The interaction and the propagation of intense and short laser pulses in nonlinear optical materials are addressed. A consistent introduction of a time-dependent ionization model into the Maxwell's equations allows one to account for the influence of strong variations of the pulse spectrum on the ionization dynamics, which in turn affects the pulse propagation. The interaction between both ionization and propagation dynamics is demonstrated for two cases of practical interest: frequency conversion and propagation of chirped pulses.

The frequencies of two nominally identical ${}^{88}{\mathrm{Sr}}^{+}$ trapped single ion optical clocks, based on the 674 nm 5$s$ ${}^2$$S_{1/2}$–4$d$ ${}^2$$D_{5/2}$ electric quadrupole clock transition, have been compared over a period of nine months. The frequencies of the two clocks were found to agree within a total uncertainty of 4 × 10${}^{-17}$, demonstrating that the individual ${}^{88}{\mathrm{Sr}}^{+}$ optical clocks are reproducible at the 3 × 10${}^{-17}$ level. The absolute frequency of the clock transition was measured to be $f$ = 444 779 044 095 486.71(24) Hz using an optical frequency comb referenced to a cesium fountain primary frequency standard. The standard uncertainty of 0.24 Hz (5.3 × 10${}^{-16}$ of the optical frequency) is dominated by measurement statistics and cesium fountain systematics and is around four times lower than previously published.

We ask and answer a basic question about the length scales involved in quantum decoherence: how far apart in space do two parts of a quantum system have to be before a common quantum environment decoheres them as if they were entirely separate? We frame this question specifically in a cold atom context. How far apart do two populations of bosons have to be before an environment of thermal atoms of a different species (“buffer gas”) responds to their two particle numbers separately? An initial guess for this length scale is the thermal coherence length of the buffer gas; we show that a standard Born-Markov treatment partially supports this guess, but predicts only inverse-square saturation of decoherence rates with distance, and not the much more abrupt Gaussian behavior of the buffer gas's first-order coherence. We confirm this Born-Markov result with a more rigorous theory, based on an exact solution of a two-scatterer scattering problem, which also extends the result beyond weak scattering. Finally, however, we show that when interactions within the buffer-gas reservoir are taken into account, an abrupt saturation of the decoherence rate does occur, exponentially on the length scale of the buffer gas's mean free path.

The spectral, dynamical, and topological properties of physical systems described by non-Hermitian (including $\mathcal{PT}$-symmetric) Hamiltonians are deeply modified by the appearance of exceptional points and spectral singularities. Here we show that exceptional points in the continuum can arise in non-Hermitian (yet admitting an entirely real-valued energy spectrum) optical lattices with engineered defects. At an exceptional point, the lattice sustains a bound state with an energy embedded in the spectrum of scattered states, similar to the von Neumann–Wigner bound states in the continuum of Hermitian lattices. However, the dynamical and scattering properties of the bound state at an exceptional point are deeply different from those of ordinary von Neumann–Wigner bound states in a Hermitian system. In particular, the bound state in the continuum at an exceptional point is an unstable state that can secularly grow by an infinitesimal perturbation. Such properties are discussed in details for transport of discretized light in a $\mathcal{PT}$-symmetric array of coupled optical waveguides, which could provide an experimentally accessible system to observe exceptional points in the continuum.

We present formulas that tighten the upper bound for the phase-flip errors in the decoy-state method by using four intensities. Our result compressed the bound to about a quarter of the known result for measurement-device-independent quantum key distribution. Based on this, we find that the key rate is improved by more than 100% given weak coherent state sources, and even more than 200% with heralded single-photon sources.

Similar to the three-qubit Greenberger-Horne-Zeilinger (GHZ) symmetry we explore the four-qubit GHZ symmetry group and its subgroup, the restricted GHZ symmetry group. While the set of symmetric states under the whole group transformation is represented by three real parameters, the set of symmetric states under the subgroup transformation is represented by two real parameters. After comparing the symmetric states for whole group and subgroup, the entanglement is examined for the latter set. It is shown that the set has only two stochastic local operations and classical communication classes, $L_{ab{c}_2}$ and $G_{abcd}$. Extension to the multiqubit system is briefly discussed.

For quantum key distribution (QKD) using spontaneous parametric-down-conversion sources (SPDCSs), the passive decoy-state protocol has been proved to be efficiently close to the theoretical limit of an infinite decoy-state protocol. In this paper, we apply a tight finite-key analysis for the passive decoy-state QKD using SPDCSs. Combining the security bound based on the uncertainty principle with the passive decoy-state protocol, a concise and stringent formula for calculating the key generation rate for QKD using SPDCSs is presented. The simulation shows that the secure distance under our formula can reach up to 182 km when the number of sifted data is ${10}^{10}$. Our results also indicate that, under the same deviation of statistical fluctuation due to finite-size effects, the passive decoy-state QKD with SPDCSs can perform as well as the active decoy-state QKD with a weak coherent source.

Atom chips made of superconducting material can generate magnetic traps with significantly reduced noise. Recently, several designs for superconducting chips have been theoretically analyzed and experimentally tested for cases with many vortices considered as an average vortex density. Here we show theoretically how the magnetic field of a single vortex, pinned by a superconducting nanodisk of radius ∼100 nm and combined with an external bias field parallel to the disk surface, yields a closed three-dimensional trap for cold atoms. The size of the trap and its height above the superconductor surface are typically tens or hundreds of nanometers. We estimate the average lifetime τ of ${}^{87}\mathrm{Rb}$ (rubidium) atoms (subject to thermal escape and Majorana spin flips) in the range 0.05–1.0 ms. We model the trap in a quantum adiabatic approximation and apply Fermi's rule to estimate the lifetime of ${}^{87}\mathrm{Rb}$ atoms in the ground state of this trap. We obtain similar lifetimes τ as in the semiclassical estimate, in the range 0.05–3.5 ms. We find that τ depends on the gradient $B_0$ of the vortex's magnetic field according to $\tau \sim B_0^{-2/3}$.

In this paper, we propose a scheme for deterministically preparing a quantum superposition $|{\psi }_s{\rangle }_b=C_0{|0\rangle }_b+C_{\mathcal{N}}{|\mathcal{N}\rangle }_b$ between vacuum and an arbitrary Fock state ${|\mathcal{N}\rangle }_b$ of mechanical oscillators via strong single-photon optomechanical coupling. We consider an optomechanical cavity which contains a Kerr medium and is driven by two lasers, with one laser tuned to the cavity resonance and the other to the $\mathcal{N}$th lower sideband of the cavity. The amplitudes $C_0$ and $C_{\mathcal{N}}$ are determined only by the drive strengths in the absence of mechanical damping and the approximate Fock state $|{\psi }_s{\rangle }_b\approx {|\mathcal{N}\rangle }_b$ can be obtained with appropriate relative strengths of the lasers. It is revealed that the superposition results from destructive quantum interference. The analytical results are confirmed by exact numerical calculation, and it is also shown that the nonclassical state is robust against thermal mechanical noise.

Quantum interference between Zeeman levels of atom placed in the structure containing left-handed materials (LHMs) and zero-index metamaterials (ZIMs) is investigated. Because of the existence of the LHM and ZIM, dipole radiation becomes highly anisotropic which is embodied by the high contrast between decay rates of the dipole component parallel to the surface and that normal to the surface. Furthermore, both decay rates are suppressed compared with those in free vacuum. Therefore, we propose the quantum interference between Zeeman levels accompanied by long lifetime. Two structures are designed to achieve such purpose. For the idealized LHM and ZIM without dissipation, a double-layer structure comprised of them is the right candidate. However, when we consider the dissipation of materials, a Fabry-Pérot cavity made of matched ZIM slabs and LHM slabs is required. Results show that we get a high degree of quantum interference and low decay rates simultaneously.

We study the Casimir-Polder (CP) force on an excited cold two-level atom in structures containing metamaterials. We adopt two kinds of metamaterials: left-handed materials (LHMs) and zero-index materials (ZIMs). The CP force on an excited atom can be divided into two parts: the dispersive force that responds to all frequencies of the electromagnetic mode and the resonant force, which is determined by the frequency at the atomic transition. Left-handed materials and ZIMs can significantly modify the resonant part of the CP force due to their unique character. It is found here that the presence of LHMs can enhance the force on the atom far away from the surface due to its phase compensation, while the presence of ZIMs can lead to a force that is independent of dipole orientation. The Casimir effect within the combination of LHMs and ZIMs leads us to realize a potential well that is insensitive to the orientation of atomic dipole. Due to the spontaneous decay, the resonant part of the CP force disappears eventually; however, the decay at the position with maximum force is inhibited. Therefore, during the time evolution, there are special positions (focuses) at which the force is significant for a longer time. Our results show the trap effect that can work on an atom with arbitrary dipole orientation. This provides a method to either trap or reflect an atom in a position far away from surface.

The resonant-state expansion, a recently developed method in electrodynamics, is generalized here to planar open optical systems with non-normal incidence of light. The method is illustrated and verified on exactly solvable examples, such as a dielectric slab and a Bragg reflector microcavity, for which explicit analytic formulas are obtained. This comparison demonstrates the accuracy and convergence of the method. Interestingly, the spectral analysis of a dielectric slab, in terms of resonant states, reveals an influence of waveguide modes in the transmission. These modes, which on-resonance do not couple to external light, surprisingly do couple to external light for off-resonant excitation.

Based on our previous classical over-barrier-ionization model, a universal scaling law of double-to-single-ionization cross-section ratios $R_{21}$ for impact by nearly stripped ions in the strong-coupling regime (0.5 < $q/$υ < 5) is found. The scaling law is consistent with extensive experimental data from proton to ${\mathrm{U}}^{92+}$. A fitting curve to the predictions of the theory is also proposed for application convenience.

We introduce a discrete $Q$ function of an $N$-qubit system projected into the space of symmetric measurements as a tool for analyzing general properties of quantum systems in the macroscopic limit. For known states the projected $Q$ function helps to visualize the results of collective measurements, and for unknown states it can be approximately reconstructed by measuring the lowest moments of the collective variables.

In this paper, we examine and compare two fundamentally different teleportation schemes: the well-known continuous-variable scheme of Vaidman, Braunstein, and Kimble (VBK) and a recently proposed hybrid scheme by Andersen and Ralph (AR). We analyze the teleportation of ensembles of arbitrary pure single-mode Gaussian states using these schemes and see how they fare against the optimal measure-and-prepare strategies—the benchmarks. In the VBK case, we allow for nonunit gain tuning and additionally consider a class of non-Gaussian resources in order to optimize performance. The results suggest that the AR scheme may likely be a more suitable candidate for beating the benchmarks in the teleportation of squeezing, capable of achieving this for moderate resources in comparison to the VBK scheme. Moreover, our quantification of resources, whereby different protocols are compared at fixed values of the entanglement entropy or the mean energy of the resource states, brings into question any advantage due to non-Gaussianity for quantum teleportation of Gaussian states.

Positronium plays a unique role in the continuing development of the techniques of bound-state QED and high-precision tests of the standard model as a Coulombic bound system that is almost free of strong and weak interaction contaminations and that exhibits large recoil and annihilation (virtual and real) effects. The present frontier is at the level of three-loop corrections to energy levels and decay rates. We have calculated the three-loop correction to the positronium hyperfine splitting due to light-by-light scattering in the exchange of two photons between the electron and positron. Our result is $\Delta E=-0.235355\left(8\right)m{\alpha }^4{\left(\frac{\alpha }{\pi }\right)}^3=-1.033\mathrm{kHz}$. As a check of our approach, we confirm earlier evaluations of the analogous correction for a bound system (such as muonium) with unequal masses.