Recently, the existence of robust three-dimensional light bullets (LBs) was predicted theoretically in the output of a laser coupled to a distant saturable absorber. In this paper, we analyze the stability and the range of existence of these dissipative localized structures and provide guidelines and realistic parameter sets for their experimental observation. In order to reduce the complexity of the analysis, we first approximate the three-dimensional problem by a reduced equation governing the dynamics of the transverse profile. This effective theory provides an intuitive picture of the LB formation mechanism. Moreover, it allows us to perform a detailed multiparameter bifurcation study and to identify the different mechanisms of instability. It is found that the LBs experience dominantly either homogeneous oscillation or symmetry-breaking transversal wave radiation. In addition, our analysis reveals several nonintuitive scaling behaviors as functions of the linewidth enhancement factors and the saturation parameters. Our results are confirmed by direct numerical simulations of the full system.

Polarization quasiprobability distribution defined in the Stokes space shares many important properties with the Wigner function for position and momentum. Most notably, they both give correct one-dimensional marginal probability distributions and therefore represent the natural choice for the probability distributions in classical hidden-variable models. In this context, negativity of the Wigner function is considered as proof of nonclassicality for a quantum state. On the contrary, the polarization quasiprobability distribution demonstrates negativity for all quantum states. This feature comes from the discrete nature of Stokes variables; however, it was not observed in previous experiments, because they were performed with photon-number averaging detectors. Here we reconstruct the polarization quasiprobability distribution of a coherent state with photon-number resolving detectors, which allows us to directly observe for the first time its negativity. Furthermore we derive a theoretical polarization quasiprobability distribution for any linearly polarized quantum state.

The quantum statistics of particles is determined by both the spins and the indistinguishability of quantum states. Here we study the quantum statistics of partially distinguishable photons by defining the multiphoton indistinguishability. The photon-bunching coefficient is formulated based on the properties of permutation symmetry and a modified Bose-Einstein statistics is presented with an indistinguishability-induced photon-bunching effect. Moreover, the statistical transition of the photon state is studied for partially distinguishable photons and the results show that the indistinguishability exhibits the same role as that observed in the generation of laser. The results will fill the gap between Bose-Einstein and Poisson statistics for photons and a formula is presented for the study of multiphoton quantum information processes.

We formulate the necessary and sufficient conditions for the existence of a pair of maximally incompatible two-outcome measurements in a finite-dimensional general probabilistic theory. The conditions are on the geometry of the state space; they require the existence of two pairs of parallel exposed faces with an additional condition on their intersections. We introduce the notion of discrimination measurement and show that the conditions for a pair of two-outcome measurements to be maximally incompatible are equivalent to requiring that a (potential, yet nonexisting) joint measurement of the maximally incompatible measurements would have to discriminate affinely dependent points. We present several examples to demonstrate our results.

Optical clock interrogation protocols, based on laser-pulse spectroscopy, suffer from probe-induced frequency shifts and their variations induced by laser power. The original hyper-Ramsey probing scheme, which was proposed to alleviate those issues, does not fully eliminate the shift, especially when decoherence and relaxation by spontaneous emission or collisions are present. We propose to solve the fundamental problem of frequency shifts induced by the laser probe by deriving the exact canonical form of a multipulse generalized hyper-Ramsey resonance, including decoherence and relaxation. We present a universal interrogation protocol based on composite laser-pulse spectroscopy with phase modulation eliminating probe-induced frequency shifts at all orders in the presence of various dissipative processes. Unlike frequency shift extrapolation based methods, a universal interrogation protocol based on $\pm \pi /4$ and $\pm 3\pi /4$ phase-modulated resonances is proposed which does not compromise the stability of the optical clock while maintaining an ultrarobust error signal gradient in the presence of substantial uncompensated ac Stark shifts. Such a scheme can be implemented in two flavors: either by inverting clock state initialization or by pulse order reversal even without a perfect quantum state initialization. This universal interrogation protocol can be applied to atomic, molecular, and nuclear frequency metrology, mass spectrometry, and the field of precision spectroscopy. It might be designed using magic-wave-induced transitions, two-photon excitation, and magnetically induced spectroscopy or it might even be implemented with quantum logic gate circuit and qubit entanglement.

The negative-ion fragmentation of formic acid (HCOOH) is studied with negative- and positive-ion coincidence spectroscopy. We report four-body ionic fragmentation where up to three positive ions are collected in coincidence with one negative ion. We report yields for 21 three-body channels and five four-body channels. More than 80% of all negative-ion fragmentation involves production of ${\mathrm{O}}^{-}$, and it is dominated by complete dissociation of all molecular bonds. Negative-ion creation is most abundant at high-Rydberg resonances and just above the molecule's core-ionization potentials. The existence of four-body fragmentation channels evidences a strong charge redistribution in the molecule.

Quantum cascaded systems offer the possibility to manipulate a target system with the quantum state of a source system. Here, we study in detail the differences between a direct quantum cascade and coherent or incoherent driving for the case of two coupled cavity-QED systems. We discuss qualitative differences between these excitations scenarios, which are particularly strong for higher-order photon-photon correlations: $g^{\left(n\right)}\left(0\right)$ with $n>2$. Quantum cascaded systems show a behavior differing from the idealized cases of individual coherent or incoherent driving and allow one to produce qualitatively different quantum statistics. Furthermore, the quantum cascaded driving exhibits an interesting mixture of quantum coherent and incoherent excitation dynamics. We develop a measure where the two regimes intermix and quantify these differences via experimentally accessible higher-order photon correlations.

We revisit the mechanisms underlying the process of spectral broadening of incoherent optical waves propagating in nonlinear media on the basis of nonequilibrium thermodynamic considerations. A simple analysis reveals that a prerequisite for the existence of a significant spectral broadening of the waves is that the linear part of the energy (Hamiltonian) has different contributions of opposite signs. It turns out that, at variance with the expected soliton turbulence scenario, an increase of the amount of disorder (incoherence) in the system does not require the generation of a coherent soliton structure. We illustrate the idea by considering the propagation of two wave components in an optical fiber with opposite dispersion coefficients. A wave turbulence approach to the problem reveals that the increase of kinetic energy in one component is offset by the negative reduction in the other component, so that the waves exhibit, as a general rule, virtually unlimited spectral broadening. More precisely, a self-similar solution of the kinetic equations reveals that the spectra of the incoherent waves tend to relax toward a homogeneous distribution in the wake of a front that propagates in frequency space with a decelerating velocity. We discuss this catastrophic process of spectral broadening in the light of different important phenomena, in particular supercontinuum generation, soliton turbulence, wave condensation, and the runaway motion of mechanical systems composed of positive and negative masses.

Projective measurement is used as a fundamental axiom in quantum mechanics, even though it is discontinuous and cannot predict which measured operator eigenstate will be observed in which experimental run. The probabilistic Born rule gives it an ensemble interpretation, predicting proportions of various outcomes over many experimental runs. Understanding gradual weak measurements requires replacing this scenario with a dynamical evolution equation for the collapse of the quantum state in individual experimental runs. We revisit the quantum trajectory framework that models quantum measurement as a continuous nonlinear stochastic process. We describe the ensemble of quantum trajectories as noise fluctuations on top of geodesics that attract the quantum state towards the measured operator eigenstates. In this effective theory framework for the ensemble of quantum trajectories, the measurement interaction can be specific to each system-apparatus pair, a context necessary for understanding weak measurements. Also in this framework, the constraint to reproduce projective measurement as per the Born rule in the appropriate limit requires that the magnitudes of the noise and the attraction are precisely related, in a manner reminiscent of the fluctuation-dissipation relation. This relation implies that both the noise and the attraction have a common origin in the underlying measurement interaction between the system and the apparatus. We analyze the quantum trajectory ensemble for the scenarios of quantum diffusion and binary quantum jump, and show that the ensemble distribution is completely determined in terms of a single evolution parameter. This trajectory ensemble distribution can be tested in weak measurement experiments. We also comment on how the required noise may arise in the measuring apparatus.

We consider the dynamics of a collisional model in which both the system and environment are embodied by spin-$1/2$ particles. In order to include non-Markovian features in our model, we introduce interactions among the environmental qubits and investigate the effect that different models of such interaction have on the degree of non-Markovianity of the system's dynamics. By extending that interaction beyond the nearest neighbor, we enhance the degree of non-Markovianity in the system's dynamics. A further significant increase can be observed if a collective interaction with the forthcoming environmental qubits is considered. However, the observed degree of non-Markovianity in this case is nonmonotonic with the increasing number of qubits included in the interaction. Moreover, one can establish a connection between the degree of non-Markovianity in the evolution of the system and the fading behavior of quantum coherence in its state as the number of collisions grows. We complement our study with an investigation of system-environment correlations and present an example of their importance on a physical upper bound on the trace distance derivative.

We address the problem of characterizing the steerability of quantum states under restrictive measurement scenarios, i.e., the problem of determining whether a quantum state can demonstrate steering when subjected to $N$ measurements of $k$ outcomes. We consider the cases of either general positive operator-valued measures (POVMs) or specific kinds of measurements (e.g., projective or symmetric). We propose general methods to calculate lower and upper bounds for the white-noise robustness of a $d$-dimensional quantum state under different measurement scenarios that are also applicable to the study of the noise robustness of the incompatibility of sets of unknown qudit measurements. We show that some mutually unbiased bases, symmetric informationally complete measurements, and other symmetric choices of measurements are not optimal for steering the isotropic states and provide candidates for the most incompatible sets of measurements in each case. Finally, we provide numerical evidence that nonprojective POVMs do not improve over projective ones for this task.

The Born rule provides a probability vector (distribution) with a quantum state for a measurement setting. For two settings, we have a pair of vectors from the same quantum state. Each pair forms a combined-probability vector that obeys certain quantum constraints, which are triangle inequalities in our case. Such a restricted set of combined vectors, called the combined-probability space, is presented here for a $d$-level quantum system (qudit). The combined space is a compact convex subset of a Euclidean space, and all its extreme points come from a family of parametric curves. Considering a suitable concave function on the combined space to estimate the uncertainty, we deliver an uncertainty relation by finding its global minimum on the curves for a qudit. If one chooses an appropriate concave (or convex) function, then there is no need to search for the absolute minimum (maximum) over the whole space; it will be on the parametric curves. So these curves are quite useful for establishing an uncertainty (or a certainty) relation for a general pair of settings. We also demonstrate that many known tight certainty or uncertainty relations for a qubit can be obtained with the triangle inequalities.

We consider a two-state system consisting of a pair of coupled ferromagnetic waveguides. A monotonically increasing bias magnetic field can dynamically manipulate the system to enter a $\mathcal{PT}$ -symmetry-broken phase and then reenter a symmetric phase. The symmetry recovery is enabled by the presence of accidental degeneracy points when the system has no loss and each degeneracy point can spawn a pair of exceptional points when asymmetric loss is introduced. We performed microwave experiments to demonstrate the presence of the exceptional point and symmetry recovery.

We address the question of whether symmetry-protected topological (SPT) order can persist at nonzero temperature, with a focus on understanding the thermal stability of several models studied in the theory of quantum computation. We present three results in this direction. First, we prove that nontrivial SPT order protected by a global onsite symmetry cannot persist at nonzero temperature, demonstrating that several quantum computational structures protected by such onsite symmetries are not thermally stable. Second, we prove that the three-dimensional (3D) cluster-state model used in the formulation of topological measurement-based quantum computation possesses a nontrivial SPT-ordered thermal phase when protected by a generalized (1-form) symmetry. The SPT order in this model is detected by long-range localizable entanglement in the thermal state, which compares with related results characterizing SPT order at zero temperature in spin chains using localizable entanglement as an order parameter. Our third result is to demonstrate that the high-error tolerance of this 3D cluster-state model for quantum computation, even without a protecting symmetry, can be understood as an application of quantum error correction to effectively enforce a 1-form symmetry.

Multipartite Einstein-Podolsky-Rosen (EPR) steering is a useful quantum resource for quantum communication in quantum networks. It has potential applications in secure quantum communication, such as one-sided device-independent quantum key distribution and quantum secret sharing. By distributing optical modes of a multipartite entangled state to space-separated quantum nodes, a local quantum network can be established. Based on the existing multipartite EPR steering in a local quantum network, secure quantum communication protocol can be accomplished. In this manuscript, we present swapping schemes for EPR steering between two space-separated Gaussian multipartite entangled states, which can be used to connect two space-separated quantum networks. Two swapping schemes, including the swapping between a tripartite Greenberger-Horne-Zeilinger (GHZ) entangled state and an EPR entangled state and that between two tripartite GHZ entangled states, are analyzed. Various types of EPR steering are presented after the swapping of two space-separated independent multipartite entanglement states without direct interaction, which can be used to implement quantum communication between two quantum networks. The presented schemes provide technical reference for more complicated quantum networks with EPR steering.

Barium monohydride (BaH) is an attractive candidate for extending laser cooling and trapping techniques to diatomic hydrides. The apparatus and high-resolution optical spectroscopy presented here demonstrate progress toward this goal. A cryogenic buffer-gas-cooled molecular beam of BaH was constructed and characterized. Pulsed laser ablation into cryogenic helium buffer gas delivers $\sim 1\times {10}^{10}$ molecules/sr/pulse in the $X{}^2\mathrm{\Sigma }^{+}$ ($v^{\prime \prime }=0,N^{\prime \prime }=1$) state of primary interest. More than $1\times {10}^7$ of these molecules per pulse enter the downstream science region with forward velocities below 100 m/s and transverse temperature of 0.1 K. This molecular beam enabled high-resolution optical spectra of BaH in quantum states relevant to laser slowing and cooling. The reported measurements include hyperfine structure and magnetic $g$ factors in the $X{}^2\mathrm{\Sigma }^{+}$, $B{}^2\mathrm{\Sigma }^{+}$, and $A{}^2\mathrm{\Pi }_{1/2}$ states.

The effect of final-state dynamic correlation is investigated for helium single ionization by 75-keV proton impact analyzing fully differential cross sections (FDCS). The final state is represented by a continuum correlated wave (CCW-PT) function which accounts for the interaction between the projectile and the residual target ion (PT interaction). This continuum correlated wave function partially includes the correlation of electron-projectile and electron-target relative motion as coupling terms of the wave equation. The transition matrix is evaluated using the CCW-PT function and the Born initial state. The analytical expression of the transition matrix has been obtained. We have shown that this series is strongly convergent and analyzed the contribution of their different terms to the FDCS within the perturbation method. Illustrative computations are performed in the scattering plane and in the perpendicular plane. Both the correlation effects and the PT interaction are checked by the preset calculations. Our results are compared with absolute experimental data as well as other theoretical models. We have shown that the dynamic correlation plays an important role in the single ionization of atoms by proton impact at intermediate projectile energies, especially at large transverse momentum transfer. While overall agreement between theory and the experimental data is encouraging, detailed agreement is lacking. The need for more theoretical and experimental work is emphasized.

In a recent experiment, Schmiegelow et al. [Nat. Commun. 7, 12998 (2016)] investigated the magnetic sublevel population of ${\mathrm{Ca}}^{+}$ ions in a Laguerre-Gaussian light beam if the target atoms were just centered along the beam axis. They demonstrated in this experiment that the sublevel population of the excited atoms is uniquely defined by the projection of the orbital angular momentum of the incident light. However, little attention has been paid so far to the question of how the magnetic sublevels are populated when atoms are displaced from the beam axis by some impact parameter $\mathit{b}$. Here, we analyze this sublevel population for different atomic impact parameters in first-order perturbation theory and by making use of the density-matrix formalism. Detailed calculations are performed especially for the $4s{}^{2}S_{1/2}\to 3d{}^{2}D_{5/2}$ transition in ${\mathrm{Ca}}^{+}$ ions and for the vector potential of a Laguerre-Gaussian beam in Coulomb gauge. It is shown that the magnetic sublevel population of the excited ${}^{2}D_{5/2}$ level varies significantly with the impact parameter and is sensitive to the polarization, the radial index, as well as the orbital angular momentum of the incident light beam.

A configuration to excite the Uller-Zenneck surface electromagnetic waves at the planar interfaces of homogeneous and isotropic dielectric materials is proposed and theoretically analyzed. The Uller-Zenneck waves are surface waves that can exist at the planar interface of two dissimilar dielectric materials of which at least one is a lossy dielectric material. In this paper, a slab of a lossy dielectric material was taken with lossless dielectric materials on both sides. A canonical boundary-value problem was set up and solved to find the possible Uller-Zenneck waves and waveguide modes. The Uller-Zenneck waves guided by the slab of the lossy dielectric material were found to be either symmetric or antisymmetric and transmuted into waveguide modes when the thickness of that slab was increased. A prism-coupled configuration was then successfully devised to excite the Uller-Zenneck waves. The results showed that the Uller-Zenneck waves are excited at the same angle of incidence for any thickness of the slab of the lossy dielectric material, whereas the waveguide modes can be excited when the slab is sufficiently thick. The excitation of Uller-Zenneck waves at the planar interfaces with homogeneous and all-dielectric materials can usher in new avenues for the applications for electromagnetic surface waves.

Single photons of subnatural linewidth and high spectral brightness are necessary for efficient light-matter interaction at the single-photon level, which lies at the heart of many quantum photonic technologies. Here we demonstrate a bright source of single photons with subnatural linewidth, controllable waveforms, and a high spectral brightness of $3.67\times {10}^5\mathrm{s}{}^{-1}\mathrm{mW}{}^{-1}\mathrm{MHz}{}^{-1}$. The interaction between the single photons and atoms is demonstrated by the controlled absorption of the single photons in an atomic vapor. Our work has potential applications in quantum information technologies.