We show that the dc Josephson effect with ultracold fermionic gases in the Bose-Einstein-condensate (BEC) regime of composite molecules can be described by a nonlinear Schrödinger equation (NLSE). By comparing our results with Bogoliubov–de Gennes calculations [Phys. Rev. Lett. 99, 040401 (2007)] we find that our superfluid NLSE, which generalizes the Gross-Pitaevskii equation taking into account the correct equation of state, is reliable in the BEC regime of the BCS-BEC crossover up to the limit of very large (positive) scattering length. We also predict that the Josephson current displays relevant beyond-mean-field effects.

We compare effects of particle interaction on Bose-Einstein condensation in inhomogeneous traps with and without optical lattice inside. Interaction pushes normal particles away from the condensate droplet, which is located in the center of the trap, toward the periphery of the trap where the trapping potential is large. In the end, the remaining normal particles are squeezed to a quasi-two-dimensional (2D) shell around the condensate droplet, thus changing the effective dimensionality of the system. In the absence of the optical lattice, the index in the temperature dependence of the condensate density at the later stages of the process is close to 2 with a weak dependence on the number of trapped particles. In the presence of the lattice inside the trap, this simple picture breaks down and the index acquires a strong dependence on the number of particles inside the trap, gradually falling from a three-dimensional to a 2D value with an increase in the number of particles. This change in index is explained by the lattice-driven spread of the condensate droplet and the localization of the narrow-band particles by the trap potential.

We study the properties of the Fraunhofer diffraction patterns produced by Gaussian beams crossing spiral phase plates. We show, both analytically and numerically, that off-axis displacements of the input beam produce asymmetric diffraction patterns. The intensity profile along the direction of maximum asymmetry shows two different peaks. We find that the intensity ratio between these two peaks decreases exponentially with the off-axis displacement of the incident beam, the decay being steeper for higher strengths of the optical singularity of the spiral phase plate. We analyze how this intensity ratio can be used to measure small misalignments of the input beam with a very high precision.

In the superlens problem, the presence of the reflected wave plays a critical role in the energy and information transfer from the object to recording device: both incident and reflected evanescent waves are required to ensure nonzero energy and information influx from the object to the recorder. Therefore an optimization is required between the image quality (characterized by a transfer function) and information transfer rate (characterized by the energy and information flux). It is shown that the introduction of the recording device may lead to the deterioration in the image quality as compared to the ideal case when no recording device is present. The decline in the image quality is due to the generation of phase-shifted reflected evanescent wave between the lens and the recorder. It is also shown that the magnitude of the energy flux depends on the amount of dissipation in the lens and the recorder in a nonmonotonous way.

General properties of linear propagation of discretized light in homogeneous and curved waveguide arrays are comprehensively investigated and compared to those of paraxial diffraction in continuous media. In particular, general laws describing beam spreading, beam decay, and discrete far-field patterns in homogeneous arrays are derived using the method of moments and the steepest-descent method. In curved arrays, the method of moments is extended to describe evolution of global beam parameters. A family of beams which propagate in curved arrays maintaining their functional shape—referred to as discrete Bessel beams—is also introduced. Propagation of discrete Bessel beams in waveguide arrays is simply described by the evolution of a complex-$q$ parameter similar to the complex-$q$ parameter used for Gaussian beams in continuous lensguide media. A few applications of the $q$ parameter formalism are discussed, including beam collimation and polygonal optical Bloch oscillations.

We present a simple scheme of atom localization in a subwavelength domain via manipulation of Raman gain process. We consider a four-level system with a pump and a weak probe field. In addition, we apply a coherent field to control the gain process. The system is similar to the one used by Agarwal and Dasgupta [Phys. Rev. A 70, 023802 (2004)] for the superluminal pulse propagation through Raman gain medium. For atom localization, we consider both pump and control fields to be the standing-wave fields of the cavity. We show that a much precise position of an atom passing through the standing-wave fields can be determined by measuring the gain spectrum of the probe field.

The fidelity and entropy in an easy-axis antiferromagnetic Heisenberg spin-1 chain are studied numerically. By using the method of density-matrix renormalization group, the effects of anisotropy on fidelity and entanglement entropy are investigated. Their relations with quantum phase transition are analyzed. It is found that the quantum phase transition from the Haldane spin liquid to Néel spin solid can be well characterized by the fidelity. The phase transition can be hardly detected by the entropy but it can be successfully detected by the first deviation of the entropy.

We report calculations of energy- and angle-resolved photoelectron distribution of ${\text{F}}^{-}$ irradiated by a linearly strong short infrared pulse, performed by evaluating the photoelectron ejection probability in the framework of a modified Keldysh theory, taking into account the temporal behavior of the pulse and the spatial inhomogeneity of the laser intensity. Results of the calculations are compared with the measurements of the photoelectron angular distribution recently appearing in the literature. The oscillations found in the experimental data are explained in terms of quantum interference effects.

The fragmentation dynamics in the ${\text{CH}}_3+\text{H}+\text{H}$ channel arising from the dissociative recombination of protonated methane, ${{\text{CH}}_5}^{+}$, has been investigated with an imaging detector at the CRYRING storage ring. The experimental results imply that this channel proceeds via two-step break-up in which the intermediate ${\text{CH}}_4$ molecule is sufficiently internally excited to further fragment. These observations could go some way to explaining the discrepancy in results reported from ion storage rings and FALP apparatus.

Anti-Stokes Raman scattering in gas-filled hollow-core photonic crystal fibers is discussed. It is shown that the efficient anti-Stokes generation observed under conditions of significant wave mismatch is caused by phase locking of the interacting fields. This leads to the establishment of a phase difference that is independent of the optical path. An optimization technique, based on the adjustment of the wave mismatch along a gas-filled hollow fiber using pressure control, is proposed. Anti-Stokes conversion efficiencies close to the theoretical maximum of 50% are predicted.

A quantum ensemble $\left\{(p_x,{\rho }_x)\right\}$ is a set of quantum states each occurring randomly with a given probability. Quantum ensembles are necessary to describe situations with incomplete a priori information, such as the output of a stochastic quantum channel (generalized measurement), and play a central role in quantum communication. In this paper, we propose measures of distance and fidelity between two quantum ensembles. We consider two approaches: the first one is based on the ability to mimic one ensemble given the other one as a resource and is closely related to the Monge-Kantorovich optimal transportation problem, while the second one uses the idea of extended-Hilbert-space (EHS) representations which introduce auxiliary pointer (or flag) states. Both types of measures enjoy a number of desirable properties. The Kantorovich measures, albeit monotonic under deterministic quantum operations, are not monotonic under generalized measurements. In contrast, the EHS measures are. This property can be regarded as a generalization of the monotonicity under deterministic maps of the trace distance and the fidelity between states. The EHS measures are equivalent to convex optimization problems and are bounded by the Kantorovich measures which are equivalent to linear programs. We present operational interpretations for both types of measures. We also show that the EHS fidelity between ensembles provides an interpretation of the fidelity between mixed states as the fidelity between all pure-state ensembles whose averages are equal to the mixed states being compared. We finally use the measures to define distance and fidelity for stochastic quantum channels and positive operator-valued measures. These quantities may be useful in the context of tomography of stochastic quantum channels and quantum detectors.

We theoretically show that continuous-variable genuine quadripartite entanglement can be generated by intracavity cascaded nonlinear optical interactions. The process consists of a parametric down-conversion, a sum-frequency generation of pump and signal and a sum-frequency generation of pump and idler. The characteristics of the quadripartite entanglement among the signal, the idler, and two sum-frequency modes are analyzed by applying a sufficient inseparability criterion for multipartite continuous-variable entanglement proposed by Van Loock and Furusawa. The threshold properties of the system are also discussed.

We consider a system of bosonic atoms in an axially symmetric harmonic trap augmented with a two-dimensional repulsive Gaussian optical potential. We find an expression for the grand free energy of the system for configurations ranging from the harmonic trap to the toroidal regime. For large tori we identify an accessible regime where the ideal-gas thermodynamics of the system are found to be independent of toroidal radius. This property is a consequence of an invariant extensive volume of the system that we identify analytically in the regime where the toroidal potential is radially harmonic. In considering corrections to the scale-invariant transition temperature, we find that the first-order interaction shift is the dominant effect in the thermodynamic limit and is also scale invariant. We also consider adiabatic loading from the harmonic-to-toroidal trap configuration, which we show to have only a small effect on the condensate fraction of the ideal gas, indicating that loading into the scale-invariant regime may be experimentally practical.

We report an experimental demonstration of a quantum controlled-NOT gate constructed entirely in optical fiber and operating on polarization-encoded single-photon qubits. We operated this gate using two heralded optical fiber single-photon sources and found an average logical fidelity of 90% and an average process fidelity of $0.83\le \overline{F}\le 0.91$. On the basis of a simple model we are able to conclude that imperfections are primarily due to the photon sources, meaning that the gate itself works with very high fidelity. Such all fiber quantum information processing will likely have important applications in future quantum networks.

It has been suggested that some strongly correlated matter might be understood qualitatively in terms of liquid crystalline phases intervening between the Fermi gas and the Wigner crystal or Mott insulator. We propose a tunable realization of this soft quantum matter physics in an ultracold gas. It uses optical lattices and dipolar interactions to realize a particularly simple model. Our analysis reveals a rich phase diagram featuring a metanematic transition where the Fermi liquid changes dimensionality; a smectic phase (stripes) and a crystalline “checkerboard” phase.

The use of decoy states in quantum key distribution (QKD) has provided a method for substantially increasing the secret key rate and distance that can be covered by QKD protocols with practical signals. The security analysis of these schemes, however, leaves open the possibility that the development of better proof techniques or better classical postprocessing methods might further improve their performance in realistic scenarios. In this paper, we derive upper bounds on the secure key rate for decoy-state QKD. These bounds are based basically only on the classical correlations established by the legitimate users during the quantum communication phase of the protocol. The only assumption about the possible postprocessing methods is that double click events are randomly assigned to single click events. Further, we consider only secure key rates based on the uncalibrated device scenario which assigns imperfections such as detection inefficiency to the eavesdropper. Our analysis relies on two preconditions for secure two-way and one-way QKD. The legitimate users need to prove that there exists no separable state (in the case of two-way QKD) or that there exists no quantum state having a symmetric extension (one-way QKD) that is compatible with the available measurements results. Both criteria have been previously applied to evaluate single-photon implementations of QKD. Here we use them to investigate a realistic source of weak coherent pulses. The resulting upper bounds can be formulated as a convex optimization problem known as a semidefinite program which can be efficiently solved. For the standard four-state QKD protocol, they are quite close to known lower bounds, thus showing that there are clear limits to the further improvement of classical postprocessing techniques in decoy-state QKD.

This work explores the possibility of controlling the dissociation of a monochromatically driven one-dimensional Morse oscillator by recreating barriers, in the form of invariant tori with irrational winding ratios, at specific locations in the phase space. The control algorithm proposed by Huang et al. [Phys. Rev. A 74, 053408 (2006)] is used to obtain an analytic expression for the control field. We show that the control term, approximated as an additional weaker field, is efficient in recreating the desired tori and suppresses the classical as well as the quantum dissociation. However, in the case when the field frequency is tuned close to a two-photon resonance the local barriers are not effective in suppressing the dissociation. We establish that in the on-resonant case quantum dissociation primarily occurs via resonance-assisted tunneling and controlling the quantum dynamics requires a local perturbation of the specific nonlinear resonance in the underlying phase space.

We report results of a systematic numerical analysis of collisions between localized three-dimensional (3D) semidiscrete complexes, viz., rhombus-shaped vortices, quadrupoles, and fundamental solitons, in the model of a bundle of fiberlike waveguides. The model also describes a 3D self-attractive Bose-Einstein condensate (BEC) loaded into a deep two-dimensional optical lattice. We identify four outcomes of the collisions: rebound of slow solitons, fusion, splitting, and, finally, quasielastic interactions of fast solitons. Diagrams which demonstrate regions of the different outcomes are reported for collisions between vortices, with equal or opposite topological charges, and quadrupoles.

High-order harmonics were generated in a two-color scheme exploiting an infrared parametric source with self-stabilization of the carrier-envelope phase. A significant cutoff extension was observed with respect to single color, 800 nm driving pulses at comparable peak intensities. Exploiting the wavelength tuning of the parametric source in the $1.5–1.6\mu \text{m}$ range, a continuous xuv spectrum extending from 36 to 70 eV was generated in krypton. A broader xuv continuum, extending beyond 100 eV, was observed in argon. These results represent a step forward in the extension of attosecond science toward the soft x-rays region and open new perspectives in the investigation of quantum effects in atoms and molecules.

We have studied the spontaneous breakup of highly elliptical laser beams into one- and two-dimensional arrays of light filaments in fused silica. Although the multiple filamentation process is initiated by random intensity modulation across the beam (amplitude noise), the output patterns exhibit a certain periodicity and high shot-to-shot reproducibility. The experimentally observed periodicity of the multiple filament arrays depends on the input beam intensity and this behavior is reproduced in detail by the numerical simulations. With the help of a simple analytical model we propose that the formation of periodic multiple filament structures could be understood within a simple framework of multistep phase-matched four-wave optical parametric amplification.