This supplemental material contains three sections:(Ⅰ)Derivation of the Floquet lattice Hamiltonian;(Ⅱ)Surface states of the Floquet lattice Hamiltonian;(Ⅲ)Evolution of Floquet Weyl points and Fermi arcs with the i...This supplemental material contains three sections:(Ⅰ)Derivation of the Floquet lattice Hamiltonian;(Ⅱ)Surface states of the Floquet lattice Hamiltonian;(Ⅲ)Evolution of Floquet Weyl points and Fermi arcs with the increase of light amplitude;(Ⅳ)Formalism for light-induced anomalous Hall effects.展开更多
Floquet engineering provides a powerful and flexible method for modifying the band structures of quantum materials.While circularly polarized light has been shown to convert curved nodal lines in three-dimensional sem...Floquet engineering provides a powerful and flexible method for modifying the band structures of quantum materials.While circularly polarized light has been shown to convert curved nodal lines in three-dimensional semimetals into Weyl points,such a transformation is forbidden for an isolated straight nodal line.In this work,we uncover a dramatic shift in this paradigm when multiple straight nodal lines intersect.We observe that circularly polarized light not only gaps them into Weyl points but also induces unprecedented surface-state Fermi arcs that extend across the entire surface Brillouin zone and form a linked topological structure.These findings advance our fundamental understanding of light-driven transitions in topological semimetals and unveil a unique Weyl semimetal phase defined by linked Fermi arcs.We discuss potential exotic phenomena arising from this phase,applications of our predictions to spin-split antiferromagnets,and the extension of this Weyl semimetal phase to classical systems.展开更多
We propose a novel approach to generate and manipulate topological Floquet bound states in the continuum(BICs)via a class of systems constructed by coupling two identical periodically driven one-dimensional Su-Schrief...We propose a novel approach to generate and manipulate topological Floquet bound states in the continuum(BICs)via a class of systems constructed by coupling two identical periodically driven one-dimensional Su-Schrieffer-Heeger chains.The formation of topological Floquet BICs can be adjusted only by tuning the driving amplitude or frequency,regardless of whether the static system has BICs or not.The interchain bias can only change the localization property of topological Floquet BICs,and a bigger bias can lead to transforming topological Floquet BICs into bound states out of the continuum(BOCs).But it does not change the topological properties of these topological Floquet states.Based on the repulsion effect of edge states,we propose to detect occurrence of topological Floquet BICs and transition point between topological Floquet BICs and BOCs using quantum walk.Our work provided a convenient and realistic approach for the experimental realization and manipulation of BICs in a single-particle quantum system.展开更多
We introduce a time-dependent generalized Floquet(TDGF)approach to calculate attosecond transient absorption spectra of helium atoms subjected to the combination of an attosecond extreme ultraviolet(XUV)pulse and a de...We introduce a time-dependent generalized Floquet(TDGF)approach to calculate attosecond transient absorption spectra of helium atoms subjected to the combination of an attosecond extreme ultraviolet(XUV)pulse and a delayed few-cycle infrared(IR)laser pulse.This TDGF approach provides a Floquet understanding of the laser-induced change of resonant absorption lineshape.It is analytically demonstrated that the phase shift of the time-dependent dipole moment that results in the lineshape changes consists of two components,the adiabatic laser-induced phase(LIP)due to the IR-induced Stark shifts of adiabatic Floquet states and the non-adiabatic phase correction due to the non-adiabatic IR-induced coupling between adiabatic Floquet states.Comparisons of the spectral lineshape calculated based on the TDGF approach with the results obtained with the LIP model[Phys.Rev.A 88033409(2013)]and the rotating-wave approximation(RWA)are presented for several typical cases,demonstrating that TDGF universally and accurately captures IR-induced lineshape changes.It is suggested that the LIP model works as long as the generalized adiabatic theorem[PRX Quantum 2030302(2021)]holds,and the RWA works when the higher-order IR-coupling effect in the formation of adiabatic Floquet states is neglectable.展开更多
Wave-particle duality is one of the key features of quantum physics,characterized by the interference pattern.Meanwhile,Floquet spectroscopy is typically studied in the high-frequency region because the Floquet sideba...Wave-particle duality is one of the key features of quantum physics,characterized by the interference pattern.Meanwhile,Floquet spectroscopy is typically studied in the high-frequency region because the Floquet sidebands are very sharp,behaving like“particles”in frequency space,and no interference phenomena are observed.Here,we consider the larger quantum fluctuation region where the Floquet sidebands are broader,making interference between them possible.With the help of an optical lattice clock experimental platform and numerical simulations,such interference of Floquet modes in frequency space is clearly observed.Additionally,it exhibits many exotic phenomena,such as large Floquet sidebands between integer ones,sensitivity to the initial phase,and corresponding emergent symmetries.To analytically elucidate this,we propose the Floquet channel interference hypothesis,which surprisingly matches quantitatively well with both experimental and numerical results.Our research paves the way for developing a new type of interferometer that could be applicable to other Floquet systems.展开更多
Non-Abelian topological insulators are characterized by matrix-valued,non-commuting topological charges with regard to more than one energy gap.Their descriptions go beyond the conventional topological band theory,in ...Non-Abelian topological insulators are characterized by matrix-valued,non-commuting topological charges with regard to more than one energy gap.Their descriptions go beyond the conventional topological band theory,in which an additive integer like the winding or Chern number is endowed separately with each(degenerate group of)energy band(s).In this work,we reveal that Floquet(time-periodic)driving could not only enrich the topology and phase transitions of non-Abelian topological matter,but also induce bulk-edge correspondence unique to nonequilibrium setups.Using a one-dimensional,three-band model as an illustrative example,we demonstrate that Floquet driving could reshuffle the phase diagram of the non-driven system,yielding both gapped and gapless Floquet band structures with non-Abelian topological charges.Moreover,by dynamically tuning the anomalous Floquet π-quasienergy gap,non-Abelian topological transitions inaccessible to static systems could arise,leading to much more complicated relations between non-Abelian topological charges and Floquet edge states.These discoveries put forth periodic driving as a powerful scheme of engineering non-Abelian topological phases and incubating unique non-Abelian band topology beyond equilibrium.展开更多
文摘This supplemental material contains three sections:(Ⅰ)Derivation of the Floquet lattice Hamiltonian;(Ⅱ)Surface states of the Floquet lattice Hamiltonian;(Ⅲ)Evolution of Floquet Weyl points and Fermi arcs with the increase of light amplitude;(Ⅳ)Formalism for light-induced anomalous Hall effects.
基金supported by the National Natural Science Foundation of China (Grant No.12174455)Guangdong Basic and Applied Basic Research Foundation (Grant No.2023B1515040023)。
文摘Floquet engineering provides a powerful and flexible method for modifying the band structures of quantum materials.While circularly polarized light has been shown to convert curved nodal lines in three-dimensional semimetals into Weyl points,such a transformation is forbidden for an isolated straight nodal line.In this work,we uncover a dramatic shift in this paradigm when multiple straight nodal lines intersect.We observe that circularly polarized light not only gaps them into Weyl points but also induces unprecedented surface-state Fermi arcs that extend across the entire surface Brillouin zone and form a linked topological structure.These findings advance our fundamental understanding of light-driven transitions in topological semimetals and unveil a unique Weyl semimetal phase defined by linked Fermi arcs.We discuss potential exotic phenomena arising from this phase,applications of our predictions to spin-split antiferromagnets,and the extension of this Weyl semimetal phase to classical systems.
基金supported by the National Natural Science Foundation of China(Grant Nos.12175315 and 12205385)。
文摘We propose a novel approach to generate and manipulate topological Floquet bound states in the continuum(BICs)via a class of systems constructed by coupling two identical periodically driven one-dimensional Su-Schrieffer-Heeger chains.The formation of topological Floquet BICs can be adjusted only by tuning the driving amplitude or frequency,regardless of whether the static system has BICs or not.The interchain bias can only change the localization property of topological Floquet BICs,and a bigger bias can lead to transforming topological Floquet BICs into bound states out of the continuum(BOCs).But it does not change the topological properties of these topological Floquet states.Based on the repulsion effect of edge states,we propose to detect occurrence of topological Floquet BICs and transition point between topological Floquet BICs and BOCs using quantum walk.Our work provided a convenient and realistic approach for the experimental realization and manipulation of BICs in a single-particle quantum system.
基金supported by the National Natural Science Foundation of China(Grant Nos.W2411002 and 12375018).
文摘We introduce a time-dependent generalized Floquet(TDGF)approach to calculate attosecond transient absorption spectra of helium atoms subjected to the combination of an attosecond extreme ultraviolet(XUV)pulse and a delayed few-cycle infrared(IR)laser pulse.This TDGF approach provides a Floquet understanding of the laser-induced change of resonant absorption lineshape.It is analytically demonstrated that the phase shift of the time-dependent dipole moment that results in the lineshape changes consists of two components,the adiabatic laser-induced phase(LIP)due to the IR-induced Stark shifts of adiabatic Floquet states and the non-adiabatic phase correction due to the non-adiabatic IR-induced coupling between adiabatic Floquet states.Comparisons of the spectral lineshape calculated based on the TDGF approach with the results obtained with the LIP model[Phys.Rev.A 88033409(2013)]and the rotating-wave approximation(RWA)are presented for several typical cases,demonstrating that TDGF universally and accurately captures IR-induced lineshape changes.It is suggested that the LIP model works as long as the generalized adiabatic theorem[PRX Quantum 2030302(2021)]holds,and the RWA works when the higher-order IR-coupling effect in the formation of adiabatic Floquet states is neglectable.
基金supported by the National Natural Science Foundation of China(Grant No.12274045)support from the National Natural Science Foundation of China(Grant Nos.12274046,11874094,12147102,and 12347101)+2 种基金the Natural Science Foundation of Chongqing(Grant No.CSTB2022NSCQ-JQX0018)the Fundamental Research Funds for the Central Universities(Grant No.2021CDJZYJH-003)the Xiaomi Foundation/Xiaomi Young Talents Program。
文摘Wave-particle duality is one of the key features of quantum physics,characterized by the interference pattern.Meanwhile,Floquet spectroscopy is typically studied in the high-frequency region because the Floquet sidebands are very sharp,behaving like“particles”in frequency space,and no interference phenomena are observed.Here,we consider the larger quantum fluctuation region where the Floquet sidebands are broader,making interference between them possible.With the help of an optical lattice clock experimental platform and numerical simulations,such interference of Floquet modes in frequency space is clearly observed.Additionally,it exhibits many exotic phenomena,such as large Floquet sidebands between integer ones,sensitivity to the initial phase,and corresponding emergent symmetries.To analytically elucidate this,we propose the Floquet channel interference hypothesis,which surprisingly matches quantitatively well with both experimental and numerical results.Our research paves the way for developing a new type of interferometer that could be applicable to other Floquet systems.
基金supported by the National Natural Science Foundation of China(Grant Nos.12275260 and 11905211)the Fundamental Research Funds for the Central Universities(Grant No.202364008)the Young Talents Project of Ocean University of China。
文摘Non-Abelian topological insulators are characterized by matrix-valued,non-commuting topological charges with regard to more than one energy gap.Their descriptions go beyond the conventional topological band theory,in which an additive integer like the winding or Chern number is endowed separately with each(degenerate group of)energy band(s).In this work,we reveal that Floquet(time-periodic)driving could not only enrich the topology and phase transitions of non-Abelian topological matter,but also induce bulk-edge correspondence unique to nonequilibrium setups.Using a one-dimensional,three-band model as an illustrative example,we demonstrate that Floquet driving could reshuffle the phase diagram of the non-driven system,yielding both gapped and gapless Floquet band structures with non-Abelian topological charges.Moreover,by dynamically tuning the anomalous Floquet π-quasienergy gap,non-Abelian topological transitions inaccessible to static systems could arise,leading to much more complicated relations between non-Abelian topological charges and Floquet edge states.These discoveries put forth periodic driving as a powerful scheme of engineering non-Abelian topological phases and incubating unique non-Abelian band topology beyond equilibrium.
