We propose two complementary approaches for solution of the coupled Maxwell-Liouville equations within the finite-difference time domain (FDTD) framework. The two methods are specifically designed to eliminate self-interaction, which often appears spuriously in simulation of the coupled Maxwell-Liouville equations, and hence can be used for modeling of single as well as ensembles of quantum emitters (such as molecules or quantum dots) in an arbitrary dielectric environment. One approach borrows from the familiar total field–scattered field technique that has been applied in the past in a different context. The second recognizes an opportunity to average over the electric field at a set of specifically chosen points around the quantum emitter. The methods introduced are applied to two problems of growing current interest that also present useful test cases. One is the modeling of spontaneous emission, where comparison with an analytical solution illustrates the accuracy and efficiency of the methodology. The second is quantum-emitter-induced transparency in a resonator formed by two gold ellipsoids, where Fano interferences suggest interesting potential applications.

We have investigated the autodetachment of electrons from rovibrationally hot SF${}_6{}^{-}$ anions using a cryogenic ion-beam trap. Extremely low residual gas densities of ${10}^4$ cm${}^{-3}$ provided undisturbed observation of the neutralization rates due to vibrational autodetachment (VAD) over almost five orders of magnitude and over times up to 100 ms. We successfully explain our experimental decay curves using statistical rate theory combined with electron attachment data and vibrational frequencies calculated for a $C_{4v}$-distorted SF${}_6{}^{-}$. The unprecedented sensitivity of the experiment to the decay constants at the VAD threshold allows us to infer from the data the adiabatic electron affinity of SF${}_6$ to be $(0.91\pm 0.07)$ eV and to confirm the recently predicted $C_{4v}$ symmetry of SF${}_6{}^{-}$.

The average-density approximation is used to construct a nonlocal kinetic energy functional for an inhomogeneous two-dimensional Fermi gas. This functional is then used to formulate a Thomas-Fermi-von Weizsäcker-like theory for the description of the ground-state properties of the system. The quality of the kinetic energy functional is tested by performing a fully self-consistent calculation for an ideal, harmonically confined, two-dimensional system. Good agreement with exact results are found, with the number and kinetic energy densities exhibiting oscillatory structure associated with the nonlocality of the energy functional. Most importantly, this functional shows a marked improvement over the two-dimensional Thomas-Fermi von Weizsäcker theory, particularly in the vicinity of the classically forbidden region.

We report on the behavior of the ionization avalanche in an ensemble of ultracold ${}^{87}\mathrm{Rb}$ atoms coupled to a high-lying Rydberg state and investigate extensions to the current model by including the effects of three-body recombination and plasma expansion. To separate the two effects we study the time dependence of the plasma formation at various densities as well as for different $nS$ and $nD$ states. At medium densities and low $n$ we observe the onset of the avalanche as has been reported in other experiments, as well as a subsequent turn-off of the avalanche for longer excitation times, which we associate with plasma expansion. At higher densities and for higher-lying Rydberg states we observe a disappearance of the avalanche signature, which we attribute to three-body recombination.

We experimentally and theoretically study the coherent quantum control of green emission in Er${}^{3+}$-doped glass by $\pi$-phase-shaped 800-nm femtosecond laser pulses. The experimental results show that the green emission intensity is enhanced over the transform-limited pulse by $\pi$-phase-shaped pulses as the laser field increases to several 10${}^{12}$ W/cm${}^2$. Coherent control of multiphoton absorption is studied based on the fourth-order perturbation theory, and the theoretical results accord well with the experimental observations.

We investigate the mean-field dynamics of a Bose-Einstein condensate described by the Gross-Pitaevskii equation (GPE) in a double-well potential with particle gain and loss, rendering the system $\mathcal{PT}$ symmetric. The stationary solutions of the system show a change from elliptically stable behavior to hyperbolically unstable behavior caused by the appearance of $\mathcal{PT}$-broken solutions of the GPE and influenced by the nonlinear interaction. The dynamical behavior is visualized using the Bloch sphere formalism. However, the dynamics is not restricted to the surface of the sphere due to the nonlinear and non-Hermitian nature of the system.

We have investigated the interaction between a strong soliton and a weak probe with certain configurations that allow optical trapping in gas-filled hollow-core photonic-crystal fibers in the presence of the shock effect. We have shown theoretically and numerically that the shock term can lead to an unbroken parity-time- ($\mathcal{PT}$-) symmetric potential in these kinds of fibers. Time irreversible behavior, a signature feature of the $\mathcal{PT}$ symmetry, is also demonstrated numerically. Our results will open different configurations and avenues for observing $\mathcal{PT}$-symmetry breaking in optical fibers, without the need to resort to complex optical systems.

Reports on experiments recently performed in Vienna [Erhard et al., Nature Phys. 8, 185 (2012)] and Toronto [Rozema et al., Phys. Rev. Lett. 109, 100404 (2012)] include claims of a violation of Heisenberg's error-disturbance relation. In contrast, we have presented and proven a Heisenberg-type relation for joint measurements of position and momentum [Phys. Rev. Lett. 111, 160405 (2013)]. To resolve the apparent conflict, we formulate here a general trade-off relation for errors in qubit measurements, using the same concepts as we did in the position-momentum case. We show that the combined errors in an approximate joint measurement of a pair of $\pm 1$-valued observables $A,B$ are tightly bounded from below by a quantity that measures the degree of incompatibility of $A$ and $B$. The claim of a violation of Heisenberg is shown to fail because it is based on unsuitable measures of error and disturbance. Finally we show how the experiments mentioned may directly be used to test our error inequality.

We analyze entanglement swapping (ES) of partially entangled pure states with arbitrary Schmidt rank from the perspective of quantum state discrimination. It is shown that the standard deterministic ES protocol is related with an optimal minimum-error strategy. In this case the amount of entanglement of the states resulting from swapping is, in general, lower than the maximum achievable for the quantum channels involved. In this regard, we show that the ES protocol can be probabilistically improved resorting to optimal maximum-confidence (MC) discrimination strategy. Additionally, we show that the success probability of achieving entanglement above a prescribed value from standard deterministic ES can be increased by applying sequential MC measurements.

We prove that enhanced entanglement percolation via lattice transformation is possible even if the new lattice is more poorly connected in that (i) the coordination number (a local property) decreases, or (ii) the classical percolation threshold (a global property) increases. In searching for protocols to transport entanglement across a network, it seems reasonable to try transformations that increase connectivity. In fact, all examples that we are aware of violate both conditions (i) and (ii). One might therefore conjecture that all good transformations must violate them. Here we introduce a method, partial entanglement swapping, and use it to construct a counterexample that satisfies conditions (i) and (ii). The example lowers the threshold, relative to all known protocols, of the amount of initial entanglement required for deterministic long-range entanglement. This result shows that a transformation may not be rejected on the basis of satisfying conditions (i) or (ii). Both the result and the method constitute steps toward answering basic questions, such as whether there is a minimum amount of local entanglement required to achieve long-range entanglement.

In the communication scenario, we consider the problem of the discrimination between the signals of the quantum pulse position modulation. We propose a receiver scheme that employs repeated local measurements in distinct temporal slots within the symbol time interval, adaptively chosen on the basis of the outcomes in the previous slots. By employing dynamic programming to optimize each measurement, we approach the theoretical performance limit much closer than existing receiver schemes.

We derive analytic expressions for the classical Casimir-Polder free energy and force for a polarizable (magnetizable) atom (microparticle) interacting with thin films, made of different materials, or graphene. It is shown that for an isolated dielectric film the free energy and force decrease quicker with separation compared to the case of an atom interacting with a thick plate (semispace). For metallic films some peculiar features depending on the model of the metal used are analyzed. For an atom interacting with graphene we demonstrate that at room temperature the classical regime is achieved at about 1.5-$\mu$m separation. In this regime the contributions to the free energy and force due to atomic magnetic polarizability are suppressed compared to the main terms caused by the atomic electric polarizability. According to our results, at separations above $5\mu$m the Casimir-Polder interaction of atoms with graphene is of the same strength as with an ideal-metal plane. The classical interaction of atoms with thin films deposited on substrates is also considered.

Estimates for the lifetime of collision complexes formed during ultracold molecular collisions based on density-of-states arguments are shown to be consistent with similar estimates based on classical trajectory calculations. In the classical version, these collisions are shown to exhibit chaos and their fractal dimension is calculated versus collision energy. From these results, a picture emerges that ultracold collisions are likely classically ergodic, justifying the density-of-states estimates for lifetimes. These results point the way toward using the techniques of classical and quantum chaos to interpret molecular collisions in the ultracold regime.

We present an experimental investigation into the angular and energy distributions of electrons set free by the interaction of hydrogen molecular ions with strong laser fields. The results extend on those presented previously [M. Odenweller et al., Phys. Rev. Lett. 107, 143004 (2011)] for circularly polarized light. Pulses of laser light ($\lambda =780$ nm, $I\approx 6\times {10}^{14}$ W cm${}^{-2}$, $\tau \approx 40$ fs) of both linear and circular polarization are focused onto an H${}_2$${}^{+}$ molecular ion beam. The momenta of the proton and electron fragments are determined in a coincidence experiment, enabling electron momentum emission patterns in the molecular frame to be deduced for specific values of internuclear distances.

The current efforts of studying many-body effects with spin-orbit coupling (SOC) using alkali-metal atoms are impeded by the heating effects due to spontaneous emission. Here, we show that even for SOCs too weak to cause any heating, dramatic many-body effects can emerge in a one-dimensional (1D) spin-$\frac{1}{2}$ Fermi gas provided the interaction is sufficiently repulsive. For weak repulsion, the effect of a weak SOC (with strength $\Omega$) is perturbative, inducing a weak spin spiral (with magnitude proportional to $\Omega$). However, as the repulsion $g$ increases beyond a critical value ($g_c\sim 1/\Omega$), the magnitude of the spin spiral rises rapidly to a value of order 1 (independent of $\Omega$). Moreover, near $g=+\infty$, the spins of neighboring fermions can interfere destructively due to quantum fluctuations of particle motion, strongly distorting the spin spiral and pulling the spins substantially away from the direction of the local field at various locations. These effects are consequences of the spin-charge separation in the strongly repulsive limit. They will also occur in other 1D quantum gases with higher spins.

We demonstrate a fully demixed (separated) robust and stable bright binary dipolar Bose-Einstein-condensate soliton in a quasi-one-dimensional setting formed due to dipolar interactions for repulsive contact interactions. For large repulsive interspecies contact interaction, the first species may spatially separate from the second species, thus, forming a demixed configuration, which can be spatially symmetric or symmetry broken. In the spatially symmetric case, one of the species occupies the central region, whereas, the other species separates into two equal parts and stays predominantly out of this central region. In the symmetry-broken case, the two species stay side by side. Stability phase diagrams for the binary solitons are obtained. The results are illustrated with realistic values of parameters in the binary ${}^{164}\mathrm{Dy}\text{−}{}^{168}\mathrm{Er}$ and ${}^{164}\mathrm{Dy}\text{−}{}^{162}\mathrm{Dy}$ mixtures. The demixed solitons are really soliton molecules formed of two types of atoms. A proposal for creating dipolar solitons in experiments is also presented.

Quantum turbulence (QT) generated by the Rayleigh-Taylor instability in binary immiscible ultracold ${}^{87}\text{Rb}$ atoms at zero temperature is studied theoretically. We show that the quantum vortex tangle is qualitatively different from previously considered superfluids, which reveals deep relations between QT and classical turbulence. The present QT may be generated at arbitrarily small Mach numbers, which is a unique property not found in previously studied superfluids. By numerical solution of the coupled Gross-Pitaevskii equations we find that the Kolmogorov scaling law holds for the incompressible kinetic energy. We demonstrate that the phenomenon may be observed in the laboratory.

We introduce an explicit scheme to realize Chern insulating phases employing cold atoms trapped in a state-dependent optical lattice and laser-induced tunneling processes. The scheme uses two internal states, a ground state and a long-lived excited state, respectively trapped in separate triangular and honeycomb optical lattices. A resonant laser coherently coupling the two internal states enables hopping between the two sublattices with a Peierls-like phase factor. Although laser-induced hopping by itself does not lead to topological bands with nonzero Chern numbers, we find that such bands emerge when adding an auxiliary lattice that perturbs the lattice structure, effectively turning it at low energies into a realization of the Haldane model: a two-dimensional honeycomb lattice breaking time-reversal symmetry. We investigate the parameters of the resulting tight-binding model using first-principles band-structure calculations to estimate the relevant regime for experimental implementation.

Photon-induced near-field electron microscopy (PINEM) enables the visualization of the plasmon fields of nanoparticles via measurement of photon-electron interaction [S. T. Park et al., New J. Phys. 12, 123028 (2010)]. In this paper, the field integral, which is a mechanical work performed on a fast electron by the total electric field, plays a key role in understanding the interaction. Here, we reexamine the field integral and give the physical meaning by decomposing the contribution of the field from the charge-density distribution. It is found that the “near-field integral” (the near-field approximation of the field integral) can be expressed as a convolution of the two-dimensional projection of the optically driven charge-density distribution in the nanoparticle with a broad radial response function. This approach, which we call the “convolution method,” is validated by applying it to Rayleigh scattering cases, where previous analytical expressions for the field integrals in near-field approximations are reproduced by the convolution method. The convolution method is applied to discrete dipole approximation calculations of a silver nanorod, and the nature of the induced charge-density distributions of its plasmons is discussed.

On-demand measurement-based schemes to control coherence transfer between interacting qubits inside a dissipative environment are considered. The measurements employed are of the types of quantum weak measurement and quantum reversal measurement of which one is carried out at the beginning of the system evolution $t=0$ and the other at a later intended time $t>0.$ The relevant questions are which type of measurement should be performed at $t=0$ and which type at $t>0$, as well as which strength of the second measurement should be chosen in dependence on the strength of the first measurement to optimally achieve a demand? We answer such questions in this work as to meet two concrete demands, namely, to make optimal (i) the transfer of coherence from the $s$th qubit to the $r$th qubit and (ii) the preservation of coherence at the $s$th qubit. Particularly, independent of the coherence degree of the $s$th qubit at $t=0,$ the coherence degree of either the $r$th qubit or the $s$th qubit at any $t>0$ can be made arbitrarily close to the maximum value equal to 1/2, but at the cost of vanishingly reduced success probability. As an application, we discuss the coherence transfer between two qubits of a bipartite system. We also analyze the influence of the controlling schemes for optimal coherence transfer on the degree of entanglement created at $t>0$ between the two qubits.