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Mean-Field Description of Multicomponent Exciton-Polariton Superfluids

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Physics of Quantum Fluids

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 177))

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Abstract

This is a review of spin-dependent (polarization) properties of multicomponent exciton-polariton condensates in conditions when quasi-equilibrium mean-field Gross-Pitaevskii description can be applied. Mainly two-component (spin states ±1) polariton condensates are addressed, but some properties of four-component exciton condensates, having both the bright (spin ±1) and the dark (spin ±2) components, are discussed. Change of polarization state of the condensate and phase transitions in applied Zeeman field are described. The properties of fractional vortices are given, in particular, I present recent results on the warping of the field around half-vortices in the presence of longitudinal-transverse splitting of bare polariton bands, and discuss the geometrical features of warped half-vortices (in the framework of the lemon, monstar, and star classification).

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Notes

  1. 1.

    The concentration of quasiparticles with the energy ϵ(k) is given by ∫(2π)−2[exp{ϵ(k)/T}−1]−1 d 2 k and the integral diverges logarithmically for small k when ϵ(k)∝k 2.

  2. 2.

    The case of the total spin 1 is irrelevant since the orbital wave function of colliding bosons is antisymmetric and it cannot be realized within the condensate.

  3. 3.

    Note, however, that this does not imply that a single vortex gives an absolute minimum of the H in the corresponding topological sector. For example, the integer vortex (1,0) can be unstable with respect to decay into the pair of \(({\frac{1}{2}},{\frac{1}{2}})\) and \(({\frac{1}{2}},-{\frac{1}{2}})\) half-vortices for m l <m t (see Sect. 4.3.2).

  4. 4.

    The tangents of polarization lines define by the direction of the main axis of polarization ellipse in each point.

  5. 5.

    Note that for the monstar all polarization lines residing within the sector −ϕ m <ϕ<ϕ m terminate in the vortex center, but only three of them are straight, i.e., are having nonzero inclination at r→0 (see [37] for the details).

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Acknowledgements

This work was supported in part by DGAPA-UNAM under the project No. IN112310 and by the EU FP7 IRSES project POLAPHEN.

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Authors and Affiliations

  1. Instituto de Energías Renovables, Universidad Nacional Autónoma de México, Temixco, Morelos, 62580, Mexico

    Y. G. Rubo

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  1. Y. G. Rubo
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Correspondence to Y. G. Rubo .

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Editors and Affiliations

  1. Université Pierre et Marie Curie, Place Jussieu 4, Paris, 75005, France

    Alberto Bramati

  2. del Pais Vasco, UPV/EHU, Dpto. de Fisica Téorica e Historia, IKERBASQUE & Universidad, Apdo. 644, Bilbao, 48080, Spain

    Michele Modugno

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Rubo, Y.G. (2013). Mean-Field Description of Multicomponent Exciton-Polariton Superfluids. In: Bramati, A., Modugno, M. (eds) Physics of Quantum Fluids. Springer Series in Solid-State Sciences, vol 177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37569-9_4

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