We provide a self-consistent electromagnetic theory of the link between spatial coherence and optical resonances in three-dimensional open and dissipative photonic systems. The theory that relies on the concept of quasinormal modes with complex frequencies provides an accurate modal expansion of the imaginary part of the Green tensor that correctly treats the effects of radiative leakage, absorption, and dispersion. It represents a powerful tool for calculating and understanding the degree of spatial coherence in complex photonic or plasmonic systems that are governed by a small number of resonances. Comparisons with fully vectorial calculations evidence the high accuracy of the predictions achieved by our semianalytical treatment in the case of coupled photonic-crystal microcavities and plasmonic nanoantennas made of metallic nanorods.

The relatively new atomic form factor for twisted (vortex) beams, which carry orbital angular momentum (OAM), is considered and compared to the conventional atomic form factor for plane-wave beams that carry only spin angular momentum. Since the vortex symmetry of a twisted photon is more complex that that of a plane wave, evaluation of the atomic form factor is also more complex for twisted photons. On the other hand, the twisted photon has additional parameters, including the OAM quantum number, $\ell$, the nodal radial number, $p$, and the Rayleigh range, $z_R$, which determine the cone angle of the vortex. This Rayleigh range may be used as a variable parameter to control the interaction of twisted photons with matter. Here we address (i) normalization of the vortex atomic form factor, (ii) displacement of target atoms away from the center of the beam vortex, and (iii) formulation of transition probabilities for a variety of photon-atom processes. We attend to features related to experiments that can test the range of validity and accuracy of calculations of these variations of the atomic form factor. Using the absolute square of the form factor for vortex beams, we introduce a vortex factor that can be directly measured.

A microwave field is used to control the interaction between pairs of optical photons stored in highly excited collective states (Rydberg polaritons). We show that strong dipole-dipole interactions induced by the microwave field destroy the coherence of polariton modes with more than one Rydberg excitation. Consequently, single-polariton modes, which correspond to single stored photons, are preferentially retrieved from the sample. Measurements of the photon statistics of the retrieved light field also reveal nontrivial propagation dynamics of the interacting polaritons.

We explore the effect of nuclear mass on the laser-driven electron localization process. We dissociate a mixed H${}_2$ and D${}_2$ target with intense, carrier-envelope-phase (CEP) stable 6 fs laser pulses and detect the products in a reaction microscope. We observe a very strong CEP-dependent asymmetry in proton and deuteron emission for low dissociation energy channels. This asymmetry is stronger for H${}_2$ than for D${}_2$. We also observe a large CEP offset between the asymmetry spectra for H${}_2$ and D${}_2$. Our theoretical simulations, based on a one-dimensional two-channel model, agree very well with the asymmetry spectra, but fail to account properly for the phase difference between the two isotopes.

Boundary-dependent corrections to the spin energy eigenvalues of an electron in a weak magnetic field and confined by a harmonic trapping potential are investigated. The electromagnetic field is quantized through a normal-mode expansion obeying the Maxwell boundary conditions at the material surface. We couple the electron to this photon field and a classical magnetic field in the Dirac equation, to which we apply the unitary Foldy-Wouthuysen transformation in order to generate a nonrelativistic approximation of the Hamiltonian to the desired order. We obtain the Schrödinger eigenstates of an electron subject to double confinement by a harmonic potential and a classical magnetic field, and then use these within second-order perturbation theory to calculate the spin energy shift that is attributable to the surface-modified quantized field. We find that a pole at the eigenfrequency of a set of generalized Landau transitions gives dominant oscillatory contributions to the energy shift in the limit of tight harmonic confinement in a weak magnetic field, which also make the energy shift preferable to the magnetic moment for a physically meaningful interpretation.

The parameters for $S$-wave elastic scattering of near-zero-energy electrons and positrons by $H_2$ molecules are calculated using the stabilization method with explicitly correlated Gaussians. The confined variational method is applied to optimize the Gaussians to describe the short-range interaction of incident $e^{\pm }$ with $H_2$ in the fixed-nuclei approximation. For $e^{+}$-$H_2$ scattering the scattering length of previous work [Phys. Rev. Lett. 103, 223202 (2009)] is substantially improved. More importantly, for $e^{-}$-$H_2$ scattering, from first principles, the scattering length is computed as a function of the internuclear distance. In the case that the two nuclei are at the equilibrium distance the results are in a good agreement with values derived from fitting experimental total and diffusion cross sections to the modified effective range theory.

In this article, coherent contributions of high-order quantum paths are proposed to generate a highly efficient and fine appearance attosecond pulse. We show how the electron dynamics of the high-order harmonics evolves so that harmonics are generated by a helium atom exposed to the two-color waveform composed of sub-one-cycle pulses. The leading and the trailing of the pulse is constructed by the near-infrared driving pulse and a midinfrared control pulse, respectively, thereby tunnel ionization and recombination are effectively manipulated. This waveform not only broadens the bandwidth but also leads to the contribution of high-order rescatterings in the generated supercontinuum and thereby enhances the harmonic yields. Whereas the effective duration of the waveform is lesser than the midinfrared pulse, with prolonging the pulse trailing, the long path of first-order rescattering is completely suppressed and high-order rescatterings of different electron trajectories appear. The most interesting feature is that under optimized conditions, the short paths of consecutive rescatterings coherently contribute in the high-order-harmonic generation process that leads to a fine appearance in the attosecond pulses.

We present an efficient method for generating maximum entanglement in one-dimensional atomic lattices. The proposed method relies on adiabatic rapid transfer into two Rydberg states with strongly asymmetric interactions. The method is suitable for Rydberg $S$ states in the absence of applied electrostatic fields. We show numerical simulations of entanglement generation in rubidium atoms using calculated van der Waals potentials under realistic experimental conditions. We study the effect of the chosen Rydberg states on the final entanglement.

We generalize the Fermi-liquid theory to $N$ component systems with $\mathrm{SU}(N)$ symmetry. We evaluate the Fermi-liquid parameters, effective mass, compressibility, and spin susceptibilities for a repulsive gas. We emphasize the important role of induced density fluctuations when $N$ is large. These fluctuations dramatically modify the properties of the gas, in particular the spin susceptibilities, from mean-field predictions.

A scheme is presented for generating unitarily multimode field squeezing, cluster entanglement, and Greenberger-Horne-Zeilinger (GHZ) entanglement via cavity quantum electrodynamics. Through a suitable laser system, we are able to engineer a squeeze field operator decoupled from the atomic degrees of freedom, yielding a large squeeze parameter proportional to the number of atoms. The physical mechanism is attributed to the multiple four-photon processes and the dispersive atom-cavity-field interaction in large detuning systems.

In this paper, we propose two protocols for generating super-resolving single-photon (SRSP) number-path-entangled states from general maximally number-path-entangled NOON states. It is our purpose to show that, contrary to popular belief, a field in a single-photon state can carry multifold phase information. We also show that both protocols generate the desired state with different probabilities depending on the type of detectors being used. Such SRSP number-path-entangled states preserve high resolving power but lack the requirement of a multiphoton absorbing resist, which may serve as a proof-of-principle prototype for quantum lithography in the future.

We present the observation of the Rb two-photon spectrum directly excited by an Er:fiber laser comb in a hot atomic vapor system. The influences of the atomic velocity distribution on direct and sequential two-photon transitions are discussed respectively and a combination of corresponding spectral control techniques is developed to eliminate the Doppler broadening background. A direct frequency comb spectroscopy is obtained with high-resolution two-photon transition lines. These techniques would benefit spectroscopy measurement in hot atomic vapor systems, and pave the way for establishing a high-stability optical frequency comb in 1.5 $\mu$m optical communication bands based on the Rb two-photon transitions.

We investigate the time evolution of the momentum of an impurity atom injected into a degenerate Tonks-Girardeau gas. We establish that given an initial momentum $p_0$ the impurity relaxes to a steady state with a nonvanishing momentum $p_{\infty }.$ The nature of the steady state is found to depend drastically on whether the masses of the impurity and the host are equal. This is due to multiple coherent scattering processes leading to a resonant interaction between the impurity and the host in the case of equal masses. The dependence of $p_{\infty }$ on $p_0$ remains nontrivial even in the limit of vanishing interaction between the impurity and host particles. In this limit $p_{\infty }\left(p_0\right)$ is found explicitly.

We introduce a computational method to determine the rate of the electron-positron pair creation triggered by a time-dependent subcritical external field. It is based on constructing a Lorentz transformation to an instantaneous rest frame, for which the pair-creation rate can be determined by standard techniques. We will discuss the accuracy and efficiency of this method by comparing its predictions with exact time-dependent quantum field theoretical solutions to the Dirac and Klein-Gordon equations for various space-time dependent external fields.

The Clauser-Horne-Shimony-Holt inequality was originally proposed as a Bell inequality to detect nonlocality in bipartite systems. However, it can also be used to certify the nonlocality of multipartite quantum states. We apply this to study the nonlocality of multipartite Greenberger-Horne-Zeilinger (GHZ), W, and graph states under local decoherence processes. We derive lower bounds on the critical local-noise strength tolerated by the states before becoming local. In addition, for the whole noisy dynamics, we derive lower bounds on the corresponding nonlocal content for the three classes of states. All the bounds presented can be calculated efficiently and, in some cases, provide significantly tighter estimates than with any other known method. For example, they reveal that $N$-qubit GHZ states undergoing local dephasing are, for all $N$, nonlocal throughout all the dephasing dynamics.

We propose an optical scheme to prepare large-scale entangled networks of $W$ states. The scheme works by simultaneously fusing three polarization-encoded $W$ states of arbitrary size via accessing only one qubit of each $W$ state. It is composed of a Fredkin gate (controlled-swap gate), two fusion gates [as proposed in S. K. Ozdemir et al., New J. Phys. 13, 103003 (2011)], and an $H$-polarized ancilla photon. Starting with three $n$-qubit $W$ states, the scheme prepares a new $W$ state with $3(n-1)$ qubits after postselection if both fusion gates operate successfully, i.e., a fourfold coincidence at the detectors. The proposed scheme reduces the cost of creating arbitrarily large $W$ states considerably when compared to previously reported schemes.

The exact dynamics of the entanglement between two harmonic modes generated by an angular momentum coupling is examined. Such a system arises when considering a particle in a rotating anisotropic harmonic trap or a charged particle in a fixed harmonic potential in a magnetic field, and it exhibits a rich dynamical structure, with stable, unstable, and critical regimes according to the values of the rotational frequency or field and trap parameters. Consequently, it is shown that the entanglement generated from an initially separable Gaussian state can exhibit quite distinct evolutions, ranging from quasiperiodic behavior in stable sectors to different types of unbounded increase in critical and unstable regions. The latter lead, respectively, to logarithmic and linear growth of the entanglement entropy with time. It is also shown that entanglement can be controlled by tuning the frequency, such that it can be increased, kept constant, or returned to a vanishing value with just stepwise frequency variations. Exact asymptotic expressions for the entanglement entropy in the different dynamical regimes are provided.

We use the dynamical algebra of a quantum system and its dynamical invariants to inverse engineer feasible Hamiltonians for implementing shortcuts to adiabaticity. These are speeded up processes that end up with the same populations as slow, adiabatic ones. As application examples, we design families of shortcut Hamiltonians that drive two- and three-level systems between initial and final configurations, imposing physically motivated constraints on the terms (generators) allowed in the Hamiltonian.

Future ultrafast x-ray light sources might image ultrafast coherent electron motion in real space and in real time. For a rigorous understanding of such an imaging experiment, we extend the theory of nonresonant x-ray scattering to the time domain. The role of energy resolution of the scattering detector is investigated in detail. We show that time-resolved nonresonant x-ray scattering with no energy resolution offers an opportunity to study time-dependent electronic correlations in nonequilibrium quantum systems. Furthermore, our theory presents a unified description of ultrafast x-ray scattering from electronic wave packets and the dynamical imaging of ultrafast dynamics using inelastic x-ray scattering by Abbamonte and co-workers. We examine closely the relation of the scattering signal and the linear density response of electronic wave packets. Finally, we demonstrate that time-resolved x-ray scattering from a crystal consisting of identical electronic wave packets recovers the instantaneous electron density.