The Casimir-Polder interaction between an atom and a metal wall is investigated under the influence of real conditions including the dynamic polarizability of the atom, finite conductivity of the wall metal, and nonzero temperature of the system. Both analytical and numerical results for the free energy and force are obtained over a wide range of atom-wall distances. Numerical computations are performed for an $\mathrm{Au}$ wall and metastable ${\mathrm{He}}^{*}$, $\mathrm{Na}$, and $\mathrm{Cs}$ atoms. For the ${\mathrm{He}}^{*}$ atom we demonstrate, as an illustration, that at short separations of about the $\mathrm{Au}$ plasma wavelength at room temperature the free energy deviates up to 35% and the force up to 57% from the classical Casimir-Polder result. Accordingly, such large deviations should be taken into account in precision experiments on atom-wall interactions. The combined account of different corrections to the Casimir-Polder interaction leads to the conclusion that at short separations the corrections due to the dynamic polarizability of an atom play a more important role than—and suppress—the corrections due to the nonideality of the metal wall. By comparison of the exact atomic polarizabilities with those in the framework of the single oscillator model, it is shown that the obtained asymptotic expressions enable calculation of the free energy and force for the atom-wall interaction under real conditions with a precision of 1%.

We propose a double-well configuration for optical trapping of ultracold two-species Fermi-Bose atomic mixtures. Two signatures of macroscopic quantum coherence attributable to a superfluid phase transition for the Fermi gas are analyzed. The first signature is based upon tunneling of Fermi pairs when the power of the deconfining laser beam is significantly reduced. The second relies on the observation of interference fringes in a regime where the fermions are trapped in two sharply separated minima of the potential. Both signatures rely on small decoherence times for the Fermi samples, which should be possible by reaching low temperatures using a Bose gas as a refrigerator, and a bichromatic optical dipole trap for confinement, with optimal heat-capacity matching between the two species.

The entropy and kinetic, potential, and interaction energies of an atomic Fermi gas in a trap are studied under the assumption of thermal equilibrium for finite temperature. A Feshbach resonance can cause the fermions to pair into diatomic molecules. The entropy and energies of mixtures of such molecules with unpaired atoms are calculated, in relation to recent experiments on molecular Bose-Einstein condensates produced in this manner. It is shown that, starting with a Fermi gas of temperature $T=0.1T_F^0$, where $T_F^0$ is the noninteracting Fermi temperature, an extremely cold degenerate Fermi gas of temperature $T\lesssim 0.01T_F^0$ may be produced without further evaporative cooling. This requires adiabatic passage of the resonance, subsequent sudden removal of unpaired atoms, and adiabatic return. We also calculate the ratio of the interaction energy to the kinetic energy, a straightforward experimental signal which may be used to determine the temperature of the atoms and indicate condensation of the molecules.

We present a local-field theory for spin and diamagnetism in linear and nonlinear optics. We examine all the processes contained in the Pauli Hamiltonian and its corresponding microscopic current density, including the terms depending on the electron spin. The resulting general real-space conductivities are presented and discussed. To quantify the implications of including the spin, we study the linear and nonlinear optical properties of free-electron metals, represented by the screened homogeneous electron gas. The real-space formalism is transformed into Fourier space, and the symmetries of the linear and nonlinear optical conductivities in a homogeneous electron gas are discussed. Numerical results are presented for the homogeneous electron gas, in which we treat $\omega$ and $q$ as independent variables, thereby opening the theory to near-field optics and the study of evanescent waves. We show that in regions of the $\omega$-$q$ spectrum, the presence of diamagnetism and spin dynamics significantly alters the response in comparison to considering only the paramagnetic response. Additionally, we discuss the effects of screening, and we finish our treatment by a discussion of how to connect the present theory to existing methods in ab initio solid-state physics.

In a recent work, Bastin and Martin [Phys. Rev. A 67, 053804 (2003)] analyzed the quantum theory of the mazer in the off-resonant case. However, our analysis of this case refutes their claim by showing that their evaluation of the coupled equations for the off-resonant case is not satisfactory. The correct expression can be obtained by applying appropriate formulas for the involved dressed-state parameters.

We refute in this Reply the criticisms made by Abdel-Aty. We show that none of them are founded and we demonstrate very explicitly what is wrong with the arguments developed by this author.

Cross sections differential in target orientation angle were measured for $19\mathrm{MeV}$ ${\mathrm{F}}^{8+}+{\mathrm{D}}_2$ collisions. Multihit position-sensitive detectors were used to isolate the double-ionization channel and determine a posteriori the full momentum vectors of both ejected ${\mathrm{D}}^{+}$ fragments. A strong dependence of the double ionization cross section on the angle between the incident ion direction and the target molecular axis is observed with a $\approx 3.5:1$ enhancement for molecules aligned perpendicular to the projectile axis. This clear asymmetry is attributed to interference effects, analogous to Young’s two-slit experiment, arising from coherent contributions to the ionization from both atomic centers. The data are compared to a simple scattering model based on two center interference.

An atom-surface interaction was detected by studying atom diffraction from a rotated material grating. A phasor diagram similar to the Cornu spiral was developed to explain why there are no missing orders in atom diffraction from material gratings. We also show that atom-surface interactions combined with rotated grating structures can produce asymmetric, i.e., blazed, diffraction patterns. Our conceptual discussion is supported by experimental observations with a sodium atom beam and silicon nitride gratings. The data are consistent with the nonretarded van der Waals interaction.

Numerical path integral calculations are performed to study the behavior of a dissipative two-level system driven by a strong monochromatic oscillatory field. It is shown that the population of an initially localized state displays persistent high-frequency oscillations at weak dissipation and low temperature. The oscillation amplitudes exhibit intricate patterns as the field parameters are varied. The observed behavior is an extension of the quantum stochastic resonance phenomenon outside the weak-field regime.

Multiphoton entanglement in the same polarization has been theoretically shown to be obtainable by type-I spontaneous parametric down-conversion (SPDC), which can generate bright pulses more easily than type-II SPDC. A quantum cryptographic protocol utilizing photon number coding of the detected type-I entangled multiphotons is described. The information capacity versus photon number is calculated after considering the transmission loss inside the optical fiber and the detector efficiency, considering possible attacks to the scheme. The result thus achieved compares very favorably with all other schemes employing entanglement.

We discuss a procedure of measurement followed by the reproduction of the quantum state of a three-level optical system—a frequency—and spatially degenerate two-photon field. The method of statistical estimation of the quantum state based on solving the likelihood equation and analyzing the statistical properties of the obtained estimates is developed. Using the root approach of estimating quantum states, the initial two-photon state vector is reproduced from the measured fourth moments in the field. The developed approach applied to quantum-state reconstruction is based on the amplitudes of mutually complementary processes. The classical algorithm of statistical estimation based on the Fisher information matrix is generalized to the case of quantum systems obeying Bohr’s complementarity principle. It has been experimentally proved that biphoton-qutrit states can be reconstructed with the fidelity of 0.995–0.999 and higher.

The Rydberg-state decay dynamics of carbon disulfide $\left(\mathrm{C}{\mathrm{S}}_2\right)$ has been investigated by $(2+1^{\prime })$ resonance-enhanced multiphoton ionization with the pump-probe technique (pump wavelength $266\mathrm{nm}$ and probe wavelength $400\mathrm{nm}$) on our homebuilt femtosecond laser system. The $\mathrm{C}{\mathrm{S}}_2$ is pumped into Rydberg state $6s{\sigma }_g$ by two $266\text{−}\mathrm{nm}$ photons, corresponding to the excitation energy $9.4\mathrm{eV}$, and then ionized by temporally delayed $400\text{−}\mathrm{nm}$ pulse. The $\mathrm{C}{\mathrm{S}}_2$ ion yield dependence on the time delay determines the excited-state lifetime to be $409\pm 6\mathrm{fs}$ for ${\mathrm{C}}^{32}{\mathrm{S}}^{32}\mathrm{S}$ and $441\pm 7\mathrm{fs}$ for ${\mathrm{C}}^{32}{\mathrm{S}}^{34}\mathrm{S}$, respectively, at $265\mathrm{nm}$ pump and the isotopically averaged lifetime $1034\pm 31\mathrm{fs}$ at $267.5\mathrm{nm}$ pump. The wavelength dependence of the lifetime may be due to the effect of electron spin on the potential energy surface—namely, separately subjected to two different mechanisms: internal conversion and intersystem crossing interaction.

Absolute differential cross sections are reported for electron capture and loss by $(1–5)\text{−}\mathrm{keV}$ oxygen atoms incident on He, ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, and ${\mathrm{O}}_2$ for scattering angles between 0.02° and 1.73° in the laboratory frame. The form of the differential cross sections is seen to vary significantly with energy and between different targets. Differences between the present O-atom electron-loss cross sections and those for H atoms reported previously imply that the underlying physical mechanism may not be the same. The integral cross sections, also reported here, are consistent with most previous studies. The consensus of the available electron-loss data suggests that the cross sections of Fogel et al. [Soviet Phys. JETP 35, 601 (1959)] are in error.

An analytic response theory formulation for the leading-order magnetic field-induced and field-dependent quadrupole splitting in nuclear magnetic resonance spectra is presented and demonstrated with first-principles calculations for ${}^{21}\mathrm{Ne}$, ${}^{36}\mathrm{Ar}$, and ${}^{83}\mathrm{Kr}$ in noble gas atoms. The case of molecules was studied for ${}^{33}\mathrm{S}$ in the sulphur hexafluoride molecule, as well as for ${}^{47∕49}\mathrm{Ti}$, ${}^{91}\mathrm{Zr}$, and ${}^{177,179}\mathrm{Hf}$ in group(IV) tetrahalides. According to our calculations, the hitherto experimentally unknown field-induced quadrupole splitting in molecules rises to ${10}^2\mathrm{Hz}$ for ${}^{177,179}\mathrm{Hf}$ nuclei in ${\mathrm{HfF}}_4$ and ${10}^1\mathrm{Hz}$ for ${}^{47∕49}\mathrm{Ti}$ in ${\mathrm{TiCl}}_4$, and is hence of observable magnitude.

We report results of quantum Monte Carlo calculations of the ground state of dilute Fermi gases with attractive short-range two-body interactions. The strength of the interaction is varied to study different pairing regimes which are characterized by the product of the $s$-wave scattering length and the Fermi wave vector, $a{k}_F$. We report results for the ground-state energy, the pairing gap $\Delta$, and the quasiparticle spectrum. In the weak-coupling regime, $1∕a{k}_F<-1$, we obtain Bardeen-Cooper-Schrieffer (BCS) superfluid and the energy gap $\Delta$ is much smaller than the Fermi gas energy $E_{\mathrm{FG}}$. When $a>0$, the interaction is strong enough to form bound molecules with energy $E_{\mathrm{mol}}$. For $1∕a{k}_F\gtrsim 0.5$, we find that weakly interacting composite bosons are formed in the superfluid gas with $\Delta$ and gas energy per particle approaching $\mid E_{\mathrm{mol}}\mid ∕2$. In this region, we seem to have Bose-Einstein condensation (BEC) of molecules. The behavior of the energy and the gap in the BCS-to-BEC transition region, $-0.5<1∕a{k}_F<0.5$, is discussed.

We examine the phase diagram of a Bose-Einstein condensate of atoms, interacting with an attractive pseudopotential, in a quadratic-plus-quartic potential trap rotating at a given rate. Investigating the behavior of the gas as a function of interaction strength and rotational frequency of the trap, we find that the phase diagram has three distinct phases: one with vortex excitation, one with center-of-mass excitation, and an unstable phase in which the gas collapses.

It is shown that matter solitons can be effectively managed by means of smooth variations of parameters of optical lattices in which the condensate is loaded. The phenomenon is based on the effect of lattice modulations on the carrier wave transporting the soliton and that is why it is well understood in terms of the effective mass approach, where a particular spatial configuration of the band structure is of primary importance. Linear, parabolic, and spatially localized modulations are considered as case examples. It is shown that these defects can originate an accelerating and oscillating motion of matter solitons as well as they can simulate soliton interactions with attractive and repulsive defects.

Topological phase imprinting is a unique technique for vortex formation in a Bose-Einstein condensate (BEC) of an alkali-metal gas, in that it does not involve rotation: the BEC is trapped in a quadrupole field with a uniform bias field which is reversed adiabatically leading to vortex formation at the center of the magnetic trap. The scenario has been experimentally verified by Leanhardt et al. employing ${}^{23}\mathrm{Na}$ atoms. Recently similar experiments have been conducted by Hirotani et al. in which a BEC of ${}^{87}\mathrm{Rb}$ atoms was used. In the latter experiments the authors found that fine-tuning of the field reverse time $T_{\mathrm{rev}}$ is required to achieve stable vortex formation. Otherwise, they often observed vortex fragmentation or a condensate without a vortex. It is shown in this paper that this behavior can be attributed to the heavy mass of the $\mathrm{Rb}$ atom. The confining potential, which depends on the eigenvalue $m_B$ of the hyperfine spin $\mathit{F}$ along the magnetic field, is now shifted by the gravitational field perpendicular to the vortex line. Then the positions of two weak-field-seeking states with $m_B=1$ and 2 deviate from each other. This effect is more prominent for BECs with a heavy atomic mass, for which the deviation is greater and, moreover, the Thomas-Fermi radius is smaller. We found, by solving the Gross-Pitaevskii equation numerically, that two condensates interact in a very complicated way leading to fragmentation of vortices, unless $T_{\mathrm{rev}}$ is properly tuned.

We present a detailed finite-temperature Hartree-Fock-Bogoliubov (HFB) treatment of the two-dimensional trapped Bose gas. We highlight the numerical methods required to obtain solutions to the HFB equations within the Popov approximation, the derivation of which we outline. This method has previously been applied successfully to the three-dimensional case and we focus on the unique features of the system which are due to its reduced dimensionality. These can be found in the spectrum of low-lying excitations and in the coherence properties. We calculate the Bragg response and the coherence length within the condensate in analogy with experiments performed in the quasi-one-dimensional regime [Richard et al., Phys. Rev. Lett. 91, 010405 (2003)] and compare to results calculated for the one-dimensional case. We then make predictions for the experimental observation of the quasicondensate phase via Bragg spectroscopy in the quasi-two-dimensional regime.