Exciton-polariton condensate in the van der Waals magnet CrSBr

The gist: The study demonstrates 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, revealing an intriguing new kind of tunable polariton non-linearity driven by the excitation of incoherent magnons.

Exciton-Polariton System and Magnetic Order

The research investigates the interplay between light-matter coupling and magnetic order in the van der Waals magnet CrSBr, which is possibly a first playground where we can study simultaneously the interaction of photons, magnons, and excitons at the quantum level The material CrSBr is of specific interest due to its ambient stability and semiconducting properties The magnetic ground state below the Néel temperature is represented by an A-type interlayer antiferromagnetic (AFM) order In AFM phase, excitons are strongly confined within the individual layer due to spin-forbidden interlayer charge transfer The magnetic order can be controlled by strain and hydrostatic pressure Out-of-plane magnetic fields can force the system into a parallel spin configuration of staggered ferromagnetic (FM) order The exciton energy changes drastically with the interlayer hybridization In presence of external magnetic fields, the excitonic landscape is further modulated by magnons, which emerge in the system and have recently been observed in pumpprobe studies First reports have verified the emergence of strongly coupled excitonpolaritons in bare CrSBr slabs However, these studies were performed in the linear regime, where exciton correlations can be widely neglected in the dilute polariton gas.

Tunable Non-linearity and Magnetic Control

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 This opens a route towards magnetically controllable quantum fluids of light, and optomagnonic devices where spin magnetism is coupled to on-chip Bose-Einstein condensates. The emergent exciton-polariton condensate is evidenced by the threshold-like emission output, and distinct via its first and second order coherence The interplay of the condensate with the magnetic order yields an intriguingly new kind of tunable polariton non-linearity that is driven by the excitation of incoherent magnons The exciton-polaritons in CrSBr show attractive and repulsive interactions in the AFM and FM orders, respectively, which might further be manipulated to trigger the formation of polaritonic droplet phase.

Experimental Setup and Measurement

For our study, we utilize a thin CrSBr flake, which we prepare via exfoliation and subsequent dry transfer on a SiO2/TiO2 distributed Bragg reflector (DBR) The thickness of the slab is determined as 312 ± 2 nm via atomic force microscopy measurements The optical transitions subject to our study thus need to be analyzed in a polaritonic picture. We use a cryogenic tunable optical microcavity with a high quality factor to acquire the necessary in-situ control of the light-matter composition of CrSBr excitonpolaritons for the transition to the non-linear regime of polariton condensation. The emergent exciton-polariton condensate is evidenced by the threshold-like emission output, and distinct via its first and second order coherence.

Magnetic Order Dependent Non-linearities

The energy shifts of the LPBs are then fitted and summarized in Figs. 9(a)-(b) For all detuning cases in the AFM order, the LPB firstly experience a moderate linear redshift, and then a giant blueshift follows until the condensate depletes However, for the detuning cases in the FM order, the energy slope of LPB at low pump powers changes sign from moderate redshift to moderate blueshift In high power regime, the LPBs have giant blueshifts for both magnetic orders and all cavity detuning scenarios. The maximum blue shift is +2.3 meV in Fig. 2(h)

Coherence and Correlation Measurements

First-order spatio-temporal coherence was measured via a Michelson interferometer The emergent interference fringes, which evolve with the polariton density, can be used to deduce the first-order spatio-temporal coherence. We see a clear development of the characteristic spatial interference fringes with the polariton density for the AFM and FM orders in the upper panels of Fig. 4(b) and Fig. 4(c), respectively, which translates to the emergence of first-order correlation that clearly enhances with the excitation power. The condensate in AFM order reaches a maximum coherence length λc= 5.1 µm at a pump power of ∼30 mW, while the condensate in FM order reaches its maximum λc= 4.8 µm much earlier at ∼25 mW.

1. Bold Header: Magnetic Phase-Dependent Non-Linearity Prediction

This improved AI system can predict whether a given exciton-polariton condensate in CrSBr will exhibit a net redshift or blueshift based on its magnetic order (AFM vs. FM) and external cavity detuning, directly leveraging the findings that The excitons in CrSBr show attractive and repulsive interactions in the AFM and FM orders, respectively.

2. Bold Header: Non-Linearity Compensation Modeling

The system can accurately calculate the polariton redshift caused by the cavity expansion by using a renormalized energy formula derived from Hopfield coefficients, specifically applying the correction: The LPB mode energy modified by the cavity drift is E'LPB = 1/2 [Ec2 + EP6 + δ - qV2/6 + (Ec2 + δ - EP6)2].

3. Bold Header: Coherence Length Estimation

The AI can estimate the spatial extension of quantum coherence in a given magnetic state by comparing the condensate in AFM order reaches a maximum coherence length λc= 5.1 µm at a pump power of ∼30 mW, while the condensate in FM order reaches its maximum λc= 4.8 µm much earlier at ∼25 mW.

4. Bold Header: Threshold Behavior Classification

The system can classify the non-linear behavior of a polariton system by observing the threshold-like emission output, distinguishing between regimes where the LPB modes of lowest energy progressively gain intensity, and eventually experience a pronounced blueshift at pump powers above 33 mW versus other behaviors.

5. Bold Header: Exciton Density Estimation

The AI can estimate the exciton density in each layer for any given pump power using the formula derived from transfer matrix simulation: d50mWX = n50mWXm·SX≃ 4.53 × 103µm−2 for a 50 mW average excitation power.

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, macroscopic occupation of the ground state 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.