We determine experimentally the spinor interaction constants of lower polaritons α1 and α2 using a resonant pump-probe spectroscopy with a spectrally narrow pump pulse. Our experimental findings are analyzed with the Bogoliubov-type theory and a mean-field two channel model based on the lower polariton and biexciton basis. We find an enhancement of the attractive interaction and a dissipative non-linearity of lower polaritons with anti-parallel spins in the vicinity of the biexciton resonance when the energy of two lower polaritons approaches energetically that of the biexciton. These observations are consistent with the existence of a scattering resonance between lower polaritons and biexcitons (polaritonic Feshbach resonance).

Feshbach resonance occurs when a pair of free particles is resonantly coupled to a molecular bound state. In the field of ultracold quantum gases, atomic Feshbach resonances [1, 2] became a usual tool for tailoring atomic interactions opening up many new applications in this field [3-8]. In a semiconductor microcavity, the Feshbach resonance appears when two lower polaritons are coupled to the molecular biexciton state [9]. Here, we demonstrate the existence of a cross Feshbach resonance for which a pair of polaritons, lower together with upper, effectively couples to the biexciton state. This demonstration is a crucial step towards the efficient generation of entangled photon pairs in a semiconductor microcavity [10, 11]. The existence of a Cross Feshbach resonance establishes the condition to convert a pair of upper and lower polaritons via the biexciton state into two lower polaritons, paving the way for the generation of momentum and polarization entangled photons.

The interaction between coherent polaritons and incoherent excitons plays an important role in polariton physics. Using resonant pump-probe spectroscopy with selective excitation of single polariton branches, we investigate the different dephasing mechanisms responsible for generating a long-lived exciton reservoir. As expected, pumping the upper polariton results in a strong dephasing process that leads to the generation of a long lived reservoir. Unexpectedly, we observe an efficient reservoir creation while exciting only the lower polariton branch when the detuning is increased towards positive detuning. We propose a simple theoretical model, the polaritonic Bloch equations, to describe the dynamics of the system.

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We present an experimental signature of the Anderson localisation of microcavity polaritons, and provide a systematic study of the dependence on disorder strength. We reveal a controllable degree of localisation, as characterised by the inverse-participation ratio, by tuning the positional disorder of arrays of interacting mesas. This constitutes the realisation of disorder-induced localisation in a driven-dissipative system. In addition to being an ideal candidate for investigating localisation in this regime, microcavity polaritons hold promise for low-power, ultra-small devices and their localisation could be used as a resource in quantum memory and quantum information processing.