Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userNon-Floquet engineering in periodically driven non-Hermitian systems
176
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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 space Floquet Hamiltonian. Here, we propose the non-Floquet theory to identify different Floquet topological phases of time periodic non-Hermitian systems via the generation of Floquet band gaps in frequency space. In non-Floquet theory, the eigenstates of non-Hermitian Floquet Hamiltonian are temporally deformed to be of Wannier-Stark localization. Remarkably, we show that different choices of starting points of driving period can result to different localization behavior, which effect can reversely be utilized to design detectors of quantum phases in dissipative oscillating fields. Our protocols establish a fundamental rule for describing topological features in non-Hermitian dynamical systems and can find its applications to construct new types of Floquet topological materials.
rate research
Read More
Models based on non-Hermitian Hamiltonians can exhibit a range of surprising and potentially useful phenomena. Physical realizations typically involve couplings to sources of incoherent gain and loss; this is problematic in quantum settings, because of the unavoidable fluctuations associated with this dissipation. Here, we present several routes for obtaining unconditional non-Hermitian dynamics in non-dissipative quantum systems. We exploit the fact that quadratic bosonic Hamiltonians that do not conserve particle number give rise to non-Hermitian dynamical matrices. We discuss the nature of these mappings from non-Hermitian to Hermitian Hamiltonians, and explore applications to quantum sensing, entanglement dynamics and topological band theory. The systems we discuss could be realized in a variety of photonic and phononic platforms using the ubiquitous resource of parametric driving.
Symmetry plays fundamental role in physics and the nature of symmetry changes in non-Hermitian physics. Here the symmetry-protected scattering in non-Hermitian linear systems is investigated by employing the discrete symmetries that classify the random matrices. The even-parity symmetries impose strict constraints on the scattering coefficients: the time-reversal (C and K) symmetries protect the symmetric transmission or reflection; the pseudo-Hermiticity (Q symmetry) or the inversion (P) symmetry protects the symmetric transmission and reflection. For the inversion-combined time-reversal symmetries, the symmetric features on the transmission and reflection interchange. The odd-parity symmetries including the particle-hole symmetry, chiral symmetry, and sublattice symmetry cannot ensure the scattering to be symmetric. These guiding principles are valid for both Hermitian and non-Hermitian linear systems. Our findings provide fundamental insights into symmetry and scattering ranging from condensed matter physics to quantum physics and optics.
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 localization transitions and mobility edges, and find the expressions of Lyapunov exponents for some models. We further introduce topological winding numbers of Floquet quasienergies to distinguish non-Hermitian quasicrystalline phases with different localization nature. Our discovery thus extend the study of quasicrystals to non-Hermitian Floquet systems, and provide an efficient way of modulating the topological and transport properties of these unique phases.
Bulk-boundary correspondence, connecting the bulk topology and the edge states, is an essential principle of the topological phases. However, the bulk-boundary correspondence is broken down in general non-Hermitian systems. In this paper, we construct one-dimensional non-Hermitian Su-Schrieffer-Heeger model with periodic driving that exhibits non-Hermitian skin effect: all the eigenstates are localized at the boundary of the systems, whether the bulk states or the zero and the $pi$ modes. To capture the topological properties, the non-Bloch winding numbers are defined by the non-Bloch periodized evolution operators based on the generalized Brillouin zone. Furthermore, the non-Hermitian bulk-boundary correspondence is established: the non-Bloch winding numbers ($W_{0,pi}$) characterize the edge states with quasienergies $epsilon=0, pi$. In our non-Hermitian system, a novel phenomenon can emerge that the robust edge states can appear even when the Floquet bands are topological trivial with zero non-Bloch band invariant, which is defined in terms of the non-Bloch effective Hamiltonian. We also show that the relation between the non-Bloch winding numbers ($W_{0,pi}$) and the non-Bloch band invariant ($mathcal{W}$): $mathcal{W}= W_{0}- W_{pi}$.
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 via counterpropagating boundary states can be tailored in ways that overcome the constraints imposed by Hermiticity. Non-Hermitian boundary state engineering specifically enables the enhancement of boundary transport relative to bulk motion, helical transport with a preferred direction, and chiral transport in the same direction on opposite boundaries. We explain the experimental relevance of our findings for the example of photonic waveguide lattices.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
