We discuss the effective interactions between two localized perturbations in one-dimensional quantum liquids. For noninteracting fermions, the interactions exhibit Friedel oscillations, giving rise to a Ruderman-Kittel-Kasuya-Yosida-type interaction familiar from impurity spins in metals. In the interacting case, at low energies, a Luttinger-liquid description applies. In the case of repulsive fermions, the Friedel oscillations of the interacting system are replaced, at long distances, by a universal Casimir-type interaction which depends only on the sound velocity and decays inversely with the separation. The Casimir-type interaction between localized perturbations embedded in a fermionic environment gives rise to a long-range coupling between quantum dots in ultracold Fermi gases, opening an alternative to couple qubits with neutral atoms. We also briefly discuss the case of bosonic quantum liquids in which the interaction between weak impurities turns out to be short ranged, decaying exponentially on the scale of the healing length.

We investigate an all-optical, pump-probe scheme for the polarization rotation of linearly polarized light in an atomic medium. A circularly polarized control light is shown to play the role of a static magnetic field via a Zeeman-like ac Stark interaction and to induce the optical Faraday rotation (OFR) of the probe light. As a model system, we consider a stationary atom with $nS\text{−}nP\text{−}nD$ level scheme without electronic or nuclear spin. In addition to OFR, we find that electromagnetically induced transparency for the three-level atom and circular dichroism also contribute to the polarization change. We characterize these three effects over different frequency ranges through an explicit calculation of the fractional transmission and the output polarization of the probe light. Our results are compared with the $nS\text{−}nP\text{−}(n+1)S$ scheme, which has been previously studied both theoretically and experimentally. We also compare the optically induced Faraday effect with the Faraday effect from a static magnetic field. We propose an experimental situation to test the theory and address the possibility of producing an atomic medium that is both optically active and transparent.

We theoretically discuss the preservation of squeezing and continuous-variable entanglement of two-mode squeezed light when the two modes are subjected to unequal transmission. One of the modes is transmitted through a slow light medium while the other is sent through an optical fiber of unit transmission. Balanced homodyne detection is used to check the presence of squeezing. It is found that loss of squeezing occurs when the mismatch in the transmission of the two modes is greater than 40% while near-ideal squeezing is preserved when the transmissions are equal. We also discuss the effect of this loss on continuous-variable entanglement using strong and weak Einstein-Podolsky-Rosen criteria and possible applications for this experimental scheme.

In 1959, Zel’dovich predicted that the bound-state spectrum of the nonrelativistic Coulomb problem distorted at small distances by a short-range potential undergoes a peculiar reconstruction whenever this potential alone supports a low-energy scattering resonance. However, documented experimental evidence of this effect has been lacking. Previous theoretical studies of this phenomenon were confined to the regime where the range of the short-ranged potential is much smaller than Bohr’s radius of the Coulomb field. We go beyond this limitation by restricting ourselves to highly excited $s$ states. This allows us to demonstrate that along the periodic table of elements, the Zel’dovich effect manifests itself as systematic periodic variation of the Rydberg spectra with a period proportional to the cubic root of the atomic number. This dependence, which is supported by an analysis of experimental and numerical data, has its origin in the binding properties of the ionic core of the atom.

The cross section for ionization of Rydberg atoms in collision with electrons at low and moderate energies is calculated using classical trajectories. The dependence of the total cross section on the initial angular momentum of the target is revealed. Low-discrepancy sequences of (quasirandom) numbers are compared with plain random numbers to confirm that they can lead to improved convergence of calculation in certain cases. A phenomenological parametrization using only two parameters is shown to describe well the classical cross section over a wide range of energies and angular momenta. Using the classical scaling law, the results are extended to any principal quantum number.

We explore connections between an operator’s matrix-element distribution and its entanglement generation. Operators with matrix-element distributions similar to those of random matrices generate states of high multipartite entanglement. This occurs even when other statistical properties of the operators do not coincide with random matrices. Similarly, operators with some statistical properties of random matrices may not exhibit random matrix element distributions and will not produce states with high levels of multipartite entanglement. Finally, we show that operators with similar matrix-element distributions generate similar amounts of entanglement.

The simple system of two atoms couple to single mode optical cavity with the phase decoherence is studied for investigating the entanglement and Bell violation between atoms and cavity or between two atoms. We show that in the resonance case (i) atom-field entanglement rapidly decays with phase decoherence and disappears in the stationary state, (ii) atom-atom entanglement is more robust against phase decoherence and survives in the stationary state. In the nonresonance case, the pairwise atom-atom and atom-field entanglement is sensitive to the detuning parameter and is not completely destroyed during evolution. On the other hand, violation of Bell-CHSH inequality is very fragile against the phase decoherence and finally disappears in the stationary state. The phenomenon that the more Bell violation, the less entanglement, or vice versa in such a realistic physical system, is revealed. This phenomenon maybe is the consequence of the choice of concurrence as the entanglement measure and the observables to build the Bell-CHSH inequality. The genuine three-partite entanglement is also analyzed by making use of the state preparation fidelity. It is shown that the genuine three-partite entanglement can appear in the evolution of the system even in the presence of the phase decoherence.

We calculated the photoelectron angular distribution (PAD) expected in the laboratory frame (LF PAD) for the ionization of ${\mathrm{N}}_2$ molecules that are aligned by an intense laser pulse. We consider two independent processes of the dynamical alignment of molecules in the electronic ground state by an intense femtosecond laser pulse $(>10\mathrm{TW}∕{\mathrm{cm}}^2)$ and one-photon ionization or $(2+1)$ resonance-enhanced multiphoton ionization of the aligned molecules by a weak laser pulse $(<10\mathrm{GW}∕{\mathrm{cm}}^2)$. We examined the variation of the LF PAD against the intensity of the alignment laser, durations of the alignment and ionization laser pulses, and the time delay between these pulses. The LF PAD obtained from the ionization of the aligned ensemble shows a semiquantitative agreement with the PAD in the molecular frame.

Ion channeling through a single-wall carbon nanotube is simulated by solving Newton’s equations for ion motion at intermediate energies, under the action of both the surface-atom repulsive forces and the polarization forces due to the dynamic perturbation of the nanotube electrons. The atomic repulsion is described by a continuum potential based on the Thomas-Fermi-Moliere model, whereas the dynamic polarization of the nanotube electrons is described by a two-dimensional hydrodynamic model, giving rise to the transverse dynamic image force and the longitudinal stopping force. In the absence of centrifugal forces, a balance between the image force and the atomic repulsion is found to give rise to ion trajectories which oscillate over peripheral radial regions in the nanotube, provided the ion impact position is not too close to the nanotube wall, the impact angle is sufficiently small, and the incident speed is not too high. Otherwise, the ion is found to oscillate between the nanotube walls, passing over a local maximum of the potential in the center of the nanotube, which results from the image interaction. The full statistical analysis of ${10}^3$ ion trajectories has been made to further demonstrate the actual effect of dynamic polarization on the ion channeling.

The strong-field approximation (SFA) can be and has been applied in both length gauge and velocity gauge with quantitatively conflicting answers. For ionization of negative ions with a ground state of odd parity, the predictions of the two gauges differ qualitatively: in the envelope of the angular-resolved energy spectrum, dips in one gauge correspond to humps in the other. We show that the length-gauge SFA matches the exact numerical solution of the time-dependent Schrödinger equation.

Single-component quantum gas confined in a harmonic potential, but otherwise isolated, is considered. From the invariance of the system of the gas under a displacement-type transformation, it is shown that the center of mass oscillates along a classical trajectory of a harmonic oscillator. It is also shown that this harmonic motion of the center has, in fact, been implied by Kohn’s theorem. If there is no interaction between the atoms of the gas, the system in a time-independent isotropic potential of frequency ${\nu }_c$ is invariant under a squeeze-type unitary transformation, which gives collective radial breathing motion of frequency $2{\nu }_c$ to the gas. The amplitudes of the oscillating and breathing motions from the exact invariances could be arbitrarily large. For a Fermi system, appearance of $2{\nu }_c$ mode of the large breathing motion indicates that there is no interaction between the atoms, except for a possible long-range interaction through the inverse-square-type potential.

The path-integral Monte Carlo method is used to simulate dilute trapped Bose gases and to investigate the equilibrium properties at finite temperatures. The quantum particles have a long-range dipole-dipole interaction and a short-range $s$-wave interaction. Using an anisotropic pseudopotential for the long-range dipolar interaction and a hard-sphere potential for the short-range $s$-wave interaction, we calculate the energetics and structural properties as a function of temperature and the number of particles. Also, in order to determine the effects of dipole-dipole forces and the influence of the trapping field on the dipolar condensate, we use two cylindrically symmetric harmonic confinements (a cigar-shaped trap and a disk-shaped trap). We find that the net effect of dipole-dipole interactions is governed by the trapping geometry. For a cigar-shaped trap, the net contribution of dipolar interactions is attractive and the shrinking of the density profiles is observed. For a disk-shaped trap, the net effect of long-range dipolar forces is repulsive and the density profiles expand.

When a single quantum of electromagnetic field excitation is added to the same spatiotemporal mode of a coherent state, a new field state is generated that exhibits intermediate properties between those of the two parents. Such a single-photon-added coherent state is obtained by the action of the photon creation operator on a coherent state and can thus be regarded as the result of the most elementary excitation process of a classical light field. Here we present and describe in depth the experimental realization of such states and their complete analysis by means of a novel ultrafast, time-domain, quantum homodyne tomography technique clearly revealing their nonclassical character.

The general theory of atomic processes stimulated by the nuclear ${\beta }^{-}$ decay is considered. The final-state probabilities are determined for a number of ${\beta }^{-}$-decaying light atoms (He-Ar) with the use of sudden approximation.

A Bose-Einstein condensate in an optical lattice exhibits parametric resonances when the intensity of the lattice is periodically modulated in time. These resonances correspond to an exponential growth of the population of counter-propagating Bogoliubov excitations. A suitable linearization of the Gross-Pitaevskii (GP) equation is used to calculate the stability diagram and the growth rates of the unstable modes. The results agree with the ones extracted from time-dependent GP simulations, supporting our previous claim [M. Krämer et al., Phys. Rev. A 71, 061602(R) (2005)] concerning the key role of parametric resonances in the response observed by Stöferle et al. [Phys. Rev. Lett. 92, 130403 (2004)] in the superfluid regime. The role of the seed excitations required to trigger the parametric amplification is discussed. The possible amplification of the quantum fluctuations present in the quasiparticle vacuum, beyond GP theory, is also addressed, finding interesting analogies with similar processes in nonlinear quantum optics and with the dynamic Casimir effect. Our results can be used in exploiting parametric instabilities for the purpose of spectroscopy, selective amplification of a particular excitation mode and for establishing a new type of thermometry.

The four-wave-mixing coherent optical oscillator is described, which is emitting light wave with regular alternation of its phase between two discrete values zero and $\pi$. Such a periodic self-modulation is a consequence of competition of photorefractive gratings formed by movable charge species of two different signs. The period of modulation depends on overthreshold coupling strength and on decay time of slow photorefractive grating. It falls to few seconds range for ${\mathrm{Sn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ crystals at ambient temperature but it can go down to microsecond range for photorefractive semiconductors.

In this work, we consider a three-dimensional model to simulate the capture velocity behavior in a sample of cold-trapped sodium atoms as a function of the trapping laser intensity. We expand on previous work [V. S. Bagnato, L. G. Marcassa, S. G. Miranda, S. R. Muniz, and A. L. de Oliveira, Phys. Rev. A 62, 013404 (2000)] by calculating the capture velocity over a broad range of light intensities considering the secondary scattering in a magneto-optical trap. Our calculations are in a good agreement with recent measured values [S. R. Muniz et al., Phys. Rev. A 65, 015402 (2001)].

This paper is motivated by the suggestion [W. Zurek, Phys. Scri. T, 76, 186 (1998)] that the chaotic tumbling of the satellite Hyperion would become nonclassical within $20\text{years}$, but for the effects of environmental decoherence. The dynamics of quantum and classical probability distributions are compared for a satellite rotating perpendicular to its orbital plane, driven by the gravitational gradient. The model is studied with and without environmental decoherence. Without decoherence, the maximum quantum-classical (QC) differences in its average angular momentum scale as ${\hslash }^{2∕3}$ for chaotic states, and as ${\hslash }^2$ for nonchaotic states, leading to negligible QC differences for a macroscopic object like Hyperion. The quantum probability distributions do not approach their classical limit smoothly, having an extremely fine oscillatory structure superimposed on the smooth classical background. For a macroscopic object, this oscillatory structure is too fine to be resolved by any realistic measurement. Either a small amount of smoothing (due to the finite resolution of the apparatus) or a very small amount of environmental decoherence is sufficient to ensure the classical limit. Under decoherence, the QC differences in the probability distributions scale as ${({\hslash }^2∕D)}^{1∕6}$, where $D$ is the momentum diffusion parameter. We conclude that decoherence is not essential to explain the classical behavior of macroscopic bodies.

We investigate decoherence channels that are modeled as a sequence of collisions of a quantum system (e.g., a qubit) with particles (e.g., qubits) of the environment. We show that collisions induce decoherence when a bipartite interaction between the system qubit and an environment (reservoir) qubit is described by the controlled-$U$ unitary transformation (gate). We characterize decoherence channels and in the case of a qubit we specify the most general decoherence channel and derive a corresponding master equation. Finally, we analyze entanglement that is generated during the process of decoherence between the system and its environment.