Exciton-polariton condensate in the van der Waals magnet CrSBr

Abstract

Van der Waals magnets are an emergent material class of paramount interest for fundamental studies in coupling light with matter excitations, which are uniquely linked to their underlying magnetic properties. Among these materials, the semiconducting magnet CrSBr is possibly a first playground where we can study simultaneously the interaction of photons, magnons, and excitons at the quantum level. Here we demonstrate a coherent macroscopic quantum phase, the bosonic condensation of exciton-polaritons, emerging in a CrSBr flake embedded in a fully tunable cryogenic open optical cavity. The Bose condensate is characterized by a highly non-linear threshold-like behavior, and coherence manifests distinctly via its first and second order quantum correlations. We find that the condensate's non-linearity is highly susceptible to the magnetic order in CrSBr. Specially, it can encounter a sign change from attractive to repulsive interactions when the intrinsic antiferromagnetic order transforms to the forced ferromagnetic order. Our findings open a route towards magnetically controllable quantum fluids of light, and optomagnonic devices where spin magnetism is coupled to on-chip Bose-Einstein condensates.

Figures (12)

• Figure 1: Exciton-polaritons of CrSBr in an external tunable cryogenic microcavity. (a) Schematics of the cryogenic open optical microcavity. Excitonic optical dipoles align to the in-plane crystallographic b-axis. (b) Schematics of the magnetic orders in CrSBr. The Cr, S and Br atoms are in blue, yellow and red colors, respectively. The green arrows indicate the intralayer net magnetization. Top panel: intrinsic anti-ferromagnetic (AFM) ground state below Néel temperature. Bottom panel: forced ferromagnetic (FM) order in an out-of-plane saturation field B$_{\mathrm{sat}}\sim$2 T. (c) bottom panel: PL measurement (black), and reflectivity (green) of a 312 nm thick CrSBr flake on the bottom DBR simulated by transfer matrix method with (green) and without (magenta) excitonic resonance (1.3655 eV). Six self-hybridized polariton states (P$_1$-P$_6$) are observed. Top panel: magneto-PL of P$_1$-P$_6$ in the bare flake. The spin canting is illustrated for a bilayer case. PL measurements with different cavity detunings (DC voltages) in (d) AFM order at 0 T and (e) FM order at 3 T. The superimposed lines are the fitting of the new polariton modes (solid), self-hybridized polaritons (dashed), and the cavity modes (dotted-dashed). The coupling strengths are summarized in Appendix B Table. I. The dots on LPBs mark the detunings for power dependent PL in Fig. 8. (f) PL spectra of the new polariton modes with same external cavity detuning marked by the white dots in (d) and (e).
• Figure 2: Stimulated polaritonic scattering at 0 T (AFM order). The threshold phenomena is clear around 20 mW pump power in (b). Note that the cavity length is slightly reduced relative to the scenarios in Fig. 1(d), to monitor the stimulated scattering in two consecutive longitudinal mode orders. An effective DC voltages above 60 V are thus used to characterize the detunings. The condensation phenomena into the LPBs with effective DC$\sim$32 V is more obvious for high pump densities.
• Figure 3: Pump power dependent PL measurements of the polariton modes in Fig. 1(f) for (a) AFM order (0 T, DC=44 V), and (b) FM order (3 T, DC=38 V). (c) Intensity, (d) linewidth, and (e) energy of the energetically lowest LPB mode in (a). (f) Intensity, (g) linewidth, and (h) energy of the energetically lowest LPB mode in (b). The Voigt fitting function yields the Gaussian (grey) and Lorentzian (red) linewidths as well as the full-width at half maxima (FWHM, blue). The error bars of the energy shifts in (e) and (h) are smaller than the symbol size. The experimentally measured polariton energy shifts that are the hollow dots in Figs. 8(a) and 8(b) are already corrected by removing the redshift of cavity thermal expansion due to increasing pump power (see Appendix C and D).
• Figure 4: Magnetic order dependent first-order correlation measurements of the exciton-polariton condensate. (a) Schematics of the Michelson interferometer. Spatial coherence measurements of the LPB in (b) AFM order and (c) FM order (spectra in Fig. 1(f)). Upper panels: power dependent spatial interference at zero-delay ($\Delta\tau=0$). Lower panels: calculated spatially-resolved first-order correlation function g$^{(1)}(\vec{r},0)$ at pump powers corresponding to the upper panels. The two dashed lines in the two bottom left graphs show a 6 $\mu$m confined region for vertical binning of g$^{(1)}(\vec{r},0)$, which is then fitted by a Gaussian function to extract the FWHM 'x$_c$' in the horizontal direction. (d) Magnetic order dependent coherence length $\lambda_c$=$\sqrt{\pi}x_c$.
• Figure 5: Magnetic order dependent second-order correlation measurements and simulations of the exciton-polariton condensate. (a) Schematics of the Hanbury Brown and Twiss setup. (b) Representative second-order correlation function measurements ${g^2(\tau)}$ of the LPBs in Fig. 1(f). The flat dashed lines at the unity mark the Poissonian level. (c) Experimental values and (d) numerical simulations of the power dependent second-order auto-correlation $\overline{g^2(0)}$ for AFM and FM orders. The simulation results are firstly averaged over independent 'numerical measurements' of $g^2(\tau)$ with corresponding standard derivation shown by the error bar. We then obtain $\overline{g^2(0)}$ by averaging $g^2(\tau)$ at the beginning of $200$ fs to account for the excitation pulse width in experiments. Typical averaged results of $g^2(\tau)$ are shown in Appendix F Figs. 12(c)-(f).