Detecting Entanglement from Macroscopic Measurements of the Electric Field and Its Fluctuations.

To address the outstanding task of detecting entanglement in large quantum systems, entanglement witnesses have emerged, addressing the separable nature of a state. Yet optimizing witnesses, or accessing them experimentally, often remains a challenge. We here introduce a family of entanglement witnesses for open quantum systems. Based on the electric field, it does not require state tomography or single-site addressing, but rather macroscopic measurements of the field quadratures and of the total fluorescence. Its efficiency is demonstrated by detecting, from almost any direction, the entanglement of collective single-photon states, such as long-lived states generated by cooperative spontaneous emission. Able to detect entanglement in large open quantum systems, and through a single continuous measurement if operating in the stationary regime, these electric-field-based witnesses can be used on any set of emitters described by the Pauli group, such as atomic systems (cold atoms and trapped ions), giant atoms, color centers, and superconducting qubits.

Matter wave speckle observed in an out-of-equilibrium quantum fluid.

We report the results of the direct comparison of a freely expanding turbulent Bose-Einstein condensate and a propagating optical speckle pattern. We found remarkably similar statistical properties underlying the spatial propagation of both phenomena. The calculated second-order correlation together with the typical correlation length of each system is used to compare and substantiate our observations. We believe that the close analogy existing between an expanding turbulent quantum gas and a traveling optical speckle might burgeon into an exciting research field investigating disordered quantum matter.