Unifying quantum mechanics and special relativity, the Dirac equation describes the behaviour of relativistic quantum particles, including imaginary-mass particles with faster-than-light speeds (e.g., tachyon). However, experimental searches for such particles remain negative so far. Fortunately, there are possibilities to investigate the relativistic quantum effects by quantum simulations using a controllable system. However, these simulations are mostly explored in closed physical systems that hinders the demonstration of imaginary-mass particles, whereas the general open framework would promise more possibilities in quantum simulations. Here, we reveal that the dynamic behaviors of imaginary-mass particles can be mapped to the transfer of wave packet in a non-Hermitian silicon optical lattice. We experimentally demonstrate a super-divergent dynamics of tachyon that travels faster than massless particles (e.g., photon). Besides, our simulation suggests another kind of imaginary-mass particles that have rarely been explored, which show non-divergent behaviors with imaginary energy. It is the first experimental quantum simulation being able to observe the imaginary-mass particles that have never been experimentally verified. Our work provides a fully controllable and extensible platform to investigate relativistic quantum phenomena at a chip-scale level, which would inspire more insightful explorations in quantum effects with non-Hermiticity.
We propose a mechanism to achieve the group velocity control of bifurcation light via an imaginary coupling effect in the non-reciprocal lattice. The physical model is composed of two-layer photonic lattices with non-reciprocal coupling in each unit cell, which can support a real energy spectrum with a pair of Dirac points in the first Brillouin zone due to the Hermicity. Furthermore, we show that the systems experience topological phase transition at the Dirac points by tuning the coupling strength, allowing the existence of topological edge states on the left or right boundaries of respectiv…
Exceptional point (EP) degeneracies in coupled cavities with gain and loss provide on-chip photonic devices with unconventional features and performance. However, such systems with realistic structures often miss the exact EPs even in simulation, and the mechanism of this EP disruption has yet to be thoroughly identified. Here, we extend the coupled-mode theory of one-dimensional non-Hermitian resonator arrays to study the effects of the imaginary part of the inter-cavity coupling, which is a second-order term and attributed to material amplification, absorption, and radiation. By taking an ap…
We investigate a uniformly coupled non-Hermitian system with asymmetric coupling amplitude. The asymmetric coupling equals to a symmetric coupling threaded by an imaginary gauge field. In a closed configuration, the imaginary gauge field leads to an imaginary magnetic flux, which induces a non-Hermitian phase transition. For an open boundary, the imaginary gauge field results in an eigenstate localization. The eigenstates under Dirac and biorthogonal norms and the scaling laws are quantitatively investigated to show the affect of asymmetric coupling induced one-way amplification. However, the …
A nonadiabatic and robust method of excitation transfer in a non-Hermitian tight-binding linear chain, assisted by an imaginary gauge field, is theoretically proposed. The gauge field undergoes a linear gradient in time, from a negative to a positive value, which results in an effective transfer of excitation between the two edge sites of the chain. An imaginary (gain and loss) gradient of site energy potentials is introduced to exactly cancel nonadiabatic effects, thus providing an effective shortcut to adiabaticity and pseudo-Hermitian dynamics. Numerical simulations indicate that the non-He…
In this paper, a non-Hermitian two-dimensional photonic crystal flat lens is proposed. The negative refraction of the second band of photonic crystal is utilized to realize super-resolution imaging of the point source. Based on the principles of non-Hermitian systems, a negative imaginary part is introduced into the imaging frequency, in which case the imaging intensity and resolution are improved. The results indicate that the non-Hermitian system provides a new method to improve the imaging performance of the photonic crystal lens.
We propose a general design strategy based on genetic optimization to realize asymmetric reflectivity in periodic and non-periodic planar structures containing dielectric and gain-loss layers. By means of an optimization algorithm, it is possible to design the imaginary (or real) part of the complex permittivity distribution from any given and arbitrary real (or imaginary) permittivity distribution, i.e to create non-Hermitian potentials intended to achieve on-demand light transport for a selected spectral range. Indeed, the asymmetric response of the obtained complex permittivity distribution…
Non-Hermitian Dirac Vortex: Minimal Theory for Topological-Cavity Surface-Emitting Laser
Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Beijing National Laboratory for Condensed Matter Physics（北京凝聚态物理国家研究中心）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Institute for Advanced Study, Tsinghua University（清华大学高等研究院）
An imaginary gauge transformation is at the core of the non-Hermitian skin effect. Here we show that such a transformation can be performed in momentum space as well, which reveals that certain gain and loss modulated systems in their parity-time (PT) symmetric phases are equivalent to Hermitian systems with real potentials. Our analysis in momentum space also distinguishes two types of exceptional points (EPs) in the same system. Besides the conventional type that leads to a PT transition upon the continuous increase of gain and loss, we find real-valued energy bands connected at a Dirac EP i…
We study numerically the localization properties of eigenstates in a one-dimensional random lattice described by a non-Hermitian disordered Hamiltonian, where both the disorder and the non-Hermiticity are inserted simultaneously in the on-site potential. We calculate the averaged participation number, the Shannon entropy and the structural entropy as a function of other parameters. We show that, in the presence of an imaginary random potential, all eigenstates are localized in the thermodynamic limit and strong anomalous Anderson localization occurs at the band center. In contrast to the usual…
Chiral symmetry provides the symmetry protection for a large class of topological edge states. It exists in non-Hermitian systems as well, and the same anti-commutation relation between the Hamiltonian and a linear chiral operator, i.e., $\{H,Π\}=0$, now warrants a symmetric spectrum about the origin of the complex energy plane. Here we show two general approaches to identify and generate chiral symmetry in non-Hermitian systems, with an emphasis on lattices with detuned on-site potentials that can vary in both their real and imaginary parts. One approach utilizes the Clifford algebra satisfie…
Optical superlattices with sublattice symmetry subjected to a synthetic imaginary gauge field undergo a topological phase transition in the Bloch energy spectrum, characterized by the change of a spectral winding number. For a narrow gap, the phase transition is of universal form and described by a non-Hermitian Dirac equation with Lorentz-symmetry violation. A simple photonic system displaying such a phase transition is discussed, which is based on light coupling in co-propagating gratings.
We investigate the propagation of Gaussian beams through optical waveguide lattices characterized by correlated non-Hermitian disorder. In the framework of coupled mode theory, we demonstrate how the imaginary part of the refractive index needs to be adjusted to achieve perfect beam transmission, despite the presence of disorder. Remarkably, the effects of both diagonal and off-diagonal disorder in the waveguides and their couplings can be efficiently eliminated by our non-Hermitian design. Waveguide arrays thus provide an ideal platform for the experimental realization of non-Hermitian phenom…
Combating the effects of disorder on light transport in micro- and nano-integrated photonic devices is of major importance from both fundamental and applied viewpoints. In ordinary waveguides, imperfections and disorder cause unwanted back-reflections, which hinder large-scale optical integration. Topological photonic structures, a new class of optical systems inspired by quantum Hall effect and topological insulators, can realize robust transport via topologically-protected unidirectional edge modes. Such waveguides are realized by the introduction of synthetic gauge fields for photons in a t…
We present a numerical study of Anderson localization in disordered non-Hermitian lattice models with flat bands. Specifically we consider one-dimensional stub and two-dimensional kagome lattices that have a random scalar potential and a uniform imaginary vector potential and calculate the spectra of the complex energy, the participation ratio, and the winding number as a function of the strength of the imaginary vector potential, $h$. The flat-band states are found to show a double transition from localized to delocalized and back to localized states with $h$, in contrast to the dispersive-ba…
By introducing the next-nearest-neighboring (NNN) intersite coupling, we investigate the eigenenergies of the $\cal PT$-symmetric non-Hermitian Su-Schrieffer-Heeger (SSH) model with two conjugated imaginary potentials at the end sites. It is found that with the strengthening of NNN coupling, the particle-hole symmetry is destroyed. As a result, the bonding band is first narrowed and then undergoes the top-bottom reversal followed by the its width's increase, whereas the antibonding band is widened monotonously. In this process, the topological state extends into the topologically-trivial regio…
In conventional Hermitian systems with the open boundary condition, Bloch's theorem is perturbatively broken down, which means although the crystal momentum is not a good quantum number, the eigenstates are the superposition of several extended Bloch waves. In this paper, we show that Bloch's theorem can be non-perturbatively broken down in some Hermitian Bosonic systems. The quasiparticles of the system are the superposition of localized non-Bloch waves, which are characterized by the complex momentum whose imaginary part determines the localization properties. Our work is a Hermitian general…
We unveil an unexpected non-Hermitian phenomenon, dubbed edge burst, in non-Hermitian quantum dynamics. Specifically, in a class of non-Hermitian quantum walk in periodic lattices with open boundary condition, an exceptionally large portion of loss occurs at the system boundary. The physical origin of this edge burst is found to be an interplay between two unique non-Hermitian phenomena: non-Hermitian skin effect and imaginary gap closing. Furthermore, we establish a universal bulk-edge scaling relation underlying the non-Hermitian edge burst. Our predictions are experimentally accessible in v…
