An official website of the United States government
Abstract An extensive number of the eigenstates can become exponentially localized at one boundary of nonreciprocal non-Hermitian systems. This effect is known as the non-Hermitian skin effect and has been studied mostly in tight-binding lattices. To extend the skin effect to continues systems beyond 1D, we introduce a quadratic imaginary vector potential in the continuous two dimensional Schrödinger equation. We find that inseparable eigenfunctions for separable nonreciprocal Hamiltonians appear under infinite boundary conditions. Introducing boundaries destroy them and hence they can only be used as quasi-stationary states in practice. We show that all eigenstates can be clustered at the point where the imaginary vector potential is minimum in a confined system.
more »
« less
Non-Hermitian Systems with a Real Spectrum and Selective Skin Effect
In this work, we first show a simple approach to constructing non-Hermitian Hamiltonians with a real spectrum, which are not obtained by a non-unitary transformation such as the imaginary gauge transformation. They are given, instead, by the product of a Hermitian Hamiltonian H0 and a positive semi-definite matrix A. Depending on whether A has zero eigenvalue(s), the resulting H can possess an exceptional point at zero energy. When A is only required to be Hermitian instead, the resulting H is pseudo-Hermitian that can have real and complex conjugate energy levels. In the special case where A is diagonal, we compare our approach to an imaginary gauge transformation, which reveals a selective non-Hermitian skin effect in our approach, i.e., only the zero mode is a skin mode and the non-zero modes reside in the bulk. We further show that this selective non-Hermitian skin mode has a much lower lasing threshold than its counterpart in the standard non-Hermitian skin effect with the same spatial profile, when we pump at the boundary where they are localized. The form of our construction can also be found, for example, in dynamical matrices describing coupled frictionless harmonic oscillators with different masses.
more »
« less
- PAR ID:
- 10504140
- Publisher / Repository:
- Innovation Discovery
- Date Published:
- Journal Name:
- Innovation Discovery
- Volume:
- 1
- Issue:
- 1
- ISSN:
- 2959-5150
- Page Range / eLocation ID:
- 4
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Zero modes are symmetry protected ones whose energy eigenvalues have zero real parts. In Hermitian arrays, they arise as a consequence of the sublattice symmetry, implying that they are dark modes. In non-Hermitian systems that naturally emerge in gain/loss optical cavities, particle-hole symmetry prevails instead; the resulting zero modes are no longer dark but feature phase jumps between adjacent cavities. Here, we report on the direct observation of zero modes in a non-Hermitian three coupled photonic crystal nanocavities array containing quantum wells. Unlike the Hermitian counterparts, the observation of non-Hermitian zero modes upon single pump spot illumination requires vanishing sublattice detuning, and they can be identified through far-field imaging and spectral filtering of the photoluminescence at selected pump locations. We explain the zero-mode coalescence as a parity-time phase transition for small coupling. These zero modes are robust against coupling disorder and can be used for laser mode engineering and photonic computing.more » « less
-
Abstract Topological and symmetry‐protected non‐Hermitian zero modes have attracted considerable interest in the past few years. Here, it is revealed that they can exhibit an unusual behavior when transitioning between the extended and localized regimes: When weakly coupled to a non‐Hermitian reservoir, such a zero mode displays a linearly decreasing amplitude as a function of space, which is not caused by an EP of a Hamiltonian, either of the entire system or the reservoir itself. Instead, this phenomenon is due to the non‐Bloch solution of a linear homogeneous recurrence relation, together with the underlying non‐Hermitian particle‐hole symmetry and the zeroness of its energy.more » « less
-
The geometrical Berry phase is key to understanding the behavior of quantum states under cyclic adiabatic evolution. When generalized to non-Hermitian systems with gain and loss, the Berry phase can become complex and should modify not only the phase but also the amplitude of the state. Here, we perform the first experimental measurements of the adiabatic non-Hermitian Berry phase, exploring a minimal two-site PT-symmetric Hamiltonian that is inspired by the Hatano-Nelson model. We realize this non-Hermitian model experimentally by mapping its dynamics to that of a pair of classical oscillators coupled by real-time measurement-based feedback. As we verify experimentally, the adiabatic non-Hermitian Berry phase is a purely geometrical effect that leads to significant amplification and damping of the amplitude also for noncyclical paths within the parameter space even when all eigenenergies are real. We further observe a non-Hermitian analog of the Aharonov-Bohm solenoid effect, observing amplification and attenuation when encircling a region of broken PT symmetry that serves as a source of imaginary flux. This experiment demonstrates the importance of geometrical effects that are unique to non-Hermitian systems and paves the way towards further studies of non-Hermitian and topological physics in synthetic metamaterials.more » « less
-
The non-Hermitian models, which are symmetric under parity (P) and time-reversal (T) operators, are the cornerstone for the fabrication of new ultra-sensitive optoelectronic devices. However, providing the gain in such systems usually demands precise control of nonlinear processes, limiting their application. In this paper, to bypass this obstacle, we introduce a class of time-dependent non-Hermitian Hamiltonians (not necessarily Floquet) that can describe a two-level system with temporally modulated on-site potential and couplings. We show that implementing an appropriate non-Unitary gauge transformation converts the original system to an effective one with a balanced gain and loss. This will allow us to derive the evolution of states analytically. Our proposed class of Hamiltonians can be employed in different platforms such as electronic circuits, acoustics, and photonics to design structures with hiddenPT-symmetry potentially without imaginary onsite amplification and absorption mechanism to obtain an exceptional point.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.53964/id.2024004
