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