Abstract

Recent experiments demonstrated that GaAs/AlAs based micropillar cavities are promising systems for quantum optomechanics, allowing the simultaneous three-dimensional confinement of near-infrared photons and acoustic phonons in the 18-100 GHz range. Here, we investigate through numerical simulations the optomechanical properties of this new platform. We evidence how the Poisson’s ratio and semiconductor/vacuum boundary conditions lead to very distinct features in the mechanical and optical three-dimensional confinement. We find a strong dependence of the mechanical quality factor and strain distribution on the micropillar radius, in great contrast to what is predicted and observed in the optical domain. The derived optomechanical coupling constants g0 reach ultra-large values in the 106 rad/s range.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  32. P. Renosi and J. S. Apriel, “Acousto-optics of semiconductor crystals and superlattices in resonance conditions,” Ultrasonics 31(5), 327–332 (1993).
    [Crossref]
  33. J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101(8), 081115 (2012).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  39. P.-L. de Assis, I. Yeo, A. Gloppe, H. A. Nguyen, D. Tumanov, E. Dupont-Ferrier, N. S. Malik, E. Dupuy, J. Claudon, J. M. Gérard, A. Auffèves, O. Arcizet, M. Richard, and J. P. Poizat, “Strain-gradient position mapping of semiconductor quantum dots,” Phys. Rev. Lett. 118(11), 117401 (2017).
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    [Crossref]

2017 (5)

S. Anguiano, A. E. Bruchhausen, B. Jusserand, I. Favero, F. R. Lamberti, L. Lanco, I. Sagnes, A. Lemaître, N. D. Lanzillotti-Kimura, P. Senellart, and A. Fainstein, “Micropillar resonators for optomechanics in the extremely high 19–95-GHz frequency range,” Phys. Rev. Lett. 118(26), 263901 (2017).
[Crossref] [PubMed]

Y. M. He, J. Liu, S. Maier, M. Emmerling, S. Gerhardt, M. Davanço, K. Srinivasan, C. Schneider, and S. Höfling, “Deterministic implementation of a bright, on-demand single photon source with near-unity indistinguishability via quantum dot imaging,” Optica 4(7), 802–808 (2017).
[Crossref] [PubMed]

M. Munsch, A. V. Kuhlmann, D. Cadeddu, J. M. Gérard, J. Claudon, M. Poggio, and R. J. Warburton, “Resonant driving of a single photon emitter embedded in a mechanical oscillator,” Nat. Commun. 8(1), 76 (2017).
[Crossref] [PubMed]

P.-L. de Assis, I. Yeo, A. Gloppe, H. A. Nguyen, D. Tumanov, E. Dupont-Ferrier, N. S. Malik, E. Dupuy, J. Claudon, J. M. Gérard, A. Auffèves, O. Arcizet, M. Richard, and J. P. Poizat, “Strain-gradient position mapping of semiconductor quantum dots,” Phys. Rev. Lett. 118(11), 117401 (2017).
[Crossref] [PubMed]

J. Restrepo, I. Favero, and C. Ciuti, “Fully coupled hybrid cavity optomechanics: quantum interferences and correlations,” Phys. Rev. A 95(2), 023832 (2017).
[Crossref]

2016 (5)

X. Ding, Y. He, Z.-C. Duan, N. Gregersen, M.-C. Chen, S. Unsleber, S. Maier, C. Schneider, M. Kamp, S. Höfling, C. Y. Lu, and J. W. Pan, “On-demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar,” Phys. Rev. Lett. 116(2), 020401 (2016).
[Crossref] [PubMed]

V. Villafañe, P. Soubelet, A. E. Bruchhausen, N. D. Lanzillotti-Kimura, B. Jusserand, A. Lemaître, and A. Fainstein, “Slow light and slow acoustic phonons in optophononic resonators,” Phys. Rev. B 94(20), 205308 (2016).
[Crossref]

V. Giesz, N. Somaschi, G. Hornecker, T. Grange, B. Reznychenko, L. De Santis, J. Demory, C. Gomez, I. Sagnes, A. Lemaître, O. Krebs, N. D. Lanzillotti-Kimura, L. Lanco, A. Auffeves, and P. Senellart, “Coherent manipulation of a solid-state artificial atom with few photons,” Nat. Commun. 7, 11986 (2016).
[Crossref] [PubMed]

N. Somaschi, V. Giesz, L. D. Santis, J. C. Loredo, M. P. Almeida, G. Hornecker, S. L. Portalupi, T. Grange, C. Antón, J. Demory, C. Gómez, I. Sagnes, N. D. Lanzillotti-Kimura, A. Lemaítre, A. Auffeves, A. G. White, L. Lanco, and P. Senellart, “Near-optimal single-photon sources in the solid state,” Nat. Photonics 10(5), 340–345 (2016).
[Crossref]

D. Garcia-Sanchez, S. Déleglise, J.-L. Thomas, P. Atkinson, C. Lagoin, and B. Perrin, “Acoustic confinement in superlattice cavities,” Phys. Rev. A 94(3), 033813 (2016).
[Crossref]

2015 (6)

T. Czerniuk, J. Tepper, A. V. Akimov, S. Unsleber, C. Schneider, M. Kamp, S. Höfling, D. R. Yakovlev, and M. Bayer, “Impact of nanomechanical resonances on lasing from electrically pumped quantum dot micropillars,” Appl. Phys. Lett. 106(4), 041103 (2015).
[Crossref]

N. D. Lanzillotti-Kimura, A. Fainstein, and B. Jusserand, “Towards GHz-THz cavity optomechanics in DBR-based semiconductor resonators,” Ultrasonics 56, 80–89 (2015).
[Crossref] [PubMed]

D. T. Nguyen, W. Hease, C. Baker, E. Gil-Santos, P. Senellart, S. Aristide Lemaître, S. Ducci, G. Leo, and I. Favero, “Improved optomechanical disk resonator sitting on a pedestal mechanical shield,” New J. Phys. 17(2), 023016 (2015).
[Crossref]

M. Gschrey, A. Thoma, P. Schnauber, M. Seifried, R. Schmidt, B. Wohlfeil, L. Krüger, J. H. Schulze, T. Heindel, S. Burger, F. Schmidt, A. Strittmatter, S. Rodt, and S. Reitzenstein, “Highly indistinguishable photons from deterministic quantum-dot microlenses utilizing three-dimensional in situ electron-beam lithography,” Nat. Commun. 6, 7662 (2015).
[Crossref] [PubMed]

H. S. Nguyen, D. Gerace, I. Carusotto, D. Sanvitto, E. Galopin, A. Lemaître, I. Sagnes, J. Bloch, and A. Amo, “Acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons,” Phys. Rev. Lett. 114(3), 036402 (2015).
[Crossref] [PubMed]

P. Sesin, P. Soubelet, V. Villafañe, A. E. Bruchhausen, B. Jusserand, A. Lemaître, N. D. Lanzillotti-Kimura, and A. Fainstein, “Dynamical optical tuning of the coherent phonon detection sensitivity in DBR-based GaAs optomechanical resonators,” Phys. Rev. B 92(7), 075307 (2015).
[Crossref]

2014 (4)

C. Baker, W. Hease, D.-T. Nguyen, A. Andronico, S. Ducci, G. Leo, and I. Favero, “Photoelastic coupling in gallium arsenide optomechanical disk resonators,” Opt. Express 22(12), 14072–14086 (2014).
[Crossref] [PubMed]

T. Jacqmin, I. Carusotto, I. Sagnes, M. Abbarchi, D. D. Solnyshkov, G. Malpuech, E. Galopin, A. Lemaître, J. Bloch, and A. Amo, “Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons,” Phys. Rev. Lett. 112(11), 116402 (2014).
[Crossref] [PubMed]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

J. Restrepo, C. Ciuti, and I. Favero, “Single-polariton optomechanics,” Phys. Rev. Lett. 112(1), 013601 (2014).
[Crossref] [PubMed]

2013 (1)

A. Fainstein, N. D. Lanzillotti-Kimura, B. Jusserand, and B. Perrin, “Strong optical-mechanical coupling in a vertical GaAs/AlAs microcavity for subterahertz phonons and near-infrared light,” Phys. Rev. Lett. 110(3), 037403 (2013).
[Crossref] [PubMed]

2012 (2)

M. Galbiati, L. Ferrier, D. D. Solnyshkov, D. Tanese, E. Wertz, A. Amo, M. Abbarchi, P. Senellart, I. Sagnes, A. Lemaître, E. Galopin, G. Malpuech, and J. Bloch, “Polariton condensation in photonic molecules,” Phys. Rev. Lett. 108(12), 126403 (2012).
[Crossref] [PubMed]

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101(8), 081115 (2012).
[Crossref]

2011 (3)

N. D. Lanzillotti-Kimura, A. Fainstein, A. Lemaitre, B. Jusserand, and B. Perrin, “Coherent control of sub-terahertz confined acoustic nanowaves: theory and experiments,” Phys. Rev. B 84(11), 115453 (2011).
[Crossref]

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “Wavelength-sized GaAs optomechanical resonators with gigahertz frequency,” Appl. Phys. Lett. 98(11), 113108 (2011).
[Crossref]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

2009 (2)

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[Crossref] [PubMed]

I. Favero and K. Karrai, “Optomechanics of deformable optical cavities,” Nat. Photonics 3(4), 201–205 (2009).
[Crossref]

2008 (3)

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
[Crossref] [PubMed]

D. Bajoni, P. Senellart, E. Wertz, I. Sagnes, A. Miard, A. Lemaître, and J. Bloch, “Polariton laser using single micropillar GaAs-GaAlAs semiconductor cavities,” Phys. Rev. Lett. 100(4), 047401 (2008).
[Crossref] [PubMed]

A. Dousse, L. Lanco, J. Suffczyński, E. Semenova, A. Miard, A. Lemaître, I. Sagnes, C. Roblin, J. Bloch, and P. Senellart, “Controlled light-matter coupling for a single quantum dot embedded in a pillar microcavity using far-field optical lithography,” Phys. Rev. Lett. 101(26), 267404 (2008).
[Crossref] [PubMed]

2000 (2)

V. B. Taranenko, I. Ganne, R. J. Kuszelewicz, and C. O. Weiss, “Patterns and localized structures in bistable semiconductor resonators,” Phys. Rev. A 61(6), 063818 (2000).
[Crossref]

R. Kuszelewicz, I. Ganne, I. Sagnes, G. Slekys, and M. Brambilla, “Optical self-organization in bulk and multiquantum well GaAlAs microresonators,” Phys. Rev. Lett. 84(26), 6006–6009 (2000).
[Crossref] [PubMed]

1998 (1)

B. Gayral, J. M. Gérard, B. Legrand, E. Costard, and V. Thierry-Mieg, “Optical study of GaAs/AlAs pillar microcavities with elliptical cross section,” Appl. Phys. Lett. 72(12), 1421–1423 (1998).
[Crossref]

1997 (2)

S. Bose, K. Jacobs, and P. L. Knight, “Preparation of nonclassical states in cavities with a moving mirror,” Phys. Rev. A 56(5), 4175–4186 (1997).
[Crossref]

S. Mancini, V. I. Man’ko, and P. Tombesi, “Ponderomotive control of quantum macroscopic coherence,” Phys. Rev. A 55(4), 3042–3050 (1997).
[Crossref]

1996 (1)

J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Appl. Phys. Lett. 69(4), 449–451 (1996).
[Crossref]

1995 (1)

J. E. Raynolds, Z. H. Levine, and J. W. Wilkins, “Strain-induced birefringence in GaAs,” Phys. Rev. B Condens. Matter 51(16), 10477–10488 (1995).
[Crossref] [PubMed]

1994 (1)

T. Rivera, F. R. Ladan, A. Izraël, R. Azoulay, R. Kuszelewicz, and J. L. Oudar, “Reduced threshold all‐optical bistability in etched quantum well microresonators,” Appl. Phys. Lett. 64(7), 869–871 (1994).
[Crossref]

1993 (1)

P. Renosi and J. S. Apriel, “Acousto-optics of semiconductor crystals and superlattices in resonance conditions,” Ultrasonics 31(5), 327–332 (1993).
[Crossref]

1974 (1)

M. A. Afromowitz, “Refractive index of Ga1-xAlxAs,” Solid State Commun. 15(1), 59–63 (1974).
[Crossref]

Abbarchi, M.

T. Jacqmin, I. Carusotto, I. Sagnes, M. Abbarchi, D. D. Solnyshkov, G. Malpuech, E. Galopin, A. Lemaître, J. Bloch, and A. Amo, “Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons,” Phys. Rev. Lett. 112(11), 116402 (2014).
[Crossref] [PubMed]

M. Galbiati, L. Ferrier, D. D. Solnyshkov, D. Tanese, E. Wertz, A. Amo, M. Abbarchi, P. Senellart, I. Sagnes, A. Lemaître, E. Galopin, G. Malpuech, and J. Bloch, “Polariton condensation in photonic molecules,” Phys. Rev. Lett. 108(12), 126403 (2012).
[Crossref] [PubMed]

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Hease, W.

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P. Sesin, P. Soubelet, V. Villafañe, A. E. Bruchhausen, B. Jusserand, A. Lemaître, N. D. Lanzillotti-Kimura, and A. Fainstein, “Dynamical optical tuning of the coherent phonon detection sensitivity in DBR-based GaAs optomechanical resonators,” Phys. Rev. B 92(7), 075307 (2015).
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N. D. Lanzillotti-Kimura, A. Fainstein, and B. Jusserand, “Towards GHz-THz cavity optomechanics in DBR-based semiconductor resonators,” Ultrasonics 56, 80–89 (2015).
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J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
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V. Giesz, N. Somaschi, G. Hornecker, T. Grange, B. Reznychenko, L. De Santis, J. Demory, C. Gomez, I. Sagnes, A. Lemaître, O. Krebs, N. D. Lanzillotti-Kimura, L. Lanco, A. Auffeves, and P. Senellart, “Coherent manipulation of a solid-state artificial atom with few photons,” Nat. Commun. 7, 11986 (2016).
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M. Gschrey, A. Thoma, P. Schnauber, M. Seifried, R. Schmidt, B. Wohlfeil, L. Krüger, J. H. Schulze, T. Heindel, S. Burger, F. Schmidt, A. Strittmatter, S. Rodt, and S. Reitzenstein, “Highly indistinguishable photons from deterministic quantum-dot microlenses utilizing three-dimensional in situ electron-beam lithography,” Nat. Commun. 6, 7662 (2015).
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M. Munsch, A. V. Kuhlmann, D. Cadeddu, J. M. Gérard, J. Claudon, M. Poggio, and R. J. Warburton, “Resonant driving of a single photon emitter embedded in a mechanical oscillator,” Nat. Commun. 8(1), 76 (2017).
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R. Kuszelewicz, I. Ganne, I. Sagnes, G. Slekys, and M. Brambilla, “Optical self-organization in bulk and multiquantum well GaAlAs microresonators,” Phys. Rev. Lett. 84(26), 6006–6009 (2000).
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J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Appl. Phys. Lett. 69(4), 449–451 (1996).
[Crossref]

T. Rivera, F. R. Ladan, A. Izraël, R. Azoulay, R. Kuszelewicz, and J. L. Oudar, “Reduced threshold all‐optical bistability in etched quantum well microresonators,” Appl. Phys. Lett. 64(7), 869–871 (1994).
[Crossref]

Kuszelewicz, R. J.

V. B. Taranenko, I. Ganne, R. J. Kuszelewicz, and C. O. Weiss, “Patterns and localized structures in bistable semiconductor resonators,” Phys. Rev. A 61(6), 063818 (2000).
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T. Rivera, F. R. Ladan, A. Izraël, R. Azoulay, R. Kuszelewicz, and J. L. Oudar, “Reduced threshold all‐optical bistability in etched quantum well microresonators,” Appl. Phys. Lett. 64(7), 869–871 (1994).
[Crossref]

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D. Garcia-Sanchez, S. Déleglise, J.-L. Thomas, P. Atkinson, C. Lagoin, and B. Perrin, “Acoustic confinement in superlattice cavities,” Phys. Rev. A 94(3), 033813 (2016).
[Crossref]

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S. Anguiano, A. E. Bruchhausen, B. Jusserand, I. Favero, F. R. Lamberti, L. Lanco, I. Sagnes, A. Lemaître, N. D. Lanzillotti-Kimura, P. Senellart, and A. Fainstein, “Micropillar resonators for optomechanics in the extremely high 19–95-GHz frequency range,” Phys. Rev. Lett. 118(26), 263901 (2017).
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S. Anguiano, A. E. Bruchhausen, B. Jusserand, I. Favero, F. R. Lamberti, L. Lanco, I. Sagnes, A. Lemaître, N. D. Lanzillotti-Kimura, P. Senellart, and A. Fainstein, “Micropillar resonators for optomechanics in the extremely high 19–95-GHz frequency range,” Phys. Rev. Lett. 118(26), 263901 (2017).
[Crossref] [PubMed]

N. Somaschi, V. Giesz, L. D. Santis, J. C. Loredo, M. P. Almeida, G. Hornecker, S. L. Portalupi, T. Grange, C. Antón, J. Demory, C. Gómez, I. Sagnes, N. D. Lanzillotti-Kimura, A. Lemaítre, A. Auffeves, A. G. White, L. Lanco, and P. Senellart, “Near-optimal single-photon sources in the solid state,” Nat. Photonics 10(5), 340–345 (2016).
[Crossref]

V. Giesz, N. Somaschi, G. Hornecker, T. Grange, B. Reznychenko, L. De Santis, J. Demory, C. Gomez, I. Sagnes, A. Lemaître, O. Krebs, N. D. Lanzillotti-Kimura, L. Lanco, A. Auffeves, and P. Senellart, “Coherent manipulation of a solid-state artificial atom with few photons,” Nat. Commun. 7, 11986 (2016).
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S. Anguiano, A. E. Bruchhausen, B. Jusserand, I. Favero, F. R. Lamberti, L. Lanco, I. Sagnes, A. Lemaître, N. D. Lanzillotti-Kimura, P. Senellart, and A. Fainstein, “Micropillar resonators for optomechanics in the extremely high 19–95-GHz frequency range,” Phys. Rev. Lett. 118(26), 263901 (2017).
[Crossref] [PubMed]

V. Giesz, N. Somaschi, G. Hornecker, T. Grange, B. Reznychenko, L. De Santis, J. Demory, C. Gomez, I. Sagnes, A. Lemaître, O. Krebs, N. D. Lanzillotti-Kimura, L. Lanco, A. Auffeves, and P. Senellart, “Coherent manipulation of a solid-state artificial atom with few photons,” Nat. Commun. 7, 11986 (2016).
[Crossref] [PubMed]

N. Somaschi, V. Giesz, L. D. Santis, J. C. Loredo, M. P. Almeida, G. Hornecker, S. L. Portalupi, T. Grange, C. Antón, J. Demory, C. Gómez, I. Sagnes, N. D. Lanzillotti-Kimura, A. Lemaítre, A. Auffeves, A. G. White, L. Lanco, and P. Senellart, “Near-optimal single-photon sources in the solid state,” Nat. Photonics 10(5), 340–345 (2016).
[Crossref]

V. Villafañe, P. Soubelet, A. E. Bruchhausen, N. D. Lanzillotti-Kimura, B. Jusserand, A. Lemaître, and A. Fainstein, “Slow light and slow acoustic phonons in optophononic resonators,” Phys. Rev. B 94(20), 205308 (2016).
[Crossref]

P. Sesin, P. Soubelet, V. Villafañe, A. E. Bruchhausen, B. Jusserand, A. Lemaître, N. D. Lanzillotti-Kimura, and A. Fainstein, “Dynamical optical tuning of the coherent phonon detection sensitivity in DBR-based GaAs optomechanical resonators,” Phys. Rev. B 92(7), 075307 (2015).
[Crossref]

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M. Gschrey, A. Thoma, P. Schnauber, M. Seifried, R. Schmidt, B. Wohlfeil, L. Krüger, J. H. Schulze, T. Heindel, S. Burger, F. Schmidt, A. Strittmatter, S. Rodt, and S. Reitzenstein, “Highly indistinguishable photons from deterministic quantum-dot microlenses utilizing three-dimensional in situ electron-beam lithography,” Nat. Commun. 6, 7662 (2015).
[Crossref] [PubMed]

Schneider, C.

Y. M. He, J. Liu, S. Maier, M. Emmerling, S. Gerhardt, M. Davanço, K. Srinivasan, C. Schneider, and S. Höfling, “Deterministic implementation of a bright, on-demand single photon source with near-unity indistinguishability via quantum dot imaging,” Optica 4(7), 802–808 (2017).
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X. Ding, Y. He, Z.-C. Duan, N. Gregersen, M.-C. Chen, S. Unsleber, S. Maier, C. Schneider, M. Kamp, S. Höfling, C. Y. Lu, and J. W. Pan, “On-demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar,” Phys. Rev. Lett. 116(2), 020401 (2016).
[Crossref] [PubMed]

T. Czerniuk, J. Tepper, A. V. Akimov, S. Unsleber, C. Schneider, M. Kamp, S. Höfling, D. R. Yakovlev, and M. Bayer, “Impact of nanomechanical resonances on lasing from electrically pumped quantum dot micropillars,” Appl. Phys. Lett. 106(4), 041103 (2015).
[Crossref]

Schulze, J. H.

M. Gschrey, A. Thoma, P. Schnauber, M. Seifried, R. Schmidt, B. Wohlfeil, L. Krüger, J. H. Schulze, T. Heindel, S. Burger, F. Schmidt, A. Strittmatter, S. Rodt, and S. Reitzenstein, “Highly indistinguishable photons from deterministic quantum-dot microlenses utilizing three-dimensional in situ electron-beam lithography,” Nat. Commun. 6, 7662 (2015).
[Crossref] [PubMed]

Seifried, M.

M. Gschrey, A. Thoma, P. Schnauber, M. Seifried, R. Schmidt, B. Wohlfeil, L. Krüger, J. H. Schulze, T. Heindel, S. Burger, F. Schmidt, A. Strittmatter, S. Rodt, and S. Reitzenstein, “Highly indistinguishable photons from deterministic quantum-dot microlenses utilizing three-dimensional in situ electron-beam lithography,” Nat. Commun. 6, 7662 (2015).
[Crossref] [PubMed]

Semenova, E.

A. Dousse, L. Lanco, J. Suffczyński, E. Semenova, A. Miard, A. Lemaître, I. Sagnes, C. Roblin, J. Bloch, and P. Senellart, “Controlled light-matter coupling for a single quantum dot embedded in a pillar microcavity using far-field optical lithography,” Phys. Rev. Lett. 101(26), 267404 (2008).
[Crossref] [PubMed]

Senellart, P.

S. Anguiano, A. E. Bruchhausen, B. Jusserand, I. Favero, F. R. Lamberti, L. Lanco, I. Sagnes, A. Lemaître, N. D. Lanzillotti-Kimura, P. Senellart, and A. Fainstein, “Micropillar resonators for optomechanics in the extremely high 19–95-GHz frequency range,” Phys. Rev. Lett. 118(26), 263901 (2017).
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N. Somaschi, V. Giesz, L. D. Santis, J. C. Loredo, M. P. Almeida, G. Hornecker, S. L. Portalupi, T. Grange, C. Antón, J. Demory, C. Gómez, I. Sagnes, N. D. Lanzillotti-Kimura, A. Lemaítre, A. Auffeves, A. G. White, L. Lanco, and P. Senellart, “Near-optimal single-photon sources in the solid state,” Nat. Photonics 10(5), 340–345 (2016).
[Crossref]

V. Giesz, N. Somaschi, G. Hornecker, T. Grange, B. Reznychenko, L. De Santis, J. Demory, C. Gomez, I. Sagnes, A. Lemaître, O. Krebs, N. D. Lanzillotti-Kimura, L. Lanco, A. Auffeves, and P. Senellart, “Coherent manipulation of a solid-state artificial atom with few photons,” Nat. Commun. 7, 11986 (2016).
[Crossref] [PubMed]

D. T. Nguyen, W. Hease, C. Baker, E. Gil-Santos, P. Senellart, S. Aristide Lemaître, S. Ducci, G. Leo, and I. Favero, “Improved optomechanical disk resonator sitting on a pedestal mechanical shield,” New J. Phys. 17(2), 023016 (2015).
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M. Galbiati, L. Ferrier, D. D. Solnyshkov, D. Tanese, E. Wertz, A. Amo, M. Abbarchi, P. Senellart, I. Sagnes, A. Lemaître, E. Galopin, G. Malpuech, and J. Bloch, “Polariton condensation in photonic molecules,” Phys. Rev. Lett. 108(12), 126403 (2012).
[Crossref] [PubMed]

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “Wavelength-sized GaAs optomechanical resonators with gigahertz frequency,” Appl. Phys. Lett. 98(11), 113108 (2011).
[Crossref]

D. Bajoni, P. Senellart, E. Wertz, I. Sagnes, A. Miard, A. Lemaître, and J. Bloch, “Polariton laser using single micropillar GaAs-GaAlAs semiconductor cavities,” Phys. Rev. Lett. 100(4), 047401 (2008).
[Crossref] [PubMed]

A. Dousse, L. Lanco, J. Suffczyński, E. Semenova, A. Miard, A. Lemaître, I. Sagnes, C. Roblin, J. Bloch, and P. Senellart, “Controlled light-matter coupling for a single quantum dot embedded in a pillar microcavity using far-field optical lithography,” Phys. Rev. Lett. 101(26), 267404 (2008).
[Crossref] [PubMed]

Sesin, P.

P. Sesin, P. Soubelet, V. Villafañe, A. E. Bruchhausen, B. Jusserand, A. Lemaître, N. D. Lanzillotti-Kimura, and A. Fainstein, “Dynamical optical tuning of the coherent phonon detection sensitivity in DBR-based GaAs optomechanical resonators,” Phys. Rev. B 92(7), 075307 (2015).
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Slekys, G.

R. Kuszelewicz, I. Ganne, I. Sagnes, G. Slekys, and M. Brambilla, “Optical self-organization in bulk and multiquantum well GaAlAs microresonators,” Phys. Rev. Lett. 84(26), 6006–6009 (2000).
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Solnyshkov, D. D.

T. Jacqmin, I. Carusotto, I. Sagnes, M. Abbarchi, D. D. Solnyshkov, G. Malpuech, E. Galopin, A. Lemaître, J. Bloch, and A. Amo, “Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons,” Phys. Rev. Lett. 112(11), 116402 (2014).
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M. Galbiati, L. Ferrier, D. D. Solnyshkov, D. Tanese, E. Wertz, A. Amo, M. Abbarchi, P. Senellart, I. Sagnes, A. Lemaître, E. Galopin, G. Malpuech, and J. Bloch, “Polariton condensation in photonic molecules,” Phys. Rev. Lett. 108(12), 126403 (2012).
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Somaschi, N.

N. Somaschi, V. Giesz, L. D. Santis, J. C. Loredo, M. P. Almeida, G. Hornecker, S. L. Portalupi, T. Grange, C. Antón, J. Demory, C. Gómez, I. Sagnes, N. D. Lanzillotti-Kimura, A. Lemaítre, A. Auffeves, A. G. White, L. Lanco, and P. Senellart, “Near-optimal single-photon sources in the solid state,” Nat. Photonics 10(5), 340–345 (2016).
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V. Giesz, N. Somaschi, G. Hornecker, T. Grange, B. Reznychenko, L. De Santis, J. Demory, C. Gomez, I. Sagnes, A. Lemaître, O. Krebs, N. D. Lanzillotti-Kimura, L. Lanco, A. Auffeves, and P. Senellart, “Coherent manipulation of a solid-state artificial atom with few photons,” Nat. Commun. 7, 11986 (2016).
[Crossref] [PubMed]

Soubelet, P.

V. Villafañe, P. Soubelet, A. E. Bruchhausen, N. D. Lanzillotti-Kimura, B. Jusserand, A. Lemaître, and A. Fainstein, “Slow light and slow acoustic phonons in optophononic resonators,” Phys. Rev. B 94(20), 205308 (2016).
[Crossref]

P. Sesin, P. Soubelet, V. Villafañe, A. E. Bruchhausen, B. Jusserand, A. Lemaître, N. D. Lanzillotti-Kimura, and A. Fainstein, “Dynamical optical tuning of the coherent phonon detection sensitivity in DBR-based GaAs optomechanical resonators,” Phys. Rev. B 92(7), 075307 (2015).
[Crossref]

Srinivasan, K.

Strittmatter, A.

M. Gschrey, A. Thoma, P. Schnauber, M. Seifried, R. Schmidt, B. Wohlfeil, L. Krüger, J. H. Schulze, T. Heindel, S. Burger, F. Schmidt, A. Strittmatter, S. Rodt, and S. Reitzenstein, “Highly indistinguishable photons from deterministic quantum-dot microlenses utilizing three-dimensional in situ electron-beam lithography,” Nat. Commun. 6, 7662 (2015).
[Crossref] [PubMed]

Suffczynski, J.

A. Dousse, L. Lanco, J. Suffczyński, E. Semenova, A. Miard, A. Lemaître, I. Sagnes, C. Roblin, J. Bloch, and P. Senellart, “Controlled light-matter coupling for a single quantum dot embedded in a pillar microcavity using far-field optical lithography,” Phys. Rev. Lett. 101(26), 267404 (2008).
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Tanese, D.

M. Galbiati, L. Ferrier, D. D. Solnyshkov, D. Tanese, E. Wertz, A. Amo, M. Abbarchi, P. Senellart, I. Sagnes, A. Lemaître, E. Galopin, G. Malpuech, and J. Bloch, “Polariton condensation in photonic molecules,” Phys. Rev. Lett. 108(12), 126403 (2012).
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Taranenko, V. B.

V. B. Taranenko, I. Ganne, R. J. Kuszelewicz, and C. O. Weiss, “Patterns and localized structures in bistable semiconductor resonators,” Phys. Rev. A 61(6), 063818 (2000).
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Tepper, J.

T. Czerniuk, J. Tepper, A. V. Akimov, S. Unsleber, C. Schneider, M. Kamp, S. Höfling, D. R. Yakovlev, and M. Bayer, “Impact of nanomechanical resonances on lasing from electrically pumped quantum dot micropillars,” Appl. Phys. Lett. 106(4), 041103 (2015).
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Thierry-Mieg, V.

B. Gayral, J. M. Gérard, B. Legrand, E. Costard, and V. Thierry-Mieg, “Optical study of GaAs/AlAs pillar microcavities with elliptical cross section,” Appl. Phys. Lett. 72(12), 1421–1423 (1998).
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J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Appl. Phys. Lett. 69(4), 449–451 (1996).
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Thoma, A.

M. Gschrey, A. Thoma, P. Schnauber, M. Seifried, R. Schmidt, B. Wohlfeil, L. Krüger, J. H. Schulze, T. Heindel, S. Burger, F. Schmidt, A. Strittmatter, S. Rodt, and S. Reitzenstein, “Highly indistinguishable photons from deterministic quantum-dot microlenses utilizing three-dimensional in situ electron-beam lithography,” Nat. Commun. 6, 7662 (2015).
[Crossref] [PubMed]

Thomas, J.-L.

D. Garcia-Sanchez, S. Déleglise, J.-L. Thomas, P. Atkinson, C. Lagoin, and B. Perrin, “Acoustic confinement in superlattice cavities,” Phys. Rev. A 94(3), 033813 (2016).
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Tombesi, P.

S. Mancini, V. I. Man’ko, and P. Tombesi, “Ponderomotive control of quantum macroscopic coherence,” Phys. Rev. A 55(4), 3042–3050 (1997).
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Tumanov, D.

P.-L. de Assis, I. Yeo, A. Gloppe, H. A. Nguyen, D. Tumanov, E. Dupont-Ferrier, N. S. Malik, E. Dupuy, J. Claudon, J. M. Gérard, A. Auffèves, O. Arcizet, M. Richard, and J. P. Poizat, “Strain-gradient position mapping of semiconductor quantum dots,” Phys. Rev. Lett. 118(11), 117401 (2017).
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Unsleber, S.

X. Ding, Y. He, Z.-C. Duan, N. Gregersen, M.-C. Chen, S. Unsleber, S. Maier, C. Schneider, M. Kamp, S. Höfling, C. Y. Lu, and J. W. Pan, “On-demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar,” Phys. Rev. Lett. 116(2), 020401 (2016).
[Crossref] [PubMed]

T. Czerniuk, J. Tepper, A. V. Akimov, S. Unsleber, C. Schneider, M. Kamp, S. Höfling, D. R. Yakovlev, and M. Bayer, “Impact of nanomechanical resonances on lasing from electrically pumped quantum dot micropillars,” Appl. Phys. Lett. 106(4), 041103 (2015).
[Crossref]

Vahala, K. J.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
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T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
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Villafañe, V.

V. Villafañe, P. Soubelet, A. E. Bruchhausen, N. D. Lanzillotti-Kimura, B. Jusserand, A. Lemaître, and A. Fainstein, “Slow light and slow acoustic phonons in optophononic resonators,” Phys. Rev. B 94(20), 205308 (2016).
[Crossref]

P. Sesin, P. Soubelet, V. Villafañe, A. E. Bruchhausen, B. Jusserand, A. Lemaître, N. D. Lanzillotti-Kimura, and A. Fainstein, “Dynamical optical tuning of the coherent phonon detection sensitivity in DBR-based GaAs optomechanical resonators,” Phys. Rev. B 92(7), 075307 (2015).
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Warburton, R. J.

M. Munsch, A. V. Kuhlmann, D. Cadeddu, J. M. Gérard, J. Claudon, M. Poggio, and R. J. Warburton, “Resonant driving of a single photon emitter embedded in a mechanical oscillator,” Nat. Commun. 8(1), 76 (2017).
[Crossref] [PubMed]

Weiss, C. O.

V. B. Taranenko, I. Ganne, R. J. Kuszelewicz, and C. O. Weiss, “Patterns and localized structures in bistable semiconductor resonators,” Phys. Rev. A 61(6), 063818 (2000).
[Crossref]

Wertz, E.

M. Galbiati, L. Ferrier, D. D. Solnyshkov, D. Tanese, E. Wertz, A. Amo, M. Abbarchi, P. Senellart, I. Sagnes, A. Lemaître, E. Galopin, G. Malpuech, and J. Bloch, “Polariton condensation in photonic molecules,” Phys. Rev. Lett. 108(12), 126403 (2012).
[Crossref] [PubMed]

D. Bajoni, P. Senellart, E. Wertz, I. Sagnes, A. Miard, A. Lemaître, and J. Bloch, “Polariton laser using single micropillar GaAs-GaAlAs semiconductor cavities,” Phys. Rev. Lett. 100(4), 047401 (2008).
[Crossref] [PubMed]

White, A. G.

N. Somaschi, V. Giesz, L. D. Santis, J. C. Loredo, M. P. Almeida, G. Hornecker, S. L. Portalupi, T. Grange, C. Antón, J. Demory, C. Gómez, I. Sagnes, N. D. Lanzillotti-Kimura, A. Lemaítre, A. Auffeves, A. G. White, L. Lanco, and P. Senellart, “Near-optimal single-photon sources in the solid state,” Nat. Photonics 10(5), 340–345 (2016).
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Wilkins, J. W.

J. E. Raynolds, Z. H. Levine, and J. W. Wilkins, “Strain-induced birefringence in GaAs,” Phys. Rev. B Condens. Matter 51(16), 10477–10488 (1995).
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Wohlfeil, B.

M. Gschrey, A. Thoma, P. Schnauber, M. Seifried, R. Schmidt, B. Wohlfeil, L. Krüger, J. H. Schulze, T. Heindel, S. Burger, F. Schmidt, A. Strittmatter, S. Rodt, and S. Reitzenstein, “Highly indistinguishable photons from deterministic quantum-dot microlenses utilizing three-dimensional in situ electron-beam lithography,” Nat. Commun. 6, 7662 (2015).
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Yakovlev, D. R.

T. Czerniuk, J. Tepper, A. V. Akimov, S. Unsleber, C. Schneider, M. Kamp, S. Höfling, D. R. Yakovlev, and M. Bayer, “Impact of nanomechanical resonances on lasing from electrically pumped quantum dot micropillars,” Appl. Phys. Lett. 106(4), 041103 (2015).
[Crossref]

Yeo, I.

P.-L. de Assis, I. Yeo, A. Gloppe, H. A. Nguyen, D. Tumanov, E. Dupont-Ferrier, N. S. Malik, E. Dupuy, J. Claudon, J. M. Gérard, A. Auffèves, O. Arcizet, M. Richard, and J. P. Poizat, “Strain-gradient position mapping of semiconductor quantum dots,” Phys. Rev. Lett. 118(11), 117401 (2017).
[Crossref] [PubMed]

Appl. Phys. Lett. (6)

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “Wavelength-sized GaAs optomechanical resonators with gigahertz frequency,” Appl. Phys. Lett. 98(11), 113108 (2011).
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T. Rivera, F. R. Ladan, A. Izraël, R. Azoulay, R. Kuszelewicz, and J. L. Oudar, “Reduced threshold all‐optical bistability in etched quantum well microresonators,” Appl. Phys. Lett. 64(7), 869–871 (1994).
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T. Czerniuk, J. Tepper, A. V. Akimov, S. Unsleber, C. Schneider, M. Kamp, S. Höfling, D. R. Yakovlev, and M. Bayer, “Impact of nanomechanical resonances on lasing from electrically pumped quantum dot micropillars,” Appl. Phys. Lett. 106(4), 041103 (2015).
[Crossref]

J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Appl. Phys. Lett. 69(4), 449–451 (1996).
[Crossref]

B. Gayral, J. M. Gérard, B. Legrand, E. Costard, and V. Thierry-Mieg, “Optical study of GaAs/AlAs pillar microcavities with elliptical cross section,” Appl. Phys. Lett. 72(12), 1421–1423 (1998).
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J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101(8), 081115 (2012).
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Nat. Commun. (3)

V. Giesz, N. Somaschi, G. Hornecker, T. Grange, B. Reznychenko, L. De Santis, J. Demory, C. Gomez, I. Sagnes, A. Lemaître, O. Krebs, N. D. Lanzillotti-Kimura, L. Lanco, A. Auffeves, and P. Senellart, “Coherent manipulation of a solid-state artificial atom with few photons,” Nat. Commun. 7, 11986 (2016).
[Crossref] [PubMed]

M. Gschrey, A. Thoma, P. Schnauber, M. Seifried, R. Schmidt, B. Wohlfeil, L. Krüger, J. H. Schulze, T. Heindel, S. Burger, F. Schmidt, A. Strittmatter, S. Rodt, and S. Reitzenstein, “Highly indistinguishable photons from deterministic quantum-dot microlenses utilizing three-dimensional in situ electron-beam lithography,” Nat. Commun. 6, 7662 (2015).
[Crossref] [PubMed]

M. Munsch, A. V. Kuhlmann, D. Cadeddu, J. M. Gérard, J. Claudon, M. Poggio, and R. J. Warburton, “Resonant driving of a single photon emitter embedded in a mechanical oscillator,” Nat. Commun. 8(1), 76 (2017).
[Crossref] [PubMed]

Nat. Photonics (2)

N. Somaschi, V. Giesz, L. D. Santis, J. C. Loredo, M. P. Almeida, G. Hornecker, S. L. Portalupi, T. Grange, C. Antón, J. Demory, C. Gómez, I. Sagnes, N. D. Lanzillotti-Kimura, A. Lemaítre, A. Auffeves, A. G. White, L. Lanco, and P. Senellart, “Near-optimal single-photon sources in the solid state,” Nat. Photonics 10(5), 340–345 (2016).
[Crossref]

I. Favero and K. Karrai, “Optomechanics of deformable optical cavities,” Nat. Photonics 3(4), 201–205 (2009).
[Crossref]

Nature (2)

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[Crossref] [PubMed]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

New J. Phys. (1)

D. T. Nguyen, W. Hease, C. Baker, E. Gil-Santos, P. Senellart, S. Aristide Lemaître, S. Ducci, G. Leo, and I. Favero, “Improved optomechanical disk resonator sitting on a pedestal mechanical shield,” New J. Phys. 17(2), 023016 (2015).
[Crossref]

Opt. Express (1)

Optica (1)

Phys. Rev. A (5)

V. B. Taranenko, I. Ganne, R. J. Kuszelewicz, and C. O. Weiss, “Patterns and localized structures in bistable semiconductor resonators,” Phys. Rev. A 61(6), 063818 (2000).
[Crossref]

S. Bose, K. Jacobs, and P. L. Knight, “Preparation of nonclassical states in cavities with a moving mirror,” Phys. Rev. A 56(5), 4175–4186 (1997).
[Crossref]

S. Mancini, V. I. Man’ko, and P. Tombesi, “Ponderomotive control of quantum macroscopic coherence,” Phys. Rev. A 55(4), 3042–3050 (1997).
[Crossref]

D. Garcia-Sanchez, S. Déleglise, J.-L. Thomas, P. Atkinson, C. Lagoin, and B. Perrin, “Acoustic confinement in superlattice cavities,” Phys. Rev. A 94(3), 033813 (2016).
[Crossref]

J. Restrepo, I. Favero, and C. Ciuti, “Fully coupled hybrid cavity optomechanics: quantum interferences and correlations,” Phys. Rev. A 95(2), 023832 (2017).
[Crossref]

Phys. Rev. B (3)

P. Sesin, P. Soubelet, V. Villafañe, A. E. Bruchhausen, B. Jusserand, A. Lemaître, N. D. Lanzillotti-Kimura, and A. Fainstein, “Dynamical optical tuning of the coherent phonon detection sensitivity in DBR-based GaAs optomechanical resonators,” Phys. Rev. B 92(7), 075307 (2015).
[Crossref]

V. Villafañe, P. Soubelet, A. E. Bruchhausen, N. D. Lanzillotti-Kimura, B. Jusserand, A. Lemaître, and A. Fainstein, “Slow light and slow acoustic phonons in optophononic resonators,” Phys. Rev. B 94(20), 205308 (2016).
[Crossref]

N. D. Lanzillotti-Kimura, A. Fainstein, A. Lemaitre, B. Jusserand, and B. Perrin, “Coherent control of sub-terahertz confined acoustic nanowaves: theory and experiments,” Phys. Rev. B 84(11), 115453 (2011).
[Crossref]

Phys. Rev. B Condens. Matter (1)

J. E. Raynolds, Z. H. Levine, and J. W. Wilkins, “Strain-induced birefringence in GaAs,” Phys. Rev. B Condens. Matter 51(16), 10477–10488 (1995).
[Crossref] [PubMed]

Phys. Rev. Lett. (11)

X. Ding, Y. He, Z.-C. Duan, N. Gregersen, M.-C. Chen, S. Unsleber, S. Maier, C. Schneider, M. Kamp, S. Höfling, C. Y. Lu, and J. W. Pan, “On-demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar,” Phys. Rev. Lett. 116(2), 020401 (2016).
[Crossref] [PubMed]

A. Dousse, L. Lanco, J. Suffczyński, E. Semenova, A. Miard, A. Lemaître, I. Sagnes, C. Roblin, J. Bloch, and P. Senellart, “Controlled light-matter coupling for a single quantum dot embedded in a pillar microcavity using far-field optical lithography,” Phys. Rev. Lett. 101(26), 267404 (2008).
[Crossref] [PubMed]

A. Fainstein, N. D. Lanzillotti-Kimura, B. Jusserand, and B. Perrin, “Strong optical-mechanical coupling in a vertical GaAs/AlAs microcavity for subterahertz phonons and near-infrared light,” Phys. Rev. Lett. 110(3), 037403 (2013).
[Crossref] [PubMed]

T. Jacqmin, I. Carusotto, I. Sagnes, M. Abbarchi, D. D. Solnyshkov, G. Malpuech, E. Galopin, A. Lemaître, J. Bloch, and A. Amo, “Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons,” Phys. Rev. Lett. 112(11), 116402 (2014).
[Crossref] [PubMed]

D. Bajoni, P. Senellart, E. Wertz, I. Sagnes, A. Miard, A. Lemaître, and J. Bloch, “Polariton laser using single micropillar GaAs-GaAlAs semiconductor cavities,” Phys. Rev. Lett. 100(4), 047401 (2008).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1 Optomechanical pillar microcavity. (a) Schematics of the micropillar structure, formed by two distributed Bragg reflectors (DBR) embedding a spacer. The number of periods in the shown DBRs is arbitrary. (b) Modulus square of the electric field distribution in a 10 periods/DBR resonator of 1.5 μm radius with a λ/2 cavity, for a mode of 921 nm of optical wavelength. (c) Modulus square of the mechanical displacement distribution corresponding to the confined acoustic mode at a resonance frequency of 18.2 GHz. Note the vertical modulation matching the one shown in (b), in addition to the radial modulation due to the free surface boundary condition. (d) Modulus of the volumetric strain. For these numerical simulations, the micropillar is considered without any GaAs substrate.
Fig. 2
Fig. 2 Dependence of the fundamental confined optical and acoustic mode frequencies on the radius of the micropillar. (a) Optical dependence showing a monotonic increase of the frequency as the radius is reduced. (b) Multiple anticrossings in the mechanical dependence originating from the coupling of vertical and radial modes due to the Poisson’s ratio. The red line is a guide to the eye to show the dependence of the frequency with the radius of the micropillars, at the center of the branches.
Fig. 3
Fig. 3 Dependence of the mechanical modes frequencies on the radius of a uniform GaAs cylinder. Curves A and B correspond to the vertical and radial mode, respectively, when ν = 0. Curves C and D correspond to the coupled hybrid vertical-radial modes (ν ≠0). Case C (D) is a breathing (volume conservative) mode. The displacement profiles are plotted for a structure of 75 nm of radius.
Fig. 4
Fig. 4 (a) Dependence of the fundamental mechanical frequency of a micropillar on the radius. (b) Fraction of radial energy in the mechanical eigenmode as a function of the radius for 10 and 20 pairs (N) of GaAs/AlAs in the DBRs. (c) and (d) show the Q-factor as a function of the radius for N = 10 and N = 20. For the 20 periods case a maximum Q-factor of ~8000 is reached. (e) Optomechanical coupling g0 as function of the radius, reaching a maximum of about 106 rad/s. Notice the strong dependence of these magnitudes near the extremes of the plotted branch.

Equations (3)

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σ zz = σ zφ = σ zr =0 at z=0 and z=2H σ rr = σ rφ = σ rz =0 at the cylindrical surface (r=R)
u z,k cos(kz) u r,q q J 1 (qr)
α= pillar 1 2 × ω 2 × | u r | 2 ×ρ×dV pillar 1 2 × ω 2 × | u | 2 ×ρ×dV

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