Scattering of a quantum particle from an oscillating barrier or well does not generally conserve the particle energy owing to energy exchange with the photon field, and an incoming particle-free state is scattered into a set of outgoing (transmitted and reflected) free states according to Floquet scattering theory. Here we introduce two families of oscillating non-Hermitian potential wells in which Floquet scattering is fully suppressed for any energy of the incident particle. The scattering-free oscillating potentials are synthesized by application of the Darboux transformation to the time-dependent Schrödinger equation. For one of the two families of scattering-free potentials, the oscillating potential turns out to be fully invisible.
Floquet engineering, modulating quantum systems in a time periodic way, lies at the central part for realizing novel topological dynamical states. Thanks to the Floquet engineering, various new realms on experimentally simulating topological materials have emerged. Conventional Floquet engineering, however, only applies to time periodic non-dissipative Hermitian systems, and for the quantum systems in reality, non-Hermitian process with dissipation usually occurs. So far, it remains unclear how to characterize topological phases of periodically driven non-Hermitian systems via the frequency sp…
Non-Hermiticity is expected to add far more physical features to the already rich Floquet topological phases of matter. Nevertheless, a systematic approach to characterize non-Hermitian Floquet topological matter is still lacking. In this work we introduce a dual scheme to characterize the topology of non-Hermitian Floquet systems in momentum space and in real space, using a piecewise quenched nonreciprocal Su-Schrieffer-Heeger model for our case studies. Under the periodic boundary condition, topological phases are characterized by a pair of experimentally accessible winding numbers that make…
We show that non-Hermiticity enables topological phases with unidirectional transport in one-dimensional Floquet chains. The topological signatures of these phases are non-contractible loops in the spectrum of the Floquet propagator that are separated by an imaginary gap. Such loops occur exclusively in non-Hermitian Floquet systems. We define the corresponding topological invariant as the winding number of the Floquet propagator relative to the imaginary gap. To relate topology to transport, we introduce the concept of regularized dynamics of non-Hermitian chains. We establish that, under the…
Non-Hermitian topological phases in static and periodically driven systems have attracted great attention in recent years. Finding dynamical probes for these exotic phases would be of great importance in the detection and application of their topological properties. In this work, we propose a systematic approach to dynamically characterize non-Hermitian Floquet topological phases in one-dimension with chiral symmetry. We show that the topological invariants of a chiral symmetric Floquet system can be fully determined by measuring the winding angles of its time-averaged spin textures. We furthe…
Majorana edge modes are candidate elements of topological quantum computing. In this work, we purpose a Floquet engineering approach to generate arbitrarily many non-Hermitian Majorana zero and $π$ modes at the edges of a one-dimensional topological superconductor. Focusing on a Kitaev chain with periodically kicked superconducting pairings and gain/losses in the chemical potential or nearest neighbor hopping terms, we found rich non-Hermitian Floquet topological superconducting phases, which are originated from the interplay between drivings and non-Hermitian effects. Each of the phases is ch…
Floquet exceptional points correspond to the coalescence of two (or more) quasi-energies and corresponding Floquet eigenstates of a time-periodic non-Hermitian Hamiltonian. They generally arise when the oscillation frequency satisfies a multiphoton resonance condition. Here we discuss the interplay between Floquet exceptional points and the chiral dynamics observed, over several oscillation cycles, in a wide class of non-Hermitian systems when they are slowly cycled in opposite directions of parameter space.
In this paper, we study the existence of Floquet topological insulators for PT symmetric non-Hermitian Hamiltonians. We consider an array of waveguide in 1D with periodically changing non-Hermitian potential and predict the existence of Floquet topological insulators in the system. We also extend the concept of Floquet topological phase to a two dimensional non-Hermitian system.
The Zeldovich hypothesis is revised and the meaning of quasi energy spectra is discussed. The observation of Floquet resonance for microobjects in quickly oscillating external fields might bring a new information about the time scale of hypothetical quantum jumps.
In the framework of the ordinary non-relativistic quantum mechanics, it is known that a quantum particle in a rapidly-oscillating bound potential with vanishing time average can be scattered off or even trapped owing to the phenomenon of dynamical (Kapitza) stabilization. A similar phenomenon occurs for scattering and trapping of optical waves. Such a remarkable result stems from the fact that, even though the particle is not able to follow the rapid external oscillations of the potential, these are still able to affect the average dynamics by means of an effective -albeit small- nonvanishing …
Periodically driven non-Hermitian systems can exhibit rich topological band structure and non-Hermitian skin effect, without analogs in their static or Hermitian counterparts. In this work we investigate the exceptional band-touching points in the Floquet quasi-energy bands, the topological characterization of such exceptions points and the Floquet non-Hermitian skin effect (FNHSE). Specifically, we exploit the simplicity of periodically quenched two-band systems in one dimension or two dimensions to analytically obtain the Floquet effective Hamiltonian as well as locations of the many excepti…
Dynamical kicking systems possess rich topological structures. In this work, we study Floquet states of matter in a non-Hermitian extension of double kicked rotor model. Under the on-resonance condition, we find various non-Hermitian Floquet topological phases, with each being characterized by a pair of topological winding numbers. A generalized mean chiral displacement is introduced to detect these winding numbers dynamically in two symmetric time frames. Furthermore, by mapping the system to a periodically quenched lattice model, we obtain the topological edge states and unravel the bulk-edg…
In Hermitian topological systems, the bulk-boundary correspondence strictly constraints boundary transport to values determined by the topological properties of the bulk. We demonstrate that this constraint can be lifted in non-Hermitian Floquet insulators. Provided that the insulator supports an anomalous topological phase, non-Hermiticity allows us to modify the boundary states independently of the bulk, without sacrificing their topological nature. We explore the ensuing possibilities for a Floquet topological insulator with non-Hermitian time-reversal symmetry, where the helical transport …
For a simple illustrative model Hamiltonian for Xenon in low frequency linearly polarized laser field we obtain a remarkable agreement between the zero-order energy as well as amplitude and phase of the zero-order Floquet states and the exact eigenvalues and eigenfunctions of the Floquet operator. Here we use as a zero-order Hamiltonian the adiabatic Hamiltonian where time is used as an instantaneous parameter. Moreover, for a variety of low laser frequencies, $ω$, the deviation of the zero-order solutions from the exact quasi-energy (QE) Floquet solutions approaches zero at the time the oscil…
Floquet phases of matter have attracted great attention due to their dynamical and topological nature that are unique to nonequilibrium settings. In this work, we introduce a generic way of taking any integer $q$th-root of the evolution operator $U$ that describes Floquet topological matter. We further apply our $q$th-rooting procedure to obtain $2^n$th- and $3^n$th-root first- and second-order non-Hermitian Floquet topological insulators (FTIs). There, we explicitly demonstrate the presence of multiple edge and corner modes at fractional quasienergies $\pm(0,1,...2^{n})π/2^{n}$ and $\pm(0,1,.…
Periodically driven non-Hermitian systems could possess exotic nonequilibrium phases with unique topological, dynamical and transport properties. In this work, we introduce an experimentally realizable two-leg ladder model subjecting to both time-periodic quenches and non-Hermitian effects, which belongs to an extended CII symmetry class. Due to the interplay between drivings and nonreciprocity, rich non-Hermitian Floquet topological phases emerge in the system, with each of them been characterized by a pair of even-integer topological invariants $(w_{0},w_π)\in2\mathbb{Z}\times2\mathbb{Z}$. U…
Time-periodic driving fields could endow a system with peculiar topological and transport features. In this work, we find dynamically controlled localization transitions and mobility edges in non-Hermitian quasicrystals via shaking the lattice periodically. The driving force dresses the hopping amplitudes between lattice sites, yielding alternate transitions between localized, mobility edge and extended non-Hermitian quasicrystalline phases. We apply our Floquet engineering approach to five representative models of non-Hermitian quasicrystals, obtain the conditions of photon-assisted localizat…
We theoretically investigate the collisional heating of a cold atom system subjected to time-periodic forces. We show within the Floquet framework that this heating rate due to two-body collisions has a general semiclassical expression $\mathcal{P}\propto ρσv_{\rm col} E_0$, depending on the kinetic energy $E_0$ associated with the shaking, particle number density $ρ$, elastic collision cross section $σ$, and an effective collisional velocity $v_{\rm col}$ determined by the dominant energy scale in the system. We further show that the collisional heating is suppressed by Pauli blocking in cold…
Wave transport and scattering in open systems can be profoundly affected by non- Hermitian dynamics. In this work we consider wave scattering in a one-dimensional tight-binding lattice with a low-frequency harmonically-vibrating complex site potential. Floquet scattering is shown to be suppressed in a range of the spectral lattice band, which is limited by a singularity in the spectral transmission/reflection amplitudes for inelastic scattering channels. Invisibility over the entire spectral band is found when the singularity is pushed at the edge of the Brillouin zone, which requires a modula…
Recent experimental advances in Floquet engineering and controlling dissipation in open systems have brought about unprecedented flexibility in tailoring novel phenomena without any static and Hermitian analogues. It can be epitomized by the various Floquet and non-Hermitian topological phases. Topological classifications of either static/Floquet Hermitian or static non-Hermitian systems based on the underlying symmetries have been well established in the past several years. However, a coherent understanding and classification of Floquet non-Hermitian (FNH) topological phases have not been ach…
We consider non-Hermitian dynamics of a quantum particle hopping on a one-dimensional tight-binding lattice made of $N$ sites with asymmetric hopping rates induced by a time-periodic oscillating imaginary gauge field. A deeply different behavior is found depending on the lattice topology. While in a linear chain (open boundary conditions) an oscillating field can lead to a complex quasi energy spectrum via a multiple parametric resonance, in a ring topology (Born-von Karman periodic boundary conditions) an entirely real quasi energy spectrum can be found and the dynamics is pseudo-Hermitian. I…
The cooperation between time-periodic driving fields and non-Hermitian effects could endow systems with distinctive spectral and transport properties. In this work, we uncover an intriguing class of non-Hermitian Floquet matter in one-dimensional quasicrystals, which is characterized by the emergence of multiple driving-induced ${\cal PT}$-symmetry breaking/restoration, mobility edges, and reentrant localization transitions. These findings are demonstrated by investigating the spectra, level statistics, inverse participation ratios and wavepacket dynamics of a periodically quenched nonreciproc…
Synthesizing Arbitrary Non-Hermitian Hamiltonian with Stochastic Floquet Engineering
College of Science, NUDT（国防科技大学理学院）；Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University（天津大学理学院量子联合研究中心与物理系）；Department of Physics, Hunan Normal University（湖南师范大学物理系）
Eigenmode coalescence imparts remarkable properties to non-hermitian time evolution, culminating in a purely non-hermitian spectral degeneracy known as an exceptional point (EP). Here, we revisit time evolution at the EP and classify two-level non-hermitian Hamiltonians in terms of the Möbius group. We then leverage that classification to study dynamical EP encircling, by applying it to periodically-modulated (Floquet) Hamiltonians. This reveals that Floquet non-hermitian systems exhibit rich physics whose complexity is not captured by an EP-encircling rule. For example, Floquet EPs can occur …
It is generally believed that non-Hermiticity can transform Weyl semimetals into Weyl-exceptional-ring semimetals. However, this belief is from the systems without skin effect. We investigate the non-Hermitian Weyl semimental and its Floquet engineering in a system with skin effect, which breaks the bulk-boundary correspondence in its Hermitian counterpart. It is found in both the static and periodically driven cases that the skin effect makes this general belief no longer valid. We discover that exotic non-Hermitian topological matters, e.g., a composite phase of Weyl semimetal and topologica…
Topological states of matter in non-Hermitian systems have attracted a lot of attention due to their intriguing dynamical and transport properties. In this study, we propose a periodically driven non-Hermitian lattice model in one-dimension, which features rich Floquet topological phases. The topological phase diagram of the model is derived analytically. Each of its non-Hermitian Floquet topological phases is characterized by a pair of integer winding numbers, counting the number of real 0- and π-quasienergy edge states at the boundaries of the lattice. Non-Hermiticity induced Floquet topolog…
The non-Hermiticity caused breakdown of the bulk-boundary correspondence (BBC) in topological phase transition was cured by the skin effect for the systems with chiral symmetry and translation invariance. However, periodic driving, as an active tool in engineering exotic topological phases, breaks the chiral symmetry, and the inevitable disorder destroys the translation invariance. Here, we propose a scheme to retrieve the BBC and establish a complete description of the topological phases of the periodically driven non-Hermitian system both with and without the translation invariance. The demo…
Non-equilibrium phases of matter have attracted much attention in recent years, among which the Floquet phase is a hot point. In this work, based on the Periodic driving Non-Hermitian model, we reveal that the winding number calculated in the framework of the Bloch band theory has a direct connection with the number of edge states even the Non-Hermiticity is present. Further, we find that the change of the phase of the hopping amplitude can induce the topological phase transitions. Precisely speaking, the increase of the value of the phase can bring the system into the larger topological phase…
We construct a two-dimensional, discrete-time quantum walk exhibiting non-Hermitian skin effects under open-boundary conditions. As a confirmation of the non-Hermitian bulk-boundary correspondence, we show that the emergence of topological edge states are consistent with Floquet winding numbers calculated using a non-Bloch band theory invoking time-dependent generalized Billouin zones. Further, the non-Bloch topological invariants associated with quasienergy bands are captured by a non-Hermitian local Chern marker in real space, defined through local biorthogonal eigen wave functions of the no…
Spatiotemporal Non-Hermitian Skin Effect with Floquet-Engineered Ultracold Atoms
Quantum Institute for Light and Atoms, School of Physics, East China Normal University（华东师范大学物理学院光与原子量子研究所）；School of Physics and Astronomy, and Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学物理与天文学院及李政道研究所）；Shanghai Branch, Hefei National Laboratory（合肥国家实验室上海分部）；Shanghai Research Center for Quantum Sciences（上海量子科学研究与创新中心）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）
We determine the relevant spinor valued wave functions for a two-dimensional quantum ring in the presence of Rashba-type spin-orbit interaction (SOI). The case of constant SOI strength is considered first, then we investigate the physical consequences of time-dependent (oscillating) SOI strength. Floquet's method is applied to find time-dependent eigenspinors, and it is shown that the Floquet quasienergies and thus their differences (the generalized Rabi frequencies) are determined by the radial boundary conditions. Time evolution of various initial states is calculated.
Second-order topological insulator (SOTI) is featured with the presence of $(d-2)$-dimensional boundary states in $d$-dimension systems. The non-Hermiticity induced breakdown of bulk-boundary correspondence (BBC) and the periodic driving on systems generally obscure the description of non-Hermitian SOTI. To prompt the applications of SOTIs, we explore the role of periodic driving in controllably creating exotic non-Hermitian SOTIs both for 2D and 3D systems. A scheme to retrieve the BBC and a complete description to SOTIs via the bulk topology of such nonequilibrium systems are proposed. It is…
A quantum particle in a slowly-changing potential well $V(x,t)=V(x-x_0(εt))$, periodically shaken in time at a slow frequency $ε$, provides an important quantum mechanical system where the adiabatic theorem fails to predict the asymptotic dynamics over time scales longer than $ \sim 1 / ε$. Specifically, we consider a double-well potential $V(x)$ sustaining two bound states spaced in frequency by $ω_0$ and periodically-shaken in complex plane. Two different spatial displacements $x_0(t)$ are assumed: the real spatial displacement $x_0(εt)=A \sin (εt)$, corresponding to ordinary Hermitian shaki…
In this paper, we study how to apply a periodic driving field to control stable spin tunneling in a non-Hermitian spin-orbit coupled bosonic double-well system. By means of a high-frequency approximation, we obtain the analytical Floquet solutions and their associated quasienergies and thus construct the general non-Floquet solutions of the dissipative spin-orbit coupled bosonic system. Based on detailed analysis of the Floquet quasienergy spectrum, the profound effect of system parameters and the periodic driving field on the stability of spin-dependent tunneling is investigated analytically …
We introduce a time-dependent perturbation method to calculate the number of created particles in a 1D cavity with an oscillating wall of the frequency $Ω. $ This method makes it easy to find the dominant part of the solution which results from the parametric resonance. The maximal number of particles are created at the mode frequency $Ω/2 . $ Using the Floquet theory, we discuss the long-time behavior of the particle creation.
Non-Hermitian Hamiltonians provide a simple picture for inspecting dissipative systems with natural or induced gain and loss. We investigate the Floquet dynamical phase transition in the dissipative periodically time driven XY and extended XY models, where the imaginary terms represent the physical gain and loss during the interacting processes with the environment. The time-independent effective Floquet non-Hermitian Hamiltonians disclose three regions by analyzing the non-Hermitian gap: pure real gap (real eigenvalues), pure imaginary gap, and complex gap. We show that each region of the sys…
