We propose an entanglement criterion based on local uncertainty relations (LURs) in a stronger form than the original LUR criterion introduced by Hofmann and Takeuchi [H. F. Hofmann and S. Takeuchi, Phys. Rev. A 68, 032103 (2003)]. Using arbitrarily chosen operators $\{{\mathrm{Â}}_k\}$ and $\{{\mathrm{B̂}}_k\}$ of subsystems A and B, the tighter LUR criterion, which may be used not only for discrete variables but also for continuous variables, can detect more entangled states than the original criterion.

Quantum-information protocols are inevitably affected by decoherence which is associated with the leakage of quantum information into an environment. In this article we address the possibility of recovering the quantum information from an environmental measurement. We investigate continuous-variable quantum information, and we propose a simple environmental measurement that under certain circumstances fully restores the quantum information of the signal state although the state is not reconstructed with unit fidelity. We implement the protocol for which information is encoded into conjugate quadratures of coherent states of light and the noise added under the decoherence process is of Gaussian nature. The correction protocol is tested using both a deterministic as well as a probabilistic strategy. The potential use of the protocol in a continuous-variable quantum-key distribution scheme as a means to combat excess noise is also investigated.

The electric quadrupole ($E2$) and magnetic octupole ($M3$) ground-state transitions in Ni-like ${\mathrm{W}}^{46+}$ have been measured using high-resolution crystal spectroscopy at the LLNL electron-beam ion trap facility. The lines fall in the soft x-ray region near $7.93$ Å and were originally observed as an unresolved feature in tokamak plasmas. Using flat ammonium dihydrogen phosphate and quartz crystals, the wavelengths, intensities, and polarizations of the two lines have been measured for various electron-beam energies and compared to intensity and polarization calculations performed using the Flexible Atomic Code (FAC).

Magnetic dipole transitions between the levels of ground $4d^N$ configurations of tungsten ions were analyzed by employing a large basis of interacting configurations. Previously introduced configuration interaction strength between two configurations was used to determine the configurations with the largest contribution to wave functions of atomic states for the considered configurations. Collisional-radiative modeling was performed for the levels of the ground configuration coupled through electric dipole transitions with $4p^{5}4d^{N+1}$ and $4d^{N-1}4f$ configurations. New identification of some lines observed in the electron-beam ion trap plasma was proposed based on calculations in which wavelength convergence was reached.

We present a theoretical investigation of coherent anti-Stokes Raman scattering (CARS) that is modulated by periodically depleting the ground-state population through Rabi oscillations driven by an additional control laser. We find that such a process generates optical sidebands in the CARS spectrum and that the frequency of the sidebands depends on the intensity of the control laser light field. We show that analyzing the sideband frequency upon scanning the beams across the sample allows one to spatially resolve emitter positions where a spatial resolution of $65$ nm, which is well below the diffraction limit, can be obtained.

The nonradiative charge-transfer process for ${\mathrm{H}}^{+}+\mathrm{K}(4s)$ collision is investigated using the quantum-mechanical molecular-orbital close-coupling method for collision energies from $1$ eV to $10$ keV. The radiative-decay and radiative charge transfer cross sections are calculated using the optical potential approach and the fully quantal method, respectively, for the energy range of ${10}^{-5}$–$10$ eV. The radiative-association cross sections are obtained by subtracting the radiative charge-transfer part from total radiative-decay cross sections. The relevant molecular data are calculated from the multireference single- and double-excitation configuration interaction approach. The nonradiative charge transfer is the dominant mechanism at energies above $2$ eV, whereas the radiative charge transfer becomes primary in the low-energy region of $E<1.5$ eV. The present radiative-decay cross sections disagree with the calculations of Watanabe et al. [Phys. Rev. A 66, 044701 (2002)]. The total charge-transfer rate coefficient is obtained in the temperature range of $1$–$20$$000$ K.

We investigate the ionization of model diatomic molecules exposed in intense laser fields both numerically and analytically. Our simulations show that, in the tunneling region, the interplay of the tunneling effect and molecular two-center structure has an important role in ionization. It can lead to the enhancement of ionization in molecules as compared to their reference atoms with similar ionization potential. Furthermore, it also plays a dominating role in the angle dependence of molecular ionization. This effect is different from that of two-center interference in ionization. The latter manifests itself remarkably in the multiphoton region and can cause the ionization suppression of molecules in this region. Our further comparisons suggest the significant influence of the orbital symmetry of the reference atom on molecular ionization comparison experiments.

We study the photodissociation of the ${\mathrm{H}}_2^{\hspace{0.5em}+}$ molecule by ultrashort Fock-state electromagnetic pulses (EMPs). We use the Born-Oppenheimer treatment combined with an explicit photon number representation via diabatic electrophoton potential surfaces for simplification of the basic equations. We discuss the issue of the number of photon states required and show that six photon states enable good accuracy for photoproduct kinetic energies of up to $3$ eV. We calculate photodissociation probabilities and nuclear kinetic-energy (KE) distributions of the photodissociation products for $800$-nm, $50$-TW$/$cm${}^2$ pulses. We show that KE distributions depend on three pulse durations of $10$, $20$, and $45$ fs and on various initial vibrational states of the molecule. We compare the Fock-state results to those obtained by “conventional,” i.e., coherent-state, laser pulses of equivalent electric fields and durations. The effects of the quantum state of EMPs on the photodissociation dynamics are especially strong for high initial vibrational states of ${\mathrm{H}}_2^{\hspace{0.5em}+}$. While coherent-state pulses suppress photodissociation for the high initial vibrational states of ${\mathrm{H}}_2^{\hspace{0.5em}+}$, the Fock-state pulses enhance it.

We study resonant nonlinear magneto-optic rotation (NMOR) in a paraffin-coated Rb vapor cell as the magnetic field is swept. At low sweep rates, the nonlinear rotation appears as a narrow resonance signal with a linewidth of about “$300$ $\mu$G” ($2\pi \times 420$ Hz). At high sweep rates, the signal shows transient response with an oscillatory decay. The decay time constant is of order $100$ ms. The behavior is different for transitions starting from the lower or the upper hyperfine level of the ground state because of optical pumping effects.

Two coupled Bose-Einstein condensates with a large population imbalance exhibit macroscopic quantum self-trapping (MQST) if the ratio of interaction energy to tunneling energy is above a critical value. Here we investigate effect of quantum fluctuations on MQST. In particular, we analyze the dynamics of a system of two elongated Bose gases prepared with a large population imbalance, where due to the quasi-one-dimensional character of the gas we no longer have true long range order, and the effect of quantum fluctuations is much more important. We show that MQST is possible in this system, but even when it is achieved it is not always dynamically stable. Using this instability one can construct states with sharply peaked momentum distributions around characteristic momenta dependent on system parameters. Our other finding is the nonmonotonic oscillating dependence of the decay rate of the MQST on the length of the wires. We also address the interesting question of thermalization in this system and show that it occurs only in sufficiently long wires.

We investigate the effect exerted by spin-polarized fermions on the interaction between superfluid bosons for a Bose-Fermi mixture residing on an optical lattice, with particular emphasis on the possibility of an induced phase separation. Using a set of microscopic parameters relevant to a ${}^{40}\mathrm{K}-{}^{87}\mathrm{Rb}$ mixture, we show how the phase-separation criterion may be directly probed by means of the critical superfluid velocity of the bosonic condensate. We report quantitative results for the magnitude of the superfluid velocity and its dependence on the trap depth, the boson-fermion interaction, and the fermionic filling fraction. All of these parameters can be controlled experimentally in a well-defined manner. We propose an experimental setup for probing the critical superfluid velocity.

We study equal mass population imbalanced two-component atomic Fermi gas with unequal trap frequencies $({\omega }_{\uparrow }\ne {\omega }_{\downarrow })$ at zero temperature using the local density approximation (LDA). We consider the strongly attracting Bose-Einstein condensation (BEC) limit where polarized (gapless) superfluid is stable. The system exhibits shell structure: unpolarized superfluid$\to$polarized superfluid$\to$normal state. Compared to the trap symmetric case, when the majority component is tightly confined the gapless superfluid shell grows in size leading to reduced threshold polarization to form a polarized (gapless) superfluid core. In contrast, when the minority component is tightly confined, we find that the superfluid phase is dominated by the unpolarized superfluid phase with the gapless phase forming a narrow shell. The shell radii for various phases as a function of polarization at different values of trap asymmetry are presented and the features are explained using the phase diagram.

We study ordinary solitons and gap solitons (GS’s) in the framework of the one-dimensional Gross-Pitaevskii equation (GPE) with a combination of both linear and nonlinear lattice potentials. The main points of the analysis are the effects of (in)commensurability between the lattices, the development of analytical methods, viz., the variational approximation (VA) for narrow ordinary solitons and various forms of the averaging method for broad solitons of both types, and also the study of the mobility of the solitons. Under the direct commensurability (equal periods of the lattices, $L_{\mathrm{lin}}=L_{\mathrm{nonlin}}$), the family of ordinary solitons is similar to its counterpart in the GPE without external potentials. In the case of the subharmonic commensurability with $L_{\mathrm{lin}}=(1/2)L_{\mathrm{nonlin}}$, or incommensurability, there is an existence threshold for the ordinary solitons and the scaling relation between their amplitude and width is different from that in the absence of the potentials. GS families demonstrate a bistability unless the direct commensurability takes place. Specific scaling relations are found for them as well. Ordinary solitons can be readily set in motion by kicking. GS’s are also mobile and feature inelastic collisions. The analytical approximations are shown to be quite accurate, predicting correct scaling relations for the soliton families in different cases. The stability of the ordinary solitons is fully determined by the Vakhitov-Kolokolov (VK) criterion (i.e., a negative slope in the dependence between the solitons’s chemical potential $\mu$ and norm $N$). The stability of GS families obeys an inverted (“anti-VK”) criterion $d\mu /\mathit{dN}>0$, which is explained by the approximation based on the averaging method. The present system provides for the unique possibility to check the anti-VK criterion, as $\mu (N)$ dependencies for GS’s feature turning points except in the case of direct commensurability.

We address quantum interference of the Zeeman atom embedded in two kinds of structures containing left-handed materials (LHM), which are a single LHM layer mounted on a single mirror (SLSM) and Fabry-Pérot cavity filled with a LHM layer by half (FPCLH). Especially, the influence of the dissipation of LHM on quantum interference has been studied in detail. Though dissipation weakens quantum interference in general, it holds nearly complete quantum interference when the thickness of the cavity is small for FPCLH. Moreover, with equivalence of left- and right- rotation polarized dipoles to two spatial orthogonal dipoles, we found the optimum orientation of two orthogonal dipoles which can realize the maximum quantum interference in a certain anisotropic environment. Our research may have potential applications in the designing of microsize devices.

The multiple filamentation of powerful light pulses in fused silica is numerically investigated for central wavelengths at $355$ nm and $1550$ nm. We consider different values for beam waist and pulse duration and compare the numerical results with behaviors expected from the plane-wave modulational instability theory. Before the nonlinear focus, the spatiotemporal intensity patterns can be explained in the framework of this theory. Once the clamping intensity is reached, for long input pulse durations ($~1$ ps), the ionization front defocuses all trailing components within a collective dynamic, and a spatial replenishment scenario takes place upon further propagation. Short pulses ($~50$ fs) undergo similar ionization fronts, before an optically turbulent regime sets in. We observe moderate changes in the total temporal extent of ultraviolet pulses and in the corresponding spectra. In contrast, infrared pulses may undergo strong temporal compression and important spectral broadening. For short input pulses, anomalous dispersion and self-steepening push all pulse components to the trailing edge, where many small-scaled filaments are nucleated. In the leading part of the pulse, different spatial landscapes, e.g., broad ring patterns, may survive and follow their own propagation dynamics.

We discuss the finite size behavior of the adiabatic Dicke model, describing the collective coupling of a set of $N$ two-level atoms (qubits) to a faster (electromagnetic) oscillator mode. The energy eigenstates of this system are shown to be directly related to those of another widely studied collective spin model, the uniaxial one. By employing an approximate continuum approach, we obtain a complete characterization of the properties of the latter, which we then use to evaluate the scaling properties of various observables for the original Dicke model near its quantum phase transition.

Propagation equations for optical pulses are needed to assist in describing applications in ever more extreme situations—including those in metamaterials with linear and nonlinear magnetic responses. Here I show how to derive a single first-order propagation equation using a minimum of approximations and a straightforward “factorization” mathematical scheme. The approach generates exact coupled bidirectional equations, after which it is clear that the description can be reduced to a single unidirectional first-order wave equation by means of a simple “slow evolution” approximation, where the optical pulse changes little over the distance of one wavelength. It also allows a direct term-to-term comparison of an exact bidirectional theory with the approximate unidirectional theory.

We consider a mixture consisting of two species of spherical nanoparticles dispersed in a liquid medium. We show that with an appropriate choice of refractive indices and particle diameters, it is possible to observe the phenomenon of optical soliton bistability in two spatial dimensions in a broad beam power range. Previously, this possibility was ruled out in the case of a single-species colloid. As a particular example, we consider the system of hydrophilic silica particles and gas bubbles generated in the process of electrolysis in water. The interaction of two soliton beams can lead to switching of the lower branch solitons to the upper branch, and the interaction of solitons from different branches is phase independent and always repulsive.

Wave modes induced by cross-phase reshaping of a probe photon in the guiding structure of a periodic train of temporal pulses are investigated theoretically with emphasis on exact solutions to the wave equation for the probe. The study has direct connection with recent advances on the issue of light control by light, the focus being on the trapping of a low-power probe by a temporal sequence of periodically matched high-power pulses of a dispersion-managed optical fiber. The problem is formulated in terms of the nonlinear optical fiber equation with averaged dispersion, coupled to a linear equation for the probe including a cross-phase modulation term. Shape-preserving modes which are robust against the dispersion are shown to be induced in the probe, they form a family of mutually orthogonal solitons the characteristic features of which are determined by the competition between the self-phase and cross-phase effects. Considering a specific context of this competition, the theory predicts two degenerate modes representing a train of bright signals and one mode which describes a train of dark signals. When the walk-off between the pump and probe is taken into consideration, these modes have finite-momentum envelopes and none of them is totally transparent vis-à-vis the optical pump soliton.

A three mode opto-acoustic parametric amplifier (OAPA) is created when two orthogonal optical modes in a high finesse optical cavity are coupled via an acoustic mode of the cavity mirror. Such interactions are predicted to occur in advanced long baseline gravitational wave detectors. They can have high positive gain, which leads to strong parametric instability. Here we show that an optical feedback scheme can enhance or suppress the parametric gain of an OAPA, allowing exploration of three-mode parametric interactions, especially in cavity systems that have insufficient optical power to achieve spontaneous instability. We derive analytical equations and show that optical feedback is capable of controlling predicted instabilities in advanced gravitational wave detectors within a time scale of $1~10$ s.