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] [PubMed]
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    [CrossRef]
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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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  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

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. Photonics6, 50–55 (2012).
[CrossRef]

2011

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,” Science332, 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

M. O. Borgh, J. Keeling, and N. G. Berloff, “Spatial pattern formation and polarization dynamics of a nonequilibrium spinor polariton condensate,” Phys. Rev. B81, 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

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. B80, 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,” Science326, 974–976 (2009).
[CrossRef] [PubMed]

2008

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

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. B74, 245316 (2006).
[CrossRef]

2005

I. Carusotto and C. Ciuti, “Spontaneous microcavity-polariton coherence across the parametric threshold: quantum Monte Carlo studies,” Phys. Rev. B72, 125335 (2005).
[CrossRef]

M. Perrin, P. Senellart, A. Lemaître, and J. Bloch, “Polariton relaxation in semiconductor microcavities: Efficiency of electron-polariton scattering,” Phys. Rev. B72, 075340 (2005).
[CrossRef]

2004

1995

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,” Science269(5221), 198–201 (1995).
[CrossRef] [PubMed]

1992

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

L. Onsager, “Statistical hidrodynamics,” Nuovo Cimento6(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,” Science332, 1167–1170 (2011).
[CrossRef] [PubMed]

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]

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,” Science269(5221), 198–201 (1995).
[CrossRef] [PubMed]

André, R.

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, 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. B80, 045317 (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,” Science326, 974–976 (2009).
[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]

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).

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. B81, 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. Photonics6, 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]

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]

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. B72, 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. B81, 235302 (2010).
[CrossRef]

Bradley, R. A.

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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,” Science332, 1167–1170 (2011).
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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,” Science332, 1167–1170 (2011).
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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).
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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. B80, 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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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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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,” Science326, 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,” Science332, 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. Photonics6, 50–55 (2012).
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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,” Science332, 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]

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. 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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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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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]

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. B72, 075340 (2005).
[CrossRef]

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. Photonics6, 50–55 (2012).
[CrossRef]

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. Photonics6, 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]

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]

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. B80, 045317 (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. Photonics6, 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]

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]

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. 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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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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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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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).

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

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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