Coupled counterrotating polariton condensates in optically defined annular potentials

Abstract

Polariton condensates are macroscopic quantum states formed by half-matter half-light quasiparticles, thus connecting the phenomena of atomic Bose-Einstein condensation, superfluidity, and photon lasing. Here we report the spontaneous formation of such condensates in programmable potential landscapes generated by two concentric circles of light. The imposed geometry supports the emergence of annular states that extend up to 100 μm, yet are fully coherent and exhibit a spatial structure that remains stable for minutes at a time. These states exhibit a petal-like intensity distribution arising due to the interaction of two superfluids counterpropagating in the circular waveguide defined by the optical potential. In stark contrast to annular modes in conventional lasing systems, the resulting standing wave patterns exhibit only minimal overlap with the pump laser itself. We theoretically describe the system using a complex Ginzburg-Landau equation, which indicates why the condensate wants to rotate. Experimentally, we demonstrate the ability to precisely control the structure of the petal condensates both by carefully modifying the excitation geometry as well as perturbing the system on ultrafast timescales to reveal unexpected superfluid dynamics.

Keywords: BEC; SQUID; interferometer; rings.

Fig. 1.

Petal-shaped polariton condensates. (A–D) Spatial images and spectra (horizontal cut at $y=0$) of annular states with increasing azimuthal index $l$. The shaded rings in C indicate the position of the pump laser. (E) Double-ring with radial index $p=1$. (F) Schematic of the experimental setup showing the phase-shaped pump laser and the resulting polariton emission. (G) Phase of the condensate wavefunction in B, extracted following the method discussed in ref. . As constant reference, one of the lobes was magnified and superimposed over the whole image. (H–K) Real- and k-space images of a petal state with $l=10$. The k-space image in K is obtained by spatially filtering the polariton emission, as shown in I.

Fig. 2.

Sample luminescence with increasing excitation power. (A–C) Spatial image of the polariton emission with increasing pumping power. Dashed blue line indicates the position of the laser as shown in C. (D and E) Power dependence of the intensity distribution along a central horizontal cut.

Fig. 3.

(A) Measured number of lobes n (green points) and spatial separation between lobes (black points) as a function of condensate radius $r_c$. Fits are obtained from simulations of the cGL equation for different pump radii (SI Appendix, SI Text 6) or the analytic expression for the density maximum of LG modes (SI Appendix, Eq. S4). (B) Simulated spatial density of a petal condensate with $n=20$ lobes and (C) corresponding phase. (D) Horizontal cut of B, indicating the relative position of the condensate and the pumping profile.

Fig. 4.

Time dynamics of a perturbed petal condensate. (A) Cylinder projection of the polariton emission around the condensate annulus at different times t. The perturbing pulse $P$ arrives at t = 0 ps. (Insets) Spatial images of the condensate ring at t = 0 ps and t = 54 ps. Dotted lines indicate the position of space cuts depicted in B and time cuts depicted in C. Dashed line is a guide to the eye. (Insets) Spatial images at different times.