Out-of-time-order correlators (OTOCs) have proven to be a useful tool for studying thermalization in quantum systems. In particular, the exponential growth of OTOCS, or scrambling, is sometimes taken as an indicator of chaos in quantum systems, despite the fact that saddle points in integrable systems can also drive rapid growth in OTOCs. By analyzing the Dicke model and a driven Bose-Hubbard dimer, we demonstrate that the OTOC growth driven by chaos can, nonetheless, be distinguished from that driven by saddle points through the long-term behavior. Besides quantitative differences in the long-term average, the saddle point gives rise to large oscillations not observed in the chaotic case. The differences are also highlighted by entanglement entropy, which in the chaotic-driven dimer matches a Page curve prediction. These results illustrate additional markers that can be used to distinguish chaotic behavior in quantum systems, beyond the initial exponential growth in OTOCs.

Non-Hermitian systems can host topological states with unusual topological invariants and bulk-edge correspondences that are distinct from conventional Hermitian systems. Here we show that two unique classes of non-Hermitian two-dimensional topological phases, a $2\mathbb{Z}$ non-Hermitian Chern insulator and a ${\mathbb{Z}}_2$ topological semimetal, can be realized by solely tuning staggered non-Hermitian or asymmetric hopping strengths in a one-dimensional (1D) superlattice. These non-Hermitian topological phases support real edge modes due to robust $\mathcal{PT}$-symmetric-like spectra and can coexist in a certain parameter regime. The proposed phases can be experimentally realized in photonic or atomic systems and may open an avenue for exploring unique classes of non-Hermitian topological phases with 1D superlattices.

Classical ghost imaging is a computational imaging technique that employs patterned illumination. It is very similar in concept to the single-pixel camera in that an image may be reconstructed from a set of measurements even though all imaging photons or particles that pass through that sample are never recorded with a position resolving detector. The method was first conceived and applied for visible-wavelength photons and was subsequently translated to other probes such as x rays, atomic beams, electrons, and neutrons. In the context of classical ghost imaging using penetrating probes that enable transmission measurement, we here consider several questions relating to the achievable signal-to-noise ratio (SNR). This is compared with the SNR for conventional imaging under scenarios of constant radiation dose and constant experiment time, considering both photon shot noise and per-measurement electronic readout noise. We show that inherent improved SNR capabilities of classical ghost imaging are limited to a subset of these scenarios and are actually due to increased dose (Fellgett advantage). An explanation is also presented for recent results published in the literature that are not consistent with these findings.

We investigate quantum walks in a noninertial frame with a Rindler metric, emulated by a nonuniform optical lattice with varying site couplings whose metric is mathematically equivalent to that of a Schwarzschild black hole near the event horizon. The optical trapping of single photons and two indistinguishable photons in such nonuniform lattices conforms to a well-known classical physical recognition due to the strong gravitational force of black holes. Counterintuitively, there is an optical escape for path-entangled photons for which one photon is captured, while the other photon escapes. Intriguingly, we find that the counterintuitive phenomenon has a distinct escape mechanism compared to Hawking radiation, which is wholly due to quantum interference. Additionally, we investigate the entanglement decay for this maximally entangled state in the emulated noninertial frame. Our study paves the way for a tabletop platform for understanding quantum effects under general relativity.

Mutually unbiased bases (MUBs) are a crucial ingredient for many protocols in quantum information processing. Measurements performed in these bases are unbiased to the maximally possible extent, which is used to prove the randomness or secrecy of measurement results. In this work we show that certain properties of sets of MUBs crucially depend on their specific choice, including, somewhat surprisingly, measurement outcome labeling. If measurements are chosen in a coherent way, the secrecy of the result can be completely lost for specific sets of MUB measurements but partially retained for others. This could potentially impact a broad spectrum of applications where MUBs are utilized.

A state-preserving quantum counting algorithm is used to obtain coefficients of a Lanczos recursion from a single ground-state wave function on the quantum computer. This is used to compute the continued fraction representation of an interacting Green's function for use in condensed matter, particle physics, and other areas. The wave function does not need to be reprepared at each iteration. The quantum algorithm represents an exponential reduction in memory over known classical methods. An extension of the method to determining the ground state is also discussed.

Electron-induced dissociative excitation (DE) is a little studied process of significant applied relevance. Our aim is to provide a theoretical counterpart to earlier experiments [M. J. Jensen, R. C. Bilodeau, O. Heber, H. B. Pedersen, C. P. Safvan, X. Urbain, D. Zajfman, and L. H. Andersen, Phys. Rev. A 60, 2970 (1999)] on DE of ${\mathrm{H}}_2{\mathrm{O}}^{+}$. For this purpose, we have performed low-energy fixed-nuclei scattering calculations, based on the R-matrix method, for over 1800 geometries of ${\mathrm{H}}_2{\mathrm{O}}^{+}$. We have identified and characterized three resonances lying above the second $\left(\tilde{B}\right)$ excited state of ${\mathrm{H}}_2{\mathrm{O}}^{+}$; their energy, lifetime, and associated quantum defect have been determined. We assess their possible contribution to the DE process.

Multiphoton ionization provides a clear window into the nature of electron correlations in the helium atom. In the present study, the final-state energy range extends up to the region near the $N=2$ and $N=3$ ionization thresholds, where two-photon ionization proceeds via continuum intermediate states above the lowest threshold. Our calculations are performed using multichannel quantum defect theory (MQDT) and the streamlined $R$-matrix method. The sum and integration over all intermediate states in the two-photon ionization amplitude is evaluated using the inhomogeneous $R$-matrix method developed by Robicheaux and Gao. The seamless connection of that method with MQDT allows us to present high-resolution spectra of the final-state Rydberg resonances. Our analysis classifies the resonances above the $N=2$ threshold in terms of their group theory quantum numbers. Their dominant decay channels are found to obey the previously conjectured propensity rule far more weakly for these even-parity states than was observed for the odd-parity states relevant to single-photon ionization.

Terahertz and third-harmonic generation by tightly focused bichromatic femtosecond pump pulses with comparable input intensities in air is studied both experimentally and theoretically. Plasma-assisted temporal shifts in the field of intense laser pulses are shown to lead to the time delay between the pump pulses in the vicinity of the focus. This delay can be compensated by the initial time delay that is evidenced by the measured as well as calculated correlation functions of the fundamental and second harmonics. The possibility to characterize the plasma channel length from the correlation function is discussed.

We analyze the dynamics of an open system coupled to a nonergodic environment for which the correlation function does not decay, leading to a failure of the weak coupling and Markov approximations standard in open systems. We show that nonergodicity appears for environments at finite temperatures that have non-Gaussian statistics and do not fulfill the eigenstate thermalization hypothesis. We illustrate our statements by considering a thermal spin-boson environment that models a gas of dye molecules, and show that nondecaying correlations are connected to a 1/f noise that extends to zero frequencies. This suggests the idea that nonergodic environments may be at the origin of the 1/f behavior observed in other hybrid environments such as the ones encountered in superconducting qubits.

The dynamics of a discrete-time quantum walk subject to time-correlated noise is studied in this paper. The noise, which goes beyond the usual telegraph noise with random variables 1 and $-1$, is modeled as a unitary coin-type operator and it is generated by a sample path of the Ornstein-Uhlenbeck process. Up to the first order in the amplitude of noise, a master equation to describe the walk is derived. The dynamics governed by the master equation is in good agreement with those given by numerical simulations within a certain number of steps, depending on the parameters of noise. Two remarkable features of long-time dynamics are observed in the numerical simulations. (1) In the slow noise regime, with the increase of the noise amplitude, the quantum coherence is suppressed, and the dynamics of noisy discrete-time quantum walk gradually transits to that of classical random walk. (2) In the fast noise regime, the walker is confined into a few lattice sites, and the width of the wave packet is much narrower compared with that in the slow noise regime.

The generation and storage of spin squeezing is an attractive topic in quantum metrology and the foundation of quantum mechanics. The major models to realize the spin squeezing are the one- and two-axis twisting models. Here, we consider a collective spin system coupled to a bosonic field, and show that proper constant-value controls in this model can simulate the dynamical behavior of these two models. More interestingly, a better performance of squeezing can be obtained when the control is time varying, which is generated via a reinforcement learning algorithm. However, this advantage becomes limited if the collective noise is involved. To deal with this, we propose a four-step strategy for the construction of a type of combined controls, which include both constant-value and time-varying controls, but performed at different time intervals. Compared to the full time-varying controls, the combined controls not only give a comparable minimum value of the squeezing parameter over time, but also provide a better lifetime and larger full amount of squeezing. Moreover, the amplitude form of a combined control is simpler and more stable than the full time-varying control. Therefore, our scheme is very promising to be applied in practice to improve the generation and storage performance of squeezing.

The static and dynamic polarizabilities of the ground state and low-lying excited states of ${\mathrm{Ba}}^{+}$ ions are calculated by using a relativistic semiempirical method: the relativistic configuration interaction plus core polarization (RCICP) method. The tune-out wavelengths of the ground state and magic wavelengths of the $6s_{1/2}\to 6p_{1/2,3/2},5d_{3/2,5/2}$ transitions are determined. One visible tune-out wavelength, 480.658(18) nm, is found. High-precision measurements on this tune-out wavelength could be used to determine the ratio of the oscillator strengths of the $6s_{1/2}\to 6p_{1/2,3/2}$ transitions. In addition, we suggest that the measurements on the magic wavelengths corresponding to the $6s_{1/2}\to 5d_{3/2,5/2}$ transitions could be used to determine the oscillator strengths of the $5d_{5/2}\to 4f_{7/2}$ and $5d_{3/2}\to 4f_{5/2}$ transitions, while the measurements of the magic wavelengths near 416 nm for the $6s_{1/2}\to 6p_{3/2}$ transition could be used to determine the ratio of the oscillator strengths of the $6p_{3/2}\to 6d_{3/2,5/2}$ transitions.

The statistics of strongly interacting, ultracold Rydberg gases are governed by the interplay of two factors: geometrical restrictions induced by blockade effects and quantum mechanical effects. To shed light on their relative roles in the statistics of Rydberg gases, we compare three models in this paper: a quantum mechanical model describing the excitation dynamics within a Rydberg gas, a random sequential adsorption (RSA) process on a random geometric graph (RGG), and a RSA process on a decomposed random intersection graph (DRIG). The last model refers to choosing a particular subgraph of a mixture of two other random graphs. Contrary to the first two models, it lends itself for a rigorous mathematical analysis, and it is built specifically to have particular structural properties of a RGG. We establish for it a fluid limit describing the time evolution of the number of Rydberg atoms and show numerically that the expression remains accurate across a wider range of particle densities than an earlier approach based on an RSA process on an Erdős-Rényi random graph (ERRG). Finally, we also develop a heuristic using random graphs that gives a recursion to describe a normalized pair-correlation function of a Rydberg gas. Our results suggest that even without dissipation, on long timescales the statistics are affected most by the geometrical restrictions induced by blockade effects, while on short timescales the statistics are affected most by quantum mechanical effects.

We consider a two-dimensional extension of the one-dimensional waveguide quantum electrodynamics and investigate the nature of linear excitations in two-dimensional arrays of qubits coupled to networks of chiral waveguides. We show that the combined effects of chirality and long-range photon-mediated qubit-qubit interactions lead to the emergence of the two-dimensional flat bands in the polaritonic spectrum, corresponding to slow strongly correlated light.

We perform atomic relativistic many-body calculations of the field isotope shifts and calculations of corresponding nuclear parameters for all stable even-even isotopes of the ${\mathrm{Yb}}^{+}$ ion. We demonstrate that if we take nuclear parameters of the Yb isotopes from a range of the state of the art nuclear models, which all predict strong quadrupole nuclear deformation, and then calculate nonlinearity of the King plot caused by the difference in the deformation in different isotopes, the result is consistent with the nonlinearity observed in the experiment [I. Counts et al., Phys. Rev. Lett. 125, 123002 (2020)]. The changes of nuclear rms radius between isotopes extracted from experiment are consistent with those obtained in the nuclear calculations.

We investigate multicomponent fermions in a flat band and predict experimental signatures of non-Fermi-liquid behavior. We use dynamical mean-field theory to obtain the density, double occupancy and entropy in a Lieb lattice for $\mathcal{N}=2$ and $\mathcal{N}=4$ components. We derive a mean-field scaling relation between the results for different values of $\mathcal{N}$, and study its breakdown due to beyond mean-field effects. The predicted signatures occur at temperatures above the Néel temperature and persists even in the presence of a trapping potential, thus they are observable in current ultracold gas experiments.

We explore two-dimensional scattering off a potential that is invariant with respect to linear symmetry transformations such as rotations, reflections, and/or coordinate exchange. The common ansatz of an incoming wave, in general, does not respect the symmetries of the potential and, therefore, the solution of the corresponding Schrödinger equation is not an eigenstate of the operator representing the respective symmetry transform. This renders it difficult to conceptually account for the imprint of the potentials' symmetry on the scattered wave field, unless the limit of an infinite distance $r\to \infty$ is taken. In the latter case, the symmetries of the potential are expressed as conditions on the scattering amplitude. In the present work, we employ the recently derived, symmetry-induced, nonlocal and divergence-free currents, which are constructed from the wave field at a point $\mathbf{r}$ and its symmetry-related image $\overline{\mathbf{r}}$, to derive general properties of the scattering solution and the associated scattering matrix. These properties originate from the requirement of a vanishing divergence for the nonlocal currents, which is in one-to-one correspondence with the presence of a symmetry in the scattering potential. In practice, they are expressed as conditions on the coefficients of the wave-field expansion with respect to the angular momentum basis in two dimensions. This, in turn, constrains the form of the related $\mathbf{S}$-matrix eigenvectors. The obtained properties are also valid at finite $\mathbf{r}$ and can be used as a tool to check upon and improve the efficiency of numerical approaches to the quantum scattering problem of interest.

We have studied the formation of ultracold RbSr molecules with laser pulses. After discussing the advantages of the Mott insulator phase for the control with pulses, we present two classes of strategies. The first class involves two electronic states. Two extensions of stimulated Raman adiabatic passage (STIRAP) for multilevel transitions are used: alternating STIRAP (A-STIRAP) and straddle STIRAP (S-STIRAP). Both transfer dynamics are modeled and compared. The second class of strategies involves only the electronic ground state and uses infrared (IR) and terahertz (THz) pulses. The molecular bond is first created by the application of a THz chirped pulse or $\pi$-pulse. Subsequently, the molecules are transferred to their rovibrational ground level using IR pulses. For this last step, different optimized pulse sequences that were obtained through optimal control techniques have been studied. The relative merits of these strategies in terms of efficiency and robustness are discussed with respect to the experimental feasibility based on present laser technologies.