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Optical nonlinearities are fundamental in several types of opticalinformation processing protocols. However, the high laser intensities neededfor implementing phase nonlinearities using conventional optical materialsrepresent a challenge for nonlinear optics in the few-photon regime. Weintroduce an infrared cavity quantum electrodynamics (QED) approach forimprinting nonlinear phase shifts on individual THz pulses in reflectionsetups, conditional on the input power. Power-dependent phase shifts on theorder of $ 0.1\, \pi$ can be achieved with femtosecond pulses of only a few$\mu$W input power. The proposed scheme involves a small number of intersubbandquantum well transition dipoles evanescently coupled to the near field of aninfrared resonator. The field evolution is nonlinear due to the dynamicaltransfer of spectral anharmonicity from material dipoles to the infraredvacuum, through an effective dipolar chirping mechanism that transientlydetunes the quantum well transitions from the vacuum field, leading to photonblockade. We develop analytical theory that describes the dependence of theimprinted nonlinear phase shift on relevant physical parameters. For a pair ofquantum well dipoles, the phase control scheme is shown to be robust withrespect to inhomogeneities in the dipole transition frequencies and relaxationrates. Numerical results based on the Lindblad quantum master equation validatethe theory in the regime where the material dipoles are populated up to thesecond excitation manifold. In contrast with conventional QED schemes for phasecontrol that require strong light-matter interaction, the proposed phasenonlinearity works best in weak coupling, increasing the prospects for itsexperimental realization using current nanophotonic technology.

Coherent anharmonicity transfer from matter to light in the THz regime