The Su-Schrieffer-Heeger (SSH) model lays the foundation of many important concepts in quantum topological matters. Here, we show that a spin-dependent double-well optical lattice allows one to couple two topologically distinct SSH chains in the bulk and realize a glided-two-leg SSH model that respects the glide reflection symmetry. Such a model gives rise to intriguing quantum phenomena beyond the paradigm of a traditional SSH model. It is characterized by Wilson lines that require non-Abelian Berry connections, and the interplay between the glide symmetry and interaction automatically leads to charge fractionalization without jointing two lattice potentials at an interface. Our work demonstrates the versatility of ultracold atoms to create new theoretical models for studying topological matters.

We study the long-time evolution of a quantum memory coupled to a bosonic environment on which quantum error correction (QEC) is performed using the surface code. The memory's evolution encompasses $N$ QEC cycles, each of them yielding a nonerror syndrome. This assumption makes our analysis independent of the recovery process. We map the expression for the time evolution of the memory onto the partition function of an equivalent statistical-mechanical spin system. In the super-Ohmic dissipation case the long-time evolution of the memory has the same behavior as the time evolution for just one QEC cycle. For this case we find analytical expressions for the critical parameters of the order-disorder phase transition of an equivalent spin system. These critical parameters determine the threshold value for the system-environment coupling below which it is possible to preserve the memory's state.

We derive a monogamy inequality for entanglement and local contextuality, for any finite bipartite system. It essentially results from the relations between the entropy of a local state and the entanglement of the global state, and between the purity of a state, in the sense of majorization, and its ability to violate a given state-dependent noncontextuality inequality. We build an explicit entanglement monotone that satisfies the found monogamy inequality. An important consequence of this inequality is that there are global states too entangled to violate the local noncontextuality inequality.

We spectroscopically investigate the hyperfine, rotational, and Zeeman structure of the vibrational levels $v^{\prime }=0,7,13$ within the electronically excited $c{}^3{\mathrm{\Sigma }}_g{}^{+}$ state of ${}^{87}\mathrm{Rb}_2$ for magnetic fields of up to $1000\text{G}$. As spectroscopic methods we use short-range photoassociation of ultracold Rb atoms as well as photoexcitation of ultracold molecules which have been previously prepared in several well-defined quantum states of the $a{}^3\mathrm{\Sigma }{}_u^{+}$ potential. As a by-product, we present optical two-photon transfer of weakly bound Feshbach molecules into $a{}^3\mathrm{\Sigma }{}_u^{+}$, $v=0$ levels featuring different nuclear spin quantum numbers. A simple model reproduces well the molecular level structures of the $c{}^3{\mathrm{\Sigma }}_g{}^{+}$ vibrational states and provides a consistent assignment of the measured resonance lines. Furthermore, the model can be used to predict the relative transition strengths of the lines. From fits to the data we extract for each vibrational level the rotational constant, the effective spin-spin interaction constant, as well as the Fermi contact parameter and the anisotropic hyperfine constant. In an alternative approach, we perform coupled-channel calculations where we fit the relevant potential energy curves, spin-orbit interactions, and hyperfine functions. The calculations reproduce the measured hyperfine level term frequencies with an average uncertainty of $\pm 9\mathrm{MHz}$, similar as for the simple model. From these fits we obtain a section of the potential energy curve for the $c{}^3{\mathrm{\Sigma }}_g{}^{+}$ state which can be used for predicting the level structure for the vibrational manifold $v^{\prime }=0$ to 13 of this electronic state.

We develop a theory of weakly interacting fermionic atoms in shaken optical lattices based on the orbital mixing in the presence of time-periodic modulations. Specifically, we focus on fermionic atoms in a circularly shaken square lattice with near-resonance frequencies, i.e., tuned close to the energy separation between the $s$ band and the $p$ bands. First, we derive a time-independent four-band effective Hamiltonian in the noninteracting limit. Diagonalization of the effective Hamiltonian yields a quasienergy spectrum consistent with the full numerical Floquet solution that includes all higher bands. In particular, we find that the hybridized $s$ band develops multiple minima and therefore nontrivial Fermi surfaces at different fillings. We then obtain the effective interactions for atoms in the hybridized $s$ band analytically and show that they acquire momentum dependence on the Fermi surface even though the bare interaction is contactlike. We apply the theory to find the phase diagram of fermions with weak attractive interactions and demonstrate that the pairing symmetry is $s+d$ wave. Our theory is valid for a range of shaking frequencies near resonance, and it can be generalized to other phases of interacting fermions in shaken lattices.

We consider spin- and density-related properties of single-particle states in a one-dimensional system with random spin-orbit coupling. We show that the presence of an additional Zeeman field $\mathrm{\Delta }$ induces both nonlinear spin polarization and delocalization of states localized at $\mathrm{\Delta }=0$, corresponding to a random macroscopic analog of the Paschen-Back effect. While the conventional Paschen-Back effect corresponds to a saturated $\mathrm{\Delta }$ dependence of the spin polarization, here the gradual suppression of the spin-orbit coupling effects by the Zeeman field is responsible both for the spin saturation and delocalization of the particles.

To explore the static properties of the one-dimensional anyon-Hubbard model for a mean density of one particle per site, we apply perturbation theory with respect to the ratio between kinetic energy and interaction energy in the Mott insulating phase. The strong-coupling results for the ground-state energy, the single-particle excitation energies, and the momentum distribution functions up to 6th order in hopping are benchmarked against the numerically exact (infinite) density-matrix renormalization group technique. Since these analytic expressions are valid for any fractional phase $\theta$ of anyons, they will be of great value for a sufficiently reliable analysis of future experiments, avoiding extensive and costly numerical simulations.

A full propagation analysis on both fold-type and cusp-type caustic optical beams under various setups of obstructions is theoretically and experimentally performed. It is demonstrated that the self-healing property of caustic optical beams that include the famous Airy beam is a quite relative property. In fact, fold-type and cusp-type beams cannot only behave as self-healing beams by blocking the main intensity peak, but also behave as self-breaking ones in a nonintuitive manner: by blocking a lateral side of the beam without touching the central intensity peak. The regeneration and rupture processes of caustic beams follow a nonlocal propagation dynamic unlike the other conventional beams. Moreover, deep differences between fold and cusp caustic beams are pointed out once facing certain obstructions. The cusp-caustic beam can be broken down by the obstacle placed in a dark zone outside the caustic region, while the fold-type one remains unaltered. This beam rupture confirms the key role of a hidden propagating field in the shadow region for cusp beams that coexist with the evanescent one. The obtained results cast down the established idea that the Airy beam is a robust self-healing beam since any caustic beam can behave in a dual manner depending on the obstruction location. These facts open up different perspectives for the applications in which the self-healing properties of the beam are relevant.

Light scattering is one of the most important elementary processes in near-field optics. We build up the Born series for scattering by dielectric bodies with sharp boundaries. The Green's function for a two-dimensional homogeneous dielectric cylinder is obtained. As an example, the formulas are derived for a scattered field of two parallel cylinders. The polar diagram is shown to agree with the numerical calculation by the known methods of discrete dipoles and boundary elements.

We demonstrate the breakdown of molecular-frame dynamics induced by the uncoupling of molecular rotation from electronic motion in molecular Rydberg states. We observe this non-Born-Oppenheimer regime in the time domain through photoelectron imaging of a coherent molecular Rydberg wave packet in ${\mathrm{N}}_2$. The photoelectron angular distribution shows a radically different time evolution than that of a typical molecular-frame-fixed electron orbital, revealing the uncoupled motion of the electron as it precesses around the averaged anisotropic potential of the rotating ion core.

We investigate the Anderson localization in non-Hermitian Aubry-André-Harper (AAH) models with imaginary potentials added to lattice sites to represent the physical gain and loss during the interacting processes between the system and environment. By checking the mean inverse participation ratio (MIPR) of the system, we find that different configurations of physical gain and loss have very different impacts on the localization phase transition in the system. In the case with balanced physical gain and loss added in an alternate way to the lattice sites, the critical region (in the case with $p$-wave superconducting pairing) and the critical value (both in the situations with and without $p$-wave pairing) for the Anderson localization phase transition will be significantly reduced, which implies an enhancement of the localization process. However, if the system is divided into two parts with one of them coupled to physical gain and the other coupled to the corresponding physical loss, the transition process will be impacted only in a very mild way. Besides, we also discuss the situations with imbalanced physical gain and loss and find that the existence of random imaginary potentials in the system will also affect the localization process while constant imaginary potentials will not.

The broad success of theoretical and experimental quantum optimal control is intimately connected to the topology of the underlying control landscape. For several common quantum control goals, including the maximization of an observable expectation value, the landscape has been shown to lack local optima if three assumptions are satisfied: (i) the quantum system is controllable, (ii) the Jacobian of the map from the control field to the evolution operator is full rank, and (iii) the control field is not constrained. In the case of the observable objective, this favorable analysis shows that the associated landscape also contains saddles, i.e., critical points that are not local suboptimal extrema. In this paper, we investigate whether the presence of these saddles affects the trajectories of gradient-based searches for an optimal control. We show through simulations that both the detailed topology of the control landscape and the parameters of the system Hamiltonian influence whether the searches are attracted to a saddle. For some circumstances with a special initial state and target observable, optimizations may approach a saddle very closely, reducing the efficiency of the gradient algorithm. Encounters with such attractive saddles are found to be quite rare. Neither the presence of a large number of saddles on the control landscape nor a large number of system states increases the likelihood that a search will closely approach a saddle. Even for applications that encounter a saddle, well-designed gradient searches with carefully chosen algorithmic parameters will readily locate optimal controls.

We propose an intuitive method, called the time-dependent population imaging (TDPI) method, to map the dynamical processes of high-order-harmonic generation (HHG) in solids by solving the time-dependent Schrödinger equation. It is shown that the real-time dynamical characteristics of HHG in solids, such as the instantaneous photon energies of emitted harmonics, can be read directly from the energy-resolved population oscillations of electrons in the TDPI picture. Meanwhile, the short and long trajectories of solid HHG are illustrated clearly from the TDPI picture. By using TDPI, we investigate the effects of the carrier-envelope phase in few-cycle pulses and demonstrate intuitively the HHG dynamics driven by two-color fields. Our results show that TDPI provides a powerful tool to study the ultrafast dynamics in strong fields for various laser-solid configurations and to gain insight into HHG processes in solids.

We consider harmonic generation from a semiconductor described in the two-band approximation. In particular, the signatures of the Floquet-Bloch states in the low-order harmonic spectra are studied. We find field-strength-dependent shifts of the position of resonant peaks. The shifts are analogous to the ponderomotive shifts in strong-field physics of atoms and molecules. We illustrate this theory by analyzing low-order harmonics generated from hexagonal boron nitride.

Surface scattering of neutral helium beams created by supersonic expansion is an established technique for measuring structural and dynamical properties of surfaces on the atomic scale. Helium beams have also been used in Fraunhofer and Fresnel diffraction experiments. Due to the short wavelength of the atom beams of typically 0.1 nm or less, Fraunhofer diffraction experiments in transmission have so far been limited to grating structures with a period (pitch) of up to 200 nm. However, larger periods are of interest for several applications, for example, for the characterization of photonic-crystal-membrane structures, where the period is typically in the micron to high submicron range. Here we present helium atom diffraction measurements of a photonic-crystal-membrane structure with a two-dimensional square lattice of $100\times 100$ circular holes. The nominal period and the hole radius were 490 and 100 nm, respectively. To our knowledge this is the largest period that has been measured with helium diffraction. The helium diffraction measurements are interpreted using a model based on the helium beam characteristics. It is demonstrated how to successfully extract values from the experimental data for the average period of the grating, the hole diameter, and the width of the virtual source used to model the helium beam.

We explore, both experimentally and theoretically, the propagation dynamics of spatially entangled photon pairs (biphotons). Characterization of entanglement is done via the Schmidt number, which is a universal measurement of the degree of entanglement directly related to the nonseparability of the state into its subsystems. We develop expressions for the terms of the Schmidt number that depend on the amplitude and phase of the commonly used double-Gaussian approximation for the biphoton wave function, and demonstrate migration of entanglement between amplitude and phase upon propagation. We then extend this analysis to incorporate both phase curvature in the pump beam and higher spatial frequency content of more realistic non-Gaussian wave functions. Specifically, we generalize the classical beam quality parameter $M^2$ to the biphotons, allowing the description of more information-rich beams and more complex dynamics. Agreement is found with experimental measurements using direct imaging and Fourier optics.

It has been found via numerical simulations that the geometric phase (GP) and fidelity susceptibility (FS) across the quantum critical points exhibit some universal scaling laws. Here we propose a singular function expansion method to find their exact singular forms and the related coefficients across the critical points. For models where the gaps are closed and reopened at special points ($k_0=0,\pi$), scaling laws can be found as a function of the system length $N$ and parameter deviation $\lambda -{\lambda }_c$, where ${\lambda }_c$ refers to one of the critical parameters. Although the GP and FS are defined in totally different ways, we find that these two measurements are essentially determined by the same physics, and as a consequence, their coefficients are closely related. Some of these exact relations are found in the anisotropic XY model and extended Ising models. We also show that the constant term in FS may be accompanied by a discontinuous jump across the critical points and, thus, does not have a universal scaling form. These findings should be in contrast to the cases where the gaps are not closed and reopened at the special points, in which some of the above scaling laws may break down as a function of the system length. Finally, we investigate the second-order derivative of GP, which may also exhibit some scaling laws across the critical point. These exact results can greatly enrich our understanding of GP and FS in the characterization of quantum phase transitions and may even find important applications in related physical quantities, such as entanglement, discord, correlation, and quantum Euler numbers, which may also exhibit scaling laws across the critical points.