The magnetic europium chalcogenide semiconductors EuTe and EuSe are investigated by the spectroscopy of second harmonic generation ͑SHG͒ in the vicinity of the optical band gap formed by transitions involving the 4f and 5d electronic orbitals of the magnetic Eu 2+ ions. In these materials with centrosymmetric crystal lattice the electric-dipole SHG process is symmetry forbidden so that no signal is observed in zero magnetic field. Signal appears, however, in applied magnetic field with the SHG intensity being proportional to the square of magnetization. The magnetic field and temperature dependencies of the induced SHG allow us to introduce a type of nonlinear optical susceptibility determined by the magnetic-dipole contribution in combination with a spontaneous or induced magnetization. The experimental results can be described qualitatively by a phenomenological model based on a symmetry analysis and are in good quantitative agreement with microscopic model calculations accounting for details of the electronic energy and spin structure.
We have experimentally observed an eddy current of exciton polaritons arising in a cylindrical GaAs/AlGaAs pillar microcavity under the nonresonant optical pumping. The polariton current manifests itself in a MachZehnder interferometry image as a characteristic spiral that occurs due to the interference of the light emitted by an exciton-polariton condensate with a reference spherical wave. We have experimentally observed the condensates with the topological charges m = +1, m = −1, and m = −2. The interference pattern corresponding to the m = −2 current represents the twin spiral emerging from the center of the micropillar. The switching between the current modes with different topological charges is achieved by a weak displacement of the pump spot.
We observe condensation of exciton polaritons in quantum states composed of concentric rings when exciting cylindrical pillar GaAs/AlGaAs microcavities non-resonantly by a focused laser beam normally incident at the center of the pillar. The number of rings depends on the pumping intensity and the pillar size, and may achieve 5 in the pillar of 40 µm diameter. Breaking the axial symmetry when moving the excitation spot away from the pillar center leads to transformation of the rings into a number of bright lobes corresponding to quantum states with nonzero angular momenta. The number of lobes, their shape and location are dependent on the spot position.We describe the out-of-equilibrium condensation of polaritons in the states with different principal quantum numbers and angular momenta with a formalism based on Boltzmann-Gross-Pitaevskii equations accounting for repulsion of polaritons from the exciton reservoir formed at the excitation spot and their spatial confinement by the pillar boundary. PACS numbers: 71.36.+c, 73.20.Mf, 78.45.+h, 78.67.-n I. INTRODUCTION. Exciton-polaritons are mixed light-matter quasiparticles that appear due to excitonphoton coupling in semiconductor crystal structures [1, 2]. They are composite bosons and demonstrate characteristic bosonic effects, in particular, stimulated scattering [3] and Bose-Einstein condensation [4, 5]. These effects are at the origin of polariton lasing which is manifested by spontaneous generation of coherent and monochromatic light by a many-body coherent state: condensate of exciton-polaritons [6, 7]. Polariton lasers are promising for applications in opto-electronics and information technologies [8]. From the point of view of fundamental physics, they represent a unique laboratory for studies of coherent many-body quantum systems. The microscopic size of polariton condensates (typically, 0.01 ÷ 0.1 mm)allows studying their shapes by optical spectroscopy methods. Another important aspect of polariton condensation is that it does not necessarily take place in the ground state. Very clear evidences of polariton condensation in excited states were given in Refs. [9][10][11]. The non-resonant optical pumping creates an excitonic reservoir localized under the excitation spot. In the mean-field approximation, the interactions of excitons from the reservoir and exciton-polaritons from the condensate may be accounted for by introducing an effective repulsive potential acting upon the polaritons [10,12,13], which pushes polaritons away from the pump spot. Exploiting this effect, in the recent years, several groups reported shaping of polariton condensates in optical traps [14,15], strain induced traps [16], laterally patterned microcavity structures realized by etching [10,[17][18][19], or metal deposition [20,21].A pattern formation in exciton-polariton condensates has been observed by several groups [18,22,23]. In particular, formation of ring condensates with large angular momenta has been demonstrated in etched rings microcavities[24] and using optically created...
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