We investigate the transient response of the generated light from four-wave mixing (FWM) in the diamond configuration using a step-down field excitation. The transients show fast decay times and oscillations that depend on the detunings and intensities of the fields. A simplified model taking into account the thermal motion of the atoms, propagation, absorption, and dispersion effects shows qualitative agreement with the experimental observations with the energy levels in rubidium ($5S_{1/2}$, $5P_{1/2}$, $5P_{3/2}$, and $6S_{1/2}$). The atomic polarization comes from all the contributions of different velocity classes of atoms in the ensemble modifying dramatically the total transient behavior of the light from FWM.

Low-energy two-dimensional scattering is particularly sensitive to the existence and the properties of weakly bound states. We show that interaction potentials $V(r)$ with the vanishing zero-momentum Born approximation $\int \mathit{dr}\hspace{0.5em}rV(r)=0$ leads to an anomalously weak bound state that crucially modifies the two-dimensional scattering properties. This anomalous case is especially relevant in the context of polar molecules in bilayer arrangements.

We study the dynamics of a two-level system driven by an off-resonance few-cycle pulse which has a phase jump $\varphi$ at $t=t_0$, in contrast to many-cycle pulses, under the nonrotating-wave approximation (NRWA). We give a closed form analytical solution for the evolution of the probability amplitude $|C_a(t)|$ for the upper level. Using the appropriate pulse parameters like the phase jump $\varphi$, jump time $t_0$, pulse width $\tau$, frequency $\nu$, and Rabi frequency ${\Omega }_0$ the population transfer after the pulse is gone can be optimized and, for the pulse considered here, an enhancement factor of ${10}^6–{10}^8$ was obtained.

Using a split-mirror stage combined with a reaction microscope, nonlinear autocorrelation traces of XUV pulses from the Free-electron LASer at Hamburg were recorded for ${\mathrm{N}}_2$ multiphoton-induced fragmentation into noncoincident ${\mathrm{N}}^{2+}$ and coincident ${\mathrm{N}}^{2+}+{\mathrm{N}}^{2+}$ channels. We find a pulse duration of $40\pm 10\hspace{0.5em}\mathrm{fs}$ along with a sharp spike pointing to a coherence time of $4\pm 1\hspace{0.5em}\mathrm{fs}$, almost twice as short as in previous observations. Both are well reproduced by a simulation based on the partial-coherence model that includes the molecular dynamics leading to an $~12-\mathrm{fs}$ substructure in the trace.

We consider a uniformly accelerated atom interacting with a vacuum electromagnetic field in the presence of an infinite conducting plane boundary and calculate separately the contributions of vacuum fluctuations and radiation reaction to the atomic energy-level shift. We analyze in detail the behavior of the total energy shift in three different regimes of the distance in both the low-acceleration and high-acceleration limits. Our results show that, in general, an accelerated atom does not behave as if immersed in a thermal bath at the Unruh temperature in terms of the atomic energy-level shifts, and the effect of the acceleration on the atomic energy-level shifts may in principle become appreciable in certain circumstances, although it may not be realistic for actual experimental measurements. We also examine the effects of the acceleration on the level shifts when the acceleration is of the order of the transition frequency of the atom and we find some features which differ from what was obtained in the existing literature.

We examine the quantum discord between two spins in the exact ground state of finite spin-1/2 arrays with anisotropic $\mathit{XY}$ couplings in a transverse field $B$. It is shown that in the vicinity of the factorizing field $B_s$, the discord approaches a common finite non-negligible limit which is independent of the pair separation and the coupling range. An analytic expression of this limit is provided. The discord of a mixture of aligned pairs in two different directions, crucial for the previous results, is analyzed in detail, including the evaluation of coherence effects, relevant in small samples and responsible for a parity splitting at $B_s$. Exact results for finite chains with first-neighbor and full-range couplings and their interpretation in terms of such mixtures are provided.

Using a merged-beam configuration, we have performed absolute measurements for the associative detachment reaction ${\mathrm{H}}^{-}+\mathrm{H}\to {\mathrm{H}}_2+e^{-}$. Our energy-resolved measurements for this process remove a long-standing discrepancy between theory and experiment for this fundamental reaction. In particular, we find excellent agreement with theoretical results which previously seemed to be ruled out by earlier experiments performed using a flowing afterglow technique.

Multielectron coincidence data for triple ionization of krypton have been recorded above the 3$d$ ionization threshold at two photon energies (140 and 150 eV). Three principal transition pathways have been observed, two involving double Auger transitions from ${\mathrm{Kr}}^{+}$, and one involving single Auger transitions from ${\mathrm{Kr}}^{2+}$ created by direct single-photon double ionization. The decay of the $3d^9$ ${}^2$$D_{5/2,3/2}$ states in ${\mathrm{Kr}}^{+}$ has been analyzed in some detail and is found to be strongly dominated by cascade processes where two electrons with well-defined energies are emitted. The decay paths leading to the $4s^2$$4p^3$ ${}^{4}S$, ${}^{2}D$, and ${}^{2}P$ states of ${\mathrm{Kr}}^{3+}$ are analyzed and energies of seven intermediate states in ${\mathrm{Kr}}^{2+}$ are given. A preliminary investigation of the decay paths from ${\mathrm{Kr}}^{+}$ $3d^9$$4p^5\mathit{nl}$ shake-up states has also been carried out.

The emission of one or two Auger electrons, following Kr $3d$ inner-shell ionization by synchrotron light, has been investigated both experimentally and theoretically. All electrons emitted in the process are detected in coincidence and analyzed in energy thanks to a magnetic-bottle electron time-of-flight spectrometer. In addition, noncoincident high-resolution electron spectra have been measured to characterize the cascade double-Auger paths more fully. Combination of the two experimental approaches and of our calculations allows a full determination of the decay pathways and branching ratios in the case of Kr $3d$ single- and double-Auger decays. The ${\mathrm{Kr}}^{3+}$ threshold is found at $74.197\pm 0.020$ eV.

We consider the Bose-Hubbard model describing attractive bosonic particles hopping across the sites of a translation-invariant lattice and compare the relevant ground-state properties with those of the corresponding symmetry-breaking semiclassical nonlinear theory. The introduction of a suitable measure allows us to highlight many correspondences between the nonlinear theory and the inherently linear quantum theory, characterized by the well-known self-trapping phenomenon. In particular we demonstrate that the localization properties and bifurcation pattern of the semiclassical ground state can be clearly recognized at the quantum level. Our analysis highlights a finite-number effect.

We investigate the entangling capacity of dynamical operations when provided with local ancilla. A comparison is made between the entangling capacity with and without the assistance of prior entanglement. An analytic solution is found for the log-negativity entangling capacity of two-qubit gates, which equals the entanglement of the Choi matrix isomorphic to the unitary operator. Surprisingly, the availability of prior entanglement does not affect this result, a property we call resource independence of the entangling capacity. We prove several useful upper bounds on the entangling capacity that hold for general qudit dynamical operations and for a whole family of entanglement monotones including log negativity and log robustness. The log-robustness entangling capacity is shown to be resource independent for general dynamics. We provide numerical results supporting a conjecture that the log-negativity entangling capacity is resource independent for all two-qudit unitary operators.

We consider the problem of improving noisy quantum measurements by suitable preprocessing strategies making many noisy detectors equivalent to a single ideal detector. For observables pertaining to finite-dimensional systems (e.g., qubits or spins) we consider preprocessing strategies that are reminiscent of quantum error correction procedures and allow one to perfectly measure an observable on a single quantum system for increasing number of inefficient detectors. For measurements of observables with an unbounded spectrum (e.g., photon number and homodyne and heterodyne detection), the purification of noisy quantum measurements can be achieved by preamplification as suggested by Yuen [Opt. Lett. 12, 789 (1987)].

We derive exact expressions for the Casimir scalar interaction energy between media-separated eccentric dielectric cylinders and for the media-separated cylinder-plane geometry using a mode-summation approach. Similarly to the electromagnetic Casimir-Lifshitz interaction energy between fluid-separated planar plates, the force between cylinders is attractive or repulsive depending on the relative values of the permittivities of the three intervening media.

Photoionization cross-section calculations are performed on potassiumlike transition metal ions (Ti${}^{3+}$, ${\mathrm{V}}^{4+}$, Cr${}^{5+}$, Mn${}^{6+}$, and Fe${}^{7+}$) using both nonrelativistic ($\mathit{LS}$-coupling) and relativistic (Breit-Pauli) $R$-matrix methods for the ground ([Ne]$3s$${}^{2}3$$p$${}^{6}3$$d$ ${}^2$$D$${}_{3/2}^e$) and the first excited ([Ne]$3s$${}^{2}3$$p$${}^{6}3$$d$ ${}^2$$D$${}_{5/2}^e$) states of each of the five ions, along with the excited $4s$ ${}^2$$S$ state of Ti${}^{3+}$. Photon energies up to the first $3p$ ionization threshold are considered. The results show that for Ti${}^{3+}$, the cross sections are dominated by the giant ($3p\to 3d$) resonances which are analyzed and identified, while for the four other ions (V${}^{4+}$, Cr${}^{5+}$, Mn${}^{6+}$, and Fe${}^{7+}$), the $3p\to 3d$ resonances lie below the ionization threshold, and the cross sections are dominated by $3p$${}^{5}3$$\mathit{dnd}$ and $3p$${}^{5}3$dn’s Rydberg series of resonances. Comparison of the Ti${}^{3+}$ results with available theoretical and experimental data shows good agreement.

We consider the degree of conservation of nuclear spin polarization in the process of optical pumping under typical spin-exchange optical pumping conditions. Previous analyses have assumed that negligible nuclear spin precession occurs during the brief periods of time in which the alkali-metal atoms are in the excited state after absorbing photons and before undergoing quenching collisions with nitrogen molecules. We include excited-state hyperfine interactions, electronic spin relaxation in collisions with He and ${\mathrm{N}}_2$, spontaneous emission, quenching collisions, and a simplified treatment of radiation trapping.

The self-organization of a Bose-Einstein condensate (BEC) in a transversely pumped optical cavity is a process akin to crystallization: when pumped by a laser of sufficient intensity, the coupled matter and light fields evolve, spontaneously, into a spatially modulated pattern, or crystal, whose lattice structure is dictated by the geometry of the cavity. In cavities having multiple degenerate modes, the quasicontinuum of possible lattice arrangements, and the continuous symmetry breaking associated with the adoption of a particular lattice arrangement, give rise to phenomena such as phonons, defects, and frustration, which have hitherto been unexplored in ultracold atomic settings involving neutral atoms. The present work develops a nonequilibrium field-theoretic approach to explore the self-organization of a BEC in a pumped, lossy optical cavity. We find that the transition is well described, in the regime of primary interest, by an effective equilibrium theory. At nonzero temperatures, the self-organization occurs via a fluctuation-driven first-order phase transition of the Brazovskii class; this transition persists to zero temperature and crosses over into a quantum phase transition. We make further use of our field-theoretic description to investigate the role of nonequilibrium fluctuations in the self-organization transition, as well as to explore the nucleation of ordered-phase droplets, the nature and energetics of topological defects, supersolidity in the ordered phase, and the possibility of frustration controlled by the cavity geometry. In addition, we discuss the range of experimental parameters for which we expect the phenomena described here to be observable, along with possible schemes for detecting ordering and fluctuations via either atomic correlations or the correlations of the light emitted from the cavity.

We study a one-dimensional Fermi gas with attractive short range-interactions in a disordered potential by the density matrix renormalization group (DMRG) technique. Our results can be tested experimentally by using cold atom techniques. We identify a region of parameters for which disorder enhances the superfluid state. As disorder is further increased, global superfluidity eventually breaks down. However this transition seems to occur before the transition to the insulator state takes place. This suggests the existence of an intermediate metallic “pseudogap” phase characterized by strong pairing but no quasi-long-range order.

We study the instability of collective excitations of a three-dimensional Bose-Einstein condensate with repulsive and attractive interactions in a shallow trap designed as a quadratic plus a quartic potential. By using a correlated many-body theory, we determine the excitation modes and probe the critical behavior of collective modes, having a crucial dependence on the anharmonic parameter. We examine the power-law behavior of monopole frequency near criticality. In Gross-Pitaevskii variational treatment [Phys. Rev. Lett. 80, 1576 (1998)] the power-law exponent is determined as one-fourth power of $(1-\frac{A}{A_{\mathit{cr}}})$, $A$ is the number of condensate atoms and $A_{\mathit{cr}}$ is the critical number near collapse. We observe that the power-law exponent becomes $\frac{1}{6}$ in our calculation for the pure harmonic trap and it becomes $\frac{1}{7}$, for traps with a small anharmonic distortion. However for large anharmonicity the power law breaks down.

We resolve the breakdown of angular momentum conservation on two-dimensional photon tunneling by considering the spin Hall effect (SHE) of light. This effect manifests itself as polarization-dependent transverse shifts of the field centroid when a classic wave packet tunnels through a prism-air-prism barrier. For the left or the right circularly polarized component, the transverse shift can be modulated by altering the refractive index gradient associated with the two prisms. We find that the SHE in conventional beam refraction can be evidently enhanced via photon tunneling mechanism. The transverse spatial shift is governed by the total angular momentum conservation law, while the transverse angular shift is governed by the total linear momentum conservation law. These findings open the possibility for developing new nanophotonic devices and can be extrapolated to other physical systems.

Recent efforts to produce single photons via heralding have relied on creating spectrally factorable two-photon states in order to achieve both high purity and high production rate. Through a careful multimode analysis, we find, however, that spectral factorability is not necessary. Utilizing single-mode detection, a similar or better performance can be achieved with nonfactorable states. This conclusion rides on the fact that even when using a broadband filter, a single-mode measurement can still be realized, as long as the coherence time of the triggering photons exceeds the measurement window of the on-off detector.