Driven Time Crystal in Low-Symmetry ENZ Conductors

Abstract

In recent years, epsilon-near-zero (ENZ) materials have attracted a great deal of attention in nonlinear optics, as they combine field enhancement with strong, ultrafast nonlinearities. In particular, transparent conducting oxides, such as ITO, have emerged as a promising class of materials and have been extensively exploited to achieve temporal optical responses varying on the femtosecond scale using an optical pump. Most of the solutions discussed so far in the literature rely on effective $χ^{(3)}$ modulations, wherein the dominant material response is controlled by the envelope of the optical pump. Here, it is shown that low-symmetry conductors can provide an interesting alternative to transparent conducting oxides and a more natural implementation of time-crystalline behavior in optical systems with optical-cycle modulation. I demonstrate that ENZ confinement, combined with the strong anomalous-velocity nonlinearity of low-symmetry conductors, enables a subwavelength nanoparticle to develop a time-crystalline response under optical pumping. For sufficiently strong pumping, this response can overcome dissipative losses and lead to parametric amplification. Furthermore, the pump can strongly tailor the scattering and extinction of a weak probe and, in extreme cases, render the extinction negative. In this regime, the driven nanoparticle effectively amplifies the probe beam.