Quantized vortices in polariton Bose-Einstein Condensates

Friday 30 April 2010

Quantized vortices are observed in a Bose-Einstein condensate of excitonic polaritons in a semiconductor. They are visualized by phase-resolved imaging of a polariton gas condensed at 20 K in a CdTe-based microcavity. Here, in contrast to the case of the Bose-Einstein condensates in liquid 4He and dilute atomic gases, the vortices are generated in the condensate ground state, and are pinned at well defined positions.

Superfluidity, first reported in liquid 4He, has received much attention in dilute atom Bose-Einstein condensates (BECs), which offer unprecedented experimental control parameters. Thus quantized vortices, a defining signature of quantum fluids, have been generated in stirred three-dimensional atom BECs or thermally activated in quasi two-dimensional atom systems following the Berezinskii-Kosterlitz-Thouless phase transition. In the solid state, polariton BECs have recently been realized in planar CdTe-based microcavities [1]. Polaritons are mixed photon-exciton bosonic quasi-particles, naturally occurring in semiconductor microcavities operating in the strong light-matter coupling regime. We have shown that the ultra light polariton mass, about 5 orders of magnitude lighter than the electron mass, has allowed condensation at critical temperatures up to around 50 K.

We have probed the spatial correlations of the polariton condensate by overlapping the condensate luminescence image with its retro-reflected image (an image symmetric with respect to its center). For a vortex free condensate, i.e. with a spatially uniform phase, the nonzero angle between the two image beams would result into a system of parallel fringes, whose intensity contrast is directly related to the condensate first order correlation function g1(r, -r) [1]. In the presence of vortices, forklike dislocations would appear in the interferogram, as can be seen in the red circle in Fig. 1.

Fig. 1: Interference pattern observed by overlapping the condensate image and its retro-reflected image. Vortex appears as a forklike dislocation in the regular fringe pattern (inside the red circle).

Since a single fringe is missing in the dislocation, the vortex charge, e. g. the multiple integer of 2π phase variation around the vortex core, is unity. This is confirmed by mapping out the spatial phase of the condensate (inset of Fig.2), using a Fourier transform processing of the interferogram. As shown in Fig. 2, the phase is found to increase exactly by 2π along a closed loop around the vortex core, independently of the distance from the core. In spite of a poor spatial resolution of about 1 µm, we have checked that the polariton density is indeed lower at the vortex core.

It should be noted that, by contrast to liquid 4He and dilute atom Bose-Einstein condensates, polariton vortices are generated in the condensate ground state, without the need of stirring the condensate. Moreover their positions and signs do not fluctuate in time, which rules out the spontaneous formation of vortices by thermal fluctuations in the Berezinskii-Kosterlitz-Thouless regime of two-dimensional BECs. Using a generalised Gross-Pitaevskii equation, we show that the deterministic vortices observed here results from the combined effect of the very short polariton lifetime (about 10-12 s) and the photonic disorder in the microcavity. The continuous pumping, required to overcome radiative decay losses, generates a constant flow of incoming polaritons within the disorder potential landscape. Depending on the details of the disorder potential, this non-equilibrium flow pattern may exhibit vortex singularities in the condensed regime. How these disorder-induced vortices are related to superfluidity in non-equilibrium BECs is yet to be understood.

[1] Kasprzak et al., Nature 443, 409 (2006)

Fig.2. Phase of the polariton condensate along closed loops (cf. the circles in the inset) around the vortex shown in Fig.1, at different distances from the core. Inset displays the 2D spatial phase around the vortex represented in false color. Circles are circulation loops used in the main plot.

Further readings: "Quantized Vortices in an Exciton-Polariton Condensate" K. G. Lagoudakis et al., Nature Physics 4, 706 (2008), in collaboration with EPFL (Switzerland) and the Universita di Trento (Italy).

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