A Photonic Tautochrone

We propose to implement an optical analogue of the tautochrone property of the cycloid to allow the focusing of ultrashort pulses inside photonic systems. This allows to enhance nonlinear effects, resulting in orders of magnitude increase of nonlinearity-induced phase shifts, while employing low irradiances. Building upon the optical-mechanical analogy, we show how to produce optical limiters for temporal light pulses, and how to implement temporal bistability and even multistability with large numbers of states. Finally, we move this concept to the quantum realm and predict a tautochrone quantum blockade regime with a stronger antibunching.