To probe the nonlinear effects of photon-photon interaction in quantum electrodynamics, we study the generation of circular polarized photons by the collision of two linearly polarized laser beams. In the framework of the Euler-Heisenberg effective Lagrangian and the quantum Boltzmann equation for the time evolution of the density matrix of polarization, we calculate the intensity of circular polarization generated by the collision of two linearly polarized laser beams and estimate the rate of generation that is proportional to ${\alpha }^2$. As a result, we show that the generated circular polarization can be experimentally measured by two head-on colliding optical laser beams of a cross-sectional area $\lesssim$$0.01$ cm${}^2$ and a laser pulse energy of $\sim$mJ, which are currently available in laboratories. Our study presents a valuable supplement to other theoretical and experimental frameworks for the study and measurment of the nonlinear effects of photon-photon interaction in quantum electrodynamics.

We propose a class of incompatibility measures for quantum observables based on quantifying the effect of a measurement of one observable on the statistics of the outcomes of another. Specifically, for a pair of observables $A$ and $B$ with purely discrete spectra, we compare the following two probability distributions: one resulting from a measurement of $A$ followed by a measurement of $B$ on a given state and the other obtained from a measurement of $B$ alone on the same state. We show that maximizing the distance between these two distributions over all states yields a valid measure of the incompatibility of observables $A$ and $B$, which is zero if and only if they commute and is strictly greater than zero (and less than or equal to one) otherwise. For finite-dimensional systems, we obtain a tight upper bound on the incompatibility of any pair of observables and show that the bound is attained when the observables are totally nondegenerate and associated with mutually unbiased bases. In the process, we also establish an important relation between the incompatibility of a pair of observables and the maximal disturbances due to their measurements. Finally, we indicate how these measures of incompatibility and disturbance can be extended to the more general class of nonprojective measurements. In particular, we obtain a nontrivial upper bound on the incompatibility of one Lüders instrument with another.

Due to omnipresent environmental interferences, quantum coherences inevitably undergo irreversible transformations over certain time scales, thus leading to the loss of encoded information. This process, known as decoherence, has been a major obstacle in realizing efficient quantum information processors. Understanding the mechanism of decoherence is crucial in developing tools to inhibit it. Here we utilize a method proposed by Teklemariam et al. [Phys. Rev. A 67, 062316 (2003)] to engineer artificial decoherence in the system qubits by randomly perturbing their surrounding ancilla qubits. Using a two-qubit nuclear magnetic resonance quantum register, we characterize the artificial decoherence by noise spectroscopy and quantum process tomography. Further, we study the efficacy of dynamical decoupling sequences in suppressing the artificial decoherence. Here we describe the experimental results and their comparisons with theoretical simulations.

We study the decay of entanglement of quantum-dot electron-spin qubits under hyperfine-interaction-mediated decoherence. We show that two-qubit entanglement of a single entangled initial state may exhibit decay characteristic of two disentanglement regimes in a single sample, when the external magnetic field is changed. The transition is manifested by the suppression of time-dependent entanglement oscillations which are superimposed on the slowly varying entanglement decay related to phase decoherence which results in oscillatory behavior of entanglement sudden death time as a function of the magnetic field. This unique behavior allows us to propose the double-quantum-dot two-electron spin Bell state as a promising candidate for precise measurements of the magnetic field.

We introduce a constructive procedure that maps all spatial correlations of a broad class of $d$-level states of $N$ parties into temporal correlations between general $d$-outcome quantum measurements performed on a single $d$-level system. This allows us to present temporal phenomena analogous to genuinely multipartite nonlocal phenomena, such as Greenberger-Horne-Zeilinger correlations, which do not exist if only projective measurements on a single qubit are considered. The map is applied to certain lattice systems in order to replace one spatial dimension with a temporal one, without affecting measured correlations. We use this map to show how repeated application of a one-dimensional (1D) cluster gate leads to universal one-way quantum computing when supplemented with general two-outcome quantum measurements. In this way, we recover a temporal version of measurement-based quantum computing performed on a sequentially recreated 1D cluster.

We study the effects of the non-$\delta$ coupling between a one-dimensional waveguide (1DW) and a side optical cavity (SOC), which is a development of previous well-studied $\delta$-coupling situations. We first find the real-space Hamiltonian of the non-$\delta$ coupling system of the 1DW and SOC, and then derive out an equation determining the energy of the hybridization state between the 1DW and SOC modes and an analytic formula for the single-photon transmission. Through them, we recognize that the single-photon transmission-dip position can be changed by adjusting the SOC size and the coupling strength between the 1DW and the SOC. The transmission spectrum strongly depends on the coupling types between the 1DW and the SOC and holds an asymmetric line shape. At last, we simulate the asymmetry of the single-photon transmission by a gold-based waveguide coupled with a rectangular SOC.

In this work we demonstrate optical control of the singlet-triplet probability distribution in the outcome of a collisional process involving lithium dimers and argon atoms. The control is achieved using the Autler-Townes effect to manipulate the spin character of a spin-orbit coupled pair of levels serving as a “gateway” between the singlet and triplet electronic state manifolds.

We study a single quantum particle in discrete spacetime evolving in a causal way. We see that in the continuum limit, any massless particle with a two-dimensional internal degree of freedom obeys the Weyl equation, provided that we perform a simple relabeling of the coordinate axes or demand rotational symmetry in the continuum limit. It is surprising that this occurs regardless of the specific details of the evolution: it would be natural to assume that discrete evolutions giving rise to relativistic dynamics in the continuum limit would be very special cases. We also see that the same is not true for particles with larger internal degrees of freedom, by looking at an example with a three-dimensional internal degree of freedom that is not relativistic in the continuum limit. In the process, we give a formula for the Hamiltonian arising from the continuum limit of massless and massive particles in discrete spacetime.

Characterization of nonclassicality or quantumness of a state is fundamental to foundations of quantum mechanics and quantum information. At the heart of the problem is the question whether there exist classical systems—howsoever complicated—that can mimic a given quantum state. Whilst this has been traditionally addressed through the violation of Bell inequality or nonseparability, we show that it is possible to go beyond them, by introducing the concept of classical simulation. Focusing on the two-qubit case, we show that, while for pure states, classical simulability is equivalent to existence of a local hidden variable (LHV) model, the conditions for simulability can be weaker for mixed states, demanding what we call only a generalized LHV description. Consequently, quantum states which defy a classical simulation—which we call exceptional—may require conditions which are more stringent than violation of Bell inequalities. We illustrate these features with a number of representative examples and discuss the underlying reasons, by employing fairly simple arguments.

The vertical positron affinity (PA) value at the equilibrium position of a formaldehyde molecule is predicted as +25(3) meV with the highly accurate quantum Monte Carlo method. Applying anharmonic vibrational analysis, we have found that the vibrational excitation of the C = O stretching mode drastically enhances the PA value, due to the increment of the molecular dipole moment along this mode. Our predictions of the vibrational averaged PA values at the fundamental and overtone states are 31 and 36 meV, respectively, which strongly supports the conclusion that a positron can bind to formaldehyde.

We have studied the evolution of Rydberg wave packets in the presence of interatomic dipole-dipole interactions in a frozen Rb gas. Rb atoms in a magneto-optical trap (MOT) are first laser excited to $ns$ Rydberg eigenstates. A picosecond THz pulse further excites them into coherent superposition states involving the initial-level and neighboring $np$ states. A second, identical, time-delayed THz pulse probes the wave-packet dynamics. As the wave packets evolve they are influenced by dipole-dipole interactions, predominantly pairwise excitation-exchange processes of the form $|s\rangle |p\rangle \leftrightarrow |p\rangle |s\rangle$. The coherent electronic evolution of the ensemble dephases due to the variation in dipole-dipole coupling strength between atom pairs in the MOT. The experimental results are in good agreement with numerical calculations that simulate the interactions between nearest neighbors in a frozen gas.

The fragmentation of spin-orbit-coupled spin-1 Bose gas with a weak interaction in external harmonic trap is explored by both exact diagonalization and mean-field theory. This fragmentation tendency, which originates from the total angular momentum conservation, is affected obviously by the spin-orbit-coupling strength and the spin-dependent interaction. Strong spin-orbit interaction raises the inverse participation ratio, which describes the number of significantly occupied single-particle states. As the spin-dependent interaction changes from antiferromagnetic to ferromagnetic, the peak values in the inverse participation ratio become lower. Without the confinement of the appointed total angular momentum, the condensate chooses a zero or finite total angular momentum ground state, which is determined by both the interaction and the spin-orbit-coupling strength.

The study of spatial dispersion of two-dimensional complex crystals, with periodic modulations of both gain-loss and the refractive index, reveals simultaneous nondiffractive-nondiffusive light propagation. Narrow light beams and light patterns propagate without dispersion while amplified through the complex material. We determine and explore nondiffractive-nondiffusive regimes for collinear and noncollinear propagation.

We demonstrate that nonlinear polarization coupling in a fiber ring laser without polarization-selective elements, subject to the effects of average anomalous dispersion, Kerr effect, and nonlinear gain saturation, can lead to the antisynchronization of spatiotemporal chaos into a wide variety of ordered laminar states of orthogonal polarization temporal domains. These antiphase polarization domains include stable lattices of soliton trains with high duty cycle at repetition rates of hundreds of MHz, as well as sparse trains of coupled dark and bright solitary waves.

We introduce an operator linked with the radial index in the Laguerre-Gauss modes of a two-dimensional harmonic oscillator in cylindrical coordinates. We discuss ladder operators for this variable, and confirm that they obey the commutation relations of the su(1,1) algebra. Using this fact, we examine how basic quantum optical concepts can be recast in terms of radial modes.

We propose a detailed stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs in whispering-gallery-mode resonators when they are pumped in either the anomalous- or normal-dispersion regime. We analyze the spatial bifurcation structure of the stationary states depending on two parameters that are experimentally tunable; namely, the pump power and the cavity detuning. Our study demonstrates that, in both the anomalous- and normal-dispersion cases, nontrivial equilibria play an important role in this bifurcation map because their associated eigenvalues undergo critical bifurcations that are actually foreshadowing the existence of localized and extended spatial dissipative structures. The corresponding bifurcation maps are evidence of a considerable richness from a dynamical standpoint. The case of anomalous dispersion is indeed the most interesting from the theoretical point of view because of the considerable variety of dynamical behavior that can be observed. For this case we study the emergence of super- and subcritical Turing patterns (or primary combs) in the system via modulational instability. We determine the areas where bright isolated cavity solitons emerge, and we show that soliton molecules can emerge as well. Very complex temporal patterns can actually be observed in the system, where solitons (or soliton complexes) coexist with or without mutual interactions. Our investigations also unveil the mechanism leading to the phenomenon of breathing solitons. Two routes to chaos in the system are identified; namely, a route via the destabilization of a primary comb, and another via the destabilization of solitons. For the case of normal dispersion, we unveil the mechanism leading to the emergence of weakly stable Turing patterns. We demonstrate that this weak stability is justified by the distribution of stable and unstable fixed points in the parameter space (flat states). We show that dark cavity solitons can emerge in the system, and also show how these solitons can coexist in the resonator as long as they do not interact with each other. We find evidence of breather solitons in this normal dispersion regime as well. The Kerr frequency combs corresponding to all these spatial dissipative structures are analyzed in detail, along with their stability properties. A discussion is led about the possibility to gain unifying comprehension of the observed spectra from the dynamical complexity of the system.

Performing exact inference on Bayesian networks is known to be $\#P$-hard. Typically approximate inference techniques are used instead to sample from the distribution on query variables given the values $e$ of evidence variables. Classically, a single unbiased sample is obtained from a Bayesian network on $n$ variables with at most $m$ parents per node in time $O\left(nmP{\left(e\right)}^{-1}\right)$, depending critically on $P\left(e\right)$, the probability that the evidence might occur in the first place. By implementing a quantum version of rejection sampling, we obtain a square-root speedup, taking $O\left(n{2}^{m}P{\left(e\right)}^{-\frac{1}{2}}\right)$ time per sample. We exploit the Bayesian network's graph structure to efficiently construct a quantum state, a q-sample, representing the intended classical distribution, and also to efficiently apply amplitude amplification, the source of our speedup. Thus, our speedup is notable as it is unrelativized—we count primitive operations and require no blackbox oracle queries.

In this work, we present a second-order Born series treatment for the double ionization of He by ion impact. In particular, we show that the well-known independent events and independent electron models naturally result from an on-shell treatment for the second-order Born approximation. A transition amplitude which coherently includes first- and second-order terms in the projectile interaction is introduced to study the role of the two-step-1, shake-off, and two-step-2 mechanisms at different impact energies. Fully differential cross sections for proton and antiproton impact are presented and analyzed for different projectile momentum transfers.

The measurements of Crandall et al. [Phys. Rev. A 10, 141 (1974)] for the polarization of light emitted during electron-impact excitation of ${\mathrm{Ba}}^{+}$ are in significant disagreement with relativistic distorted wave scattering theory calculations of Sharma et al. [Phys. Rev. A 83, 062701 (2011)]. The relativistic convergent close-coupling (RCCC) method is applied to the problem and the discrepancy between theory and experiment is resolved across the full range of energies measured. Furthermore, the oscillations in the polarization fraction measurements at low energies near threshold are reproduced by the RCCC calculations and linked to the formation of autoionizing states of neutral Ba.