We reinvestigate the modulation inversion of angular distribution of high-order harmonic generation (HHG) from impulsively aligned ${\text{CO}}_2$ molecules. The angular distribution is found to be sensitive to both the harmonic order and the intensity of the driving laser pulse for HHG. The roles of intramolecular quantum interference and the laser intensity are clarified. A laser-field-related recombination interference model is proposed to explain the modulation inversion of harmonic yield with respect to the molecular alignment. We conclude that the two-center interference in the recombination process can be manipulated by changing the laser intensity.

We describe interacting mixtures of ultracold bosonic and fermionic atoms in harmonically confined optical lattices. For a suitable choice of parameters we study the emergence of superfluid and Fermi-liquid (noninsulating) regions out of Bose-Mott and Fermi-band insulators due to finite boson and fermion hoppings. We obtain the shell structure for the system and show that angular momentum can be transferred to the noninsulating regions from Laguerre-Gaussian beams, which combined with Bragg spectroscopy can reveal all superfluid and Fermi-liquid shells.

We consider the thermodynamic properties of the squeezed vacuum state of a frequency-modulated quantum harmonic oscillator. We analytically relate the squeezing parameter to the irreversible work and the degree of nonadiabaticity of the frequency transformation. We furthermore determine the optimal modulation that leads to maximal squeezing, and discuss its implementation as well as the detection of squeezing in single cold ion traps.

The Casimir force due to a scalar field in a cylinder of radius $r$ with a spherical cap of radius $R>r$ is computed numerically in the world-line approach. A geometrical subtraction scheme gives the finite interaction energy that determines the Casimir force. The spectral function of convex domains is obtained from a probability measure on convex surfaces that is induced by the Wiener measure on Brownian bridges the convex surfaces are the hulls of. Due to reflection positivity, the vacuum force on the piston by a scalar field satisfying Dirichlet boundary conditions is attractive in these geometries, but the strength and short-distance behavior of the force depend strongly on the shape of the piston casing. For a cylindrical casing with a hemispherical head, the force on the piston does not depend on the dimension of the casing at small piston elevation $a⪡R$ and numerically approaches ${\mathcal{F}}_{\text{cas}}\left(a⪡R\right)=-0.00326\left(4\right)\hslash c/a^2$. Semiclassically this asymptotic force is due to short, closed, and nonperiodic trajectories that reflect just once off the piston near its periphery. A semiclassical estimate reproduces the numerical results for the small-distance behavior of the force within statistical errors, whereas the proximity force approximation is off by one order of magnitude when $R\sim r$.

The variance of an observable in a quantum state is usually used to describe Heisenberg uncertainty relation. For mixed states, the variance includes quantum and classical uncertainties. By means of the skew information and the decomposition of the variance, a stronger uncertainty relation was presented by Luo [Phys. Rev. A 72, 042110 (2005)]. In this paper, by using Wigner-Yanase-Dyson information which is a generalization of the skew information, we propose a general uncertainty relation of mixed states.

We investigate entanglement in a linear chain of $N$ polar molecules interacting by dipole forces. Entanglement is computed using two different methods, one of which is directly related to collective spatial orientation, an observable that can be experimentally measured for molecular systems. We discuss on applications of our results on quantum communications and we analyze different experimental systems where our ideas can be implemented.

We introduce a physically motivated classification of pure quantum states describing $n$ qubits. We characterize all multipartite states which can be maximally entangled to local auxiliary systems using controlled operations. A state has this property if and only if one can construct out of it an orthonormal basis by applying independent local unitary operations. This implies that those states can be used to encode locally the maximum amount of $n$ independent bits. Examples of these states are the so-called stabilizer states, which are used for quantum error correction and one-way quantum computing. We give a simple characterization of these states and construct a complete set of commuting unitary observables which characterize the state uniquely. Furthermore we show how these states can be prepared and discuss their applications.

The high resilience to decoherence shown by a recently discovered macroscopic quantum superposition (MQS) generated by a quantum-injected optical parametric amplifier and involving a number of photons in excess of $5\times {10}^4$ motivates the present theoretical and numerical investigation. The results are analyzed in comparison with the properties of the MQS based on $|\alpha ⟩$ and N-photon maximally entangled states (NOON), in the perspective of the comprehensive theory of the subject by Zurek. In that perspective the concepts of “pointer state” and “environment-induced superselection” are applied to the new scheme.

We consider elastic single-particle scattering from a one-dimensional trapped two-component superfluid Fermi gas when the incoming projectile particle is identical to one of the confined species. Our theoretical treatment is based on the Hartree-Fock ground state of the trapped gas and a configuration-interaction description of the excitations. We determine the scattering phase shifts for the system and predict Fano-type scattering resonances that are a direct consequence of interatomic pairing. We describe the main characteristics of the scattering resonances and make a comparison with the results of BCS mean-field theory.

We report the results of ab initio calculations of cross sections and molecular-frame photoelectron angular distributions for $\text{C}1s$ ionization of ${\text{CO}}_2$ and propose a mechanism for the recently observed asymmetry of those angular distributions with respect to the ${\text{CO}}^{+}$ and ${\text{O}}^{+}$ ions produced by subsequent Auger decay. The fixed-nuclei, photoionization amplitudes were constructed using variationally obtained electron-molecular ion scattering wave functions. We have also carried out electronic structure calculations which identify a dissociative state of the ${\text{CO}}_2^{2+}$ dication that is likely populated following Auger decay and which leads to ${\text{O}}^{+}+{\text{CO}}^{+}$ fragment ions. We show that a proper accounting of vibrational motion in the computation of the photoelectron angular distributions, along with reasonable assumptions about the nuclear dissociation dynamics, gives results in good agreement with recent experimental observations. We also demonstrate that destructive interference between different partial waves accounts for sudden changes with photon energy in the observed angular distributions.

Atomic and molecular ions generated by a strong optical laser pulse are not in general in the electronic ground state. The density matrix for such ions is characterized by the electronic quantum-state populations and by the coherences among the electronic quantum states. Nonvanishing coherences signal the presence of coherent electronic wave-packet dynamics in the laser-generated ions. For noble-gas atoms heavier than helium, the most important channels populated via strong-field ionization are the outer-valence single-hole states with a total angular momentum of $j=3/2$ or $j=1/2$. For this case, we develop a time-dependent multichannel theory of strong-field ionization. We derive the ion density matrix and express the hole density in terms of the elements of the ion density matrix. Our wave-packet calculations demonstrate that neon ions generated in a strong optical field (800 nm) are almost perfectly coherent. In strong-field-generated xenon ions, however, the coherence is substantially suppressed.

It is well known that a finite level quantum system is controllable if and only if the Lie algebra of its generators has full rank. When the rank of the Lie algebra is not full, there is a rich mathematical and physical structure to the subalgebra that to date has been analyzed only in special cases. We show that uncontrollable systems can be classified into reducible and irreducible ones. The irreducible class is the more subtle and can be related to a notion of generalized entanglement. We give a general prescription for revealing irreducible uncontrollable systems: the fundamental representation of $\text{su}\left(N\right)$, where $N$ is the number of levels, must remain irreducible in the subalgebra of $\text{su}\left(N\right)$. We illustrate the concepts with a variety of physical examples.

Experimental signals of nonlinear magneto-optical resonances at $D_1$ excitation of natural rubidium in a vapor cell have been obtained and described with experimental accuracy by a detailed theoretical model based on the optical Bloch equations. The $D_1$ transition of rubidium is a challenging system to analyze theoretically because it contains transitions that are only partially resolved under Doppler broadening. The theoretical model took into account all nearby transitions, the coherence properties of the exciting laser radiation, and the mixing of magnetic sublevels in an external magnetic field and also included averaging over the Doppler profile. The experimental signals were reproduced very well at each hyperfine transition and over a wide range of laser power densities, beam diameters, and laser detunings from the exact transition frequency. The bright resonance expected at the $F_g=1\to F_e=2$ transition of ${}^{87}\text{R}\text{b}$ has been observed. A bright resonance was observed at the $F_g=2\to F_e=3$ transition of ${}^{85}\text{R}\text{b}$, but displaced from the exact position of the transition due to the influence of the nearby $F_g=2\to F_e=2$ transition, which is a dark resonance whose contrast is almost 2 orders of magnitude larger than the contrast of the bright resonance at the $F_g=2\to F_e=3$ transition. Even in this very delicate situation, the theoretical model described in detail the experimental signals at different laser detunings.

We investigate ferromagnetic ordering in an itinerant ultracold atomic Fermi gas with repulsive interactions and population imbalance. In a spatially uniform system, we show that at zero temperature the transition to the itinerant magnetic phase transforms from first to second order with increasing population imbalance. Drawing on these results, we elucidate the phases present in a trapped geometry, finding three characteristic types of behavior with changing population imbalance. Finally, we outline the potential experimental implications of the findings.

The ability to interferometrically detect inertial rotations via the Sagnac effect has been a strong stimulus for the development of atom interferometry because of the potential ${10}^{10}$ enhancement of the rotational phase shift in comparison to optical Sagnac gyroscopes. Here we analyze ballistic transport of matter waves in a one-dimensional chain of $N$ coherently coupled quantum rings in the presence of a rotation of angular frequency $\Omega$. We show that the transmission probability, $T$, exhibits zero transmission stop gaps as a function of the rotation rate interspersed with regions of rapidly oscillating finite transmission. With increasing $N$, the transition from zero transmission to the oscillatory regime becomes an increasingly sharp function of $\Omega$ with a slope $\partial T/\partial \Omega \sim N^2$. The steepness of this slope dramatically enhances the response to rotations in comparison to conventional single ring interferometers such as the Mach-Zehnder interferometer and leads to a phase sensitivity well below the quantum shot-noise limit typical of atom interferometers.

We study families of one-dimensional matter-wave bright solitons supported by the competition of contact and dipole-dipole (DD) interactions of opposite signs. Soliton families are found, and their stability is investigated in the free space and in the presence of an optical lattice (OL). Free-space solitons may exist with an arbitrarily weak local attraction if the strength of the DD repulsion is fixed. In the case of the DD attraction, solitons do not exist beyond a maximum value of the local-repulsion strength. In the system which includes the OL, a stability region for subfundamental solitons is found in the second finite band gap. For the existence of gap solitons (GSs) under the attractive DD interaction, the contact repulsion must be strong enough. In the opposite case of the DD repulsion, GSs exist if the contact attraction is not too strong. Collisions between solitons in the free space are studied too. In the case of the local attraction, they merge or pass through each other at small and large velocities, respectively. In the presence of the local repulsion, slowly moving solitons bounce from each other.

We present a one-dimensional scattering theory which enables us to describe a wealth of effects arising from the coupling of the motional degree of freedom of scatterers to the electromagnetic field. Multiple scattering to all orders is taken into account. The theory is applied to describe the scheme of a Fabry-Perot resonator with one of its mirrors moving. The friction force, as well as the diffusion, acting on the moving mirror is derived. In the limit of a small reflection coefficient, the same model provides for the description of the mechanical effect of light on an atom moving in front of a mirror.

We demonstrate analytically a linear optical property of photonic crystals—diffraction-induced incident optical pulse splitting in two pulses propagating with different group velocities in a linear photonic crystal. The reason of this phenomenon is in spatially inhomogeneous field localization within the photonic crystal in case of the Bragg diffraction at the Laue scheme. The field of the fast first pulse is mainly localized within low refractive index layers, whereas the slow second pulse field is mostly in high refractive index layers. Changing optical properties of either high-index or low-index layers of periodical multilayer structure, it is possible to control parameters of each propagating pulse separately. The distance between two transmitted and two diffractively reflected output pulses can be controlled by varying the crystal thickness and modulation depth of the refractive index.

We present the first-principles theory of the existence and stability of TE and TM spatial solitons in a subwavelength periodic semiconductor-dielectric structure. We have found that for the wavelength of 1550 nm and the interface separation close to and less than 100 nm the band structure of the linear TE and TM waves becomes similar to the band structure of a homogeneous medium. The properties of TE solitons change accordingly. However, the transverse profiles of the TM solitons continue to reflect the subwavelength geometry of the structure and develop dominant intensity peaks inside the low-index dielectric slots. Our stability analysis based on the linearized Maxwell equations indicates that the nonlinear TM waves can be approximated as the evanescently coupled modes of the slot waveguides with the low-index dielectric core and the high-index semiconductor cladding. Transition to the regime where the slot waveguides start to determine properties of TM waves is associated with the so-called Brewster condition.

We present a systematic theoretical study of spatial mode dynamics in wide-aperture semiconductor quantum-dot lasers within the Maxwell-Bloch formalism. Our opto-electro-thermal model self-consistently captures the essential dynamical coupling between field, polarization, and carrier density in both thermal and nonthermal regimes, providing detailed description of the complex spatiotemporal modal intensity structure and spectra in these novel devices and broad area edge-emitting lasers in general. Using linear stability analysis and high resolution adaptive-grid finite element numerical simulation, we show that in the nonthermal regime, the presence of inhomogeneous broadening in quantum-dot active media leads to suppressed filamentation and enhanced spatial coherence compared to conventional quantum well devices with comparable phase-amplitude coupling (alpha parameter). Increasing the degree of inhomogeneous broadening in the active medium leads to further improvement in spatial coherence. In the thermal regime, there is further suppression of filamentation in the inhomogeneously broadened quantum-dot active medium; however, the spatial coherence aided by inhomogeneous broadening is partly lost due to the effect of temperature on cavity detuning. We propose that device designs based on optimized inhomogeneous broadening of quantum-dot gain medium could ultimately lead to diffraction-limited outputs in the quasi-cw regime which are still very difficult to achieve in conventional wide-aperture designs.