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.
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.
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.
Introduction The propagation of light in periodically ordered photonic crystals bears a strong analogy to the wave propagation of conduction electrons in atomic crystals. The development of Bloch modes and dispersion are determined by the interference of waves that are diffracted by lattice planes [19, 52]. The periodicity commensurate with the wavelength (a ≈ λ/2) gives rise to Bragg diffraction that is associated with frequency windows for which waves are forbidden to propagate in a particular direction. Such stop gaps have long been known to arise for electromagnetic waves, notably for X-rays in atomic crystals [214]. At optical frequencies, the stop gaps that occur in one-dimensional periodic structures, known as Bragg stacks, are widely used in optical laboratories as broadband highly reflecting dielectric mirrors [556]. The distinguishing feature of three-dimensional (3D) photonic crystals is that a common stop gap can be achieved for all directions and for all polarizations simultaneously: the widely pursued 3D photonic band gap . Historically a 3D band gap has never been considered for the propagation of X-rays in periodic media, since a gap requires a high refractive index contrast of order unity, whereas the refractive index varies by less then 10 −4 in the X-ray range. At frequencies inside the 3D photonic band gap, the density of optical states (DOS) completely vanishes. As the density of states can also be interpreted as the density of vacuum fluctuations [334], a 3D band gap thus serves as an effective shield to these fluctuations. The total absence of optical modes in a photonic band gap has implications beyond classical optics that break the analogy between the behavior of light in photonic crystals and the behavior of electrons in atomic crystals. 3D photonic band gap crystals play an important role in cavity quantum electrodynamics (cQED) [64, 549], where they offer at least five prospects for new physics. Firstly, probably the most eagerly pursued phenomenon is the complete inhibition of spontaneous emission: an excited quantum emitter – such as an atom, molecule, or quantum dot – embedded in a crystal with its transition frequency tuned to within the 3D band gap remains forever excited since it cannot decay to the ground state by emitting a photon.
Optical phenomena in materials with a space modulation of dielectric constant at distances close to the light wavelengths (so called photonic band-gap structures or photonic crystals) are of a great interest now because of the existence of band gaps in their photonic band structure (Bykov, 1972; Yablonovitch, 1987; John, 1987). These band gaps represent frequency regions where electromagnetic waves are forbidden, irrespective of the spatial propagation directions. Inside the band gaps, the photon density of states is equal to zero and so the emission of light sources embedded in these crystals should be inhibited in these spectral regions (Vats et al., 2002). Since the time the effect is predicted, many experiments have been devoted to studies of spontaneous emission of molecules embedded in photonic crystals (Gaponenko et al., 1999; Gorelik, 2007). Typical structures of photonic crystals and calculations of corresponding photonic band structures are presented in a book by Prof. Joannopoulos (Joannopoulos et al., 2008). Besides the emission inhibition effect, a number of new optical phenomena in 3D photonic crystals, interesting from the applied point of view, are under intensive study now. The main research directions are the following: Effects of light localisation (John, 1987; Kaliteevskii et al., 2005; Vignolini et al., 2008). Radiation of photonic crystals filled with organic (rhodamine 6G, 1,8-naphthoylene1’,2’-benzimidazole, stilbene) and inorganic (ZnO, ZnS, rare-earth ions Eu3+, Tb3+, Er3+) luminophores near by the edges of photonic band-gap (Gaponenko et al., 1999; Aliev et al., 2002; Emel’chenko et al., 2005; Li et al., 2007). Radiation of CdTe, CdSe/ZnS quantum dots in photonic crystal volume (Gruzintsev et al., 2009; Ambrozevich et al., 2009). Quantum optics phenomena in nano-structured materials based on photonic crystals and nonlinear optical substances (Lin & Vuckovic, 2010). Effects of the radiation field amplification in photonic crystals (Lin & Vuckovic, 2010). Increase of solar cells efficiency with the use of photonic crystals (Florescu et al., 2007).
Abstract Time is, figuratively and literally, becoming the new dimension for crystalline matter. In a key recent advance, temporal and spatiotemporal crystals that exhibit periodicity in time and space-time, respectively, were reported, with unique properties such as spectra containing gaps not only in energy but also in momentum. Conversely, the field of topological physics, which has led to celebrated discoveries such as topological insulators featuring protected conducting surface states with immunity to backscattering, has so far been based on the notion of energy gaps and spatial boundaries only. Fundamentally rethinking the role of time, which in contrast to space exhibits a unique unidirectionality called the ‘arrow of time’, thus promises a new dimension for topological physics, setting paradigms of time and space-time topology based on the topological properties of momentum and energy–momentum gaps. Indeed, previous work has shown simulations of states which arise through the topology of momentum gaps and localize at temporal interfaces. Here we enter this new dimension of time and space-time topology. First, using discrete-time quantum walks on synthetic photonic lattices in coupled optical fibre loops, we observe such time topological states. We find a time-topological invariant and establish its relation to the observed time topological states. Transcending the separate concepts of space and time topology, we then propose and implement a system with an energy–momentum gap and introduce the concept of space-time topology, leading to topological states that are localized in both space and time, thus forming space-time topological events. We demonstrate that these are associated with unique effects such as causality-suppressed coupling or the limited collapse of space-time localization. Our study provides a model of time and space-time topology, highlighting an interplay of momentum and energy gap topology with applicability beyond photonics. In the field of topological physics, we anticipate a new role of causality and non-Hermiticity inspired by time and space-time topology. These concepts further invite exploration of connections to other fields where the arrow of time plays an important role. Moreover, our results enable the topological shaping of waves in space and time, with applications in spatiotemporal wave control for imaging or communication and topological lasers, for example.
We present a comprehensive investigation of entanglement dynamics in multi-level V-type atomic systems embedded within photonic crystals. We mainly focus on the synergistic roles of resonant dipole-dipole interactions and quantum interference through analytical modeling and numerical simulations using the Schrodinger equation. Key findings reveal that resonant interaction dominates when the interatomic distance is comparable to the localization length of photon-atom bound states lying in the bandgap region. For atoms with anti-parallel dipole orientations, both initially entangled and separable states exhibit robust entanglement preservation due to strong collective interactions. Conversely, when dipoles are oriented orthogonally, initially entangled states exhibit unique oscillatory patterns in their entanglement dynamics. This effect arises from the formation of dark states due to destructive interference within the structured photonic environment, with resonant dipole-dipole interactions sustaining non-Markovian dynamics. We further demonstrate that positioning the atomic excited states deeper within the photonic bandgap accelerates the decay of entanglement oscillations due to the exponential suppression of resonant energy exchange mediated by evanescent modes. Our analysis establishes resonant dipole-dipole interactions and quantum interference as potential tools for tailoring entanglement dynamics, paving the way for controlled quantum coherence in photonic crystal platforms.