Abstract

Observation of quantized vortices in non-equilibrium polariton condensates has been reported either by spontaneous formation and pinning in the presence of disorder or by imprinting them onto the signal or idler of an optical parametric oscillator (OPO). Here, we report a detailed analysis of the creation and annihilation of polariton vortex-antivortex pairs in the signal state of a polariton OPO by means of a short optical Gaussian pulse at a certain finite pump wave-vector. A time-resolved, interferometric analysis of the emission allows us to extract the phase of the perturbed condensate and to reveal the dynamics of the supercurrents created by the pulsed probe. This flow is responsible for the appearance of the topological defects when counter-propagating to the underlying currents of the OPO signal.

© 2012 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  28. G. Tosi, F. M. Marchetti, D. Sanvitto, C. Antón, M. H. Szymańska, A. Berceanu, C. Tejedor, L. Marrucci, A. Lemaître, J. Bloch, and L. Viña, “Onset and dynamics of vortex-antivortex pairs in polariton optical parametric oscillator superfluids,” Phys. Rev. Lett. 107, 036401 (2011).
    [CrossRef] [PubMed]
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    [CrossRef]
  30. The detuning δ is defined as the difference between the bare cavity mode, EC, and exciton, EX, energies at k = 0.
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  32. For the supercurrent calculations, eventual phase jumps between 0 and 2π, where the gradient of the phase is not well defined, (see, for example the region between the white arrows in the Fig. 3(a)), are circumvented using ∇Φs (r,t) = −i∇ exp(iΦs (r,t)) / exp (iΦs (r,t)).

2012 (1)

M. Sich, D. N. Krizhanovskii, M. S. Skolnick, A. V. Gorbach, R. Hartley, D. V. Skryabin, E. A. Cerda-Méndez, K. Biermann, R. Hey, and P. V. Santos, “Observation of bright polariton solitons in a semiconductor microcavity,” Nat. Photonics 6, 50–55 (2012).
[CrossRef]

2011 (6)

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science 332, 1167–1170 (2011).
[CrossRef] [PubMed]

G. Grosso, G. Nardin, F. Morier-Genoud, Y. Léger, and B. Deveaud-Plédran, “Soliton instabilities and vortex street formation in a polariton quantum fluid,” Phys. Rev. Lett. 107, 245301 (2011).
[CrossRef]

G. Nardin, G. Grosso, Y. Léger, B. Piȩtka, F. Morier-Genoud, and B. Deveaud-Plédran, “Hydrodynamic nucleation of quantized vortex pairs in a polariton quantum fluid,” Nat. Phys. 7, 635–641 (2011).
[CrossRef]

F. Manni, K. G. Lagoudakis, B. Piȩtka, L. Fontanesi, M. Wouters, V. Savona, R. André, and B. Deveaud-Plédran, “Polariton condensation in a one-dimensional disordered potential,” Phys. Rev. Lett. 106, 176401 (2011).
[CrossRef] [PubMed]

K. G. Lagoudakis, F. Manni, B. Piȩtka, M. Wouters, T. C. H. Liew, V. Savona, A. V. Kavokin, R. André, and B. Deveaud-Plédran, “Probing the dynamics of spontaneous quantum vortices in polariton superfluids,” Phys. Rev. Lett. 106, 115301 (2011).
[CrossRef] [PubMed]

G. Tosi, F. M. Marchetti, D. Sanvitto, C. Antón, M. H. Szymańska, A. Berceanu, C. Tejedor, L. Marrucci, A. Lemaître, J. Bloch, and L. Viña, “Onset and dynamics of vortex-antivortex pairs in polariton optical parametric oscillator superfluids,” Phys. Rev. Lett. 107, 036401 (2011).
[CrossRef] [PubMed]

2010 (5)

M. O. Borgh, J. Keeling, and N. G. Berloff, “Spatial pattern formation and polarization dynamics of a nonequilibrium spinor polariton condensate,” Phys. Rev. B 81, 235302 (2010).
[CrossRef]

D. N. Krizhanovskii, D. M. Whittaker, R. A. Bradley, K. Guda, D. Sarkar, D. Sanvitto, L. Viña, E. Cerda, P. Santos, K. Biermann, R. Hey, and M. S. Skolnick, “Effect of interactions on vortices in a nonequilibrium polariton condensate,” Phys. Rev. Lett. 104, 126402 (2010).
[CrossRef] [PubMed]

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lematre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nature Phys. 6, 527–533 (2010).
[CrossRef]

G. Tosi, M. Baudisch, D. Sanvitto, L. Viña, A Lemaître, J. Bloch, E. Karimi, B. Piccirillo, and L. Marrucci, “Optical induced vortices and persistent currents in polariton condensates,” J. Phys.: Conf. Ser. 210, 012023 (2010).
[CrossRef]

G. Roumpos, M. D. Fraser, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, “Single vortex-antivortex pair in an exciton-polariton condensate,” Nat. Phys. 7, 129–133 (2010).
[CrossRef]

2009 (4)

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and L. S. Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B 80, 045317 (2009).
[CrossRef]

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature (London) 457, 291–295 (2009).
[CrossRef]

A. Amo, J. Lefrère, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
[CrossRef]

K. G. Lagoudakis, T. Ostatnický, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 326, 974–976 (2009).
[CrossRef] [PubMed]

2008 (2)

J. Keeling and N. G. Berloff, “Spontaneous rotating vortex lattices in a pumped decaying condensate,” Phys. Rev. Lett. 100, 250401 (2008).
[CrossRef] [PubMed]

K. G. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. André, L. S. Dang, and B. Deveaud-Plédran, “Quantized vortices in an exciton-polariton condensate,” Nat. Phys. 4, 706–710 (2008).
[CrossRef]

2006 (2)

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L. S. Dang, “Bose-Einstein condensation of exciton polaritons,” Nature (London) 443, 409–412 (2006).
[CrossRef]

M. Wouters and I. Carusotto, “Absence of long-range coherence in the parametric emission of photonic wires,” Phys. Rev. B 74, 245316 (2006).
[CrossRef]

2005 (2)

I. Carusotto and C. Ciuti, “Spontaneous microcavity-polariton coherence across the parametric threshold: quantum Monte Carlo studies,” Phys. Rev. B 72, 125335 (2005).
[CrossRef]

M. Perrin, P. Senellart, A. Lemaître, and J. Bloch, “Polariton relaxation in semiconductor microcavities: Efficiency of electron-polariton scattering,” Phys. Rev. B 72, 075340 (2005).
[CrossRef]

2004 (1)

1995 (1)

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose-Einstein condensation in a dilute atomic vapor,” Science 269(5221), 198–201 (1995).
[CrossRef] [PubMed]

1992 (1)

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69, 3314–3317 (1992).
[CrossRef] [PubMed]

1949 (1)

L. Onsager, “Statistical hidrodynamics,” Nuovo Cimento 6(Suppl. 2), 279–287 (1949).
[CrossRef]

Adrados, C.

A. Amo, J. Lefrère, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
[CrossRef]

Amo, A.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science 332, 1167–1170 (2011).
[CrossRef] [PubMed]

A. Amo, J. Lefrère, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
[CrossRef]

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature (London) 457, 291–295 (2009).
[CrossRef]

Anderson, M. H.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose-Einstein condensation in a dilute atomic vapor,” Science 269(5221), 198–201 (1995).
[CrossRef] [PubMed]

André, R.

F. Manni, K. G. Lagoudakis, B. Piȩtka, L. Fontanesi, M. Wouters, V. Savona, R. André, and B. Deveaud-Plédran, “Polariton condensation in a one-dimensional disordered potential,” Phys. Rev. Lett. 106, 176401 (2011).
[CrossRef] [PubMed]

K. G. Lagoudakis, F. Manni, B. Piȩtka, M. Wouters, T. C. H. Liew, V. Savona, A. V. Kavokin, R. André, and B. Deveaud-Plédran, “Probing the dynamics of spontaneous quantum vortices in polariton superfluids,” Phys. Rev. Lett. 106, 115301 (2011).
[CrossRef] [PubMed]

K. G. Lagoudakis, T. Ostatnický, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 326, 974–976 (2009).
[CrossRef] [PubMed]

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and L. S. Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B 80, 045317 (2009).
[CrossRef]

K. G. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. André, L. S. Dang, and B. Deveaud-Plédran, “Quantized vortices in an exciton-polariton condensate,” Nat. Phys. 4, 706–710 (2008).
[CrossRef]

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L. S. Dang, “Bose-Einstein condensation of exciton polaritons,” Nature (London) 443, 409–412 (2006).
[CrossRef]

Antón, C.

G. Tosi, F. M. Marchetti, D. Sanvitto, C. Antón, M. H. Szymańska, A. Berceanu, C. Tejedor, L. Marrucci, A. Lemaître, J. Bloch, and L. Viña, “Onset and dynamics of vortex-antivortex pairs in polariton optical parametric oscillator superfluids,” Phys. Rev. Lett. 107, 036401 (2011).
[CrossRef] [PubMed]

Arakawa, Y.

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69, 3314–3317 (1992).
[CrossRef] [PubMed]

Baas, A.

K. G. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. André, L. S. Dang, and B. Deveaud-Plédran, “Quantized vortices in an exciton-polariton condensate,” Nat. Phys. 4, 706–710 (2008).
[CrossRef]

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L. S. Dang, “Bose-Einstein condensation of exciton polaritons,” Nature (London) 443, 409–412 (2006).
[CrossRef]

Ballarini, D.

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature (London) 457, 291–295 (2009).
[CrossRef]

Baudisch, M.

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lematre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nature Phys. 6, 527–533 (2010).
[CrossRef]

G. Tosi, M. Baudisch, D. Sanvitto, L. Viña, A Lemaître, J. Bloch, E. Karimi, B. Piccirillo, and L. Marrucci, “Optical induced vortices and persistent currents in polariton condensates,” J. Phys.: Conf. Ser. 210, 012023 (2010).
[CrossRef]

Baumberg, J. J.

A. Kavokin, J. J. Baumberg, G. Malpuech, and F. P. Laussy, Microcavities (Oxford University Press, 2007).
[CrossRef]

Berceanu, A.

G. Tosi, F. M. Marchetti, D. Sanvitto, C. Antón, M. H. Szymańska, A. Berceanu, C. Tejedor, L. Marrucci, A. Lemaître, J. Bloch, and L. Viña, “Onset and dynamics of vortex-antivortex pairs in polariton optical parametric oscillator superfluids,” Phys. Rev. Lett. 107, 036401 (2011).
[CrossRef] [PubMed]

Berloff, N. G.

M. O. Borgh, J. Keeling, and N. G. Berloff, “Spatial pattern formation and polarization dynamics of a nonequilibrium spinor polariton condensate,” Phys. Rev. B 81, 235302 (2010).
[CrossRef]

J. Keeling and N. G. Berloff, “Spontaneous rotating vortex lattices in a pumped decaying condensate,” Phys. Rev. Lett. 100, 250401 (2008).
[CrossRef] [PubMed]

Biermann, K.

M. Sich, D. N. Krizhanovskii, M. S. Skolnick, A. V. Gorbach, R. Hartley, D. V. Skryabin, E. A. Cerda-Méndez, K. Biermann, R. Hey, and P. V. Santos, “Observation of bright polariton solitons in a semiconductor microcavity,” Nat. Photonics 6, 50–55 (2012).
[CrossRef]

D. N. Krizhanovskii, D. M. Whittaker, R. A. Bradley, K. Guda, D. Sarkar, D. Sanvitto, L. Viña, E. Cerda, P. Santos, K. Biermann, R. Hey, and M. S. Skolnick, “Effect of interactions on vortices in a nonequilibrium polariton condensate,” Phys. Rev. Lett. 104, 126402 (2010).
[CrossRef] [PubMed]

Bloch, J.

G. Tosi, F. M. Marchetti, D. Sanvitto, C. Antón, M. H. Szymańska, A. Berceanu, C. Tejedor, L. Marrucci, A. Lemaître, J. Bloch, and L. Viña, “Onset and dynamics of vortex-antivortex pairs in polariton optical parametric oscillator superfluids,” Phys. Rev. Lett. 107, 036401 (2011).
[CrossRef] [PubMed]

G. Tosi, M. Baudisch, D. Sanvitto, L. Viña, A Lemaître, J. Bloch, E. Karimi, B. Piccirillo, and L. Marrucci, “Optical induced vortices and persistent currents in polariton condensates,” J. Phys.: Conf. Ser. 210, 012023 (2010).
[CrossRef]

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lematre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nature Phys. 6, 527–533 (2010).
[CrossRef]

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature (London) 457, 291–295 (2009).
[CrossRef]

M. Perrin, P. Senellart, A. Lemaître, and J. Bloch, “Polariton relaxation in semiconductor microcavities: Efficiency of electron-polariton scattering,” Phys. Rev. B 72, 075340 (2005).
[CrossRef]

Blu, T.

Borgh, M. O.

M. O. Borgh, J. Keeling, and N. G. Berloff, “Spatial pattern formation and polarization dynamics of a nonequilibrium spinor polariton condensate,” Phys. Rev. B 81, 235302 (2010).
[CrossRef]

Bradley, R. A.

D. N. Krizhanovskii, D. M. Whittaker, R. A. Bradley, K. Guda, D. Sarkar, D. Sanvitto, L. Viña, E. Cerda, P. Santos, K. Biermann, R. Hey, and M. S. Skolnick, “Effect of interactions on vortices in a nonequilibrium polariton condensate,” Phys. Rev. Lett. 104, 126402 (2010).
[CrossRef] [PubMed]

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and L. S. Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B 80, 045317 (2009).
[CrossRef]

Bramati, A.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science 332, 1167–1170 (2011).
[CrossRef] [PubMed]

A. Amo, J. Lefrère, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
[CrossRef]

Carusotto, I.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science 332, 1167–1170 (2011).
[CrossRef] [PubMed]

A. Amo, J. Lefrère, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
[CrossRef]

K. G. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. André, L. S. Dang, and B. Deveaud-Plédran, “Quantized vortices in an exciton-polariton condensate,” Nat. Phys. 4, 706–710 (2008).
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M. Wouters and I. Carusotto, “Absence of long-range coherence in the parametric emission of photonic wires,” Phys. Rev. B 74, 245316 (2006).
[CrossRef]

I. Carusotto and C. Ciuti, “Spontaneous microcavity-polariton coherence across the parametric threshold: quantum Monte Carlo studies,” Phys. Rev. B 72, 125335 (2005).
[CrossRef]

Cerda, E.

D. N. Krizhanovskii, D. M. Whittaker, R. A. Bradley, K. Guda, D. Sarkar, D. Sanvitto, L. Viña, E. Cerda, P. Santos, K. Biermann, R. Hey, and M. S. Skolnick, “Effect of interactions on vortices in a nonequilibrium polariton condensate,” Phys. Rev. Lett. 104, 126402 (2010).
[CrossRef] [PubMed]

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M. Sich, D. N. Krizhanovskii, M. S. Skolnick, A. V. Gorbach, R. Hartley, D. V. Skryabin, E. A. Cerda-Méndez, K. Biermann, R. Hey, and P. V. Santos, “Observation of bright polariton solitons in a semiconductor microcavity,” Nat. Photonics 6, 50–55 (2012).
[CrossRef]

Ciuti, C.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science 332, 1167–1170 (2011).
[CrossRef] [PubMed]

A. Amo, J. Lefrère, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
[CrossRef]

I. Carusotto and C. Ciuti, “Spontaneous microcavity-polariton coherence across the parametric threshold: quantum Monte Carlo studies,” Phys. Rev. B 72, 125335 (2005).
[CrossRef]

Cornell, E. A.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose-Einstein condensation in a dilute atomic vapor,” Science 269(5221), 198–201 (1995).
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R. Spano, J. Cuadra, C. Lingg, D. Sanvitto, M. D. Martín, P. R. Eastham, M. van der Poel, J. M. Hvam, and L. Viña, “Build up of off-diagonal long-range order in microcavity exciton-polaritons across the parametric threshold,” arXiv:1111.4894 (2011).

Dang, L. S.

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and L. S. Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B 80, 045317 (2009).
[CrossRef]

K. G. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. André, L. S. Dang, and B. Deveaud-Plédran, “Quantized vortices in an exciton-polariton condensate,” Nat. Phys. 4, 706–710 (2008).
[CrossRef]

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L. S. Dang, “Bose-Einstein condensation of exciton polaritons,” Nature (London) 443, 409–412 (2006).
[CrossRef]

del Valle, E.

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature (London) 457, 291–295 (2009).
[CrossRef]

Deveaud, B.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L. S. Dang, “Bose-Einstein condensation of exciton polaritons,” Nature (London) 443, 409–412 (2006).
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Deveaud-Plédran, B.

G. Grosso, G. Nardin, F. Morier-Genoud, Y. Léger, and B. Deveaud-Plédran, “Soliton instabilities and vortex street formation in a polariton quantum fluid,” Phys. Rev. Lett. 107, 245301 (2011).
[CrossRef]

G. Nardin, G. Grosso, Y. Léger, B. Piȩtka, F. Morier-Genoud, and B. Deveaud-Plédran, “Hydrodynamic nucleation of quantized vortex pairs in a polariton quantum fluid,” Nat. Phys. 7, 635–641 (2011).
[CrossRef]

F. Manni, K. G. Lagoudakis, B. Piȩtka, L. Fontanesi, M. Wouters, V. Savona, R. André, and B. Deveaud-Plédran, “Polariton condensation in a one-dimensional disordered potential,” Phys. Rev. Lett. 106, 176401 (2011).
[CrossRef] [PubMed]

K. G. Lagoudakis, F. Manni, B. Piȩtka, M. Wouters, T. C. H. Liew, V. Savona, A. V. Kavokin, R. André, and B. Deveaud-Plédran, “Probing the dynamics of spontaneous quantum vortices in polariton superfluids,” Phys. Rev. Lett. 106, 115301 (2011).
[CrossRef] [PubMed]

K. G. Lagoudakis, T. Ostatnický, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 326, 974–976 (2009).
[CrossRef] [PubMed]

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and L. S. Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B 80, 045317 (2009).
[CrossRef]

K. G. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. André, L. S. Dang, and B. Deveaud-Plédran, “Quantized vortices in an exciton-polariton condensate,” Nat. Phys. 4, 706–710 (2008).
[CrossRef]

Eastham, P. R.

R. Spano, J. Cuadra, C. Lingg, D. Sanvitto, M. D. Martín, P. R. Eastham, M. van der Poel, J. M. Hvam, and L. Viña, “Build up of off-diagonal long-range order in microcavity exciton-polaritons across the parametric threshold,” arXiv:1111.4894 (2011).

Ensher, J. R.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose-Einstein condensation in a dilute atomic vapor,” Science 269(5221), 198–201 (1995).
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Fontanesi, L.

F. Manni, K. G. Lagoudakis, B. Piȩtka, L. Fontanesi, M. Wouters, V. Savona, R. André, and B. Deveaud-Plédran, “Polariton condensation in a one-dimensional disordered potential,” Phys. Rev. Lett. 106, 176401 (2011).
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Forchel, A.

G. Roumpos, M. D. Fraser, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, “Single vortex-antivortex pair in an exciton-polariton condensate,” Nat. Phys. 7, 129–133 (2010).
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Fraser, M. D.

G. Roumpos, M. D. Fraser, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, “Single vortex-antivortex pair in an exciton-polariton condensate,” Nat. Phys. 7, 129–133 (2010).
[CrossRef]

Giacobino, E.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science 332, 1167–1170 (2011).
[CrossRef] [PubMed]

A. Amo, J. Lefrère, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
[CrossRef]

Gorbach, A. V.

M. Sich, D. N. Krizhanovskii, M. S. Skolnick, A. V. Gorbach, R. Hartley, D. V. Skryabin, E. A. Cerda-Méndez, K. Biermann, R. Hey, and P. V. Santos, “Observation of bright polariton solitons in a semiconductor microcavity,” Nat. Photonics 6, 50–55 (2012).
[CrossRef]

Grosso, G.

G. Grosso, G. Nardin, F. Morier-Genoud, Y. Léger, and B. Deveaud-Plédran, “Soliton instabilities and vortex street formation in a polariton quantum fluid,” Phys. Rev. Lett. 107, 245301 (2011).
[CrossRef]

G. Nardin, G. Grosso, Y. Léger, B. Piȩtka, F. Morier-Genoud, and B. Deveaud-Plédran, “Hydrodynamic nucleation of quantized vortex pairs in a polariton quantum fluid,” Nat. Phys. 7, 635–641 (2011).
[CrossRef]

Guda, K.

D. N. Krizhanovskii, D. M. Whittaker, R. A. Bradley, K. Guda, D. Sarkar, D. Sanvitto, L. Viña, E. Cerda, P. Santos, K. Biermann, R. Hey, and M. S. Skolnick, “Effect of interactions on vortices in a nonequilibrium polariton condensate,” Phys. Rev. Lett. 104, 126402 (2010).
[CrossRef] [PubMed]

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and L. S. Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B 80, 045317 (2009).
[CrossRef]

Hartley, R.

M. Sich, D. N. Krizhanovskii, M. S. Skolnick, A. V. Gorbach, R. Hartley, D. V. Skryabin, E. A. Cerda-Méndez, K. Biermann, R. Hey, and P. V. Santos, “Observation of bright polariton solitons in a semiconductor microcavity,” Nat. Photonics 6, 50–55 (2012).
[CrossRef]

Hey, R.

M. Sich, D. N. Krizhanovskii, M. S. Skolnick, A. V. Gorbach, R. Hartley, D. V. Skryabin, E. A. Cerda-Méndez, K. Biermann, R. Hey, and P. V. Santos, “Observation of bright polariton solitons in a semiconductor microcavity,” Nat. Photonics 6, 50–55 (2012).
[CrossRef]

D. N. Krizhanovskii, D. M. Whittaker, R. A. Bradley, K. Guda, D. Sarkar, D. Sanvitto, L. Viña, E. Cerda, P. Santos, K. Biermann, R. Hey, and M. S. Skolnick, “Effect of interactions on vortices in a nonequilibrium polariton condensate,” Phys. Rev. Lett. 104, 126402 (2010).
[CrossRef] [PubMed]

Hivet, R.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science 332, 1167–1170 (2011).
[CrossRef] [PubMed]

Höfling, S.

G. Roumpos, M. D. Fraser, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, “Single vortex-antivortex pair in an exciton-polariton condensate,” Nat. Phys. 7, 129–133 (2010).
[CrossRef]

Houdré, R.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science 332, 1167–1170 (2011).
[CrossRef] [PubMed]

A. Amo, J. Lefrère, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
[CrossRef]

Hvam, J. M.

R. Spano, J. Cuadra, C. Lingg, D. Sanvitto, M. D. Martín, P. R. Eastham, M. van der Poel, J. M. Hvam, and L. Viña, “Build up of off-diagonal long-range order in microcavity exciton-polaritons across the parametric threshold,” arXiv:1111.4894 (2011).

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C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69, 3314–3317 (1992).
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J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L. S. Dang, “Bose-Einstein condensation of exciton polaritons,” Nature (London) 443, 409–412 (2006).
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Karimi, E.

G. Tosi, M. Baudisch, D. Sanvitto, L. Viña, A Lemaître, J. Bloch, E. Karimi, B. Piccirillo, and L. Marrucci, “Optical induced vortices and persistent currents in polariton condensates,” J. Phys.: Conf. Ser. 210, 012023 (2010).
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Kasprzak, J.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L. S. Dang, “Bose-Einstein condensation of exciton polaritons,” Nature (London) 443, 409–412 (2006).
[CrossRef]

Kavokin, A.

A. Kavokin, J. J. Baumberg, G. Malpuech, and F. P. Laussy, Microcavities (Oxford University Press, 2007).
[CrossRef]

Kavokin, A. V.

K. G. Lagoudakis, F. Manni, B. Piȩtka, M. Wouters, T. C. H. Liew, V. Savona, A. V. Kavokin, R. André, and B. Deveaud-Plédran, “Probing the dynamics of spontaneous quantum vortices in polariton superfluids,” Phys. Rev. Lett. 106, 115301 (2011).
[CrossRef] [PubMed]

K. G. Lagoudakis, T. Ostatnický, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 326, 974–976 (2009).
[CrossRef] [PubMed]

Keeling, J.

M. O. Borgh, J. Keeling, and N. G. Berloff, “Spatial pattern formation and polarization dynamics of a nonequilibrium spinor polariton condensate,” Phys. Rev. B 81, 235302 (2010).
[CrossRef]

J. Keeling and N. G. Berloff, “Spontaneous rotating vortex lattices in a pumped decaying condensate,” Phys. Rev. Lett. 100, 250401 (2008).
[CrossRef] [PubMed]

Keeling, J. M. J.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L. S. Dang, “Bose-Einstein condensation of exciton polaritons,” Nature (London) 443, 409–412 (2006).
[CrossRef]

Krizhanovskii, D. N.

M. Sich, D. N. Krizhanovskii, M. S. Skolnick, A. V. Gorbach, R. Hartley, D. V. Skryabin, E. A. Cerda-Méndez, K. Biermann, R. Hey, and P. V. Santos, “Observation of bright polariton solitons in a semiconductor microcavity,” Nat. Photonics 6, 50–55 (2012).
[CrossRef]

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lematre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nature Phys. 6, 527–533 (2010).
[CrossRef]

D. N. Krizhanovskii, D. M. Whittaker, R. A. Bradley, K. Guda, D. Sarkar, D. Sanvitto, L. Viña, E. Cerda, P. Santos, K. Biermann, R. Hey, and M. S. Skolnick, “Effect of interactions on vortices in a nonequilibrium polariton condensate,” Phys. Rev. Lett. 104, 126402 (2010).
[CrossRef] [PubMed]

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and L. S. Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B 80, 045317 (2009).
[CrossRef]

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature (London) 457, 291–295 (2009).
[CrossRef]

Kundermann, S.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L. S. Dang, “Bose-Einstein condensation of exciton polaritons,” Nature (London) 443, 409–412 (2006).
[CrossRef]

Lagoudakis, K. G.

F. Manni, K. G. Lagoudakis, B. Piȩtka, L. Fontanesi, M. Wouters, V. Savona, R. André, and B. Deveaud-Plédran, “Polariton condensation in a one-dimensional disordered potential,” Phys. Rev. Lett. 106, 176401 (2011).
[CrossRef] [PubMed]

K. G. Lagoudakis, F. Manni, B. Piȩtka, M. Wouters, T. C. H. Liew, V. Savona, A. V. Kavokin, R. André, and B. Deveaud-Plédran, “Probing the dynamics of spontaneous quantum vortices in polariton superfluids,” Phys. Rev. Lett. 106, 115301 (2011).
[CrossRef] [PubMed]

K. G. Lagoudakis, T. Ostatnický, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 326, 974–976 (2009).
[CrossRef] [PubMed]

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and L. S. Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B 80, 045317 (2009).
[CrossRef]

K. G. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. André, L. S. Dang, and B. Deveaud-Plédran, “Quantized vortices in an exciton-polariton condensate,” Nat. Phys. 4, 706–710 (2008).
[CrossRef]

Laussy, F. P.

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lematre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nature Phys. 6, 527–533 (2010).
[CrossRef]

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature (London) 457, 291–295 (2009).
[CrossRef]

A. Kavokin, J. J. Baumberg, G. Malpuech, and F. P. Laussy, Microcavities (Oxford University Press, 2007).
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Lefrère, J.

A. Amo, J. Lefrère, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
[CrossRef]

Léger, Y.

G. Nardin, G. Grosso, Y. Léger, B. Piȩtka, F. Morier-Genoud, and B. Deveaud-Plédran, “Hydrodynamic nucleation of quantized vortex pairs in a polariton quantum fluid,” Nat. Phys. 7, 635–641 (2011).
[CrossRef]

G. Grosso, G. Nardin, F. Morier-Genoud, Y. Léger, and B. Deveaud-Plédran, “Soliton instabilities and vortex street formation in a polariton quantum fluid,” Phys. Rev. Lett. 107, 245301 (2011).
[CrossRef]

Lemaître, A

G. Tosi, M. Baudisch, D. Sanvitto, L. Viña, A Lemaître, J. Bloch, E. Karimi, B. Piccirillo, and L. Marrucci, “Optical induced vortices and persistent currents in polariton condensates,” J. Phys.: Conf. Ser. 210, 012023 (2010).
[CrossRef]

Lemaître, A.

G. Tosi, F. M. Marchetti, D. Sanvitto, C. Antón, M. H. Szymańska, A. Berceanu, C. Tejedor, L. Marrucci, A. Lemaître, J. Bloch, and L. Viña, “Onset and dynamics of vortex-antivortex pairs in polariton optical parametric oscillator superfluids,” Phys. Rev. Lett. 107, 036401 (2011).
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M. Perrin, P. Senellart, A. Lemaître, and J. Bloch, “Polariton relaxation in semiconductor microcavities: Efficiency of electron-polariton scattering,” Phys. Rev. B 72, 075340 (2005).
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Lematre, A.

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lematre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nature Phys. 6, 527–533 (2010).
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G. Tosi, M. Baudisch, D. Sanvitto, L. Viña, A Lemaître, J. Bloch, E. Karimi, B. Piccirillo, and L. Marrucci, “Optical induced vortices and persistent currents in polariton condensates,” J. Phys.: Conf. Ser. 210, 012023 (2010).
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D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and L. S. Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B 80, 045317 (2009).
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K. G. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. André, L. S. Dang, and B. Deveaud-Plédran, “Quantized vortices in an exciton-polariton condensate,” Nat. Phys. 4, 706–710 (2008).
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G. Roumpos, M. D. Fraser, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, “Single vortex-antivortex pair in an exciton-polariton condensate,” Nat. Phys. 7, 129–133 (2010).
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K. G. Lagoudakis, T. Ostatnický, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 326, 974–976 (2009).
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A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science 332, 1167–1170 (2011).
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D. N. Krizhanovskii, D. M. Whittaker, R. A. Bradley, K. Guda, D. Sarkar, D. Sanvitto, L. Viña, E. Cerda, P. Santos, K. Biermann, R. Hey, and M. S. Skolnick, “Effect of interactions on vortices in a nonequilibrium polariton condensate,” Phys. Rev. Lett. 104, 126402 (2010).
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M. Sich, D. N. Krizhanovskii, M. S. Skolnick, A. V. Gorbach, R. Hartley, D. V. Skryabin, E. A. Cerda-Méndez, K. Biermann, R. Hey, and P. V. Santos, “Observation of bright polariton solitons in a semiconductor microcavity,” Nat. Photonics 6, 50–55 (2012).
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Sanvitto, D.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science 332, 1167–1170 (2011).
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G. Tosi, F. M. Marchetti, D. Sanvitto, C. Antón, M. H. Szymańska, A. Berceanu, C. Tejedor, L. Marrucci, A. Lemaître, J. Bloch, and L. Viña, “Onset and dynamics of vortex-antivortex pairs in polariton optical parametric oscillator superfluids,” Phys. Rev. Lett. 107, 036401 (2011).
[CrossRef] [PubMed]

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lematre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nature Phys. 6, 527–533 (2010).
[CrossRef]

D. N. Krizhanovskii, D. M. Whittaker, R. A. Bradley, K. Guda, D. Sarkar, D. Sanvitto, L. Viña, E. Cerda, P. Santos, K. Biermann, R. Hey, and M. S. Skolnick, “Effect of interactions on vortices in a nonequilibrium polariton condensate,” Phys. Rev. Lett. 104, 126402 (2010).
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G. Tosi, M. Baudisch, D. Sanvitto, L. Viña, A Lemaître, J. Bloch, E. Karimi, B. Piccirillo, and L. Marrucci, “Optical induced vortices and persistent currents in polariton condensates,” J. Phys.: Conf. Ser. 210, 012023 (2010).
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A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature (London) 457, 291–295 (2009).
[CrossRef]

R. Spano, J. Cuadra, C. Lingg, D. Sanvitto, M. D. Martín, P. R. Eastham, M. van der Poel, J. M. Hvam, and L. Viña, “Build up of off-diagonal long-range order in microcavity exciton-polaritons across the parametric threshold,” arXiv:1111.4894 (2011).

Sarkar, D.

D. N. Krizhanovskii, D. M. Whittaker, R. A. Bradley, K. Guda, D. Sarkar, D. Sanvitto, L. Viña, E. Cerda, P. Santos, K. Biermann, R. Hey, and M. S. Skolnick, “Effect of interactions on vortices in a nonequilibrium polariton condensate,” Phys. Rev. Lett. 104, 126402 (2010).
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F. Manni, K. G. Lagoudakis, B. Piȩtka, L. Fontanesi, M. Wouters, V. Savona, R. André, and B. Deveaud-Plédran, “Polariton condensation in a one-dimensional disordered potential,” Phys. Rev. Lett. 106, 176401 (2011).
[CrossRef] [PubMed]

K. G. Lagoudakis, F. Manni, B. Piȩtka, M. Wouters, T. C. H. Liew, V. Savona, A. V. Kavokin, R. André, and B. Deveaud-Plédran, “Probing the dynamics of spontaneous quantum vortices in polariton superfluids,” Phys. Rev. Lett. 106, 115301 (2011).
[CrossRef] [PubMed]

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L. S. Dang, “Bose-Einstein condensation of exciton polaritons,” Nature (London) 443, 409–412 (2006).
[CrossRef]

Senellart, P.

M. Perrin, P. Senellart, A. Lemaître, and J. Bloch, “Polariton relaxation in semiconductor microcavities: Efficiency of electron-polariton scattering,” Phys. Rev. B 72, 075340 (2005).
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Sich, M.

M. Sich, D. N. Krizhanovskii, M. S. Skolnick, A. V. Gorbach, R. Hartley, D. V. Skryabin, E. A. Cerda-Méndez, K. Biermann, R. Hey, and P. V. Santos, “Observation of bright polariton solitons in a semiconductor microcavity,” Nat. Photonics 6, 50–55 (2012).
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Skolnick, M. S.

M. Sich, D. N. Krizhanovskii, M. S. Skolnick, A. V. Gorbach, R. Hartley, D. V. Skryabin, E. A. Cerda-Méndez, K. Biermann, R. Hey, and P. V. Santos, “Observation of bright polariton solitons in a semiconductor microcavity,” Nat. Photonics 6, 50–55 (2012).
[CrossRef]

D. N. Krizhanovskii, D. M. Whittaker, R. A. Bradley, K. Guda, D. Sarkar, D. Sanvitto, L. Viña, E. Cerda, P. Santos, K. Biermann, R. Hey, and M. S. Skolnick, “Effect of interactions on vortices in a nonequilibrium polariton condensate,” Phys. Rev. Lett. 104, 126402 (2010).
[CrossRef] [PubMed]

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lematre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nature Phys. 6, 527–533 (2010).
[CrossRef]

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and L. S. Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B 80, 045317 (2009).
[CrossRef]

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature (London) 457, 291–295 (2009).
[CrossRef]

Skryabin, D. V.

M. Sich, D. N. Krizhanovskii, M. S. Skolnick, A. V. Gorbach, R. Hartley, D. V. Skryabin, E. A. Cerda-Méndez, K. Biermann, R. Hey, and P. V. Santos, “Observation of bright polariton solitons in a semiconductor microcavity,” Nat. Photonics 6, 50–55 (2012).
[CrossRef]

Spano, R.

R. Spano, J. Cuadra, C. Lingg, D. Sanvitto, M. D. Martín, P. R. Eastham, M. van der Poel, J. M. Hvam, and L. Viña, “Build up of off-diagonal long-range order in microcavity exciton-polaritons across the parametric threshold,” arXiv:1111.4894 (2011).

Staehli, J. L.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L. S. Dang, “Bose-Einstein condensation of exciton polaritons,” Nature (London) 443, 409–412 (2006).
[CrossRef]

Szymanska, M. H.

G. Tosi, F. M. Marchetti, D. Sanvitto, C. Antón, M. H. Szymańska, A. Berceanu, C. Tejedor, L. Marrucci, A. Lemaître, J. Bloch, and L. Viña, “Onset and dynamics of vortex-antivortex pairs in polariton optical parametric oscillator superfluids,” Phys. Rev. Lett. 107, 036401 (2011).
[CrossRef] [PubMed]

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lematre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nature Phys. 6, 527–533 (2010).
[CrossRef]

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L. S. Dang, “Bose-Einstein condensation of exciton polaritons,” Nature (London) 443, 409–412 (2006).
[CrossRef]

F. M. Marchetti and M. H. Szymańska, “Vortices in polariton OPO superfluids,” arXiv:1107.4487 (2012).

Tejedor, C.

G. Tosi, F. M. Marchetti, D. Sanvitto, C. Antón, M. H. Szymańska, A. Berceanu, C. Tejedor, L. Marrucci, A. Lemaître, J. Bloch, and L. Viña, “Onset and dynamics of vortex-antivortex pairs in polariton optical parametric oscillator superfluids,” Phys. Rev. Lett. 107, 036401 (2011).
[CrossRef] [PubMed]

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lematre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nature Phys. 6, 527–533 (2010).
[CrossRef]

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature (London) 457, 291–295 (2009).
[CrossRef]

Tosi, G.

G. Tosi, F. M. Marchetti, D. Sanvitto, C. Antón, M. H. Szymańska, A. Berceanu, C. Tejedor, L. Marrucci, A. Lemaître, J. Bloch, and L. Viña, “Onset and dynamics of vortex-antivortex pairs in polariton optical parametric oscillator superfluids,” Phys. Rev. Lett. 107, 036401 (2011).
[CrossRef] [PubMed]

G. Tosi, M. Baudisch, D. Sanvitto, L. Viña, A Lemaître, J. Bloch, E. Karimi, B. Piccirillo, and L. Marrucci, “Optical induced vortices and persistent currents in polariton condensates,” J. Phys.: Conf. Ser. 210, 012023 (2010).
[CrossRef]

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lematre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nature Phys. 6, 527–533 (2010).
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Unser, M.

van der Poel, M.

R. Spano, J. Cuadra, C. Lingg, D. Sanvitto, M. D. Martín, P. R. Eastham, M. van der Poel, J. M. Hvam, and L. Viña, “Build up of off-diagonal long-range order in microcavity exciton-polaritons across the parametric threshold,” arXiv:1111.4894 (2011).

Viña, L.

G. Tosi, F. M. Marchetti, D. Sanvitto, C. Antón, M. H. Szymańska, A. Berceanu, C. Tejedor, L. Marrucci, A. Lemaître, J. Bloch, and L. Viña, “Onset and dynamics of vortex-antivortex pairs in polariton optical parametric oscillator superfluids,” Phys. Rev. Lett. 107, 036401 (2011).
[CrossRef] [PubMed]

D. N. Krizhanovskii, D. M. Whittaker, R. A. Bradley, K. Guda, D. Sarkar, D. Sanvitto, L. Viña, E. Cerda, P. Santos, K. Biermann, R. Hey, and M. S. Skolnick, “Effect of interactions on vortices in a nonequilibrium polariton condensate,” Phys. Rev. Lett. 104, 126402 (2010).
[CrossRef] [PubMed]

G. Tosi, M. Baudisch, D. Sanvitto, L. Viña, A Lemaître, J. Bloch, E. Karimi, B. Piccirillo, and L. Marrucci, “Optical induced vortices and persistent currents in polariton condensates,” J. Phys.: Conf. Ser. 210, 012023 (2010).
[CrossRef]

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lematre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nature Phys. 6, 527–533 (2010).
[CrossRef]

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature (London) 457, 291–295 (2009).
[CrossRef]

R. Spano, J. Cuadra, C. Lingg, D. Sanvitto, M. D. Martín, P. R. Eastham, M. van der Poel, J. M. Hvam, and L. Viña, “Build up of off-diagonal long-range order in microcavity exciton-polaritons across the parametric threshold,” arXiv:1111.4894 (2011).

Weisbuch, C.

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69, 3314–3317 (1992).
[CrossRef] [PubMed]

Whittaker, D. M.

D. N. Krizhanovskii, D. M. Whittaker, R. A. Bradley, K. Guda, D. Sarkar, D. Sanvitto, L. Viña, E. Cerda, P. Santos, K. Biermann, R. Hey, and M. S. Skolnick, “Effect of interactions on vortices in a nonequilibrium polariton condensate,” Phys. Rev. Lett. 104, 126402 (2010).
[CrossRef] [PubMed]

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and L. S. Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B 80, 045317 (2009).
[CrossRef]

Wieman, C. E.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose-Einstein condensation in a dilute atomic vapor,” Science 269(5221), 198–201 (1995).
[CrossRef] [PubMed]

Wouters, M.

F. Manni, K. G. Lagoudakis, B. Piȩtka, L. Fontanesi, M. Wouters, V. Savona, R. André, and B. Deveaud-Plédran, “Polariton condensation in a one-dimensional disordered potential,” Phys. Rev. Lett. 106, 176401 (2011).
[CrossRef] [PubMed]

K. G. Lagoudakis, F. Manni, B. Piȩtka, M. Wouters, T. C. H. Liew, V. Savona, A. V. Kavokin, R. André, and B. Deveaud-Plédran, “Probing the dynamics of spontaneous quantum vortices in polariton superfluids,” Phys. Rev. Lett. 106, 115301 (2011).
[CrossRef] [PubMed]

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and L. S. Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B 80, 045317 (2009).
[CrossRef]

K. G. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. André, L. S. Dang, and B. Deveaud-Plédran, “Quantized vortices in an exciton-polariton condensate,” Nat. Phys. 4, 706–710 (2008).
[CrossRef]

M. Wouters and I. Carusotto, “Absence of long-range coherence in the parametric emission of photonic wires,” Phys. Rev. B 74, 245316 (2006).
[CrossRef]

Yamamoto, Y.

G. Roumpos, M. D. Fraser, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, “Single vortex-antivortex pair in an exciton-polariton condensate,” Nat. Phys. 7, 129–133 (2010).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys.: Conf. Ser. (1)

G. Tosi, M. Baudisch, D. Sanvitto, L. Viña, A Lemaître, J. Bloch, E. Karimi, B. Piccirillo, and L. Marrucci, “Optical induced vortices and persistent currents in polariton condensates,” J. Phys.: Conf. Ser. 210, 012023 (2010).
[CrossRef]

Nat. Photonics (1)

M. Sich, D. N. Krizhanovskii, M. S. Skolnick, A. V. Gorbach, R. Hartley, D. V. Skryabin, E. A. Cerda-Méndez, K. Biermann, R. Hey, and P. V. Santos, “Observation of bright polariton solitons in a semiconductor microcavity,” Nat. Photonics 6, 50–55 (2012).
[CrossRef]

Nat. Phys. (4)

G. Nardin, G. Grosso, Y. Léger, B. Piȩtka, F. Morier-Genoud, and B. Deveaud-Plédran, “Hydrodynamic nucleation of quantized vortex pairs in a polariton quantum fluid,” Nat. Phys. 7, 635–641 (2011).
[CrossRef]

A. Amo, J. Lefrère, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
[CrossRef]

G. Roumpos, M. D. Fraser, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, “Single vortex-antivortex pair in an exciton-polariton condensate,” Nat. Phys. 7, 129–133 (2010).
[CrossRef]

K. G. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. André, L. S. Dang, and B. Deveaud-Plédran, “Quantized vortices in an exciton-polariton condensate,” Nat. Phys. 4, 706–710 (2008).
[CrossRef]

Nature (London) (2)

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L. S. Dang, “Bose-Einstein condensation of exciton polaritons,” Nature (London) 443, 409–412 (2006).
[CrossRef]

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature (London) 457, 291–295 (2009).
[CrossRef]

Nature Phys. (1)

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lematre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nature Phys. 6, 527–533 (2010).
[CrossRef]

Nuovo Cimento (1)

L. Onsager, “Statistical hidrodynamics,” Nuovo Cimento 6(Suppl. 2), 279–287 (1949).
[CrossRef]

Phys. Rev. B (5)

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and L. S. Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B 80, 045317 (2009).
[CrossRef]

I. Carusotto and C. Ciuti, “Spontaneous microcavity-polariton coherence across the parametric threshold: quantum Monte Carlo studies,” Phys. Rev. B 72, 125335 (2005).
[CrossRef]

M. Wouters and I. Carusotto, “Absence of long-range coherence in the parametric emission of photonic wires,” Phys. Rev. B 74, 245316 (2006).
[CrossRef]

M. O. Borgh, J. Keeling, and N. G. Berloff, “Spatial pattern formation and polarization dynamics of a nonequilibrium spinor polariton condensate,” Phys. Rev. B 81, 235302 (2010).
[CrossRef]

M. Perrin, P. Senellart, A. Lemaître, and J. Bloch, “Polariton relaxation in semiconductor microcavities: Efficiency of electron-polariton scattering,” Phys. Rev. B 72, 075340 (2005).
[CrossRef]

Phys. Rev. Lett. (7)

G. Tosi, F. M. Marchetti, D. Sanvitto, C. Antón, M. H. Szymańska, A. Berceanu, C. Tejedor, L. Marrucci, A. Lemaître, J. Bloch, and L. Viña, “Onset and dynamics of vortex-antivortex pairs in polariton optical parametric oscillator superfluids,” Phys. Rev. Lett. 107, 036401 (2011).
[CrossRef] [PubMed]

J. Keeling and N. G. Berloff, “Spontaneous rotating vortex lattices in a pumped decaying condensate,” Phys. Rev. Lett. 100, 250401 (2008).
[CrossRef] [PubMed]

K. G. Lagoudakis, F. Manni, B. Piȩtka, M. Wouters, T. C. H. Liew, V. Savona, A. V. Kavokin, R. André, and B. Deveaud-Plédran, “Probing the dynamics of spontaneous quantum vortices in polariton superfluids,” Phys. Rev. Lett. 106, 115301 (2011).
[CrossRef] [PubMed]

F. Manni, K. G. Lagoudakis, B. Piȩtka, L. Fontanesi, M. Wouters, V. Savona, R. André, and B. Deveaud-Plédran, “Polariton condensation in a one-dimensional disordered potential,” Phys. Rev. Lett. 106, 176401 (2011).
[CrossRef] [PubMed]

D. N. Krizhanovskii, D. M. Whittaker, R. A. Bradley, K. Guda, D. Sarkar, D. Sanvitto, L. Viña, E. Cerda, P. Santos, K. Biermann, R. Hey, and M. S. Skolnick, “Effect of interactions on vortices in a nonequilibrium polariton condensate,” Phys. Rev. Lett. 104, 126402 (2010).
[CrossRef] [PubMed]

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69, 3314–3317 (1992).
[CrossRef] [PubMed]

G. Grosso, G. Nardin, F. Morier-Genoud, Y. Léger, and B. Deveaud-Plédran, “Soliton instabilities and vortex street formation in a polariton quantum fluid,” Phys. Rev. Lett. 107, 245301 (2011).
[CrossRef]

Science (3)

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose-Einstein condensation in a dilute atomic vapor,” Science 269(5221), 198–201 (1995).
[CrossRef] [PubMed]

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science 332, 1167–1170 (2011).
[CrossRef] [PubMed]

K. G. Lagoudakis, T. Ostatnický, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 326, 974–976 (2009).
[CrossRef] [PubMed]

Other (6)

F. M. Marchetti and M. H. Szymańska, “Vortices in polariton OPO superfluids,” arXiv:1107.4487 (2012).

The detuning δ is defined as the difference between the bare cavity mode, EC, and exciton, EX, energies at k = 0.

For the supercurrent calculations, eventual phase jumps between 0 and 2π, where the gradient of the phase is not well defined, (see, for example the region between the white arrows in the Fig. 3(a)), are circumvented using ∇Φs (r,t) = −i∇ exp(iΦs (r,t)) / exp (iΦs (r,t)).

A. Kavokin, J. J. Baumberg, G. Malpuech, and F. P. Laussy, Microcavities (Oxford University Press, 2007).
[CrossRef]

R. Feynman, Progress in Low Temperature Physics (Elsevier, 1955), Vol. 1.
[CrossRef]

R. Spano, J. Cuadra, C. Lingg, D. Sanvitto, M. D. Martín, P. R. Eastham, M. van der Poel, J. M. Hvam, and L. Viña, “Build up of off-diagonal long-range order in microcavity exciton-polaritons across the parametric threshold,” arXiv:1111.4894 (2011).

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Figures (5)

Fig. 1
Fig. 1

Experimental lower-polariton-branch dispersion relation under non-resonant weak excitation conditions, energy versus in-plane k momentum. The blue-shifted conditions used for the OPO-pump and pulsed-probe are: pump laser Ep = 1.5283 eV and kp = 1.4 μm−1 (red ring); probe beam Es = 1.5268 eV either with kpb = 0 or kpb = 0.5 μm−1 (red/blue dashed arrows depict the corresponding pair-scattering process).

Fig. 2
Fig. 2

(a) Signal emission |s|2 recorded from the unexpanded interferometer arm, showing a typical vortex. (b) Interference pattern |s + r|2 with a fork-like dislocation that reveals the position of the vortex (white dotted line is a guide to the eye). (c) Extracted phase, Φs, with the Fourier procedure detailed in the text, black arrows schematically depict polariton circulation around the vortex core. The same sample position and scale are used for the three images. (d) Supercurrents stream-plot (orange arrows) of an unperturbed OPO-signal superimposed on its emission shown in a false color scale.

Fig. 3
Fig. 3

(a–d)/(e–h) Phase maps at different times after the probe disappearance for kpb = 0.5/kpb = 0 μm−1. Same false color scale for all plots from 0 to 2π. The white arrows in (a) point to a phase jump between 0 and 2π. The black curved arrows in (b,c) depict the circulation around the V and AV cores.

Fig. 4
Fig. 4

Supercurrents stream-plot superimposed on the gain at the OPO-signal (orange arrows). (a–d) Evolution of the polariton bullet at kpb = 0.5 μm−1. The dotted white line is a guide to the eye to follow the movement of the bullet. Spatial extension of each snapshot is 40 × 55 μm2. (e–h) Same as (a–d) for kpb = 0, the probe size is sketched by the dotted white line. Spatial extension of each snapshot is 40 × 40 μm2. The gain in each figure is rescaled according to its false color bar.

Fig. 5
Fig. 5

Time evolution of the mean supercurrents along the Y -direction under two probe configurations. Solid dots (open dots) correspond to kpb = 0.5 μm−1 (kpb = 0) with a dot-dashed (dashed) line as a guide to the eyes. The red gaussian peak depicts the 2 ps-pulsed probe arrival. The full black line indicates the value of the mean current along the Y -axis in the steady state OPO-signal (as obtained from Fig. 2(d)).

Equations (3)

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| s + r | 2 = ( | s | 2 + | r | 2 ) + s * r + r * s .
j ( r , t ) = h ¯ m | ( r , t ) | 2 Φ ( r , t ) = | ( r , t ) | 2 v s ( r , t ) ,
( Φ s ) y ( t ) 1 N x N y l , m = 1 N x , N y ( Φ s ( ( l , m ) , t ) ) y ,

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