Dynamical d-wave condensation of exciton–polaritons in a two-dimensional square-lattice potential

Abstract

Macroscopic order appears as the collective behaviour of many interacting particles. Prime examples are superfluidity in helium 1 , atomic Bose-Einstein condensation 2 , s-wave 3 and d-wave superconductivity 4 and metal-insulator transitions 5. Such physical properties are tightly linked to spin and charge degrees of freedom and are greatly enriched by orbital structures 6. Moreover, high-orbital states of bosons exhibit exotic orders distinct from the orders with real-valued bosonic ground states 7. Recently, a wide range of related phenomena have been studied using atom condensates in optical lattices 8-10 , but the experimental observation of highorbital orders has been limited to momentum space 11,12. Here we establish microcavity exciton-polariton condensates as a promising alternative for exploring high-orbital orders. We observe the formation of d-orbital condensates on a square lattice and characterize their coherence properties in terms of population distributions both in real and momentum space. Exciton-polaritons emerge from the strong light-matter coupling in semiconductor quantum wells embedded in a planar microcavity structure. They behave as degenerate Bose gases in the low-density and low-temperature limit 13. Exciton-polaritons have undergone a dynamic phase transition, in which a macroscopic number of particles are accumulated in the lowest-energy single-particle state with a long-range order 14-17. Owing to their very light effective mass, the phase transition temperatures of exciton-polaritons are eight to nine orders of magnitude higher than those of atomic Bose-Einstein condensates. Coherence properties of exciton-polariton condensates have been characterized by the direct optical access in spatial and momentum spaces 14-16,18. Modern solid-state physics has studied quantum many-body phenomena whose properties reflect exotic orbital nature, another intrinsic degree of freedom, which interplays with charge and spin degrees of freedom. Its energy degeneracy and spatial anisotropy generate rich dynamics in weakly interacting many-body systems. For example, a key role of d-orbital nature has been actively investigated in salient phenomena including metal-insulator transitions 5 , colossal magnetoresistance 6,19 , and recently discovered iron-pnictide superconductors 20,21. These orbital ordering phenomena originate from the strong correlation effects of electrons in the anisotropic degenerate d-orbitals. Theoretical modelling of such

Geometrically locked vortex lattices in semiconductor quantum fluids

“…This pump geometry thus provides a way to generate periodic 2D structures in polariton condensates, with no need of a built-in periodic potential 27 . The interacting topological defects move around on the dark lines in this square matrix, while quantized values of vortex charge can also be restricted to specific positions in this lattice (see Supplementary Fig.…”

Spin-Orbit Coupling for Photons and Polaritons in Microstructures

“…In combination with the strong spin-dependent interactions naturally present in microcavity-polariton devices and the possibility of scaling up to lattices of arbitrary geometry [16][17][18], the realization of such a coupling in semiconductor microcavities would open the way to the simulation of many-body effects in a new quantum optical context [19]. Some examples would be the controlled nucleation of fractional topological excitations [20,21], the formation of polarization patterns [22,23], the simulation of spin models using photons [24], topological insulation [25,26], or the generation of fractional quantum Hall states for light [27,28].…”

Polariton lasing in high-quality selenide-based micropillars in the strong coupling regime

“…4 Refined etching and microstructuring techniques have been developed for GaAs-based microcavity, allowing the fabrication of high quality micropillars, 5,6 mesas, 7 as well as advanced polaritonic circuits elements like waveguides, interferometers, optical gates, [8][9][10] and lattices with direct applications for quantum simulations. [11][12][13][14][15] This approach is likely to be successful in the upcoming years; however, for practical use, its drawback is to be stuck to cryogenic temperatures. A way around this problem is the use of large bandgap materials, where the exciton binding energy is larger, and hence stable at room temperature.…”