Abstract

Modulational instabilities play a key role in a wide range of nonlinear optical phenomena, leading, e.g., to the formation of spatial and temporal solitons, rogue waves, and chaotic dynamics. Here, we experimentally demonstrate the existence of a modulational instability in condensates of cavity polaritons, quasi-particles arising from the strong coupling of cavity photons with quantum well excitons. For this purpose, we investigate the spatiotemporal coherence properties of polariton condensates in GaAs-based microcavities under continuous-wave pumping. The chaotic behavior of the instability results in a strongly reduced spatial and temporal coherence and a significantly inhomogeneous density. Additionally, we show how the instability can be tamed by introducing a periodic potential so that condensation occurs in negative mass states, leading to largely improved coherence and homogeneity. These results pave the way to the exploration of long-range order in dissipative quantum fluids of light within a controlled platform.

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2018 (3)

N. Bobrovska, M. Matuszewski, K. S. Daskalakis, S. A. Maier, and S. Kéna-Cohen, “Dynamical instability of a nonequilibrium exciton-polariton condensate,” ACS Photon. 5, 111–118 (2018).
[Crossref]

S. Ravets, P. Knüppel, S. Faelt, O. Cotlet, M. Kroner, W. Wegscheider, and A. Imamoglu, “Polaron polaritons in the integer and fractional quantum Hall regimes,” Phys. Rev. Lett. 120, 057401 (2018).
[Crossref]

C. Whittaker, E. Cancellieri, P. Walker, D. Gulevich, H. Schomerus, D. Vaitiekus, B. Royall, D. Whittaker, E. Clarke, I. Iorsh, I. A. Shelykh, M. S. Skolnick, and D. N. Krizhanovskii, “Exciton polaritons in a two-dimensional Lieb lattice with spin-orbit coupling,” Phys. Rev. Lett. 120, 097401 (2018).
[Crossref]

2017 (6)

D. Ballarini, D. Caputo, C. S. Muñoz, M. De Giorgi, L. Dominici, M. H. Szymańska, K. West, L. N. Pfeiffer, G. Gigli, F. P. Laussy, and D. Sanvitto, “Macroscopic two-dimensional polariton condensates,” Phys. Rev. Lett. 118, 215301 (2017).
[Crossref]

S. Klembt, T. H. Harder, O. A. Egorov, K. Winkler, H. Suchomel, J. Beierlein, M. Emmerling, C. Schneider, and S. Höfling, “Polariton condensation in s-and p-flatbands in a two-dimensional Lieb lattice,” Appl. Phys. Lett. 111, 231102 (2017).
[Crossref]

M. Ramezani, A. Halpin, A. I. Fernández-Domínguez, J. Feist, S. R.-K. Rodriguez, F. J. Garcia-Vidal, and J. G. Rivas, “Plasmon-exciton-polariton lasing,” Optica 4, 31–37 (2017).
[Crossref]

M. Sidler, P. Back, O. Cotlet, A. Srivastava, T. Fink, M. Kroner, E. Demler, and A. Imamoglu, “Fermi polaron-polaritons in charge-tunable atomically thin semiconductors,” Nat. Phys. 13, 255–261 (2017).
[Crossref]

J. H. Nguyen, D. Luo, and R. G. Hulet, “Formation of matter-wave soliton trains by modulational instability,” Science 356, 422–426 (2017).
[Crossref]

M. Khamehchi, K. Hossain, M. Mossman, Y. Zhang, T. Busch, M. M. Forbes, and P. Engels, “Negative-mass hydrodynamics in a spin-orbit-coupled Bose-Einstein condensate,” Phys. Rev. Lett. 118, 155301 (2017).
[Crossref]

2016 (3)

L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, “Self-organized instability in graded-index multimode fibres,” Nat. Photonics 10, 771–776 (2016).
[Crossref]

F. Selmi, S. Coulibaly, Z. Loghmari, I. Sagnes, G. Beaudoin, M. G. Clerc, and S. Barbay, “Spatiotemporal chaos induces extreme events in an extended microcavity laser,” Phys. Rev. Lett. 116, 013901 (2016).
[Crossref]

F. Baboux, L. Ge, T. Jacqmin, M. Biondi, E. Galopin, A. Lemaître, L. Le Gratiet, I. Sagnes, S. Schmidt, H. E. Türeci, A. Amo, and J. Bloch, “Bosonic condensation and disorder-induced localization in a flat band,” Phys. Rev. Lett. 116, 066402 (2016).
[Crossref]

2015 (10)

K. Ji, V. N. Gladilin, and M. Wouters, “Temporal coherence of one-dimensional nonequilibrium quantum fluids,” Phys. Rev. B 91, 045301 (2015).
[Crossref]

X. Liu, T. Galfsky, Z. Sun, F. Xia, E.-C. Lin, Y.-H. Lee, S. Kéna-Cohen, and V. M. Menon, “Strong light-matter coupling in two-dimensional atomic crystals,” Nat. Photonics 9, 30–34 (2015).
[Crossref]

S. Dufferwiel, S. Schwarz, F. Withers, A. Trichet, F. Li, M. Sich, O. Del Pozo-Zamudio, C. Clark, A. Nalitov, D. Solnyshkov, G. Malpuech, K. S. Novoselov, J. M. Smith, M. S. Skolnick, D. N. Krizhanovskii, and A. I. Tartakovskii, “Exciton-polaritons in van der Waals heterostructures embedded in tunable microcavities,” Nat. Commun. 6, 8579 (2015).
[Crossref]

K. S. Daskalakis, S. A. Maier, and S. Kéna-Cohen, “Spatial coherence and stability in a disordered organic polariton condensate,” Phys. Rev. Lett. 115, 035301 (2015).
[Crossref]

M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9, 151–162 (2015).
[Crossref]

T. C. H. Liew, O. A. Egorov, M. Matuszewski, O. Kyriienko, X. Ma, and E. A. Ostrovskaya, “Instability-induced formation and nonequilibrium dynamics of phase defects in polariton condensates,” Phys. Rev. B 91, 085413 (2015).
[Crossref]

N. Bobrovska and M. Matuszewski, “Adiabatic approximation and fluctuations in exciton-polariton condensates,” Phys. Rev. B 92, 035311 (2015).
[Crossref]

L. He, L. M. Sieberer, E. Altman, and S. Diehl, “Scaling properties of one-dimensional driven-dissipative condensates,” Phys. Rev. B 92, 155307 (2015).
[Crossref]

E. Altman, L. M. Sieberer, L. Chen, S. Diehl, and J. Toner, “Two-dimensional superfluidity of exciton polaritons requires strong anisotropy,” Phys. Rev. X 5, 011017 (2015).
[Crossref]

G. Dagvadorj, J. M. Fellows, S. Matyjaśkiewicz, F. M. Marchetti, I. Carusotto, and M. H. Szymańska, “Nonequilibrium phase transition in a two-dimensional driven open quantum system,” Phys. Rev. X 5, 041028 (2015).
[Crossref]

2014 (6)

V. N. Gladilin, K. Ji, and M. Wouters, “Spatial coherence of weakly interacting one-dimensional nonequilibrium bosonic quantum fluids,” Phys. Rev. A 90, 023615 (2014).
[Crossref]

N. Bobrovska, E. A. Ostrovskaya, and M. Matuszewski, “Stability and spatial coherence of nonresonantly pumped exciton-polariton condensates,” Phys. Rev. B 90, 205304 (2014).
[Crossref]

L. A. Smirnov, D. A. Smirnova, E. A. Ostrovskaya, and Y. S. Kivshar, “Dynamics and stability of dark solitons in exciton-polariton condensates,” Phys. Rev. B 89, 235310 (2014).
[Crossref]

W. H. Nitsche, N. Y. Kim, G. Roumpos, C. Schneider, M. Kamp, S. Höfling, A. Forchel, and Y. Yamamoto, “Algebraic order and the Berezinskii-Kosterlitz-Thouless transition in an exciton-polariton gas,” Phys. Rev. B 90, 205430 (2014).
[Crossref]

J. Fischer, I. G. Savenko, M. D. Fraser, S. Holzinger, S. Brodbeck, M. Kamp, I. A. Shelykh, C. Schneider, and S. Höfling, “Spatial coherence properties of one dimensional exciton-polariton condensates,” Phys. Rev. Lett. 113, 203902 (2014).
[Crossref]

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2013 (5)

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2012 (4)

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2011 (1)

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2010 (1)

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2008 (2)

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2007 (5)

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2006 (1)

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2005 (1)

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2001 (2)

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2000 (1)

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1998 (1)

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1986 (1)

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In our lattice, we note that due to the large interpillar spacing (required to obtain a band with large negative mass) the optical overlap between pillars is small. In this limit, the additional Lieb sites are only weakly coupled and play a minor role, so that the band structure resembles that of a simple linear chain of pillars of period a′=a/2. In the case of such a simple linear chain, there is a single band that takes a negative curvature at the edges of the Brillouin zone, located at k=±π/a′=±2π/a, i.e., at the same absolute wavevector position than for the Lieb lattice we consider here.

The density of the interference fringes is fixed by the relative angle between both arms of the interferometer. In Figs. 3(d) and 5(h), we used for convenience a higher fringe density to be able to measure a sufficient number of fringes within the small spatial areas occupied by the condensate. This does not affect the fringe contrast, which is the only relevant quantity to extract the coherence.

More formally, three independent analytical conditions need to be fulfilled so as to apply the adiabatic approximation, as shown in Ref. [34].

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Supplementary Material (1)

NameDescription
» Supplement 1       Details on the modeling and additional theoretical and experimental data.

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Figures (5)

Fig. 1.
Fig. 1. (a) Scanning electron micrograph of 1D wire cavities. (b)–(c) Far-field emission (TM polarization) of a moderate Q wire cavity at pump power (b) below and (c) above the condensation threshold (P=2Pth). (d) Real space image of the condensate. (e) Interferogram obtained by superposing two mirror-symmetric images of the condensate in a Michelson interferometer. (f) Measured and (g) calculated spatial coherence g(1) at t=0 (red), compared to the spatial profile of the condensate (black) and of the pump spot (blue). (h)–(k) Same quantities as (d)–(g) obtained in a high Q wire cavity. (l) Measured and (m) calculated evolution of the x=0 temporal coherence, for the moderate (green line) and high Q wire cavity (blue line).
Fig. 2.
Fig. 2. (a) Scanning electron micrograph of a 1D Lieb lattice of micropillars. (b)–(c) Far-field emission (TM polarization) of a moderate Q Lieb lattice at pump power (b) below and (c) above the condensation threshold (P=1.5Pth). (d) Real space image and (e) interferogram of the condensate. Positions of the micropillars are indicated by black circles. (f) Measured and (g) calculated spatial coherence g(1) at t=0 (red), compared to the spatial profile of the condensate (black) and of the pump spot (blue). (h) Measured and (i) calculated evolution of the x=0 temporal coherence.
Fig. 3.
Fig. 3. (a)–(b) Far-field emission of a moderate Q Lieb lattice at pump power (a) below and (b) above the condensation threshold (P=1.5Pth) when condensation is triggered into a positive mass state. (c) Real-space image and (d) interferogram of the condensate. (e) Measured spatial coherence g(1) at t=0 (red), compared to the spatial profile of the condensate (black). (f) Measured evolution of the x=0 temporal coherence.
Fig. 4.
Fig. 4. (a)–(b) Imaginary part of the Bogoliubov excitation spectrum calculated under the adiabatic approximation, for a positive (a) and negative (b) mass condensate of moderate Q factor, assuming a constant polariton linewidth γ0. (c)–(f) Same quantities calculated with the full model of coupled Eqs. (1),(2), with a constant linewidth (c, d) and with a momentum-dependent linewidth (e, f). Formulas and parameters are given in the Supplement 1.
Fig. 5.
Fig. 5. Condensation in 2D cavities. (a) Real-space image and (b) interferogram of the condensate in a planar cavity with moderate Q factor. (c) Cuts of the condensate density and of the spatial coherence profiles along the horizontal axis indicated in (a)–(b). (d)–(f) Similar measurements performed on a high Q planar cavity. (g)–(i) Similar measurements performed on a high Q honeycomb lattice of coupled micropillars.

Equations (3)

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iψt=[2Δ2m+g|ψ|2+2gRnR+i2(RnRγ)]ψ,
nRt=P(r)(γR+R|ψ|2)nR,
geff=g2gRγγRPthP.

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