Research
Anderson Localization in Photonic Time Crystals
Solutions of the wave equations for time-independent disordered media can exhibit Anderson localization where instead of wave propagation we observe their localization around different points in space. Photonic time crystals are spatially homogeneous media in which the refractive index changes periodically in time, leading to the formation of bands in the wave number domain. By analogy to Anderson localization in space, one might expect that the presence of temporal disorder in photonic time crystals would lead to Anderson localization in the time domain. Here, we show that indeed periodic modulations of the refractive index with the addition of temporal disorder lead to Anderson localization in time, where an electromagnetic field can emerge from the temporally modulated medium at a certain moment in time and then decay exponentially over time. Thus, we are dealing with a situation where, in a fluctuating three-dimensional medium, the birth and death of waves can occur, and the mechanism of this phenomenon corresponds to Anderson localization.
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Towards Timetronics with Photonic Systems
Periodic driving of systems of particles can create crystalline structures in time. Such systems can be used to study solid-state physics phenomena in the time domain. In addition, it is possible to engineer the wave-number band structure of optical systems and to realize photonic time crystals by periodic temporal modulation of the material properties of the electromagnetic wave propagation medium. We introduce here a versatile averaged-permittivity approach which empowers emulating various condensed matter phases in the time dimension in a traveling wave resonator. This is achieved by utilizing temporal modulation of permittivity within a small segment of the resonator and the spatial shape of the segment. The required frequency and depth of the modulation are experimentally achievable, opening a pathway for research into the practical realisation of crystalline structures in time utilising microwave and optical systems.
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Topologically protected quantized changes of the distance between atoms
Thouless pumping enables the transport of particles in a one-dimensional periodic potential if the potential is slowly and periodically modulated in time. The change in the position of particles after each modulation period is quantized and depends solely on the topology of the pump cycle, making it robust against perturbations. Here, we demonstrate that Thouless pumping also allows for the realization of topologically protected quantized changes of the distance between atoms if the atomic s-wave scattering length is properly modulated in time.
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Classical Phase Space Crystals in Open Environment
It was recently discovered that a crystalline many-body state can exist in the phase space of a closed dynamical system. Phase space crystal can be anomalous Chern insulator that supports chiral topological transport without breaking physical time-reversal symmetry [L. Guo et al., Phys. Rev. B 105, 094301 (2022)]. In this work, we further study the effects of open dissipative environment with thermal noise, and identify the existence condition of classical phase space crystals in realistic scenarios. By defining a crystal order parameter, we plot the phase diagram in the parameter space of dissipation rate, interaction and temperature. Our present work paves the way to realise phase space crystals and explore anomalous chiral transport in experiments.
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Topological Molecules and Topological Localization of a Rydberg Electron on a Classical Orbit
It is common knowledge that atoms can form molecules if they attract each other. Here we show that it is possible to create molecules where bound states of atoms are not the result of the attractive interactions but have the topological origin. That is, bound states of atoms correspond to topologically protected edge states of a topological model. Such topological molecules can be realized if the interaction strength between ultra-cold atoms is properly modulated in time. Similar mechanism allows one to realize topologically protected localization of an electron on a classical orbit if a Rydberg atom is perturbed by a properly modulated microwave field.
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Homogeneous Floquet time crystal from weak ergodicity breaking
Recent works on observation of discrete time-crystalline signatures throw up major puzzles on the necessity of localization for stabilizing such out-of-equilibrium phases. Motivated by these studies, we delve into a clean interacting Floquet system whose quasi-spectrum conforms to the ergodic Wigner-Dyson distribution, yet with an unexpectedly robust, long-lived time-crystalline order in the absence of fine-tuning or any explicit local constraint. We relate such behavior to a measure zero set of nonthermal Floquet eigenstates with long- range spatial correlations, which coexist with otherwise thermal states at near-infinite temperature and develop a high overlap with a family of translationally invariant, symmetry-broken initial conditions. This resembles the notion of “dynamical scar states” that remain robustly localized throughout a thermalizing Floquet spectrum with fractured structure. We dub such a long-lived discrete time crystal formed in partially nonergodic systems, “scarred discrete time crystal” which is distinct by nature from those stabilized by either many-body localization or prethermalization mechanism.