First experimental realization of the Dirac oscillator

Optical trimer: a theoretical physics approach to waveguide couplers

We study electromagnetic field propagation through an ideal, passive, three-dimensional, triangular three-waveguide coupler using a symmetry-based approach that capitalizes on the underlying su(3) symmetry. The planar version of this platform has already demonstrated its utility in photonic circuit design, enabling optical sampling, filtering, modulating, multiplexing, and switching. We aim to provide a practical tutorial on using group theory for the analysis of photonic lattices for those less familiar with abstract algebra methods. This approach serves as a powerful tool for optical designs. To illustrate this, we focus on the equilateral trimer, connected to the discrete Fourier transform, and the isosceles trimer, related to the golden ratio, providing stable single waveguide output. We also explore a scenario where the coupling in an equilateral coupler changes linearly with propagation distance. Going beyond the standard optical-quantum analogy, we show that coupled-mode equations for intensity and phase allows us to calculate envelopes for inputs within an intensity class, as well as individual input field amplitudes. This approach streamlines the design process by eliminating the need for point-to-point propagation calculations, highlighting the power of group theory in the field of photonic design.

Realization of Gapped and Ungapped Photonic Topological Anderson Insulators

It is commonly believed that topologically nontrivial one-dimensional systems support edge states rather than bulk states at zero energy. In this work, we find an unanticipated case of topological Anderson insulator (TAI) phase where two bulk modes are degenerate at zero energy, in addition to degenerate edge modes. We term this "ungapped TAI" to distinguish it from the previously known gapped TAIs. Our experimental realization of both gapped and ungapped TAIs relies on coupled photonic resonators, in which the disorder in coupling is judiciously engineered by adjusting the spacing between the resonators. By measuring the local density of states both in the bulk and at the edges, we demonstrate the existence of these two types of TAIs, together forming a TAI plateau in the phase diagram. Our experimental findings are well supported by theoretical analysis. In the ungapped TAI phase, we observe stable coexistence of topological edge states and localized bulk states at zero energy, highlighting the distinction between TAIs and traditional topological insulators.

The generalized relativistic harmonic oscillator with a point interaction

We study the perturbation of the one-dimensional generalized relativistic harmonic oscillator (GRHO) by a Lorentz scalar delta-shaped interaction. By exactly solving the implied Dirac equation, we show that the presence of the singular potential brings about drastic changes in the structure of the energy spectrum of the system. Particularly, an apparent anomaly of doubly degenerate energy levels is noted when the strength of the local term becomes infinite and energy eigenvalues in the range [ - m c 2 , m c 2 ] are obtained for some negative values of the delta-coupling and for all settings of the oscillator parameters.

Relativistic Measurement Backaction in the Quantum Dirac Oscillator

An elegant method to circumvent quantum measurement backaction is the use of quantum mechanics free subsystems (QMFS), with one approach involving the use of two oscillators with effective masses of opposite signs. Since negative energies, and hence masses, are a characteristic of relativistic systems a natural question is to what extent QMFS can be realized in this context. Using the example of a one-dimensional Dirac oscillator we investigate conditions under which this can be achieved, and identify Zitterbewegung or virtual pair creation as the physical mechanism that fundamentally limits the feasibility of the scheme. We propose a tabletop implementation of a Dirac oscillator system based on a spin-orbit coupled ultracold atomic sample that allows for a direct observation of the corresponding analog of virtual pair creation on quantum measurement backaction.

Selective enhancement of topologically induced interface states in a dielectric resonator chain

The recent realization of topological phases in insulators and superconductors has advanced the search for robust quantum technologies. The prospect to implement the underlying topological features controllably has given incentive to explore optical platforms for analogous realizations. Here we realize a topologically induced defect state in a chain of dielectric microwave resonators and show that the functionality of the system can be enhanced by supplementing topological protection with non-hermitian symmetries that do not have an electronic counterpart. We draw on a characteristic topological feature of the defect state, namely, that it breaks a sublattice symmetry. This isolates the state from losses that respect parity-time symmetry, which enhances its visibility relative to all other states both in the frequency and in the time domain. This mode selection mechanism naturally carries over to a wide range of topological and parity-time symmetric optical platforms, including couplers, rectifiers and lasers.

At interfaces between systems with topologically distinct band structure, robust symmetry protected states emerge. Here, Poli et al. control such states in a coupled dielectric resonator chain with parity-time symmetry and exploit their topological nature to protect them from absorptive losses.

Transparent lattices and their solitary waves

We provide a family of transparent tight-binding models with nontrivial potentials and site-dependent hopping parameters. Their feasibility is discussed in electromagnetic resonators, dielectric slabs, and quantum-mechanical traps. In the second part of the paper, the arrays are obtained through a generalization of supersymmetric quantum mechanics in discrete variables. The formalism includes a finite-difference Darboux transformation applied to the scattering matrix of a periodic array. A procedure for constructing a hierarchy of discrete Hamiltonians is indicated and a particular biparametric family is given. The corresponding potentials and hopping functions are identified as solitary waves, pointing to a discrete spinorial generalization of the Korteweg-deVries family.

Optimal control of effective Hamiltonians

We present a systematic scheme for the optimization of quantum simulations. Specifically, we show how polychromatic driving can be used to significantly improve the driving of Raman transitions in the Lambda system, which opens new possibilities for controlled driving-induced effective dynamics.