The unitary design formation in random circuits has attracted considerable attention due to its wide range of practical applications and relevance to fundamental physics. While the formation rates in Haar random circuits have been extensively studied in previous works, it remains an open question how these rates are affected by the choice of local randomizers. In this Letter, we prove that the circuit depths required for general non-Haar random circuits to form unitary designs are upper bounded by those for the corresponding Haar random circuits, up to a constant factor independent of the system size. This result is derived in a broad range of circuit structures, including one- and higher-dimensional lattices, geometrically nonlocal configurations, and even extremely shallow circuits with patchwork architectures. We provide specific applications of these results in randomized benchmarking and random circuit sampling, and also discuss their implications for quantum many-body physics. Our results lays the foundation for flexible and robust randomness generation in real-world experiments, and offers new insights into chaotic dynamics in complex quantum systems.

We present an algorithm utilizing midcircuit measurement and feedback that prepares Dicke states with polylogarithmically many ancillae and polylogarithmic depth. Our algorithm uses only global midcircuit projective measurements and adaptively chosen global rotations. This improves over prior work that was only efficient for Dicke states of low weight or was not efficient in both depth and width. Our algorithm can also naturally be implemented in a cavity QED context using logarithmic time, zero ancillae, and atom-photon coupling scaling with the square root of the system size.

We investigate the full spectrum of twisted bilayer optical lattices (TBOLs) across all possible twist angles. Our calculation departs from the conventional moiré physics paradigm, which focuses on continuum theory at a fixed small twist angle. We discover that the full spectrum of a TBOL exhibits an astonishing fractal structure that resembles Hofstadter’s butterfly but with vanishing first Chern number. Yet unlike conventional butterfly band structures, these fractal bands emerge purely from the geometric moiré effects and do not require any external magnetic field. By mapping TBOL to a generalized Hofstadter model with long-range hopping, we reveal a universal algebraic structure underlying both systems. We also provide numerical evidence on the infinite recursive structures of the spectrum and present the algorithm for computing these structures.

Topological materials exhibit topologically protected surface states (TSS) characterized by helical spin texture and high charge-spin conversion efficiency, making them promising for high-performance spintronic devices. However, achieving gate control to switch between up and down spin-polarized states of TSS has been a significant challenge for developing spin field-effect transistors (FETs). Additionally, the limited density of states of TSS restricts the on-state spin signals and, consequently, the spin on-off ratio. Here, we demonstrate gate-tunable spin textures in the topological semimetal ${\mathrm{Cd}}_3{\mathrm{As}}_2$ achieved through surface modification with gold atoms, which induces the Rashba spin-splitting states (RSS) alongside the intrinsic TSS. The dominant spin textures are modulated by gate voltages, enabling the realization of spin-polarized current FETs. The incorporation of RSS enhances spin polarization signals, particularly in the conduction band, resulting in a gate-tunable on-off ratio of 72 000%, and exhibiting a highly efficient field-effect spin switching. Moreover, the emergent RSS generate a significant bilinear magnetoelectric resistance, which reverses its sign from the electron to hole regime. Our Letter presents a promising surface engineering approach for implementing spin FETs in topological materials, paving the way for advancements in spintronics.

We present an explicit Bethe-ansatz wave function to a 1D spin-$1/2$ interacting fermion system, manifesting a many-body resonance resulting from the interplay between interaction and non-Hermitian spin-orbit coupling. In the dilute limit, the Bethe-ansatz wave function is factorized into Slater determinants and a Jastrow factor. An effective thermodynamic distribution is constructed with an effective Hamiltonian including a repulsion resulting from Pauli’s exclusion principle and a distinctive zigzag potential arising from the resonance. The competition between these effects leads to a transition from a uniformly distributed configuration to a phase separation. Clustering of particles with identical spins is observed in the latter phase, demonstrating that the many-body resonance effect is enhanced by the repulsive interaction.

The LEGEND Collaboration is searching for neutrinoless double-beta ($0\nu \beta \beta$) decay by operating high-purity germanium detectors enriched in ${}^{76}\mathrm{Ge}$ in a low-background liquid argon environment. Building on key technological innovations from the GERmanium Detector Array (GERDA) experiment and the MAJORANA DEMONSTRATOR experiment, LEGEND-200 has performed a first $0\nu \beta \beta$ decay search based on 61.0 kg yr of data. Over half of this exposure comes from our highest performing detectors, including newly developed inverted-coaxial detectors, and is characterized by an estimated background level of ${0.5}_{-0.2}^{+0.3}\mathrm{cts}/(\mathrm{keV}\mathrm{ton}\mathrm{yr})$ in the $0\nu \beta \beta$ decay signal region. A combined analysis of data from GERDA, the MAJORANA DEMONSTRATOR, and LEGEND-200, characterized by a 90% confidence level exclusion sensitivity of $2.8\times {10}^{26}\mathrm{yr}$ on the half-life of $0\nu \beta \beta$ decay, reveals no evidence for a signal and sets a new observed lower limit at $T_{1/2}^{0\nu }>1.9\times {10}^{26}\mathrm{yr}$ (90% confidence level). Assuming the decay is mediated by Majorana neutrinos, this corresponds to an upper limit on the effective Majorana mass in the range $m_{\beta \beta }<75–200\mathrm{meV}$, depending on the adopted nuclear matrix element.

We investigate the recently discovered multiple superconducting states in rhombohedral graphene quarter metal. We demonstrate that one of these states features a single-spin, single-valley, single-band, single-Fermi-pocket parent state and is most likely a chiral topological pair-density wave, characterized by an ultra-small Fermi pocket and an ultra-large pairing momentum. This novel state exhibits three defining features: a 2D periodic modulation of the pairing phase compatible with the threefold symmetry; unpaired Majorana zero modes localized at edges, vortices, and pairing-phase dislocations; and an anomalous spin-polarized intrinsic superconducting diode effect.

We propose an entanglement protocol where ions illuminated by optical tweezers serve as control qubits. We experimentally demonstrate this proposal with a controlled Mölmer-Sörensen operation on a three-ion chain, analogous to the canonical Toffoli gate. Our demonstration features cases in which the control qubit was in one of its logical basis states, and not in their superposition, due to dephasing by tweezer beam intensity fluctuations. Finally, we discuss how our protocol generalizes to a broad class of unitary operations and larger qubit systems, enabling a single-pulse implementation of $n$-controlled unitaries.

Rapidly rotating black-hole spacetimes outside general relativity are key to many tests of Einstein’s theory. We here develop an efficient spectral method to represent such spacetimes analytically, in closed-form, and to high accuracy, in a large class of effective-field-theory extensions of general relativity. We exemplify this method by constructing, for the first time, closed-form and analytic representations of spinning black holes in scalar-Gauss-Bonnet, dynamical Chern-Simons, and axidilaton gravity to an accuracy better than ${10}^{-8}$ for all dimensionless spins below 0.99.

Trapped ions provide a highly controlled platform for quantum sensors, clocks, simulators, and computers, all of which depend on cooling ions close to their motional ground state. Existing methods like Doppler, resolved sideband, and dark resonance cooling balance trade-offs between the final temperature and cooling rate. A traveling polarization gradient has been shown to cool multiple modes quickly and in parallel, but utilizing a stable polarization gradient can achieve lower ion energies, while also allowing tailorable light-matter interactions in the sub-wavelength regime. In this Letter, we demonstrate cooling of a trapped ion below the Doppler limit using a phase-stable polarization gradient created using trap-integrated photonic devices. At an axial frequency of $2\pi \times 1.45\mathrm{MHz}$ we achieve $⟨n⟩=1.56\pm 0.07$ in $150\mathrm{\mu }\mathrm{s}$ and cooling rates of $\sim 0.3\mathrm{quanta}/\mathrm{\mu }\mathrm{s}$. We examine ion dynamics under different polarization gradient phases, detunings, and intensities, showing reasonable agreement between experimental results and a multilevel model. Cooling is fast and power efficient, with lower average motional Fock state occupation when compared to simulated operation under the corresponding running wave configuration. Our results demonstrate a well-controlled test bed for studying the dynamics of multilevel atomic systems in a phase-stable polarization gradient.

Dirac points, arising from intrinsic space-group symmetry in hexagonal lattices, have been extensively explored in graphene and photonic crystals. However, their characteristic scales, confined either to atomic level ($\sim \AA$) or limited by the operational wavelength ($\sim \lambda$), pose fundamental challenges for precisely engineering their topological properties and thus freely controlling the wave-transport behaviors in such systems. Here, beyond the conventional lattice-dependent paradigm, we demonstrate a type-I photonic Dirac point in the surface modes of an electromagnetic metasurface. This realization, governed by the intrinsic properties of constitutional units rather than the global crystalline symmetry, enables us to control Dirac physics in deep-subwavelength scales. Owing to the vanishing density of states at the type-I Dirac degeneracy, by strategically integrating inhomogeneous local symmetry breaking as an artificial gauge field, we experimentally observe supersymmetric Landau levels and chiral zero modes with deep-subwavelength precision in the microwave regime. Such a platform offers a branch-new approach to freely control surface waves through precisely engineering the spatial distribution of the gauge field imposed, with bending, focusing, and spreading of surface waves experimentally demonstrated. By harnessing the mode-tuning flexibility of metasurfaces, our Letter establishes a versatile platform for topology-driven optical manipulation.