We report the experimental observation of a cross-Kerr nonlinearity in a free-space medium based on resonantly-excited, interacting Rydberg atoms and electromagnetically induced transparency. The nonlinearity is used to implement cross-phase modulation between two optical pulses. The nonlinear phase written onto the probe pulse is measured to be as large as 8 mrad per nW of signal power, corresponding to a χ (3) of 10 −8 m 2 V 2 . Potential applications range from optical quantum information processing to quantum non-demolition measurement of photon number.

As the separation between two emitters is decreased below the Rayleigh limit, the information that can be gained about their separation using traditional imaging techniques, photon counting in the image plane, reduces to nil. Assuming the sources are of equal intensity, Rayleigh's 'curse' can be alleviated by making phase-sensitive measurements in the image plane. However, with unequal and unknown intensities the curse returns regardless of the measurement, though the ideal scheme would still outperform image plane counting (IPC), i.e. recording intensities on a screen. We analyze the limits of the super-resolved position localization by inversion of coherence along an edge (SPLICE) phase measurement scheme as the intensity imbalance between the emitters grows. We find that SPLICE still outperforms IPC for moderately disparate intensities. For larger intensity imbalances we propose a hybrid of IPC and SPLICE, which we call 'adapted SPLICE', requiring only simple modifications. Using Monte Carlo simulation, we identify regions (emitter brightness, separation, intensity imbalance) where it is advantageous to use SPLICE over IPC, and when to switch to the adapted SPLICE measurement. We find that adapted SPLICE can outperform IPC for large intensity imbalances, e.g. 10 000:1, with the advantage growing with greater disparity between the two intensities. Finally, we also propose additional phase measurements for estimating the statistical moments of more complex source distributions. Our results are promising for implementing phase measurements in sub-Rayleigh imaging tasks such as exoplanet detection.

We offer a perspective on recent advances in picosecond-timescale all-optical switching with applications in quantum optics. The switch is based on polarization rotation in standard single-mode fiber via the optical Kerr effect. By using ultrafast laser pulses and short (∼10 cm) fibers, this technique can achieve a switching duration of ≲1 ps, at the repetition rate of 80 MHz or above. This high repetition rate is well-suited to quantum optics where experiments operate in the photon-counting regime. The switch efficiency can be ≳99% with a noise floor of just ∼10−4 photons/pulse, enabling high fidelity operations on quantum states of light, with negligible generation of spurious noise photons. We highlight the capabilities of this technique in four early applications: switching of heralded single photons, time-bin to polarization conversion of photonic qubits, noise gating for quantum key distribution, and pulse carving.