We present a robust approach for interpreting the physics of Fano resonances in planar oligomer structures of both metallic and dielectric nanoparticles. We reveal a key mechanism for Fano resonances by demonstrating that such resonances can be generated purely from the interference of nonorthogonal collective eigenmodes, which are clearly identified based on the coupled-dipole approximation. We prove analytically a general theorem to identify the number of collective eigenmodes that can be excited in ring-type nanoparticle oligomers and further demonstrate that no dark-mode excitation is necessary for the existence of Fano resonances in symmetric oligomers. As a consequence, we unify the understanding of Fano resonances for both plasmonic and all-dielectric oligomers.

An efficient method for assessing the quality of quantum state tomography is developed. Special attention is paid to the tomography of multipartite systems in terms of unbiased measurements. Although the overall reconstruction errors of different sets of mutually unbiased bases are the same, differences appear when particular aspects of the measured system are contemplated. This point is illustrated by estimating the fidelities of genuinely tripartite entangled states.

We study the effect of the rotating-wave approximation (RWA) and the secular approximation (SA) on the non-Markovian behavior in the spin-boson model at zero temperature. We find that both the RWA and SA lead to a dramatic reduction in the observed non-Markovianity. In general, non-Markovian dynamics is observed for the whole relaxation time of the system, whereas the RWA and SA lead to such dynamics only on the short time scale of the environmental correlation time. Thus, the RWA and SA are not necessarily justified in the studies of non-Markovianity, although they can estimate the state of the system precisely. Furthermore, we derive an accurate analytical expression for the non-Markovianity measure without the RWA or SA. This expression yields important insight into the physics of the problem.

We study the effect of the acceleration of the observer on a parameter estimation protocol using NOON states. An inertial observer, Alice, prepares a NOON state in Unruh modes of the quantum field, and sends it to an accelerated observer, Rob. We calculate the quantum Fisher information of the state received by Rob. We find the counterintuitive result that the single-rail encoding outperforms the dual rail. The NOON states have an optimal $N$ for the maximum information extractable by Rob, given his acceleration. This optimal $N$ decreases with increasing acceleration.

We propose a quantum method to judge whether two spatially separated clocks have been synchronized within a specific accuracy $\sigma$. If the measurement result of the experiment is clearly a nonzero value, the time difference between two clocks is smaller than $\sigma$; otherwise, the difference is beyond $\sigma$. Upon sharing the 2$N$-qubit bipartite maximally entangled state in this scheme, the accuracy of judgment can be enhanced to $\sigma \sim \pi /\left[\omega \right(N+1\left)\right]$. This criterion is consistent with Heisenberg scaling, which can be considered as the beating standard quantum limit; moreover, the unbiased estimation condition is not necessary. In particular, we demonstrate that this scheme is still feasible when suffering the loss of qubits.

We present a detailed study of the exact-exchange (EXX) kernel of time-dependent density-functional theory with an emphasis on its discontinuity at integer particle numbers. It was recently found that this exact property leads to sharp peaks and step features in the kernel that diverge in the dissociation limit of diatomic systems [Hellgren and Gross, Phys. Rev. A 85, 022514 (2012)]. To further analyze the discontinuity of the kernel, we here make use of two different approximations to the EXX kernel: the Petersilka Gossmann Gross (PGG) approximation and a common energy denominator approximation (CEDA). It is demonstrated that whereas the PGG approximation neglects the discontinuity, the CEDA includes it explicitly. By studying model molecular systems it is shown that the so-called field-counteracting effect in the density-functional description of molecular chains can be viewed in terms of the discontinuity of the static kernel. The role of the frequency dependence is also investigated, highlighting its importance for long-range charge-transfer excitations as well as inner-shell excitations.

We demonstrate a technique for investigation of a strongly perturbed atomic system, which is an extension of standard radio-frequency spectroscopy. Analogous to “relaxation in the dark” experiments, this technique allows a reconstruction of the population distribution of the unperturbed atomic state by observing the rf spectroscopy signal after an abrupt switch-off of the perturbing light. The evolution and relaxation dynamics of the individual magnetic sublevels is investigated. Experimental observations are supported with numerical modeling based on a full density-matrix calculation performed in the presence of spin-exchange collisions and homogeneous relaxation.

Photoassociation resonances in the ${}^{87}$Rb${}_2$ $1_g$ state dissociating to $5{}^{2}S+5{}^2{P}_{1/2}$ were produced by the excitation of colliding ${}^{87}$Rb atoms in a far-off resonance trap. Levels down to 31 cm${}^{-1}$ below the dissociation limit were measured with resonance linewidths of 15 to 20 MHz, and have been located to a one-sigma combined systematic and statistical uncertainty of 50 MHz relative to the $5{}^{2}S+5{}^2{P}_{1/2}$ limit. Electron and nuclear spins were fixed to a space-fixed axis by circularly polarized optical pumping, so that only states with total nuclear spin $I=3$ were excited, thereby greatly simplifying the spectrum. The analysis of the data yielded hyperfine coupling parameters $A\left(v\right)$, vibrational $G\left(v\right)$, and rotational $B\left(v\right)$ parameters. The $G\left(v\right)$ parameters could be fit to an rms accuracy of about 0.01 cm${}^{-1}$ to a potential constructed from current $C_3$ and $C_6$ long-range dispersion parameters plus an ab initio potential that was adjusted in depth and with quadratic terms in the internuclear distance added to the inner wall.

A high-resolution technique for direct in-source laser spectroscopy within a hot cavity laser ion source has been demonstrated by applying Doppler free two-photon resonance ionization spectroscopy. An injection-locked narrow-bandwidth pulsed titanium:sapphire laser operating in high repetition rate was used for resonance ionization of silicon. The isotope shift of ${}^{28}$Si, ${}^{29}$Si, and ${}^{30}$Si as well as the hyperfine structure of all two-photon transitions of the $3s^{2}3p^2{}^3{P}_{0,1,2}\to 3s^{2}3p4p{}^3{P}_{0,1,2}$ multiplet for ${}^{29}$Si were recorded at an overall experimental spectral linewidth of 90 MHz.

We review briefly the recent work on dissociative electron attachment (DEA) to formic acid. Using Feshbach resonance theory we present results calculating the forces on various atoms during resonance processes that can arise at different electron impact energies. The conclusion is that DEA to formic acid happens through a short-lived ${\sigma }^{*}$ resonance with minimal involvement from $\pi$-$\sigma$ symmetry breaking as suggested elsewhere. We conclude that rehybridization on a C atom caused by the $\pi$-$\sigma$ mixing is too far from the O—H bond to detect its effect on the DEA cross section. A recent experimental confirmation is also reported.

State-selective and total single-electron capture cross sections in fast collisions of a bare projectile with a heliumlike target are examined in the four-body formalism. A special emphasis is given to a proper inclusion of dynamic electron-electron correlation effects. For this purpose, the post form of the four-body boundary-corrected first Born approximation (CB1-4B) is utilized. With regard to our related previous study, where the prior version has been considered, in the present work an extensive analytical study of the post-transition amplitude for electron capture into the arbitrary final states $n^f{l}^f{m}^f$ of the projectile is carried out. The post-transition amplitude for single charge exchange encompassing symmetric and asymmetric collisions is derived in terms of five-dimensional integrals over real variables. The dielectronic interaction $V_{12}=1/r_{12}\equiv 1/|{\vec{r}}_1-{\vec{r}}_2|$ explicitly appears in the perturbation potential $V_f$ of the post-transition probability amplitude $T_{if}^{+},$ such that the CB1-4B method can provide information about the relative significance of the dynamic interelectron correlation in the collisions under study. An illustrative computation is performed involving state-selective and total single capture cross sections for the $p-\mathrm{He}$ collisions at intermediate and high impact energies. The so-called post-prior discrepancy, which plagues almost all the existing distorted wave approximations, is presently shown to be practically nonexistent in the CB1-4B method. The validity of our findings is critically assessed in comparisons with the available experimental data for both state-selective and total cross sections summed over all the discrete energy levels of the hydrogenlike atom formed with the projectile. Overall, excellent performance of the CB1-4B method is recorded, thus robustly establishing this formalism as the leading first-order description of high-energy single charge exchange, which is a collision of paramount theoretical and practical importance across interdisciplinary fields ranging from astrophysics to medicine.

The carrier-envelope-phase (CEP) dependence of electron angular distributions in double ionization of He by an arbitrarily polarized, few-cycle, intense XUV pulse is formulated using perturbation theory (PT) in the pulse amplitude. Owing to the broad pulse bandwidth, interference of first- and second-order PT amplitudes produces asymmetric angular distributions sensitive to the CEP. The PT parametrization is shown to be valid by comparing with results of solutions of the full-dimensional, two-electron time-dependent Schrödinger equation for the case of linear polarization.

Here we analyze the collective excitations as well as the expansion of a trapped Bose-Einstein condensate with a vortex line at its center. To this end, we propose a variational method where the variational parameters have to be carefully chosen in order to produce reliable results. Our variational calculations agree with numerical simulations of the Gross-Pitaevskii equation. The system considered here turns out to exhibit four collective modes of which only three can be observed at a time depending on the trap anisotropy. We also demonstrate that these collective modes can be excited using well established experimental methods such as modulation of the $s$-wave scattering length.

We report the effects of interaction on thermodynamic properties of a repulsive Bose-Einstein condensate confined in a harmonic trap by using the correlated potential harmonics expansion method. This many-body technique permits the use of a realistic interactomic interaction, which gives rise to the effective long-range interaction of the condensate in terms of the $s$-wave scattering length. We have computed temperature ($T$) dependence of the chemical potential, specific heat, condensate fraction, entropy, pressure, and the average energy per particle of a system containing a large number ($A$) of ${}^{87}$Rb atoms in the Joint Institute for Laboratory Astrophysics (JILA) trap. The repulsion among the interacting bosons results in a small but measurable drop of condensate fraction and critical temperature ($T_c$), compared to those of a noninteracting condensate. These are in agreement with the experiment. Although all thermodynamic quantities have a strong dependence on $A$ and to a smaller extent on the interatomic interaction, our numerical calculation appears to show that a thermodynamic quantity per particle follows a universal behavior as a function of $T/T_c$. This shows the importance of $T_c$ for all thermodynamic properties of the condensate. As expected, for $T>T_c$, these properties follow those of a trapped noncondensed Bose gas.

This paper reports the results of a theoretical and experimental study of how the initial circulation of ring-shaped Bose-Einstein condensates (BECs) can be probed by time-of-flight (TOF) images. We have studied the dynamics of a BEC after release from a toroidal trap potential by solving the three-dimensional Gross-Pitaevskii (GP) equation. The trap and condensate characteristics matched those of a recent experiment. The circulation, experimentally imparted to the condensate by stirring, was simulated by imprinting a linear azimuthal phase on the initial condensate wave function. The simulated TOF images were in good agreement with the experimental data. We find that upon release the dynamics of the ring-shaped condensate proceeds in two distinct phases. First, the condensate expands rapidly inward, filling in the initial hole until it reaches a minimum radius that depends on the initial circulation. In the second phase, the density at the inner radius increases to a maximum after which the hole radius begins slowly to expand. During this second phase a series of concentric rings appears due to the interference of ingoing and outgoing matter waves from the inner radius. The results of the GP equation predict that the hole area is a quadratic function of the initial circulation when the condensate is released directly from the trap in which it was stirred and is a linear function of the circulation if the trap is relaxed before release. These scalings matched the data. Thus hole size after TOF can be used as a reliable probe of initial condensate circulation. This connection between circulation and hole size after TOF will facilitate future studies of atomtronic systems that are implemented in ultracold quantum gases.

In a recent experiment [Vogt et al., Phys. Rev. Lett. 108, 070404 (2012)], quadrupole and breathing modes of a two-dimensional Fermi gas were studied. We model these collective modes by solving the Boltzmann equation via the method of phase-space moments up to fourth order, including in-medium effects on the scattering cross section. In our analysis, we use a realistic Gaussian potential deformed by the presence of gravity and magnetic field gradients. We conclude that the origin of the experimentally observed damping of the quadrupole mode, especially in the weakly interacting (or even noninteracting) case, cannot be explained by these mechanisms.

We study the coherent propagation of light whose dynamics is governed by the effective Schrödinger equation derived in a magneto-optically manipulated atomic ensemble with a four-level tripod configuration for electromagnetically induced transparency (EIT). The small transverse deflection of an optical beam, which is ultrasensitive to the EIT effect, could be drastically amplified via a weak measurement with an appropriate preselection and postselection of the polarization state. The physical mechanism is explained as the effect of wave-packet reshaping, which results in an enlarged group velocity in the transverse direction.

Unitary non-Gaussian nonlinearity is one of the key components required for quantum computation and other developing applications of quantum information processing. Sufficient operation of this kind is still not available, but it can be approximatively implemented with the help of a specifically engineered resource state constructed from individual photons. We present experimental realization and thorough analysis of such quantum resource states and confirm that the state does indeed possess properties of a state produced by unitary dynamics driven by cubic nonlinearity.

In the actively coupled (AC) pair of waveguides, the growth of small perturbations is saturated by the focusing nonlinearity that couples the linearly growing mode to the linearly damped mode. On the other hand, in the $\mathcal{PT}$-symmetric coupler, the focusing nonlinearity promotes the blow-up of stationary light beams. The purpose of this study is to compare the nonlinear dynamics and explain the opposite effect of the same nonlinearity in the two systems. We show that, while the blow-up regimes are stable in the $\mathcal{PT}$-symmetric pair of waveguides, they are unstable and hence cannot be observed in the AC dimer.

In the quantum metrology protocol described by Tacla et al. [Tacla, Boixo, Datta, Shaji, and Caves, Phys. Rev. A 82, 053636 (2010)] where a two-mode Bose-Einstein condensate (BEC) is used for parameter estimation, the measured quantity is to be obtained by doing a one-parameter fit of the observed data to a theoretically expected signal. Here we look at different levels of approximation used to model the two-mode BEC to see how the estimate improves when increasing the level of detail is added to the theory while at the same time keeping the expected signal computable.