We propose initial conditions that could facilitate the excitation of rogue waves. Understanding the initial conditions that foster rogue waves could be useful both in attempts to avoid them by seafarers and in generating highly energetic pulses in optical fibers.

Phase matching of high-order harmonic generation is investigated experimentally for various parameters in a semi-infinite gas-cell (SIGC) geometry. The optimized harmonic yield is identified using two different noble gases (Xe and He) and its parameter dependence is studied in a systematic way. Beside the straightforward setup of the SIGC, this geometry promises a high photon flux due to a large interaction region. Moreover, since the experimental parameters within this cell are known accurately, direct comparison to simulations is performed. Spectral splitting and blueshift of high-order harmonics are observed.

The second-order Talbot effect is analyzed for a periodic object illuminated by entangled photon pairs in both the quantum imaging and quantum lithography configurations. The Klyshko picture is applied to describe the quantum imaging scheme, in which self-images of the object that may or may not be magnified can be observed nonlocally in the photon coincidences but not in the singles count rate. In the quantum lithography setup, we find that the second-order Talbot length is half that of the classical first-order case, thus the resolution may be improved by a factor of 2.

Amplified dispersive Fourier transformation (ADFT) is a powerful technique that maps the spectrum of an optical pulse into a time-domain waveform using group-velocity dispersion (GVD) and simultaneously amplifies it in the optical domain. It replaces a diffraction grating and detector array with a dispersive fiber and single photodetector, greatly simplifying the system and, more importantly, enabling ultrafast real-time spectroscopic measurements. Here we present a theory of ADFT by deriving the general equation and spectral resolution for ADFT and studying the evolution of the pulse spectrum into time, the effect of GVD coefficients on ADFT, and the requirement for dispersion. This theory is expected to lend valuable insights into the process and implementation of ADFT.

With photon-number resolving detectors, we show compression of interference fringes with increasing photon numbers for a Fabry-Perot interferometer. This feature provides a higher precision in determining the position of the interference maxima compared to a classical detection strategy. We also theoretically show supersensitivity if $N$-photon states are sent into the interferometer and a photon-number resolving measurement is performed.

We calculate the rate of two-photon absorption for frequency-entangled photons in a tapered optical fiber whose diameter is comparable to the wavelength of the light. The confinement of the electric field in the transverse direction increases the intensity associated with a single photon, while the two-photon absorption rate is further enhanced by the fact that the sum of the frequencies of the two photons is on resonance with the upper atomic state, even though each photon has a relatively broad linewidth. As a result, the photons are effectively confined in all three dimensions and the two-photon absorption rate for frequency-entangled photons in a tapered fiber was found to be comparable to that for unentangled photons in a microcavity with a small mode volume.

We consider a system consisting of a large number of interacting qubits and study the geometric phase of one of them. The many body interaction is analyzed within a mean-field approach when the reduced dynamics of a single qubit is described by a nonlinear Hartree equation. Generally, the geometric phase is highly sensitive to the type and the strength of interaction. However, we identify regimes where the geometric phase is almost independent of the qubit-qubit coupling.

The hyperfine-structure constants of the lowest $s$ and $p_{1/2}$ states of superheavy elements $Z=119$ and $Z={120}^{+}$ are calculated using ab initio approach. Core polarization and dominating correlation effects are included to all orders. Breit and quantum electrodynamic effects are also considered. Similar calculations for Cs, Fr, ${\text{Ba}}^{+}$, and ${\text{Ra}}^{+}$ are used to control the accuracy. The dependence of the hyperfine-structure constants on the nuclear radius is discussed.

We consider a quantum above-barrier reflection of a Bose-Einstein condensate by a one-dimensional rectangular potential barrier, or by a potential well, for nonlinear Schrödinger equation (Gross-Pitaevskii equation) with a small nonlinearity. The most interesting case is realized in resonances when the reflection coefficient is equal to zero for the linear Schrödinger equation. Then the reflection is determined only by small nonlinear term in the Gross-Pitaevskii equation. A simple analytic expression has been obtained for the reflection coefficient produced only by the nonlinearity. An analytical condition is found when common action of potential barrier and nonlinearity produces a zero reflection coefficient. The reflection coefficient is derived analytically in the vicinity of resonances which are shifted by nonlinearity.

We propose a scheme to realize Zitterbewegung (ZB) with cold atoms in an Abelian vector potential. Two dark states can be created by interacting alkali-metal atoms with three coaxial Gaussian beams. Atoms moving in the subspace spanned by the two dark states feel a vector gauge potential that is nonvanishing only along the laser axis. We show that cold atoms in this Abelian vector potential undergo ZB with a large amplitude detectable in experiment.

Correlations between particles can lead to subtle and sometimes counterintuitive phenomena. We analyze one such case, occurring during the sudden expansion of fermions in a lattice when the initial state has a strong admixture of double occupancies. We promote the notion of quantum distillation: during the expansion and in the case of strongly repulsive interactions, doublons group together, forming a nearly ideal band insulator, which is metastable with low entropy. We propose that this effect could be used for cooling purposes in experiments with two-component Fermi gases.

We investigate optimal discrimination between two projective quantum measurements on a single qubit. We consider a scenario where the measurement that should be identified can be performed twice and we show that adaptive discrimination strategy, entangled probe states, and feed forward all help to increase the probability of correct identification of the measurement. We also experimentally demonstrate the studied discrimination strategies and test their performance. The employed experimental setup involves projective measurements on polarization states of single photons and preparation of required probe two-photon polarization states by the process of spontaneous parametric downconversion and passive linear optics.

We introduce four new molecules—YbRb, YbCs, ${\text{YbSr}}^{+}$, and ${\text{YbBa}}^{+}$—that may prove fruitful in experimental searches for the electric-dipole moment (EDM) of the electron. These molecules can, in principle, be prepared at extremely low temperatures by photoassociating ultracold atoms and therefore may present an advantage over molecular-beam experiments. Here we discuss properties of these molecules and assess the effective electric fields they contribute to an electron EDM measurement.

We introduce two active-electron classical trajectory Monte Carlo models for ion-He collisions, in which the electron-electron force is smoothed using a Gaussian kernel approximation for the pointwise classical particles. A first model uses independent pairs of Gaussian electrons, while a second one employs time-dependent mean-field theory to define an averaged electron-electron repulsion force. These models are implemented for prototypical $p+\text{He}$ collisions and the results are compared to available experimental and theoretical data.

We investigate the energy-loss spectra of high-energy electrons incident on Ar atoms using linear density response theory with a self-interaction correction. The energy region of the spectra covers from 24.5 to 30.0 eV, where many $ns$, $np$, and $nd$ autoionizing resonant states from the $3s$ orbital of Ar exist with the continuum background from the $3p$ orbital. We compare the calculated spectra to recent energy-loss spectra measurements and identify the observed autoionizing resonant states. We also discuss the dependence of the spectra on the scattering angles and their physical meanings.

We calculate the dynamic structure factor $S(q,\omega )$ of a one-dimensional (1D) interacting Bose gas confined in a harmonic trap. The effective interaction depends on the strength of the confinement enforcing the (1D) motion of atoms; interaction may be further enhanced by superimposing an optical lattice on the trap potential. In the compressible state, we find that the smooth variation in the gas density around the trap center leads to softening of the singular behavior of $S(q,\omega )$ at the first Lieb excitation mode compared to the behavior predicted for homogeneous 1D systems. Nevertheless, the density-averaged response $\overline{S}(q,\omega )$ remains a nonanalytic function of $q$ and $\omega$ at the first Lieb excitation mode in the limit of weak trap confinement. The exponent of the power-law nonanalyticity is modified due to the inhomogeneity in a universal way and thus bears unambiguously the information about the (homogeneous) Lieb-Liniger model. A strong optical lattice causes formation of Mott phases. Deep in the Mott regime, we predict a semicircular peak in $S(q,\omega )$ centered at the on-site repulsion energy, $\omega =U$. Similar peaks of smaller amplitudes exist at multiples of $U$ as well. We explain the suppression of the dynamic response with entering into the Mott regime, observed recently by Clément et al. [Phys. Rev. Lett. 102, 155301 (2009)], based on an $f$-sum rule for the Bose-Hubbard model.

We study the superfluid phase of the one-band attractive Hubbard model of fermions as a prototype of a strongly correlated $s$-wave fermion superfluid on a lattice. We show that the collective mode spectrum of this superfluid exhibits, in addition to the long wavelength sound mode, a sharp roton mode over a wide range of densities and interaction strengths. We compute the sound velocity and the roton gap within a generalized random phase approximation (GRPA) and show that the GRPA results are in good agreement, at strong coupling, with a spin-wave analysis of the appropriate strong-coupling pseudospin model. We also investigate, using this two-pronged approach, the breakdown of superfluidity in the presence of a supercurrent. We find that the superflow can break down at a critical flow momentum via several distinct mechanisms—depairing, Landau instabilities or dynamical instabilities—depending on the dimension, the interaction strength and the fermion density. The most interesting of these instabilities is a charge modulation dynamical instability which is distinct from previously studied dynamical instabilities of Bose superfluids. The charge order associated with this instability can be of two types: (i) a commensurate checkerboard modulation driven by softening of the roton mode at the Brillouin zone corner, or, (ii) an incommensurate density modulation arising from superflow-induced finite momentum pairing of Bogoliubov quasiparticles. We elucidate the dynamical phase diagram showing the critical flow momentum of the leading instability over a wide range of fermion densities and interaction strengths and point out implications of our results for experiments on cold atom fermion superfluids in an optical lattice.

We investigate the spatial quantum properties of the light emitted by a perfectly spatially degenerate optical parametric oscillator (self-imaging optical parametric oscillator). We show that this device produces local squeezing for areas bigger than a coherence area that depends on the crystal length and pump width. Furthermore, it generates local EPR beams in the far field. We show, calculating the eigenmodes of the system, that it is highly multimode for realistic experimental parameters.

We discuss the inevitable dissipation of energy that must accompany the creation of a pulse-medium excitation state in a passive dielectric. We show that there is a minimum amount of energy that an optical pulse must deposit in the medium to create a given pulse-medium state and that energy deposited beyond this minimum value must be dissipated in the medium. We compare this notion of dissipation to a related concept found by determining the fraction of energy stored in a medium that is irrecoverable by future fields. These two notions of dissipation are model-independent and form upper and lower bounds for real-time loss. Any model-dependent notion of loss that falls outside these bounds has serious conceptual difficulties. We show that a traditional notion of real-time loss based on a multiple-Lorentz oscillator model fails to give reasonable results in classes of passive linear media near EIT, while the notions of loss we introduce give sensible results for all passive media.

We explicitly construct a quantum circuit, which exactly generates random three-qubit states. The optimal circuit consists of three CNOT gates and fifteen single-qubit elementary rotations, parametrized by fourteen independent angles. The explicit distribution of these angles is derived, showing that the joint distribution is a product of independent distributions of individual angles apart from four angles.