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Spin-Orbit Coupling for Photons and Polaritons in Microstructures

Sala, V. G., Solnyshkov, D. D., Carusotto, I., Jacqmin, T., Lemaître, A., Terças, H., Nalitov, A., Abbarchi, M., Galopin, E., Sagnes, I., Bloch, J., Malpuech, G., Amo, A.·2015·Physical Review X
DOI 10.1103/physrevx.5.011034
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FIG. 1 Photonic molecular states. (a) Scanning electron microscope image of the polaritonic molecule. (b) Polarization-insensitive emission spectrum in momentum space at kx ¼ 0 . 2 μ mandlowexcitation power (7 mW), showing the four molecular states E ð 0 Þ ; … ; E ð 3 Þ arising from the coupling of the lowest energy mode of each single micropillar. (c) Scheme of the phase winding of the eigenfunctions of the E ð l Þ states without accounting for the spin. (d) Measured polarization-insensitive real-space emission. (e) Interference pattern and (f) extracted phase for each of the individual emission lines. The solid arrow points the pillar used for the phase reference in the interference experiment. (g) Measured polarization-insensitive momentum-space emission. (h) Simulated momentum-space emission obtained by Fourier transforming the tight-binding model eigenfunctions with a Gaussian distribution over each lobe.
FIG. 1 Photonic molecular states. (a) Scanning electron microscope image of the polaritonic molecule. (b) Polarization-insensitive emission spectrum in momentum space at kx ¼ 0 . 2 μ mandlowexcitation power (7 mW), showing the four molecular states E ð 0 Þ ; … ; E ð 3 Þ arising from the coupling of the lowest energy mode of each single micropillar. (c) Scheme of the phase winding of the eigenfunctions of the E ð l Þ states without accounting for the spin. (d) Measured polarization-insensitive real-space emission. (e) Interference pattern and (f) extracted phase for each of the individual emission lines. The solid arrow points the pillar used for the phase reference in the interference experiment. (g) Measured polarization-insensitive momentum-space emission. (h) Simulated momentum-space emission obtained by Fourier transforming the tight-binding model eigenfunctions with a Gaussian distribution over each lobe.CC-BY · From the PDF
Image 2
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FIG. 3 Power dependence of the condensation process. (a) -(f) Energy- and momentum-resolved emission of the molecule as a function of the excitation power, indicated in each panel. At low power (a), the E ð 0 Þ ; … ; E ð 3 Þ energy levels are visible along with higher energy states (above the dashed line) arising from the coupling of higher energy modes of each individual pillar [32]. When increasing the excitation power, polariton condensation occurs first in one of the states of the multiplet E ð 2 Þ (c) and then in one of the states of the multiplet E ð 1 Þ (e,f). In (d), the double line in E ð 2 Þ arises from fluctuations in the position of the pump spot during the measurement (see Sec. E of Ref. [32]). These fluctuations were absent in the experiments shown in Figs. 4 and 5. (g) Emitted intensity of the E ð 1 Þ and E ð 2 Þ states as a function of the excitation power. The circles indicate the power at which the experiments shown in Figs. 4 and 5 were performed.
FIG. 3 Power dependence of the condensation process. (a) -(f) Energy- and momentum-resolved emission of the molecule as a function of the excitation power, indicated in each panel. At low power (a), the E ð 0 Þ ; … ; E ð 3 Þ energy levels are visible along with higher energy states (above the dashed line) arising from the coupling of higher energy modes of each individual pillar [32]. When increasing the excitation power, polariton condensation occurs first in one of the states of the multiplet E ð 2 Þ (c) and then in one of the states of the multiplet E ð 1 Þ (e,f). In (d), the double line in E ð 2 Þ arises from fluctuations in the position of the pump spot during the measurement (see Sec. E of Ref. [32]). These fluctuations were absent in the experiments shown in Figs. 4 and 5. (g) Emitted intensity of the E ð 1 Þ and E ð 2 Þ states as a function of the excitation power. The circles indicate the power at which the experiments shown in Figs. 4 and 5 were performed.CC-BY · From the PDF
FIG. 4 Condensation in the k ¼ 0 state of the E ð 1 Þ manifold. (a,b) Real space emission in the σ þ and σ -circular polarizations for a polariton condensate in the state j ψ lower ð k ¼ 0 Þi , at a pumping intensity of 84 mW. Each polarization component contains a vortical current in the clockwise ( σ þ ) and counterclockwise ( σ -) directions, evidenced in the forklike dislocations apparent in the interferometric measurements shown in (c) and (d), respectively, and in the extracted phase gradients in (e) and (f). The phase changes from 0 to ∓ 2 π when circumventing the molecule. (g) The green traces show the plane of linear polarization of the emission measured locally, superimposed to the total emitted intensity of the molecule. The condensate shows azimuthal linear polarization. Solid lines depict the contour of the microstructure. (h) Spatially resolved emission spectrum.
FIG. 4 Condensation in the k ¼ 0 state of the E ð 1 Þ manifold. (a,b) Real space emission in the σ þ and σ -circular polarizations for a polariton condensate in the state j ψ lower ð k ¼ 0 Þi , at a pumping intensity of 84 mW. Each polarization component contains a vortical current in the clockwise ( σ þ ) and counterclockwise ( σ -) directions, evidenced in the forklike dislocations apparent in the interferometric measurements shown in (c) and (d), respectively, and in the extracted phase gradients in (e) and (f). The phase changes from 0 to ∓ 2 π when circumventing the molecule. (g) The green traces show the plane of linear polarization of the emission measured locally, superimposed to the total emitted intensity of the molecule. The condensate shows azimuthal linear polarization. Solid lines depict the contour of the microstructure. (h) Spatially resolved emission spectrum.CC-BY · From the PDF
FIG. 5 Condensation in the k ¼ 3 state of the E ð 2 Þ manifold. (a,b) Real space emission in the σ þ and σ -circular polarizations for a polariton condensate in the state j ψ lower ð k ¼ 3 Þi , at 25 mW. Each polarization component contains a vortical current of double phase charge in the counterclockwise ( σ þ ) and clockwise ( σ -) directions, evidenced in the double forklike dislocations apparent in the interferometric measurements shown in (c) and (d), respectively, and in the extracted phase gradients in (e) and (f). The phase changes from 0 to  4 π when circumventing the molecule. (g) The green traces show the plane of linear polarization of the emission measured locally, superimposed to the total emitted intensity of the molecule. At the center of each micropillar, the condensate shows a linear polarization pattern pointing radially. Solid lines depict the contour of the microstructure. (h) Spatially resolved emission spectrum.
FIG. 5 Condensation in the k ¼ 3 state of the E ð 2 Þ manifold. (a,b) Real space emission in the σ þ and σ -circular polarizations for a polariton condensate in the state j ψ lower ð k ¼ 3 Þi , at 25 mW. Each polarization component contains a vortical current of double phase charge in the counterclockwise ( σ þ ) and clockwise ( σ -) directions, evidenced in the double forklike dislocations apparent in the interferometric measurements shown in (c) and (d), respectively, and in the extracted phase gradients in (e) and (f). The phase changes from 0 to  4 π when circumventing the molecule. (g) The green traces show the plane of linear polarization of the emission measured locally, superimposed to the total emitted intensity of the molecule. At the center of each micropillar, the condensate shows a linear polarization pattern pointing radially. Solid lines depict the contour of the microstructure. (h) Spatially resolved emission spectrum.CC-BY · From the PDF

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Citations

Cites

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Metadata

Authors
Sala, V. G., Solnyshkov, D. D., Carusotto, I., Jacqmin, T., Lemaître, A., Terças, H., Nalitov, A., Abbarchi, M., Galopin, E., Sagnes, I., Bloch, J., Malpuech, G., & Amo, A.
Venue
Physical Review X
Publisher
American Physical Society (APS)
Published
2015-03-25
Volume
5
Issue
1
ISSN
2160-3308
DOI
10.1103/physrevx.5.011034
Cited by
172
References
9
Language
en
Licence
creativecommons.org/licenses/by/3.0/ (vor)
Funders
  • Agence Nationale de la Recherche (ANR-11-BS10-001, ANR-11-LABX-0014)
  • Seventh Framework Programme (235114, 289968, 246912)
  • European Research Council
  • French RENATECH
  • RTRA Triangle de la Physique
  • POLATOM ESF Network
  • Nanosaclay Labex

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