Topological aspects of photonic time crystals

Lustig, Eran; Sharabi, Yonatan; Segev, Mordechai

doi:10.1364/optica.5.001390

Cited by 227 publications

(139 citation statements)

References 44 publications

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“…Such devices may find practical usage in quantum communication protocols requiring conversion of visible photons to infrared 51 and in classical coherent optical communications 52,53 . We anticipate that the large time-refraction effect, we report here, can be exploited to engineer magnet-free nonreciprocal devices 54,55 , spatiotemporal metasurfaces 13 , and to investigate photonic time crystals and other topological effects in the time domain 16,56 using free-space or on-chip ENZ-based structures.…”

Section: Discussionmentioning

confidence: 84%

“…Thus, a highly nonlinear low-index medium is a natural platform with which to generate a large frequency translation using time refraction. In addition to frequency conversion, a timevarying medium with a large index change can also be used to investigate many novel effects in the time domain such as alloptical nonreciprocity 12,13 , negative refraction 14 , photonic topological insulators 15 , photonic time crystals 16 , achromatic optical switches 17 , and the dynamic Casimir effect 18 .…”

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confidence: 99%

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Broadband frequency translation through time refraction in an epsilon-near-zero material

et al. 2020

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Space-time duality in paraxial optical wave propagation implies the existence of intriguing effects when light interacts with a material exhibiting two refractive indexes separated by a boundary in time. The direct consequence of such time-refraction effect is a change in the frequency of light while leaving the wavevector unchanged. Here, we experimentally show that the effect of time refraction is significantly enhanced in an epsilon-near-zero (ENZ) medium as a consequence of the optically induced unity-order refractive index change in a sub-picosecond time scale. Specifically, we demonstrate broadband and controllable shift (up to 14.9 THz) in the frequency of a light beam using a time-varying subwavelength-thick indium tin oxide (ITO) film in its ENZ spectral range. Our findings hint at the possibility of designing (3 + 1)D metamaterials by incorporating time-varying bulk ENZ materials, and they present a unique playground to investigate various novel effects in the time domain.

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Section: Discussionmentioning

confidence: 84%

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confidence: 99%

Broadband frequency translation through time refraction in an epsilon-near-zero material

et al. 2020

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“…After the submission of the present manuscript we learned about the work on a similar topic but in photonic materials [95].…”

Section: Note Addedmentioning

confidence: 99%

Topological time crystals

et al. 2019

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By analogy with the formation of space crystals, crystalline structures can also appear in the time domain. While in the case of space crystals we often ask about periodic arrangements of atoms in space at a moment of a detection, in time crystals the role of space and time is exchanged. That is, we fix a space point and ask if the probability density for detection of a system at this point behaves periodically in time. Here, we show that in periodically driven systems it is possible to realize topological insulators, which can be observed in time. The bulk-edge correspondence is related to the edge in time, where edge states localize. We focus on two examples: Su-Schrieffer-Heeger model in time and Bose Haldane insulator which emerges in the dynamics of a periodically driven many-body system. 5 Note that due to the negative effective mass m eff , the first energy band is the highest in energy. 2 New J. Phys. 21 (2019) 052003 where = ¢ J J i 2and J 2i−1 =J, which is identical to the SSH model [86]. The latter describes spinless fermions hopping on a 1D-lattice with staggered hopping amplitudes. Changing the ratio λ 1 /λ in (1), allows one to control the ratio ¢ J J . This effective Hamiltonian belongs to the BDI class of the periodic table of the topological insulators and superconductors [87] and is characterized by a  topological invariant, the winding number ν. For an infinite system with ¢ > J J ( ¢ < J J ), the system is in a topological (trivial) phase with winding number ν=1 (ν=0). For a finite system, the topological phase exhibits zero energy edge states protected by the topology of the bulk. The SSH model has been experimentally realized in quantum simulators and both the presence of edge states and the winding number have been measured [63][64][65]. Let us emphasize that the Wannier states w i (x, t) of equation (2) are localized wavepackets of the effective SSH Hamiltonian of equation (3). We then discuss how such states allow one to detect the topology of the SSH Hamiltonian. corresponding to quasi-energies closest to zero, see top panel. In the topological phase, these eigenstates have zero quasi-energy and are linear combinations of the edge states localized at the edge of time. That is, in the laboratory frame, a detector is placed close to the oscillating mirror (x≈0) and the probability density of clicking of the detector is shown versus time for different values of the ratio ¢ J J of the tunneling amplitudes in (3). This behavior is repeated with the period 2π/ω. At sωt/(2π)=1 and sωt/(2π)=40 there are edges where the eigenstate localizes if ¢ > J J 1. The results correspond to ω=0.067, λ=0.06 in (1) and are obtained within the quantum secular approach [84], see the appendix.

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“…The resulting systems are often referred to as Chern insulators, as their topological gaps can support uni-directional modes, whose transport is protected by the topological invariant of Chern numbers. Another important method to break reciprocity is through temporal modulation 12 , yet the understanding of topological phases in dynamically driven optical systems is often limited to tight-binding models of coupled resonators 13–15 or waveguides 16–18 .…”

Section: Introductionmentioning

confidence: 99%

Floquet Chern insulators of light

Addison

Jin

et al. 2019

Nat Commun

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Achieving topologically-protected robust transport in optical systems has recently been of great interest. Most studied topological photonic structures can be understood by solving the eigenvalue problem of Maxwell’s equations for static linear systems. Here, we extend topological phases into dynamically driven systems and achieve a Floquet Chern insulator of light in nonlinear photonic crystals (PhCs). Specifically, we start by presenting the Floquet eigenvalue problem in driven two-dimensional PhCs. We then define topological invariant associated with Floquet bands, and show that topological band gaps with non-zero Chern number can be opened by breaking time-reversal symmetry through the driving field. Finally, we numerically demonstrate the existence of chiral edge states at the interfaces between a Floquet Chern insulator and normal insulators, where the transport is non-reciprocal and uni-directional. Our work paves the way to further exploring topological phases in driven optical systems and their optoelectronic applications.

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Topological aspects of photonic time crystals

Cited by 227 publications

References 44 publications

Broadband frequency translation through time refraction in an epsilon-near-zero material

Broadband frequency translation through time refraction in an epsilon-near-zero material

Topological time crystals

Floquet Chern insulators of light

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