Multipartite entangled states are great resources for quantum networks. In this work, we study the distribution, or routing, of entangled states over fixed, but arbitrary, physical networks. Our simplified model represents each use of a quantum channel as the sharing of a Bell pair; local operations and classical communications are considered to be free. We introduce two protocols to distribute, respectively, Greenberger-Horne-Zeilinger (GHZ) states and arbitrary graph states over arbitrary quantum networks. The GHZ states' distribution protocol takes a single step and is optimal in terms of the number of Bell pairs used; the graph states' distribution protocol uses, at most, twice as many Bell pairs and steps as the optimal routing protocol for the worst-case scenario.

We discuss electron diffraction from two standing waves with two different frequencies. The effects of increasing the frequency of the second laser beam and changing the laser amplitudes on the form and period of the Rabi oscillation are studied theoretically. The corresponding scattering probabilities for certain incident electron momenta are obtained by an analytical Rabi matrix and numerical solution of the Dirac equation. We show that at high intensities, $\ge {10}^{20}$ W ${\mathrm{cm}}^{-2}$, the process with an even number of photons involved in the Kapitza-Dirac effect can be used as a spin filter for free electrons. On the other hand, the process with an odd number photons and an electron with momentum along the laser polarization preserves the initial spin of the electron.

We present extreme ultraviolet spectra of Ag-like ${\mathrm{W}}^{27+}$ observed with an electron beam ion trap. In the spectra, the $4f_{7/2,5/2}–5s$ electric octupole transitions are identified. Our theoretical investigation shows that the emission line intensity is strongly and specifically enhanced at the atomic number 74 by the anomalous behavior of the cascading contribution to $5s$ via $5p\leftarrow 5d$.

We consider binary-encounter electron emission in relativistic ion-atom collisions in the presence of a monochromatic low-frequency plane-wave electromagnetic field of circular polarization. The parameters of the field—its intensity and frequency—are chosen in such a way that the field per se has a negligible effect on the initial (ground) state of the atom. The results show, however, that this field may have a profound effect on the electron emission spectra, which is mainly caused by an enormous energy exchange between the emitted electron and the field.

Dissociative tunneling ionization of nitric oxide (NO) in linearly polarized phase-locked two-color femtosecond intense laser fields (45 fs, $\lambda =800$ and 400 nm, total field intensity $I=1\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$) has been studied by three-dimensional ion momentum imaging. The ${\mathrm{N}}^{+}$ fragment produced by the dissociative ionization, $\mathrm{NO}\to \mathrm{N}{\mathrm{O}}^{+}+e^{-}\to {\mathrm{N}}^{+}+\mathrm{O}+e^{-}$, exhibits a butterflylike momentum distribution peaked at finite angles with respect to the laser polarization direction. In addition, a clear dependence on the relative phase between the two laser fields is observed, showing that the tunneling ionization occurs efficiently when the electric field points from N to O. For the highest kinetic energy component, the observed orientation dependence is well explained with theoretical calculations by the weak-field asymptotic theory for the 2π highest occupied molecular orbital (HOMO). On the other hand, the peak angle shifts toward the laser polarization direction as the kinetic energy decreases, indicating that pathways other than direct ionization from the HOMO contribute to the dissociative ionization.

Strong synthetic magnetic fields have been successfully implemented in periodically driven optical lattices. However, the interplay of the driving and interactions introduces detrimental heating, and for this reason it is still challenging to reach a fractional quantum Hall state in cold-atom setup. By performing a numerical study, we investigate stability of a bosonic Laughlin state in a small atomic sample exposed to driving. We identify an optimal regime of microscopic parameters, in particular interaction strength $U$ and the driving frequency $\omega$, such that the stroboscopic dynamics supports the basic $\nu =1/2$ Laughlin state. Moreover, we explore slow ramping of a driving term and show that the considered protocol allows for the preparation of the Laughlin state on experimentally realistic time-scales.

Inspired by the recent experiment of Hamsen et al. [Phys. Rev. Lett. 118, 133604 (2017)], which demonstrated two-photon blockade in a driven nonlinear system (composed of a harmonic cavity with a driven atom), we show that two-photon blockade and other nonstandard types of photon blockade and photon-induced tunneling can be generated in a driven harmonic cavity without an atom or any other kind of nonlinearity, but instead coupled to a nonlinear (i.e., squeezed) reservoir. We also simulate these single- and two-photon effects with squeezed coherent states and displaced squeezed thermal states.

We introduce the concept of Kadison-Schwarz-divisible dynamical maps. It turns out that it is a natural generalization of the well-known CP-divisibility which characterizes quantum Markovian evolution. It is proved that Kadison-Schwarz-divisible maps are fully characterized in terms of time-local dissipative generators. Simple qubit evolution illustrates the concept.

A well-known property of quantum nonlocality is monogamy. However, recent research by Silva et al. shows that multiple observers can share the nonlocality by using weak measurements [Phys. Rev. Lett. 114, 250401 (2015)]. In this paper, we deeply discuss nonlocality sharing for an arbitrary two-qubit state via weak measurements. Two types of nonlocality sharing, passive nonlocality sharing and active nonlocality sharing, which is another type of double violation of Clauser-Horne-Shimony-Holt (CHSH) inequality with many counterintuitive results existing, are fully analyzed. The two types are quite distinct. Active nonlocality sharing can be observed when Bob1 performs strong measurements only except for the ideal strong measurements. Also, a double violation still can be observed in the active nonlocality sharing even using a square pointer type for weak measurements of Bob1, which is impossible in the passive one. As a special example, for a Bell state, a double violation of Clauser-Horne-Shimony-Holt inequality can be always observed in a broad range whether the weak measurement of Bob1 is with an optimal pointer or a square pointer.

We study the steady-state entanglement and correlations of an open system comprising two coupled fermions in the equilibrium or nonequilibrium environments and distill the nonequilibrium contribution to the quantum correlations. We show that in the equilibrium condition, the steady-state quantum correlations exhibit nonmonotonic behavior, while in the nonequilibrium case, the monotonicity is determined by many parameters. The entanglement vanishes abruptly upon the increase of the temperature (bias) and chemical potential bias, and it witnesses a critical chemical potential above which the concurrence always remains positive. In the fermionic reservoirs, quantum correlations reach the maximal values when one chemical potential of the reservoirs matches the system frequency. We separate the quantum correlation generation due to the averaged effect from the pure nonequilibrium effect. In contrast with previous results, when the averaged effect is separated out, the nonequilibrium generation of quantum correlation shows a distinctive monotonic behavior. The difference between the large-tunneling regime with decaying correlations and the small-tunneling with increasing correlations is discussed. Near the boundary of the two regimes, the entanglement behavior is a mixture of two extremes, and it resurrects with the increase of chemical potential bias after its previous drop to zero.

Binding energies of fine structure levels of the negative ion of gallium have been determined both experimentally and theoretically, resolving long-standing discrepancies for the electron affinity of gallium. The relative photodetachment cross section from ${\mathrm{Ga}}^{-}$ ($4p^2{}^{3}P_{0,1,2}$) was measured using tunable laser spectroscopy over the photon energy range 270–400 meV (4600–3100 nm). Observed photodetachment thresholds were used to measure the electron affinity of Ga to be 301.20(11) meV and the fine structure splittings of ${\mathrm{Ga}}^{-}$ to be 23.31(19) meV for $J=0-1$ and 62.4(5) meV for $J=0-2$. The binding energies of the negative ion states were independently calculated using the multireference extrapolated intermediate Hamiltonian relativistic Fock space coupled cluster method in large, converged four-component Gaussian-spinor basis sets. The Dirac-Fock-Breit Hamiltonian was used, and leading quantum electrodynamic effects were added. All calculations were carried out in spherical symmetry, correlating all electrons and fully including core effects. The calculated electron affinity is 302(3) meV, and the fine structure splittings are 22(2) meV for $J=0-1$ and 60(2) meV for $J=0-2$, which are all in excellent agreement with the present measurements. These results substantially improve both the accuracy and precision of the Ga electron affinity and provide a determination of the fine structure of ${\mathrm{Ga}}^{-}$.

Here we report on spectroscopic measurements of the aluminum monofluoride molecule (AlF; boson) that are relevant to laser cooling and trapping experiments. We measure the detailed energy-level structure of AlF in the $X{}^1{\mathrm{\Sigma }}^{+}$ electronic ground state, in the $A{}^1\mathrm{\Pi }$ state, and in the metastable $a{}^3\mathrm{\Pi }$ state. We determine the rotational, vibrational, and electronic branching ratios from the $A{}^1\mathrm{\Pi }$ state. We also study how the rotational levels split and shift in external electric and magnetic fields. We find that AlF is an excellent candidate for laser cooling on any $Q$ line of the $A{}^1\mathrm{\Pi }$ - $X{}^1{\mathrm{\Sigma }}^{+}$ transition and for trapping at high densities. The energy levels in the $X{}^1{\mathrm{\Sigma }}^{+},v=0$ state and within each $\mathrm{\Omega }$ manifold in the $a{}^3\mathrm{\Pi },v=0$ state are determined with a relative accuracy of a few kHz, using laser-radio-frequency multiple resonance and ionization detection schemes in a jet-cooled, pulsed molecular beam. To determine the hyperfine and $\mathrm{\Lambda }$-doubling parameters we measure transitions throughout the 0.1-MHz–66-GHz range, between rotational levels in the $X{}^1{\mathrm{\Sigma }}^{+},v=0$ state, and between rotational and $\mathrm{\Lambda }$-doublet levels in all three spin-orbit manifolds of the $a{}^3\mathrm{\Pi },v=0$ state. We measure the hyperfine splitting in the $A{}^1\mathrm{\Pi }$ state using continuous wave (cw) laser-induced fluorescence spectroscopy of the $A{}^1\mathrm{\Pi },v=0\leftarrow X{}^1{\mathrm{\Sigma }}^{+},v^{″}=0$ band. The resolution is limited by the short radiative lifetime of the $A{}^1\mathrm{\Pi },v=0$ state, which we experimentally determine to be $1.90\pm 0.03$ ns. The hyperfine mixing of the lowest rotational levels in the $A{}^1\mathrm{\Pi }$ state causes a small loss from the main laser cooling transition of ${10}^{-5}$. The off-diagonal vibrational branching from the $A{}^1\mathrm{\Pi },v=0$ state is measured to be $(5.60\pm 0.02)\times {10}^{-3}$ in good agreement with theoretical predictions. The strength of the spin-forbidden $A{}^1\mathrm{\Pi },v=0\to a{}^3\mathrm{\Pi },v^{\prime }=0$ transition is measured to be seven orders of magnitude lower than the strength of the $A{}^1\mathrm{\Pi },v=0\to X{}^1{\mathrm{\Sigma }}^{+},v^{″}=0$ transition. We determine the electric dipole moments $\mu \left(\mathrm{X}\right)=1.515\pm 0.004$ Debye, $\mu \left(a\right)=1.780\pm 0.003$ Debye and $\mu \left(\mathrm{A}\right)=1.45\pm 0.02$ Debye in $X{}^1{\mathrm{\Sigma }}^{+}$, $v=0$, $a{}^3\mathrm{\Pi },v=0$ and $A{}^1\mathrm{\Pi },v=0$, respectively, by recording cw laser excitation spectra in electric fields up to 150 kV/cm.

We present experimental and theoretical cross sections for elastic electron scattering from ${\mathrm{CHCl}}_3$. This is an important target because of its relevance to environmental chemistry and the plasma etching industry as a source of chlorine radicals. The experimental results were obtained at incident electron energies ranging from 0.5 to 800 eV in the ${10}^{\circ }$–${130}^{\circ }$ scattering angle range. Theoretically, the scattering cross sections in the low-energy region were obtained by using the Schwinger multichannel method with pseudopotentials in the static-exchange plus polarization approximation. Additionally, in the low- and intermediate-energy ranges, theoretical calculations were also performed using a molecular complex optical potential and a single-center expansion method combined with Padé approximation. Further calculations using the independent atom model were also made at intermediate energies. Momentum-transfer cross sections were derived by integrating the differential cross sections. In general, there is a good agreement between the experimental data and the theoretical results. Moreover, the calculations reveal the presence of three shape resonances in the elastic channel, located at 0.5, 2, and 8 eV. The two higher-lying resonances were confirmed by the present experiments, whereas the positions of the two lower-lying resonances agree well with previous results of electron attachment experiments.

Coherent control experiments in molecules are often done with shaped laser fields. The electric field is described classically and control over the time evolution of the system is achieved by shaping the laser pulses in the time or frequency domain. Moving on from a classical to a quantum description of the light field allows one to engineer the quantum state of light to steer chemical processes. The quantum field description of the photon mode allows one to manipulate the light-matter interaction directly in phase space. In this paper we demonstrate the basic principle of coherent control with quantum light on the avoided crossing in lithium fluoride. Using a quantum description of light together with the nonadiabatic couplings and vibronic degrees of freedoms opens up alternative perspective on quantum control. We show the deviations from control with purely classical light field and how back-action of the light field becomes important in a few-photon regime.

Temperature-dependent characteristics of a midinfrared quantum cascade laser (QCL) including the threshold current, the output power, the modulation bandwidth, and the relative intensity noise (RIN) exhibit a deterioration with temperature from 77 to 300 K. Based on a comprehensive temperature-dependent model we show that optical injection locking can be applied to surpass the intrinsically limited thermal characteristics of a QCL through the modification of the carrier density in the active region. A modulation bandwidth improvement of $\approx 35\%$ and an almost temperature-independent RIN behavior for an injection-locked laser have been achieved compared to a free-running slave laser at room temperature. A threshold current reduction of $\approx 20\%$ has also been obtained at 300 K. Results indicate that the locking boundaries of an injection-locked QCL are suppressed with temperature. The output power and the small-signal characteristics of the laser have also been analyzed in the entire stable locking range.

We observe a density-dependent collective suppression of optical pumping between the hyperfine ground states in an array of submicrometer-sized clouds of dense and cold rubidium atoms. The suppressed Raman transition rate can be explained by strong resonant dipole-dipole interactions that are enhanced by increasing atom density, and are already significant at densities of $\gtrsim 0.1k^3$, where $k$ denotes the resonance wave number. The observations are consistent with stochastic electrodynamics simulations that incorporate the effects of population transfer via internal atomic levels embedded in a coupled-dipole model.

According to classical theory, a system with two or more macroscopically distinct states available to it is in one of those states at all times. Quantum mechanics gives a different interpretation where the system can be in a superposition of such states. In this paper, we derive criteria in the form of inequalities to detect this effect, referred to as mesoscopic quantum coherence, where the states are (at least) mesoscopically distinct. Such criteria are also signatures of a mesoscopic Schrödinger cat paradox. We extend the treatment to consider definitions and criteria for mesoscopically entangled states, which are a subset of the states exhibiting mesoscopic quantum coherence. It is shown how the criteria (referred to as type I criteria) can be applied to detect the mesoscopic entanglement of systems prepared in NOON states, Greenberger-Horne-Zeilinger states, and entangled cat states involving coherent states. Here, a larger system $C$ is entangled with a second system $S$, which can be small. The proposed definition of mesoscopic (macroscopic) entanglement involves the Schmidt decomposition, and can be applied to systems in a superposition of many states, only some pairs of which are mesoscopically (macroscopically) distinguishable. We prove that a higher-order Hillery-Zubairy entanglement criterion will detect mesoscopic entanglement of this type, and use this to demonstrate the mesoscopic entanglement of the ground state of a two-mode Bose-Einstein condensate. Finally, we explain how a subset of the type I criteria (called type II criteria) are EPR steering inequalities allowing realization of a mesoscopic or macroscopic version of the Einstein-Podolsky-Rosen paradox for macroscopic superposition states. Where the two systems $C$ and $S$ are spatially separated, we then use results from the literature to point out it is not possible to complete quantum mechanics using hidden-variable theories compatible with the assumption of locality between the two systems. The violation of certain Bell inequalities is sufficient to prove this result, which gives a stricter signature of the Schrödinger cat paradox and of mesoscopic quantum coherence. We call such signatures type III criteria.

Exceptional points, at which two or more eigenfunctions of a Hamiltonian coalesce, occur in non-Hermitian systems and lead to surprising physical effects. In particular, the behavior of a system under parameter variation can differ significantly from the familiar Hermitian case in the presence of exceptional points. Here we analytically derive the probability of a nonadiabatic transition in a two-level system driven through two consecutive exceptional points at finite speed. The system is Hermitian far away from the exceptional points. In the adiabatic limit an equal redistribution between the states coalescing in the exceptional point is observed, which can be interpreted as a loss of information when passing through the exceptional point. For finite parameter variation this is modified. We demonstrate how the transition through the exceptional points can be experimentally addressed in a $PT$-symmetric lattice using Bloch oscillations.

Characterization of topological invariants in experiments is at the heart of understanding topological quantum phases. We experimentally demonstrate a dynamical classification approach for investigation of topological quantum phases using a solid-state spin system through nitrogen vacancy (NV) center in diamond. Similar to the bulk-boundary correspondence in real space at equilibrium, we observe a dynamical bulk-surface correspondence in the momentum space from a dynamical quench process. An emergent dynamical topological invariant is precisely measured in experiment by imaging the dynamical spin textures on the recently defined band-inversion surfaces, with high topological numbers being implemented. Importantly, the dynamical classification approach is shown to be independent of quench ways and robust to the dephasing effects, offering a powerful strategy for dynamical topology characterization, especially for high-dimensional gapped topological phases.

Non-Gaussian operations on two-mode squeezed vacuum states in continuous-variable (CV) measurement-device-independent (MDI) quantum key distribution (QKD) protocols have been shown to effectively increase the total transmission distances drastically. In this paper we show that photon subtraction on a two-mode squeezed coherent (PSTMSC) state can further improve the transmission distances remarkably. To that end we also provide a generalized covariance matrix corresponding to the PSTMSC state. We show that coherence, defined as the amount of displacement of the vacuum state, along with non-Gaussianity can help improve the performance of prevalent CV MDI QKD protocols. Furthermore, since we use realistic parameters, our technique is experimentally feasible and can be readily implemented.