Large broadening of short optical pulses due to fiber dispersion leads to a strong overlap in information data streams resulting in statistical deviations of the local power from its average. We present a theoretical analysis of rare events of high-intensity fluctuations—optical freak waves—that occur in fiber communication links using bit-overlapping transmission. Although the nature of the large fluctuations examined here is completely linear, as compared to commonly studied freak waves generated by nonlinear effects, the considered deviations inherit from rogue waves the key features of practical interest—random appearance of localized high-intensity pulses. We use the term “rogue wave” in an unusual context mostly to attract attention to both the possibility of purely linear statistical generation of huge amplitude waves and to the fact that in optics the occurrence of such pulses might be observable even with the standard Gaussian or even rarer-than-Gaussian statistics, without imposing the condition of an increased probability of extreme value events.

We consider the average distance between four bases in six dimensions. The distance between two orthonormal bases vanishes when the bases are the same, and the distance reaches its maximal value of unity when the bases are unbiased. We perform a numerical search for the maximum average distance and find it to be strictly smaller than unity. This is strong evidence that no four mutually unbiased bases exist in six dimensions. We also provide a two-parameter family of three bases which, together with the canonical basis, reach the numerically found maximum of the average distance, and we conduct a detailed study of the structure of the extremal set of bases.

We introduce the informational power of a quantum measurement as the maximum amount of classical information that the measurement can extract from any ensemble of quantum states. We prove the additivity by showing that the informational power corresponds to the classical capacity of a quantum-classical channel. We restate the problem of evaluating the informational power as the maximization of the accessible information of a suitable ensemble. We provide a numerical algorithm to find an optimal ensemble and quantify the informational power.

We investigate superradiance of an ensemble of atoms coupled to an integrated superconducting $\mathit{LC}$ circuit. Particular attention is paid to the effect of inhomogeneous coupling constants. Combining perturbation theory in the inhomogeneity and numerical simulations, we show that inhomogeneous coupling constants can significantly affect the superradiant relaxation process. Incomplete relaxation terminating in “dark states” can occur, from which the only escape is through individual spontaneous emission on a much longer time scale. The relaxation dynamics can be significantly accelerated or retarded, depending on the distribution of the coupling constants. On the technical side, we also generalize the previously known propagator of superradiance for identical couplings in the completely symmetric sector to the full exponentially large Hilbert space.

Binding energies of high-$L$ Rydberg states ($L$ ⩾ 7) of Th${}^{2+}$ with $n$ $=$ 27–29 were studied using the resonant excitation Stark ionization spectroscopy (RESIS) method. The core of the Th${}^{2+}$ Rydberg ion is the Fr-like ion Th${}^{3+}$ whose ground state is a 5 ${}^2$$F$${}_{5/2}$ level. The large-core angular momentum results in a complex Rydberg fine-structure pattern consisting of six levels for each value of $L$ that is only partially resolved in the RESIS excitation spectrum. The pattern is further complicated, especially for the relatively-low-$L$ levels, by strong nonadiabatic effects due to the low-lying 6d levels. Analysis of the observed RESIS spectra leads to determination of five properties of the Th${}^{3+}$ ion: its electric quadrupole moment $Q$ $=$ 0.54(4); its adiabatic scalar and tensor dipole polarizabilities ${\alpha }_d$${}_{,0}$ $=$ 15.42(17) and ${\alpha }_d$${}_{,2}$ $=$ -3.6(1.3); and the dipole matrix elements connecting the ground 5 ${}^2$$F_{5/2}$ level to the low-lying 6  ${}^2$$D$${}_{3/2}$ and 6  ${}^2$$D$${}_{5/2}$ levels, $|\langle 5\hspace{0.5em}{}^2{F}_{5/2}|\left|D\right||6{}^2{D}_{3/2}\rangle |=1.435(10)$ and $|\langle 5{}^2{F}_{5/2}|\left|D\right||6{}^2{D}_{5/2}\rangle |=0.414(24)$. All are in atomic units. These are compared with theoretical calculations.

We give results for the order-$\alpha$ radiative corrections to several polarization-related effects involving the decay of ortho-positronium (o-Ps) to three photons. Specifically, we consider the decays of spin-polarized o-Ps from states of specified spin component $m$ into final states where the direction of the normal to the decay plane is measured, the linear polarization of one photon is observed, and the two variables giving the energies, or equivalently the relative orientations of the photons in the decay plane, are measured.

Fully relativistic distorted-wave theory has been applied to study the electron-impact excitation of the ${\mathit{ns}}_{1/2}$-${\mathit{np}}_{1/2}$ and ${\mathit{ns}}_{1/2}$-${\mathit{np}}_{3/2}$ resonance transitions of singly charged metal ions with one valence electron, viz., Mg${}^{+}$ ($n=3$), Ca${}^{+}$ ($n=4$), Zn${}^{+}$ ($n=4$), Cd${}^{+}$ ($n=5$), and Ba${}^{+}$ ($n=6$). Calculations are performed in the range of incident electron energies up to 300 eV for differential and integrated cross sections as well as for the linear polarization of the photon emissions following the decay of excited ${\mathit{np}}_{3/2}$ states. Results are compared with the available experimental data and previous nonrelativistic theoretical calculations. Moreover, analytic fits to our integrated cross sections are provided for potential applications in modeling plasma sources and environments.

Laser-cooled arrays or crystals of ${}^{171}\mathrm{Yb}$${}^{+}$ ions containing a single impurity, ${}^{172}\mathrm{Yb}$${}^{+}$ isotope, are confined in a linear radio-frequency Paul trap. Site-to-site hopping of the impurity ion, distinguished by a lack of fluorescence, is studied as a function of the ${}^{171}\mathrm{Yb}$${}^{+}$ laser-cooling parameters and as a function of the anisotropy of the trapping potential. Imaging of the independently resolved crystal sites permits the extraction of the impurity’s hopping trajectory, from which the dwell times at a given site can be obtained as well as the spatial distribution of hopping rate and hopping destination. The onset of rapid hopping is found to occur at average thermal energies approaching a significant fraction of the Coulomb potential energy. Furthermore, the hopping rate is enhanced at trap anisotropies near the critical value for the structural phase transition to a two-dimensional zigzag phase. Finally, the hopping mobility of the impurity ion is observed to be highest near the center of the crystal, which may have an intrinsic cause related to the crystal structure and dynamics near the zigzag transition.

We present a scheme for nonadiabatically loading a Bose-Einstein condensate into the ground state of a one-dimensional optical lattice within a few tens of microseconds, i.e., typically in less than half the Talbot period. This technique of coherent control is based on sequences of pulsed perturbations, and the experimental results demonstrate its feasibility and effectiveness. As the loading process is much shorter than the traditional adiabatic loading time scale, this method may find many applications.

We present results on coherent control of ultracold trap-loss collisions using 40-ns pulses of nonlinearly frequency-chirped light. The chirps, either positive or negative, sweep $~$1 GHz in 100 ns and are centered at various detunings below the $D_2$ line of ${}^{85}\mathrm{Rb}$. At each center detuning, we compare the collisional rate constant $\beta$ for chirps that are linear in time, concave-down, and concave-up. For positive chirps, we find that $\beta$ generally depends very little on the shape of the chirp. For negative chirps, however, we find that $\beta$ can be enhanced by up to 50(20)$\%$ for the case of the concave-down shape. This occurs at detunings where the evolution of the wave packet is expected to be coherent. An enhancement at these detunings is also seen in quantum-mechanical simulations of the collisional process.

We use a coherent Bragg diffraction method to impart an external momentum to ultracold bosonic atoms trapped in a one-dimensional optical lattice. This method is based on the application of a single light pulse, with conditions where scattering of photons can be resonantly amplified by atomic density grating. An oscillatory behavior of the momentum distribution resulting from the time evolution in the lattice potential is then observed. By measuring the oscillating frequencies, we extract multiband energy structures of single-particle excitations with zero pseudomomentum transfer for a wide range of lattice depths. The excitation energy structures reveal the interaction effect through the whole range of lattice depths.

We consider the propagation of circularly polarized few-cycle pulses (FCPs) in Kerr media beyond the slowly varying envelope approximation. Assuming that the frequency of the transition is far above the characteristic wave frequency (long-wave-approximation regime), we show that propagation of FCPs, taking into account the wave polarization, is described by the nonintegrable complex modified Korteweg–de Vries (cmKdV) equation. By direct numerical simulations, we get robust localized solutions to the cmKdV equation, which describe circularly polarized few-cycle-optical solitons and strongly differ from the breather soliton of the modified Korteweg–de Vries equation, which represents linearly polarized FCP solitons. The circularly polarized FCP soliton becomes unstable when the angular frequency is less than 1.5 times the inverse of the pulse length. The unstable subcycle pulses decay into linearly polarized half-cycle pulses, the polarization direction of which slowly rotates around the propagation axis.

We study the field correlation functions and the natural laser spectrum for a slow-inversion laser with the thresholdless intensity fluctuations. In such a laser, the spontaneous-emission-driven relaxation oscillations are responsible for some unique features: The field correlation function oscillates with the frequency of relaxation oscillations ${\omega }_r$ and the laser line changes its profile. We show that appreciably above threshold the laser spectrum consists of three lines. In addition to the main line at the frequency of the lasing mode ${\omega }_c$ appear two lines at frequencies ${\omega }_c+{\omega }_r$ and ${\omega }_c-{\omega }_r$. The spontaneous emission noise in such lasers gives rise to nonlinear stochastic effects: Quantum noise affects the oscillation frequency ${\omega }_r$ and the decay rates of the field correlation function.

We explore experimentally if light’s orbital angular momentum (OAM) interacts with chiral nematic polymer films. Specifically, we measure the circular dichroism of such a material using light beams with different OAM. We investigate the case of strongly focused, nonparaxial light beams, where the spatial and polarization degrees of freedom are coupled. Within the experimental accuracy, we cannot find any influence of the OAM on the circular dichroism of cholesteric polymers.

In this paper we derived a necessary and sufficient condition for classical correlated states and proposed a norm-based measurement $Q$ of quantum correlation. Using the max norm of operators, we gave the expression of the quantum correlation measurement $Q$ and investigated the dynamics of $Q$ in Markovian and non-Markovian cases, respectively. $Q$ decays exponentially and vanishes only asymptotically in the Markovian case and causes periodical death and rebirth in the non-Markovian case. In the pure state, the quantum correlation $Q$ is always larger than the entanglement, which was different from other known measurements. In addition, we showed that locally broadcastable and broadcastable are equivalent and reproved the density of quantum correlated states.

We propose a way for generating $n$-qubit Greenberger-Horne-Zeilinger (GHZ) entangled states with a three-level qubit system and $(n-1)$ four-level qubit systems in a cavity. This proposal does not require identical qubit-cavity coupling constants and thus is tolerant to qubit-system parameter nonuniformity and nonexact placement of qubits in a cavity. The proposal does not require adjustment of the qubit-system level spacings during the entire operation. Moreover, it is shown that entanglement can be deterministically generated using this method and the operation time is independent of the number of qubits. The present proposal is quite general, which can be applied to physical systems such as various types of superconducting devices coupled to a resonator or atoms trapped in a cavity.

We study theoretically the instability of countersuperflow, i.e., two counterpropagating miscible superflows, in uniform two-component Bose-Einstein condensates. Countersuperflow instability causes mutual friction between the superfluids, causing a momentum exchange between the two condensates, when the relative velocity of the counterflow exceeds a critical value. The momentum exchange leads to nucleation of vortex rings from characteristic density patterns due to the nonlinear development of the instability. Expansion of the vortex rings drastically accelerates the momentum exchange, leading to a highly nonlinear regime caused by intervortex interaction and vortex reconnection between the rings. For a sufficiently large interaction between the two components, rapid expansion of the vortex rings causes isotropic turbulence and the global relative motion of the two condensates relaxes. The maximum vortex line density in the turbulence is proportional to the square of the relative velocity.

We study the asymptotic interaction between two half-quantized vortices in two-component Bose-Einstein condensates. When two vortices in different components are placed at distance $2R$, the leading order of the force between them is found to be $(\ln R/\xi -1/2)/R^3$, in contrast to $1/R$ between vortices placed in the same component. We derive it analytically using the Abrikosov ansatz and the profile functions of the vortices, confirmed numerically with the Gross-Pitaevskii model. We also find that the short-range cutoff of the intervortex potential linearly depends on the healing length.

The Berry phase, which was discovered more than two decades ago, provides very deep insight into the geometric structure of quantum mechanics. Its classical counterpart, Hannay’s angle, is defined if closed curves of action variables return to the same curves in phase space after a time evolution. In this paper we study the Berry phase and Hannay’s angle in a quantum-classical hybrid system under the Born-Oppenheimer approximation. By the term quantum-classical hybrid system, we mean a composite system consists of a quantum subsystem and a classical subsystem. The effects of subsystem-subsystem couplings on the Berry phase and Hannay’s angle are explored. The results show that the Berry phase has been changed sharply by the couplings, whereas the couplings have a small effect on the Hannay’s angle.