beamforms a confining potential to polaritons. This potentialcauses steady radial flow away from the ring, both inwardsand outwards. Weak spatial overlap of polariton wavefunction with the ring-shaped pumped reservoir can inducethe instability of polariton condensate confined in thispotential. The radial inward flowbased on circular symmetryis predicted to be unstable and nonzero net circulation can begenerated [41,43]. The rotational invariance originally pre-sented in the pump beam is spontaneously broken in theresulting polariton fluid with the direction of the circulationchosen at random. Our result from the incident beam withl ¼ 0 shows no such effect, so we are clearly not in thisregime. However, injection of orbital angular momentumfrom the LG beam (ring shape) could induce this instabilitythat would not be present otherwise. The induced instability(a small residual asymmetry) in an exciton reservoir can beenhanced by stimulated scattering in the bottom of the LPB.Once the symmetric polariton flow becomes unstable, theinjected OAM could further nudge the polariton fluid tofollow the chirality and OAM of the incident beam.Alternatively, the multistate nature of the condensate

could hold the key to this OAM transfer. The fact that someof the condensates are in the ground state with zero linearand angular momentum indicates that part of the total OAMinitially transferred from the laser is lost. If the OAM iscompletely lost during the relaxation process, the wholesystem would condense substantially in the ground state.However, as long as some fraction of OAM survives therelaxation process, the quantized nature of the vortices couldbe forcing the condensate to split into the ground state withzero OAM and the excited states with quantized OAM.

The exact mechanism through which phase informationof the nonresonant laser is transferred in the polaritonsuperfluid is not well understood and merits a furtherinvestigation, e.g., parametric scattering mediated with hotexciton or bosonic stimulated scattering as approachablefrom other possible mechanisms. For future studies,advanced theoretical models are needed to describe energyrelaxation related to carriers, excitons, and polaritons.In conclusion, excellent controllability of polariton

OAM through a simple manipulation of incident light’sOAM is demonstrated, which paves the way for developinga nonequilibrium Abrikosov lattice formation and studyingits dynamics. The ease of control also provides a newmeans to study all optical memory devices [44,45]such as vortex memory [46] and simple quantum simulators[47–50].

The authors wish to thank L. S. Dang, M. Richard(CNRS, Grenoble, France), I. Savenko (IBS, Daejeon,Republic of Korea), C. Park, and M. Kim (KAIST,Daejeon, Republic of Korea) for helpful discussions.This research was supported by National ResearchFoundation (NRF) of Korea through Projects No. NRF-2016R1A2A1A05005320, No. 2015R1C1A1A01055813and No. 2016R1A5A1008184, and the Climate ChangeResearch Hub of KAIST (Grant No. N11160013). Theauthors in KIST acknowledge the support from KISTinstitutional program of flagship.

B. Y. O. and M. S. K contributed equally to this work.

B. Y. O. and M. S. K performed the experiment andcarried out analysis. S. H. G designed the sample whichwas grown by H. K. K, S. K., and J. D. S. S. H. G. also setup the experiments with J. H. K, B. Y. O., and M. S. K. H. Cand Y. H. C conceived the project and supervised it. Allauthors contributed to the editing of the manuscript.

*Corresponding author.yhc@kaist.ac.kr

†Corresponding author.h.choi@kaist.ac.kr

‡Present address: Department of Physics & School ofNatural Science, UNIST, Ulsan 44919, Republic of Korea.

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