We investigate the $\mathcal{P}\mathcal{T}$-symmetric Talbot effect in a temporal mesh lattice constructed by two coupled fiber loops, in which the $\mathcal{P}\mathcal{T}$ symmetry is introduced through temporally controlling the gain and loss of the loops. The Talbot self-imaging exists only if the period of input pulse train is chosen as two- or fourfold compared to the time interval caused by the length difference between the two loops. Through varying the gain and loss, we can tailor the lattice band structure and thus flexibly manipulate the Talbot distance, which can further be tuned by imposing a linear phase distribution on the input pulse train. In addition, the power oscillations are found in the Talbot imaging process, and the oscillation amplitude is associated with the gain and loss and the gradient of the linear phase modulation. Especially, the power oscillations possess significant amplitude as the modes near the exceptional points are excited. The study may find potential applications in pulse repetition rate multiplication, temporal cloaking, and tunable intensity amplifiers.

The nonlinear Schrödinger equation (NSE) provides a powerful tool for the analysis of ultrafast nonlinear-optical dynamics, including a vast class of optical solitons. Here, we show, however, that the photon-number integral of the NSE differs from the physical number of photons, conserved by more general field evolution equations. This difficulty is traced to the optical shock term, which is dropped in the NSE, making nonlinear coupling in NSE-based models frequency independent and leading to unphysical predictions for ultrabroadband, octave-spanning field waveforms.

Given two states $|\psi \rangle$ and $|\varphi \rangle$ of a quantum many-body system, one may use the overlap or fidelity $|\langle \psi |\varphi \rangle |$ to quantify how similar they are. To further resolve the similarity of $|\psi \rangle$ and $|\varphi \rangle$ in space, one can consider their reduced density matrices $\rho$ and $\sigma$ on various regions of the system and compute the Uhlmann fidelity $F(\rho ,\sigma )=Tr\sqrt{\sqrt{\rho }\sigma \sqrt{\rho }}$. In this paper, we show how computing such subsystem fidelities can be done efficiently in many cases when the two states are represented as tensor networks. Formulated using Uhlmann's theorem, such subsystem fidelities appear as natural quantities to extract for certain subsystems of matrix product states and tree tensor networks, and evaluating them is algorithmically simple and computationally affordable. We demonstrate the usefulness of evaluating subsystem fidelities with three example applications: studying local quenches, comparing critical and noncritical states, and quantifying convergence in tensor network simulations.

The multipartite correlations derived from local measurements on some composite quantum systems are inconsistent with those reproduced classically. This inconsistency is known as the quantum nonlocality and shows a milestone in the foundations of quantum theory. Still, it is NP hard to decide a nonlocal quantum state. We investigate an extended question as to how to characterize the nonlocal properties of quantum states that are distributed and measured in networks. We first prove the generic tripartite nonlocality of chain-shaped quantum networks using semiquantum nonlocal games. We then introduce an approach to prove the generic activated nonlocality as a result of entanglement swapping for all the bipartite entangled states. The result is further applied to show the multipartite nonlocality and activated nonlocality for all the nontrivial quantum networks consisting of any entangled states. Our results provide the nonlocality witnesses and quantum superiorities of all the connected quantum networks or nontrivial hybrid networks in contrast to classical networks.

Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by imperfect knowledge of the system. We present a procedure to simultaneously characterize quantum states and measurements that mitigates systematic errors by use of a single high-fidelity state preparation and a limited set of high-fidelity unitary operations. Such states and operations are typical of many state-of-the-art systems. For this situation we design a set of experiments and an optimization algorithm that alternates between maximizing the likelihood with respect to the states and measurements to produce estimates of each. In some cases, the procedure does not enable unique estimation of the states. For these cases, we show how one may identify a set of density matrices compatible with the measurements and use a semidefinite program to place bounds on the state's expectation values. We demonstrate the procedure on data from a simulated experiment with two trapped ions.

A combined experimental and theoretical spectroscopic study of high-$n, 30\lesssim n\lesssim 100$, triplet $S$ and $D$ Rydberg states in ${}^{87}\mathrm{Sr}$ is presented. ${}^{87}\mathrm{Sr}$ has a large nuclear spin $I=9/2$, and at high-$n$ the hyperfine interaction becomes comparable to, or even larger than, the fine structure and singlet-triplet splittings, which poses a considerable challenge both for precision spectroscopy and for theory. For high-$n S$ states, the hyperfine shifts are evaluated nonperturbatively, taking advantage of earlier spectroscopic data for the $I=0$ isotope ${}^{88}\mathrm{Sr}$, which results in good agreement with the present measurements. For the $D$ states, this procedure is reversed by first extracting from the present ${}^{87}\mathrm{Sr}$ measurements the energies of the ${}^3{D}_{1,2,3}$ states to be expected for isotopes without hyperfine structure (${}^{88}\mathrm{Sr}$), which allows the determination of corrected quantum defects in the high-$n$ limit.

We report on the existence and stability of multidimensional bound solitonic states in harmonically trapped scalar Bose-Einstein condensates. Their equilibrium separation, as a measure of the strength of the soliton-soliton or the solitonic vortex-vortex interaction, is provided for varying chemical potential $\mu$. Static bound dark solitons are shown to be dynamically stable in elongated condensates within a range of intermediate (repulsive) interparticle-interaction strength. Beyond this range the snaking instability manifests during the time evolution of the planar solitons and produces the decay into nonstationary vortex states. A subsequent dynamical recurrence of solitons and vortices can be observed at low $\mu$. At equilibrium, the bifurcations of bound dark solitons are bound solitonic vortices. Among them, both two-open and two-ring vortex lines are demonstrated to exist with both counter- and co-rotating steady velocity fields. The latter flow configurations evolve, for high chemical potential, into a stationary three-dimensional (3D)-chain-shaped vortex and a three vortex-antivortex-vortex ring sequence that arrest the otherwise increasing angular or linear momentum respectively. As a feature common to the bifurcated families of vortex states, their excitation spectra present unstable modes with associated oscillatory dynamics. In spite of this, the family of two-open counter-rotating vortices support dynamically stable 3D states.

We show that cavity-field fluctuations can induce interesting magnetic phases and phase transitions in an atom-cavity coupled system. Adopting a numerical density-matrix-renormalization-group method, we study the steady state of a two-component Fermi gas subject to cavity-assisted Raman coupling in a one-dimensional lattice at half filling. The cavity-enhanced atom-photon coupling introduces a dynamic long-range interaction in the atoms, which competes with the short-range on-site interactions and leads to a rich phase diagram with a variety of magnetic orders. Importantly, as all the phase transitions take place outside the superradiant regime, the magnetic orders are associated with cavity-field fluctuations with a vanishing number of photons on the mean-field level.

We investigate realizations of topological insulators with spin-1 bosons loaded in a honeycomb optical lattice and subjected to a $\text{SU}\left(3\right)$ spin-orbit coupling—a situation which can be realized experimentally using cold atomic gases. In this paper, we focus on the topological properties of the single-particle band structure, namely, Chern numbers (lattice with periodic boundary conditions) and edge states (lattice with strip geometry) and their connection to time-reversal symmetry and the sublattice symmetry. While $\text{SU}\left(2\right)$ spin-orbit couplings always lead to time-reversal symmetric tight-binding models, and thereby to topologically trivial band structures, suitable $\text{SU}\left(3\right)$ spin-orbit couplings can break time-reversal symmetry and lead to topologically nontrivial bulk band structures and to edge states in the strip geometry. In addition, we show that one can trigger a series of topological transitions (i.e., integer changes of the Chern numbers) that are specific to the geometry of the honeycomb lattice by varying a single parameter in the Hamiltonian.

We show how a generalized kind of chiral symmetry can be used to construct highly efficient reservoir engineering protocols for bosonic lattices. These protocols exploit only a single squeezed reservoir coupled to a single lattice site; this is enough to stabilize the entire system in a pure, entangled steady state. Our approach is applicable to lattices in any dimension and does not rely on translational invariance. We show how the relevant symmetry operation directly determines the real-space correlation structure in the steady state and give several examples that are within reach in several one- and two-dimensional quantum photonic platforms.

We present the design of a chiral photonic quantum link, where distant atoms interact by exchanging photons propagating in a single direction in free space. This is achieved by coupling each atom in a laser-assisted process to an atomic array acting as a quantum phased-array antenna. This provides a basic building block for quantum networks in free space, i.e., without requiring cavities or nanostructures, which we illustrate with high-fidelity quantum state transfer protocols. Our setup can be implemented with neutral atoms using Rydberg-dressed interactions.

We report a family of solutions of the homogeneous free-space scalar wave equation. These solutions are determined by linear combinations of the half-integer order Bessel functions. We call these beams “combined half-integer Bessel-like beams.” It is shown that, by selecting suitable combinations of the half-integer order Bessel functions, a wide set of beams can be produced in which they may carry the orbital angular momentum (OAM) or not. We show that this family of beams satisfies a “radial structured” boundary condition at $z=0$ plane, therefore they can be produced by the diffraction of a plane wave from suitable “radial structures.” Some specific examples of the half-integer Bessel-like beams are introduced. Especially, a set of spatially asymmetric beams, having half-integer OAM, is introduced that can be used to make the concentration of the absorbing and dielectric micro- or nanoparticles in a microsolution inhomogeneous. Also, by manipulating the Fourier series of the radial structures, three subfamily of beams can be produced including the radial carpet, petallike, and ringlike vortex beams. The intensity profile of the petallike beams forms two dimensional optical latices with polar symmetry at the transverse plane. The ringlike vortex beams carry OAM. Here, by solving the wave equation we present the full image of the radial carpet beams. All the presented beams have nondiffracting, accelerating, and self-healing features. The combined half-integer Bessel-like beams can be considered in other areas of wave phenomena, ranging from sound and elastic waves to many other kinds of classical waves. Therefore, this work has profound implications in many linear wave systems in nature.

We experimentally investigate the manifestations of broken inversion symmetry in solids in two-color interferometric measurements. Polarization-resolved, high-order harmonic spectra of ${\mathrm{SiO}}_2$ with different levels of crystallinity are obtained. In amorphous and polycrystalline ${\mathrm{SiO}}_2$, both even and odd harmonics of the two-color interferogram beat four times per fundamental period, which is similar to what was observed in atomic gases or nonoriented molecules. In contrast, when a crystalline ${\mathrm{SiO}}_2$ sample is utilized, the competition between the contributions of broken inversion symmetries of the medium and the incident electric field results in a distinctive feature: Both odd and even harmonics beat two times per fundamental period [as predicted in Phys. Rev. B 94, 115164 (2016)]. Our observations are explained by an intuitive model. Moreover, they are fully supported by numerical simulations based on semiclassical transport theory. Our experiments highlight the considerable potential of polarimetry in two-color interferometric measurements, which allow pure and unambiguous characterization of the complex polarization response and thus consequent studies of electron dynamics in solids.

Machine learning employs dynamical algorithms that mimic the human capacity to learn, where the reinforcement learning ones are among the most similar to humans in this respect. On the other hand, adaptability is an essential aspect to perform any task efficiently in a changing environment, and it is fundamental for many purposes, such as natural selection. Here, we propose an algorithm based on successive measurements to adapt one quantum state to a reference unknown state, in the sense of achieving maximum overlap. The protocol naturally provides many identical copies of the reference state, such that in each measurement iteration more information about it is obtained. In our protocol, we consider a system composed of three parts, the “environment” system, which provides the reference state copies; the register, which is an auxiliary subsystem that interacts with the environment to acquire information from it; and the agent, which corresponds to the quantum state that is adapted by digital feedback with input corresponding to the outcome of the measurements on the register. With this proposal we can achieve an average fidelity between the environment and the agent of more than $90\%$ with less than 30 iterations of the protocol. In addition, we extend the formalism to $d$-dimensional states, reaching an average fidelity of around $80\%$ in less than 400 iterations for $d=11$, for a variety of genuinely quantum and semiclassical states. This work paves the way for the development of quantum reinforcement learning protocols using quantum data and for the future deployment of semiautonomous quantum systems.

We report the formation of a negative energy flux in the case of tight focusing of an arbitrary-order radially polarized annular beam. We consider not only the longitudinal component of the Poynting vector (energy flux density) and the region of its negative values, but also the local inverse energy flux as an integral characteristic over the region of negative values. Theoretically, the Richards-Wolf formulas in the Debye approximation are used to maximize the negative value of the energy flux density on the optical axis in the focal region for the second-order radial polarization ($m=2$). In this case, the local inverse energy flux, an integral characteristic in the bulk region of negative values, increases with increasing radial polarization order, i.e., for $m>2$. Jones matrices are employed to show that the result obtained will be valid for azimuthal polarization, as well as for a circularly polarized vortex beam. The results of numerical simulation are in good agreement with theoretical calculations. In addition, taking into account the approximate nature of the Richards-Wolf formulas, we also additionally model the tight focusing of a circular beam based on the solution of Maxwell's equation using the finite element method. It is shown that the local inverse energy flux in the case of the second-order radial polarization will be 1.5 times less than that in the case of the third-order radial polarization. In turn, the use of the fourth-order radial polarization makes it possible to increase the local inverse energy flux by a factor of 2.

We present a general, second quantization procedure for multitransverse-spatial-mode Gaussian-beam dynamics in nonlinear interactions. Previous treatments have focused on the spectral density and angular distribution of spatial modes. Here we go a layer deeper by investigating the complex transverse spatial mode in each angular spatial mode. Furthermore, to implement the theory, we simulate four-wave mixing and parametric down-conversion schemes, showing how one can elucidate and tailor the underlying multitransverse-spatial-mode structure along with its quantum properties.

Weak potential wells (or traps) in one and two dimensions, and the potential wells slightly deeper than the critical ones in three dimensions, feature shallow bound states with localization length much larger than the well radii. We address a simple fundamental question of how many repulsively interacting bosons can be localized by such traps. We find that under rather generic conditions, for both weakly and strongly repulsive particles, in two and three dimensions—but not in one-dimension—the potential well will trap infinitely many bosons. For example, even hard-core repulsive interactions do not prevent this “trapping collapse” phenomenon from taking place. A quantum system acquires the phenomenon along with the universal (asymptotically exact) classical-field behavior at large distances, allowing generic description by the Gross-Pitaevskii equation. We also discuss the possibility of having a transition between the infinite and finite number of trapped particles when strong repulsive interparticle correlations are increased.

We suggest an improved version of the Robertson–Schrödinger uncertainty relation for canonically conjugate variables by taking into account a pair of characteristics of states: non-Gaussianity and mixedness quantified by using fidelity and entropy, respectively. This relation is saturated by both Gaussian and Fock states and provides a strictly improved bound for any non-Gaussian states or mixed states. For the case of Gaussian states, it is reduced to the entropy-bounded uncertainty relation derived by Dodonov. Furthermore, we consider readily computable measures of both characteristics and find a weaker but more readily accessible bound. With its generalization to the case of two-mode states, we show applicability of the relation to detect entanglement of non-Gaussian states.

We present a direct excitation of the presumably ultranarrow $1001-\mathrm{nm}$ ground-state transition in atomic dysprosium. By using resonance ionization spectroscopy with pulsed Ti:sapphire lasers at a hot cavity laser ion source, we were able to measure the isotopic shifts in the $1001-\mathrm{nm}$ line between all seven stable isotopes. Furthermore, we determined the upper level energy from the atomic transition frequency of the ${}^{164}\mathrm{Dy}$ isotope as $9991.004\left(1\right){\mathrm{cm}}^{-1}$ and confirm the level energy listed in the NIST database. Since a sufficiently narrow natural linewidth is an essential prerequisite for high-precision spectroscopic investigations for fundamental questions, we furthermore determined a lower limit of $2.9\left(1\right)\mu \mathrm{s}$ for the lifetime of the excited state.

Circular Rydberg states with $n=70$ have been prepared in helium using a modified version of the crossed-fields method. This approach to the preparation of high-$n$ circular Rydberg states overcomes limitations of the standard crossed-fields method which arise at this, and higher, values of $n$. The experiments were performed with atoms traveling in pulsed supersonic beams that were initially laser photoexcited from the metastable $1s2s{}^{3}S_1$ level to the $1s73s{}^{3}S_1$ level by resonance-enhanced two-color two-photon excitation in a magnetic field of 16.154 G. These excited atoms were then polarized using a perpendicular electric field of 0.844 V/cm, and transferred by a pulse of microwave radiation to the state that, when adiabatically depolarized, evolves into the $n=70$ circular state in zero electric field. The excited atoms were detected by state-selective electric field ionization. Each step of the circular state preparation process was validated by comparison with the calculated atomic energy-level structure in the perpendicular electric and magnetic fields used. Of the atoms initially excited to the $1s73s{}^{3}S_1$ level, $\sim 80\%$ were transferred to the $n=70$ circular state. At these high values of $n, \mathrm{\Delta }n=1$ circular-to-circular Rydberg state transitions occur at frequencies below 20 GHz. Consequently, atoms in these states, and the circular state preparation process presented here, are well suited to hybrid cavity QED experiments with Rydberg atoms and superconducting microwave circuits.