Topological phases of matter that have been recently extended to topological phases of sound can confine acoustic energy at the corners of higher-order topological insulators. We broaden this concept by incorporating parity-time symmetry and show new topologically protected confinement rules that are dictated by the geometrical arrangement of gain and loss units. Particularly, our findings reveal how sound trapping occurs at all corners when parity-time symmetry is intact, beyond the exceptional point within the broken phase; however, opposite corners sustain either sink-or sourcelike states that could lead to novel non-Hermitian guides for sound.

We study photoelectron angular distributions (PADs) near the ionization threshold with a newly developed Coulomb quantum-orbit strong-field approximation (CQSFA) theory. The CQSFA simulations exhibit an excellent agreement with the result from the time-dependent Schrödinger equation. We show that the low-energy fan-shaped pattern in the PADs corresponds to a subcycle time-resolved holographic structure and stems from the significant influence of the Coulomb potential on the phase of the forward-scattered electron trajectories, which affects different momenta and scattering angles unequally. Our work provides a direct explanation of how the fan-shaped structure is formed, based on the quantum interference of direct and forward-scattered orbits. Moreover, our work shows that the fan-shaped pattern can be used to extract information on the target structure, as the number of fringes in the PADs depends strongly on the symmetry of the electronic bound state.

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We unambiguously identify, in experiment and theory, an overlooked holographic interference pattern in strong-field ionization, dubbed "the spiral," stemming from two trajectories where the potential and laser field are equally critical. Because of the strong interaction with the core of the two trajectories, the spiral could be employed as an optimal tool for probing the target after ionization and for revealing obfuscated phases in the bound states. We find that the spiral is responsible for interference carpets, formerly ascribed to direct trajectories, and that the carpet-interference condition is derived from the field symmetry. This case of mistaken identity may have prevented the spiral from being used as a holographic tool.