The surfaces of intrinsic magnetic topological insulators (TIs) host magnetic moments exchange-coupled to Dirac electrons. We study the magnetic phases arising from tuning the electron density using variational and exact diagonalization approaches. In the dilute limit, we find that magnetic skyrmions are formed, which bind to electrons, leading to a skyrmion Wigner crystal phase while at higher densities spin spirals accompanied by chiral one-dimensional channels of electrons are formed. The binding of electrons to textures raises the possibility of manipulating textures with electrostatic gating. We determine the phase diagram capturing the competition of intrinsic spin-spin interactions and carrier density and comment on the possible application to experiments in magnetic TIs and spintronic devices such as skyrmion-based memory.

The phase behavior of liquids confined in a slit geometry does not reveal a crossover from a three- to a two-dimensional behavior as the gap size decreases. Indeed, the prototypical two-dimensional hexatic phase only occurs in liquids confined to a monolayer. Here, we demonstrate that the dimensionality crossover is apparent in the lateral size dependence of the relaxation dynamics of confined liquids, developing a Debye model for the density of vibrational states of confined systems and performing extensive numerical simulations. In confined systems, Mermin-Wagner fluctuations enhance the amplitude of vibrational motion—or the Debye-Waller factor—by a quantity scaling as the inverse gap width and proportional to the logarithm of the aspect ratio, as a clear signature of a two-dimensional behavior. As the temperature or lateral system size increases, the crossover to a size-independent relaxation dynamics occurs when structural relaxation takes place before the vibrational modes with the longest wavelength develop.

We preform dynamic state evolution on an IBM quantum computer using a simulation of braiding Majorana zero modes as a benchmark for success. We find the native quantum gates introduce too much noise to observe braiding. Instead, we use Qiskit Pulse to develop scaled 2-qubit quantum gates that better match the unitary time evolution operator and enable us to observe braiding. This paper demonstrates that quantum computers can be used for simulation, and highlights the use of pulse-level control for programming quantum computers and constitutes the first experimental evidence of braiding via dynamical Hamiltonian evolution.

Experimental results on the phase transfer from structured beams to parametric light, generated by inducing four-wave mixing in an atomic gas, are reported. Near-infrared, Mathieu, and Gaussian pump beams yield a blue coherent Mathieu electromagnetic field and an infrared beam. Two complementary techniques enable full characterization of the up-converted modes. The unambiguous and efficient phase heritage of these complex quasipropagation invariant modes to up-converted photons is demonstrated. The presented data enable a quantitative study of dynamical variables related to Mathieu beams. These include elliptic angular momentum, a generalization of the orbital angular momentum of light, which is also up-converted through the nonlinear process.

We introduce a thermodynamically consistent, minimal stochastic model for complementary logic gates built with field-effect transistors. We characterize the performance of such gates with tools from information theory and study the interplay between accuracy, speed, and dissipation of computations. With a few universal building blocks, such as the not and nand gates, we are able to model arbitrary combinatorial and sequential logic circuits, which are modularized to implement computing tasks. We find generically that high accuracy can be achieved provided sufficient energy consumption and time to perform the computation. However, for low-energy computing, accuracy and speed are coupled in a way that depends on the device architecture and task. Our work bridges the gap between the engineering of low dissipation digital devices and theoretical developments in stochastic thermodynamics, and provides a platform to study design principles for low dissipation digital devices.

The Bethe-Salpeter equation plays a crucial role in understanding the physics of correlated fermions, relating to optical excitations in solids as well as resonances in high-energy physics. Yet, it is notoriously difficult to control numerically, typically requiring an effort that scales polynomially with energy scales and accuracy. This puts many interesting systems out of computational reach. Using the intermediate representation and sparse modeling for two-particle objects on the Matsubara axis, we develop an algorithm that solves the Bethe-Salpeter equation in $\mathcal{O}\left(L^8\right)$ time with $\mathcal{O}\left(L^4\right)$ memory, where $L$ grows only logarithmically with inverse temperature, bandwidth, and desired accuracy. This opens the door for computations in hitherto inaccessible regimes. We benchmark the method on the Hubbard atom and on the multiorbital weak-coupling limit, where we observe the expected exponential convergence to the analytical results. We then showcase the method for a realistic impurity problem.

Within a Dirac model in $1+1$ dimensions, a prototypical model to describe low-energy physics for a wide class of lattice models, we propose a field-theoretical version for the representation of Wannier functions, the Zak-Berry connection, and the geometric tensor. In two natural Abelian gauges we present universal scaling of the Dirac Wannier functions in terms of four fundamental scaling functions that depend only on the phase $\gamma$ of the gap parameter and the charge correlation length $\xi$ in an insulator. The two gauges allow for a universal low-energy formulation of the surface charge and surface fluctuation theorem, relating the boundary charge and its fluctuations to bulk properties. Our analysis describes the universal aspects of Wannier functions for the wide class of one-dimensional generalized Aubry-André-Harper lattice models. In the low-energy regime of small gaps we demonstrate universal scaling of all lattice Wannier functions and their moments in the corresponding Abelian gauges. In particular, for the quadratic spread of the lattice Wannier function, we find the universal result $Za\xi /8$, where $Za$ is the length of the unit cell. This result solves a long-standing problem providing further evidence that an insulator is only characterized by the two fundamental length scales $Za$ and $\xi$. Finally, we discuss also non-Abelian lattice gauges and find that lattice Wannier functions of maximal localization show universal scaling and are uniquely related to the Dirac Wannier function of the lower band. In addition, via the winding number of the determinant of the non-Abelian transformation, we establish a bulk-boundary correspondence for the number of edge states up to the bottom of a certain band, which requires no symmetry constraints. Our results present evidence that universal aspects of Wannier functions and of the boundary charge are uniquely related and can be elegantly described within universal low-energy theories.

We develop a strong-coupling theory of Bose-Einstein condensate-mediated superconductivity in a hybrid system, which consists of a two-dimensional electron gas with either: (i) parabolic spectrum or (ii) relativistic Dirac spectrum in the vicinity of a two-dimensional solid-state condensate of indirect excitons. The Eliashberg equations are derived, and the expressions for the electron pairing self-energy due to the exchange interaction between electrons mediated by a single Bogoliubov excitation (a bogolon) and the bogolon pairs are found. Furthermore, we find the superconducting order parameter and estimate the critical temperature of the superconducting transition. The critical temperature reveals its linear dependence on the dimensionless coupling constant. It is shown that the bogolon-pair-mediated interaction is the dominant mechanism of electron pairing in hybrid systems in both the weak- and the strong-coupling regimes. We calculate the effective bogolon-electron interaction constant for both parabolic and linear electron dispersions and examine the dependence of the critical temperature of the superconducting transition on exciton condensate density.

We present a study of the Rydberg spectrum in ${}^{166}\mathrm{Er}$ for series connected to the $4f^{12}\left({}^{3}H_6\right)6s$, $J_c=13/2$, and $J_c=11/2$ ionic core states using an all-optical detection based on electromagnetically induced transparency in an effusive atomic beam. Identifying approximately 550 individual states, we find good agreement with a multichannel quantum defect theory (MQDT) which allows assignment of most states to $ns$ or $nd$ Rydberg series. We provide an improved accuracy for the lowest two ionization thresholds to $E_{\mathrm{IP},J_c=13/2}=49260.750\left(1\right){\mathrm{cm}}^{-1}$ and $E_{\mathrm{IP},J_c=11/2}=49701.184\left(1\right){\mathrm{cm}}^{-1}$ as well as the corresponding quantum defects for all observed series. We identify Rydberg states in five different isotopes, and states between the two lowest ionization thresholds. Our results open the way for future applications of Rydberg states for quantum simulation using erbium and exploiting its special open-shell structure.

The entanglement resource required for quantum information processing comes in a variety of forms, from Bell states to multipartite GHZ states or cluster states. Purifying these resources after their imperfect generation is an indispensable step towards using them in quantum architectures. While this challenge, both in the case of Bell pairs and more general multipartite entangled states, is mostly overcome in the presence of perfect local quantum hardware with unconstrained qubit register sizes, devising optimal purification strategies for finite-size realistic noisy hardware has remained elusive. Here we depart from the typical purification paradigm for multipartite states explored in the last 20 years. We present cases where the hardware limitations are taken into account and, surprisingly, find that smaller “sacrificial” states, such as Bell pairs, can be more useful in the purification of multipartite states than additional copies of these same states. This drastically simplifies the requirements and presents a fundamentally different pathway to leverage near-term networked quantum hardware.

There is indeed a finite-size issue in computer simulations of the correlation decay in a quasi-one-dimensional system of hard disks. The correlation function obtained from the exact canonical $NVT$ partition function shows a decay which is much slower and more complex than the exponential one, presented in the Comment.

Huerta et al. [Phys. Rev. Research 2, 033351 (2020)] report a power-law decay of positional order in numerical simulations of hard disks confined within hard parallel walls, which they interpret as a Kosterlitz-Thouless (KT)-type caging-uncaging transition. The proposed existence of such a transition in a quasi-one-dimensional system, however, contradicts long-held physical expectations. To clarify if the proposed ordering persists in the thermodynamic limit, we introduce an exact transfer matrix approach to expeditiously generate configurations of very large subsystems that are typical of equilibrium thermodynamic (infinite-size) systems. The power-law decay of positional order is found to extend only over finite distances. We conclude that the numerical simulation results reported are associated with a crossover unrelated to KT-type physics, and not with a proper thermodynamic phase transition.

We develop a microscopic theory of multipole interactions and orderings in $5d^2$ transition metal ion compounds. In a cubic environment, the ground state of $5d^2$ ions is a non-Kramers $E_g$ doublet, which is nonmagnetic but hosts quadrupole and octupole moments. We derive low-energy pseudospin one-half Hamiltonians describing various spin-orbital exchange processes between these ions. Direct overlap of the $t_{2g}$ orbitals results in bond-dependent pseudospin interactions similar to those for $e_g$ orbitals in manganites, except for different orientations of the pseudospin easy axes. On the other hand, the superexchange process, where two different $t_{2g}$ orbitals communicate via oxygen ions, generates new types of pairwise interactions. In perovskites with ${180}^{\circ }$ bonding, we find nearly equal mixture of Heisenberg and $e_g$ orbital compass-type couplings. The ${90}^{\circ }$ superexchange in compounds with edge-shared octahedra is most unusual: Despite highly anisotropic shapes of the $E_g$ wave functions, the pseudospin interactions have no bond dependence. We consider the $E_g$ pseudospin models on various lattices and obtain their ground state properties using analytical and numerical methods. On the honeycomb lattice, we observe a duality with the extended Kitaev model, and use it to uncover a critical point where the quadrupole and octupole states are exactly degenerate. On the triangular lattice, an exotic pseudospin state, corresponding to the coherent superposition of vortex-type quadrupole and ferri-type octupole orders, is realized due to geometrical frustration. This state breaks both spatial and time-reversal symmetries, but possesses no dipolar magnetism. We also consider Jahn-Teller coupling effects and lattice mediated interactions between $E_g$ pseudospins, and find that they support quadrupole order. Possible implications of the results for recent experiments on double perovskite osmates are discussed, including effects of local distortions on the pseudospin wave functions and interactions.

In transport of micro- or nanosized particles through a confined structure driven by thermal fluctuations and external forcing—a situation that arises commonly in a variety of fields in physical and biological sciences, efficient and controllable separation of particles of different sizes is an important but challenging problem. We study, numerically and analytically, the diffusion dynamics of Brownian particles through the biologically relevant setting of a spatially periodic structure, subject to static and temporally periodic forcing. Molecular dynamical simulations reveal that the mean velocity in general depends sensitively on the particle size. The phenomenon of current reversal is uncovered, where particles larger than or smaller than a critical size diffuse in exactly opposite directions. This striking behavior occurs in a wide range of the forcing amplitude and provides a mechanism to separate the Brownian particles of different sizes. Besides the forcing amplitude, other parametric quantities characterizing the forcing profile, such as the temporal asymmetry, can also be exploited to modulate or control the transport dynamics of particles of different sizes. To gain a theoretical understanding, we exploit the Fick-Jacobs approximation to obtain a one-dimensional description of the diffusion problem, which enables key quantities characterizing the diffusion process, such as the mean velocity, to be predicted. In the regime of weak forcing, a reasonable agreement between theory and numerical results is achieved. Beyond the weakly forcing regime, the diffusion approximation breaks down, causing the theoretical predictions to deviate from the numerical results, into which we provide physical insights. Our findings have potential applications in optimizing transport in microfluidic devices or through biological channels.

We propose an integrated photonic approach to generating guided space-time wave packets in a conventional multimode waveguide using multilevel interband photonic transitions. It can generate broadband propagation-invariant space-time wave packets with arbitrary group velocity and tailored field profiles. Our work reveals an important connection between the study of time-varying media and space-time optics.

In a noncentrosymmetric system, an intrinsic electric polarization is allowed and may lead to unusual nonreciprocal charge transport phenomena. As a result, a current-dependent resistance, arising from the magnetoelectric anisotropy term of $k·\vec{E}\times \vec{B}$, appears and acts as a current rectifier with the amount of rectification being linearly proportional to the magnitude of both current and applied magnetic field. In this work, a different type of nonreciprocal transport effect was demonstrated in a graphene-based device, which requires no external magnetic field. Due to the unique pseudospin (valley) degree of freedom in chiral fermions with trigonal warping, a large nonreciprocal transport effect was uncovered in a gapped bilayer graphene, where electric-field tunabilities of the band gap and valley polarization play an important role. The exact cancellation of nonreciprocal effect between two different valleys is effectively removed by breaking the inversion symmetry via electric gatings. The magnitude of the current rectification appears to be at a maximum when the Fermi surface undergoes a Lifshitz transition near the band edges, which is proportional to the current and the displacement field strength. The full electric-field tuning of the nonreciprocal transport effect without a magnetic field opens up a new direction for valleytronics in two-dimensional-based devices.

A steady-state magneto-optical trap (MOT) of fermionic strontium atoms operating on the $7.5\text{-kHz}$-wide ${}^{1}S_0\text{−}{}^{3}P_1$ transition is demonstrated. This MOT contains $8.4\times {10}^7\mathrm{atoms}$, a loading rate of $1.3\times {10}^7\mathrm{atoms}/\mathrm{s}$, and an average temperature of $12\mu \mathrm{K}$. These parameters make it well suited to serve as a source of atoms for continuous-wave superradiant lasers operating on strontium's mHz-wide clock transition. Such lasers have only been demonstrated using pulsed Sr sources, limiting their range of applications. Our MOT makes an important step toward continuous operation of these devices, paving the way for continuous active optical clocks.