The dressed states that are linear combinations of two bare levels of an atom (e.g., an alkali-metal atom) can be realized by a strong-coupling laser beam. As the dressed states have mixed parities, both electric- and magnetic-dipole-allowed transitions can occur between the dressed states and a third level with a definite (pure) parity. It is shown that such dressed-state mixed-parity transitions in an atomic vapor (the concept also applies in the solid state) can give rise to a negative refractive index. The produced negative refractive index is isotropic with atomic-scale microscopic structure units, and the negative real part can emerge in the optical frequency band. Also examined is the case of a fully quantized probe photonic field which interrogates the bottom dressed state and the third-level state. Similarities between the semiclassical approach for the weaker probe field and its fully quantum mechanical second-quantization treatment are discussed in regard to the off-diagonal density matrix element for the reduced $2\times 2$ manifold, and its implications for the refractive index.

We have developed a technique for measuring the atomic recoil frequency using a single-state echo-type atom interferometer that manipulates laser-cooled atoms in the ground state. The interferometer relies on momentum-state interference due to two standing-wave pulses that produce density gratings. The interference is modified by applying a third standing-wave pulse during the interferometer pulse sequence. As a result, the grating contrast exhibits periodic revivals at the atomic recoil frequency ${\omega }_r$ as a function of the time at which the third pulse is applied, allowing ${\omega }_r$ to be measured easily and precisely. The contrast is accurately described by a coherence function, which is the Fourier transform of the momentum distribution, produced by the third pulse and by the theory of echo formation. If the third pulse is a traveling wave, loss of grating contrast is observed, an effect also described by a coherence function. The decay of the grating contrast as a function of continuous-wave light intensity is used to infer the cross section for photon absorption.

Despite the great importance of quantum entanglement, a computationally practical, physically motivated, and experimentally implementable way to estimate the amount of entanglement associated with a general (mixed) state of a bipartite quantum system is still lacking. An entanglement lower bound recently advanced by Mintert and Buchleitner [Phys. Rev. Lett. 98, 140505 (2007)] was proposed as a possible tool for the aforementioned task. Mintert and Buchleitner presented evidence indicating that, due to its tightness, in some important cases the alluded bound can be used as an entanglement measure. From the physical point of view, what makes this bound particularly appealing as an entanglement measure is that it is based on an observable quantity. For this last reason, and also because of its other attractive feature, mathematical simplicity, this promising bound and its possible use as an entanglement estimator certainly deserve to be the focus of careful attention. The usefulness of the bound as an entanglement measure, however, depends on its degree of tightness. Here we perform a systematic survey of the behavior of the alluded bound in state space, in order to determine its typical properties (in particular its tightness) and thus assess its value as an entanglement estimator.

We present the kinetic energy contribution to the exchange-correlation energy functional of the extended constrained-search (ECS) theory by means of the generalized Bauer’s relation. Due to the nature of the exchange-correlation energy functional being a function of the Bohr radius and $e^2$, three kinds of expressions for the kinetic energy contribution are obtained. These can be utilized as constraints in developing and/or evaluating the approximate form of the exchange-correlation energy functional of the ECS theory. Furthermore, by combining three expressions with the virial relation, we derive other useful relations that include not the kinetic energy contribution but only the exchange-correlation energy functional.

We demonstrate that the entanglement in a class of two-mode non-Gaussian states obtained by subtracting photons from Gaussian twin beams can be bounded from above and from below by functionals of the second moments only. Knowledge of the covariance matrix thus suffices for an entanglement quantification with appreciable precision. The absolute error in the entanglement estimation scales with the non-Gaussianity of the considered states.

We demonstrate accurate single-qubit control in an ensemble of atomic qubits trapped in an optical lattice. The qubits are driven with microwave radiation, and their dynamics tracked by optical probe polarimetry. Real-time diagnostics is crucial to minimize systematic errors and optimize the performance of single-qubit gates, leading to fidelities of 0.99 for single-qubit $\pi$ rotations. We show that increased robustness to large, deliberately introduced errors can be achieved through the use of composite rotations. However, during normal operation the combination of very small intrinsic errors and additional decoherence during the longer pulse sequences precludes any significant performance gain in our current experiment.

Some properties of small and medium sodium clusters are described within the random-phase approximation (RPA) approach using a projected spherical single-particle basis. The oscillator strengths calculated with a Schiff-type dipole transition operator and folded with Lorentzian functions are used to calculate the photoabsorption cross-section spectra. The results are further employed to establish the dependence of the plasmon frequency on the number of cluster components. Static electric polarizabilities of the clusters excited in a RPA dipole state are also calculated. Comparison of our results with the corresponding experimental data shows an overall good agreement.

We present an extension of the basis generator method, which was successfully used for ion-atom collisions in previous works, and apply it to a laser-molecule problem. As test system, we have chosen the one-electron, diatomic and asymmetric molecule $\mathrm{He}{\mathrm{H}}^{2+}$ in a short (approximately fs) intense laser field. Due to the asymmetry of the molecule, excitation and ionization probabilities are different if the main peak of the laser pulse is parallel or antiparallel to the molecular dipole moment. Our results are in fair agreement with previous calculations for this system.

We develop an analytical model of correlated two-electron ionization in strong infrared laser fields. The model includes all relevant interactions between the electrons, the laser field, and the ionic core nonperturbatively. We focus on the deeply quantum regime, where the energy of the active electron driven by the laser field is insufficient to collisionally ionize the parent ion, and the assistance of the laser field is required to create a doubly charged ion. In this regime, the electron-electron and the electron-ion interactions leave distinct footprints in the correlated two-electron spectra, recording the mutual dynamics of the escaping electrons.

We show, numerically, that a single photon trapped by a soliton in a Kerr nonlinear medium can be transferred from one soliton to another when the captor soliton undergoes collision with a second soliton. Soliton collisions can also be used in this way to realize a beam splitter, as well as a mode-separating beam splitter, analogous to the usual polarizing beam splitter. We discuss briefly the feasibility of an optical fiber implementation and possible applications to quantum-information processing.

Within numerical analysis, we have demonstrated the existence of a type of solitonic solutions with the same intensity profile, but with different phase structures and topological charges. These solutions, which are in the form of necklaces, appear in optically induced square photonic lattices and oscillate during propagation in a way that neighboring pearls exchange power periodically, with the intensity beam profiles being self-similar. Due to the phase distribution, these solitons are azimuthons or soliton clusters.

We study the violation of the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality for two-spin systems, of arbitrary spins $j_1$ and $j_2$, prepared in an entanglement of spin-coherent states of each of the spins. We show that the Bell-CHSH inequality is quite robustly violated for a wide range of values of the parameters that specify the spin-coherent states, and, for a particular choice of these parameters, maximal violations are obtained. That is, the violations can reach the Tsirelson bound, $2\sqrt{2}$, for any choices of the spins.

We present filtering equations for single-shot parameter estimation using continuous quantum measurement. By embedding parameter estimation in the standard quantum filtering formalism, we derive the optimal Bayesian filter for cases when the parameter takes on a finite range of values. Leveraging recent convergence results [R. van Handel, e-print arXiv:0709.2216], we give a condition which determines the asymptotic convergence of the estimator. For cases when the parameter is continuous valued, we develop quantum particle filters as a practical computational method for quantum parameter estimation.

We report photoabsorption measurements from the $4p$ inner shell of singly ionized strontium in the spectral region between 26.0 and $37.4\mathrm{eV}$. More than 60 levels of $\mathrm{Sr}\mathrm{II}$ are reported which are interpreted as singly excited inner-shell transitions $4p^{6}5s$ ${}^{2}S_{1∕2}\to 4p^{4}5s({}^{1}P,{}^{3}P)ns$, $md$ and doubly excited transitions $4p^{6}5s$ ${}^{2}S_{1∕2}\to 4p^{5}4d({}^{1}P,{}^{3}P,{}^{3}D)nl$. Multiconfiguration Hartree-Fock calculations are performed in $jj$ coupling and the levels are arranged into Rydberg series converging on seven limits, allowing the identification of two levels in $\mathrm{Sr}\mathrm{III}$.

The puzzling phenomenon of no suppression observed in experiments on strong-field ionization of laser-irradiated diatomic ${\mathrm{F}}_2$ molecules (as compared to its atomic counterpart Ar of nearly equal ionization potential) is addressed within the velocity-gauge formulation of molecular strong-field approximation (SFA). The approach essentially exploits the density-functional-theory (DFT) method applied for numerical composition of initial (laser-free) molecular states using the modified van Leuwen–Baerends (LB-$\alpha$) intramolecular binding potential, which incorporates both the exchange and correlation local-spin-density approximation (LSDA) potentials and also allows for construction of initial (laser-free) wave function correctly reproducing molecular and/or atomic valence shells and respective binding energies. Unlike the respective results of earlier alternative strong-field considerations (all predicting a high suppression in ${\mathrm{F}}_2$ ionization), our DFT SFA based calculation results unambiguously demonstrate no suppression in strong-field ionization of ${\mathrm{F}}_2$ versus its atomic (Ar) and molecular $\left({\mathrm{N}}_2\right)$ counterparts. Our presented results also suggest that the predominant contribution to ${\mathrm{F}}_2$ ionization will always be from the $1{\pi }_g$ highest occupied molecular orbital (HOMO, corresponding to the outermost valence shell) and allow for quite a transparent physical interpretation. Namely, the phenomenon of no suppression in ${\mathrm{F}}_2$ ionization is just explained by the closed-shell nature of its $1{\pi }_g$ HOMO (and thus by its substantially more enhanced and pronounced electron-correlated response to an incident laser field). Quantitatively, the latter becomes manifest through equally large contributions from the correlation and exchange parts of the intramolecular LSDA potential to ${\mathrm{F}}_2$ and ${\mathrm{N}}_2$ valence shells, in contrast to ${\mathrm{O}}_2$ valence shells, to which the exchange part of the LSDA potential proved to contribute well, predominantly resulting in a high suppression of ionization relative to the atomic counterpart Xe.

We study the zero sound and the first sound in a dilute and ultracold disk-shaped normal Fermi gas with a strong harmonic confinement along the axial direction and uniform in the two planar directions. Working at zero temperature we calculate the chemical potential $\mu$ of the fermionic fluid as a function of the uniform planar density $\rho$ and find that $\mu$ changes its slope in correspondence to the filling of harmonic axial modes (shell effects). Within the linear response theory, and under the random phase approximation, we calculate the velocity $c_s^0$ of the zero sound. We find that also $c_s^0$ changes its slope in correspondence of the filling of the harmonic axial modes and that this effect depends on the Fermi-Fermi scattering length $a_F$. In the collisional regime, we calculate the velocity $c_s$ of first sound showing that $c_s$ displays jumps at critical densities fixed by the scattering length $a_F$. Finally, we discuss the experimental achievability of these zero sound and first sound waves with ultracold alkali-metal atoms.

Quantum interferometers are generally set so that phase differences between paths in coordinate space combine constructively or destructively. Indeed, the interfering paths can also meet in momentum space leading to momentum-space fringes. We propose and analyze a method to produce interference in momentum space by phase imprinting part of a trapped atomic cloud with a detuned laser. For one-particle wave functions analytical expressions are found for the fringe width and shift versus the phase imprinted. The effects of unsharpness or displacement of the phase jump are also studied, as well as many-body effects, to determine the potential applicability of momentum-space interferometry. For a broad range of parameters and conditions it is found that a “dark notch” in the momentum distribution depends linearly on the phase imprinted, with maximal sensitivity for noninteracting atoms in the ground state of tight traps.

We study an experimental scheme to generate Gaussian two-mode entangled states via beam splitter. Specifically, we consider a nonclassical Gaussian state (squeezed state) and a thermal state as two input modes, and evaluate the degree of entanglement at the output. Experimental conditions to generate entangled outputs are completely identified and the critical thermal noise to destroy entanglement is analytically obtained. By doing so, we discuss the possibility to link the resistance to noise in entanglement generation with the degree of single-mode nonclassicality.

We demonstrate a technique that allows full control of the bandwidth of entangled photons independently of the frequency band of interest and of the nonlinear crystal. We theoretically show that this technique allows generating nearly transform-limited biphotons with almost one octave of bandwidth (hundreds of terahertz) which corresponds to correlation times of just a few femtoseconds. The presented method becomes an enabling tool for attosecond entangled-photons quantum optics. The technique can also be used to generate paired photons with a very high degree of entanglement.

We experimentally investigate the photon correlations in resonance fluorescence from a few atoms into the guided modes of the nanofiber. We show that, when the photons are emitted in the same direction, the photon correlation varies from antibunching to bunching with increasing atom number and, when the photons are emitted in the opposite directions, the photon correlation is always antibunchinglike regardless of the number of atoms. The effect of excitation geometry on the photon correlations is also discussed.