Polaritonic Feshbach resonance

A Feshbach resonance occurs when the energy of two interacting free particles comes into resonance with a molecular bound state. When approaching this resonance, marked changes in the interaction strength between the particles can arise. Feshbach resonances provide a powerful tool for controlling the interactions in ultracold atomic gases, which can be switched from repulsive to attractive1–4, and have allowed a range of many-body quantum physics e ects to be explored5,6. Here we demonstrate a Feshbach resonance based on the polariton spinor interactions in a semiconductor microcavity. By tuning the energy of two polaritons with anti-parallel spins across the biexciton bound state energy, we show an enhancement of attractive interactions and a prompt change to repulsive interactions. A mean-field two-channel model quantitatively reproduces the experimental results. This observation paves the way for a new tool for tuning polariton interactions and to move forward into quantum correlated polariton physics. A semiconductor microcavity is a unique system where exciton–polaritons emerge from the strong coupling between an exciton and a photon. The demonstration of Bose–Einstein condensation of exciton–polaritons in a semiconductor microcavity7 has attracted much attention and opened a wide field of research on polariton quantum fluids, such as superfluidity8, quantum vortices9 and Bogoliubov dispersion10–12. Many more examples could be proposed to highlight the fact that polaritons provide a concrete realization of a bosonic interacting many-body quantum system, complementing the work performed on ultracold atom systems. Furthermore, polaritons exhibit a polarization degree of freedom, with a one-to-one connection to two counter circular polarizations for their photonic part. The different excitonic content of both polarization states results in asymmetric spinor interactions. Such spinor interactions offer a wide range of effects and a very rich physics to explore in semiconductor microcavities13–18. In this work, we demonstrate a Feshbach resonance in a polariton semiconductor microcavity. Feshbach biexcitonic resonant scattering is investigated through spectrally resolved circularly polarized pump–probe spectroscopy on a III–V basedmicrocavity (Methods). To bring the energy of a two-lower polariton state into resonance with the biexciton state we change the cavity exciton detuning (Fig. 1a,c). We evidence the resonant polariton scattering by probing the anti-parallel spin polariton interactions when scanning the two-polariton energy across the bound biexciton state. We clearly show the enhancement of polariton interactions and the change of their character from attractive to repulsive. Moreover, we observe a decrease of the polariton resonance amplitude when the lower polariton energy is in the vicinity of the biexciton energy. The results are modelled by numerical simulations based on a meanfield two-channel model that includes coupling between polaritons and biexcitons as a key ingredient. It is worth mentioning that several works19–22 have already reported observations of coupling between polaritons and biexcitons without reaching the regime of the Feshbach resonance reported here. The expected signatures of the Feshbach resonance phenomenon are twofold. First, a strong variation of the strength and sign of the scattering amplitude; second, a reduction of the free particle density through the coupling with the molecular bound state. Both are sensitive to the energy difference between the free particles and the molecular states. These two energy states refer, in our system, to the state of two anti-parallel spin lower polaritons and the biexciton state, respectively. We investigate both experimental signatures of the Feshbach resonance. This coherent effect requires working in the coherent regime, therefore we set a zero delay between pump and probe (results from experiments with different pump–probe delays are presented in SupplementaryMethods). For a given pump power, we measure through the transmitted probe beam the energy shift and the amplitude variation of the lower polariton resonance induced by the presence of the polariton population generated by the pump (Fig. 1b,d,e). From negative to positive cavity detuning, the energy of the two lower polaritons (2LP, one from the σ+ polariton cloud created by the pump, and one σ− polariton coming from the probe) ranges from below to above the molecular biexciton state energy, passing through the resonance (Fig. 1c). In Fig. 2a, we plot the lower polariton energy shift versus exciton-cavity detuning for a polariton density of 5.1× 1010 polaritons cm−2 generated by the pump. This result clearly shows a dispersive shape, characteristic of the resonant scattering. Indeed, in dilute atomic gas systems the Feshbach resonances are evidenced by a dispersive shape of the scattering length at resonance3. In these atomic systems, the dispersive shape diverges in the case of magnetic Feshbach resonances with very long molecular lifetime1,3. Here, however, a smooth dispersive shape shows up, similar to the case of optical Feshbach resonances with finite molecular lifetime3,4. For polaritons, the finite lifetime of the molecular biexciton state prevents the dispersive shape form diverging at the resonance. Note that the sign and amplitude of the energy shift are related to the character and strength of the polariton interaction respectively. Our result directly shows that, at resonance, the energy shift switches from redshift to blueshift, demonstrating the drastic modification of the interaction character from attractive to repulsive. This measured shape provides clear evidence for a Feshbach resonance. In Fig. 2b, we plot the variation of the polariton resonance amplitude as a function of the cavity detuning. This result shows the resonant conversion of two polaritons with anti-parallel spins into a biexciton. The simultaneous observations of the change of the polariton interaction character from attractive to repulsive together with the enhanced polariton loss through the coupling with the molecular biexciton state gives direct evidence for the polaritonic Feshbach resonant scattering. The resonance effect shown in Fig. 2a,b is located at an exciton-cavity detuning energy