Photonic time crystals are exotic materials characterized by effective parameters that are uniform in space yet periodically vary over time. Recently, these materials have been the subject of extensive study from both theoretical and experimental perspectives. However, the quantum characteristics of light within photonic time crystals remain largely uncharted territory. In this presentation, we explore the interaction of light with these materials through the lens of quantum optics, addressing various topics ranging from mode operator transformation to the photon statistics of light in photonic time crystals.
Photonic time crystals are exotic materials characterized by effective parameters that are uniform in space yet periodically vary over time. Recently, these materials have been the subject of extensive study from both theoretical and experimental perspectives. However, the quantum characteristics of light within photonic time crystals remain largely uncharted territory. In this presentation, we explore the interaction of light with these materials through the lens of quantum optics, addressing various topics ranging from mode operator transformation to the photon statistics of light in photonic time crystals.
Photonic time crystals host a variety of intriguing phenomena, from wave amplification and mixing to exotic band structures, all stemming from the time-periodic modulation of optical properties. While these features have been well described classically, their quantum manifestation when coupled to an atomic electric dipole has remained elusive. Here, we introduce a quantum electrodynamical model of photonic time crystals that reveals a deeper connection between classical and quantum pictures: the classical momentum gap arises from a localization-delocalization quantum phase transition in a Floquet-photonic synthetic lattice. Leveraging an effective Hamiltonian perspective, we pinpoint the critical momenta and highlight how classical exponential field growth manifests itself as wave-packet acceleration in the quantum synthetic space. Remarkably, when a two-level atom is embedded in such a photonic time crystal, its Rabi oscillations undergo irreversible decay to a half-and-half mixed state-a previously unobserved phenomenon driven by photonic delocalization within the momentum gap, even with just a single frequency mode. Our findings establish photonic time crystals as versatile platforms for studying nonequilibrium quantum photonics and suggest new avenues for controlling light matter interactions through time domain engineering.
In this presentation, we shed light on electromagnetic time interfaces using the principles of quantum optics. We begin by explaining the transformation of bosonic mode operators in response to a temporal discontinuity in the macroscopic parameters. Accordingly, our discussion extends to the general analysis of photon statistics and the degree of second-order coherence of the generated forward and backward modes. Focusing on input number states, we meticulously detail the quantum states produced after the time interface, elucidating the associated probability distributions. By virtue of this study, we specifically highlight the controllable nature of photon statistics of the output forward mode for particular input states. We show that this capability, in general, is not present for the backward mode generated through the time interface. Also, we reveal that photon-pair generation is a fundamental inherent feature of the time interface. By unveiling all these insights, we aim to pave the way for exploring photonic time crystals within the domain of quantum optics.
Photonic crystals are optical materials that have an intricate structure with length scales of the order of the wavelength of light. The flow of photons is controlled in a manner analogous to how electrons propagate through semiconductor crystals, i.e., by Bragg diffraction and the formation of band structures. If the interaction between light and matter is made strong, multiple diffraction and multiple scattering effects dominate. A main research goal is the realization of a "photonic band gap", that is, a frequency range for which no light can propagate in a crystal in any direction, which causes radical modifications of the density of radiative states. Important consequences of photonic band gaps are the complete control over spontaneous and stimulated emission of light, as well as over the propagation of light, in particular photon localization. This opens up the possibility to achieve a "cage for light": trap photons and do with them whatever one chooses. In this talk we will also review means for making such structures, and recent experimental advances in optical experiments.
Over the last few decades, the predominant strategies for controlling spontaneous emission have involved tailoring the spatial surroundings of quantum emitters or atoms to create resonant or spatially periodic photonic structures. However, the rise of time-varying photonics has prompted a reevaluation of spontaneous emission in dynamically changing environments, especially within photonic time crystals, where optical properties undergo time-periodic modulation. Here, we apply classical light-matter interaction theory together with Floquet analysis to reveal a substantial enhancement of the spontaneous emission decay rate at the momentum gap frequency in photonic time crystals. Moreover, our findings suggest that photonic time crystals enable a nonequilibrium light-matter interaction process: the spontaneous excitation of an atom from its ground state to an excited state, accompanied by the concurrent emission of a photon, referred to as spontaneous emission excitation.
Modulating macroscopic parameters of materials in time offers innovative avenues for manipulating electromagnetic waves. Due to such enticing prospects, the general research subject of time-varying systems is expanding today in different branches of electromagnetism and optics. However, compared with the research efforts and progresses that have taken place in the realm of classical electrodynamics, the quantum aspects of this emerging subject have been less explored. Here, through the lens of quantum optics, we study the scattering of electromagnetic fields from an isotropic and nondispersive material with a suddenly changing refractive index, creating a time interface. We revisit the transformation of the bosonic mode operators and corresponding quantum states due to this interface, governed by the two-mode squeeze operator. Building on this foundation, at the core of the investigation, our analysis focuses on the quantum state engineering and photon statistics of the scattered light. Notably, such an analysis reveals and connects various quantum optical phenomena and opportunities arising from the time interface, including photon-pair production and destruction, photon bunching and antibunching, vacuum generation, quantum state discrimination, and quantum state freezing. To bridge theory and experiment, we propose a possible circuit quantum electrodynamics approach for validating our theoretical predictions. We hope that our work inspires experimental investigations of such quantum state engineering and photon statistics phenomena, as well as further quantum optical explorations of electromagnetic field interaction with photonic time crystals or with dispersive time-varying materials.
Temporal modulation of materials offers unprecedented control over light, sparking recent interest in the quantum theory of light interaction with time-varying materials. In this presentation, through the lens of quantum optics, we evaluate the von Neumann entropy transformation induced by an electromagnetic time interface, in which the refractive index of an isotropic, homogeneous, nondispersive dielectric medium uniformly undergoes an abrupt change in time. We demonstrate that the entropy increases across such an interface, with the magnitude of the increase correlating positively with the refractive index contrast. Additionally, we analyze how photon population in the incident modes governs entropy evolution. We hope that our study advances both the fundamental physics of time interfaces and their potential applications in quantum information technology.