We address characterization of many-body superradiant systems and establish a fundamental connection between quantum criticality and the possibility of locally estimating the coupling constant, i.e., extracting its value by probing only a portion of the whole system. In particular, we consider Dicke-like superradiant systems made of an ensemble of two-level atoms interacting with a single-mode radiation field at zero effective temperature, and address estimation of the coupling by measurements performed only on radiation. At first, we obtain analytically the quantum Fisher information (QFI) and show that optimal estimation of the coupling may be achieved by tuning the frequency of the radiation field to drive the system toward criticality. The scaling behavior of the QFI at the critical point is obtained explicitly upon exploiting the symplectic formalism for Gaussian states. We then analyze the performances of feasible detection schemes performed only on the radiation subsystem, namely homodyne detection and photon counting, and show that the corresponding Fisher informations (FIs) approach the global QFI in the critical region. We thus conclude that criticality is a twofold resource. On the one hand, global QFI diverges at the critical point, i.e., the coupling may be estimated with the arbitrary precision. On the other hand, the FIs of feasible local measurements (which are generally smaller than the QFI out of the critical region), show the same scaling of the global QFI; i.e., optimal estimation of coupling may be achieved by locally probing the system, despite its strongly interacting nature.

Exciton-polaritons in semiconductor microcavities constitute the archetypal realization of a quantum fluid of light. Under coherent optical drive, remarkable effects such as superfluidity, dark solitons or the nucleation of vortices have been observed, and can be all understood as specific manifestations of the condensate collective excitations. In this work, we perform a Brillouin scattering experiment to measure their dispersion relation directly. The results, such as a speed of sound which is apparently twice too low, cannot be explained upon considering the polariton condensate alone. In a combined theoretical and experimental analysis, we demonstrate that the presence of an excitonic reservoir alongside the polariton condensate has a dramatic influence on the characteristics of the quantum fluid, and explains our measurement quantitatively. This work clarifies the role of such a reservoir in polariton quantum hydrodynamics. It also provides an unambiguous tool to determine the condensate-to-reservoir fraction in the quantum fluid, and sets an accurate framework to approach ideas for polariton-based quantum-optical applications.

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In this section, we review the driven-dissipative Gross-Pitaevskii equation that is currently used to describe the hydrodynamics of exciton-polaritons fluids under a co-arXiv:1905.05855v2 [cond-mat.quant-gas]