We analyze some aspects of the fluidity of Bose-Einstein (BE) condensed systems. We show that a two-fluid picture of a condensed system holds true. The condensate is a quantum fluid component of the system. This component of the fluid satisfies the continuity equation and a generalized Bernoulli equation. Under certain conditions, the condensate component becomes a classical superfluid. We suggest that condensed systems might exhibit mechanochalorical and thermomechanical effects, in close analogy with superfluid helium-4. Quantized vortices are also expected to appear in a BE condensed system. We discuss the structure of quantized vortices.

We investigate systematically pump-probe spectroscopy of cold ${}^{87}\mathrm{Rb}$ atoms produced by a magneto-optical trap. The pump-probe spectra are measured without the presence of the trapping beams or any optical molasses. Various polarization configurations of the probe and pump fields result in very different spectra of probe absorption. The observed spectra exhibit a dispersive profile, a dispersionlike profile, a Lorentzian profile, or a dispersive profile plus a Lorentzian profile. The widths of all the spectral profiles are narrower than the natural linewidth of the excited state. Our work clarifies the mechanisms behind these different spectral profiles and provides essential information for the pump-probe spectroscopy of cold atoms.

The spontaneous-emission rate of a radiating atom reaches its time-independent equilibrium value after an initial transient regime. In this paper, we consider the associated relaxation effects of the spontaneous-decay rate of atoms in dispersive and absorbing dielectric media for atomic-transition frequencies near material resonances. A quantum mechanical description of such media is furnished by a damped-polariton model in which absorption is taken into account through coupling to a bath. We show how all field and matter operators in this theory can be expressed in terms of the bath operators at an initial time. The consistency of these solutions for the field and matter operators are found to depend on the validity of certain velocity sum rules. The transient effects in the spontaneous-decay rate are studied with the help of several specific models for the dielectric constant, which are shown to follow from the general theory by adopting particular forms of the bath coupling constant.

The nuclear forward scattering of synchrotron radiation (SR) of two spatially separated stainless-steel foils has been investigated. Immediately after the SR pulse a nuclear exciton extending over both targets is formed, which then decays under the influence of radiative coupling of the nuclear oscillators both within and between the targets. Cooling one target to low temperatures causes the Mössbauer linewidth to increase by inhomogeneous broadening, which leads to a rapid dephasing of the nuclear oscillators of this system. In general, the influence of the radiation field of the upstream oscillators on the oscillators of the downstream target causes the latter to radiate at a high decay rate (steep slope) at early times. Surprisingly, for the combined targets, the initial decay can be less steep than that of the inhomogeneously broadened sample alone if this broadening is sufficiently large. In addition, when the upstream oscillators are broadened in energy they may cause the downstream oscillators to emit only very little intensity at late times. In the experiments, this influence on the downstream sample was changed by varying the inhomogeneous resonance broadening and the resonance frequencies of the targets. Drastic changes of the time evolution of the nuclear forward scattering were observed, which are discussed within the dynamical theory.

We present a time-dependent calculation for four-wave mixing using a combination of long, short, and time delayed laser pulses in the context of electromagnetically induced transparency. Two transform limited nanosecond lasers are used to create a highly coherent mixture of the ground state and an excited state via a two-photon process. Once the induced transparency is established, a laser with short pulse length is injected after a suitable delay to generate four-wave mixing. We show that the wave mixing process is phase matched for all detunings, and with appropriately selected atomic coherence and populations, near 100% photon flux conversion efficiency can be obtained, independent of the intensity of the short pulse laser. In addition, we show that for small detunings for the short pulse laser, the four-wave mixing field travels with the speed of light in vacuum and suffers no pulse distortion even though the medium is highly dispersive at the frequency of the generated wave. These advantages open a door for future applications of the scheme for highly efficient, very stable UV generation.

The recently reported precise experimental determination of the dipole polarizability of the ${\mathrm{H}}_2^{+}$ molecular ion ground state [P.L. Jacobson, R.A. Komara, W.G. Sturrus, and S.R. Lundeen, Phys. Rev. A 62, 012509 (2000)] reveals a discrepancy between theory and experiment of about ${0.0007a}_0^3,$ which has been attributed to relativistic and QED effects. In the present work we analyze an influence of the relativistic effects on the scalar dipole polarizability of an isolated ${\mathrm{H}}_2^{+}$ molecular ion. Our conclusion is that it accounts for only 1/5 of the measured discrepancy.

We describe a dramatic decrease of the critical velocity in elongated cylindrical Bose-Einstein condensates which originates from the nonuniform character of the radial density profile. We discuss this mechanism with respect to recent measurements at MIT.

Correction to the hyperfine constant $A$ of an external $s-\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{n}$ in many-electron atom caused by the Breit interaction is calculated analytically: $\delta A/A=0.68Z{\alpha }^2.$ The physical mechanism for this correction is polarization of the internal electronic shells (mainly ${1s}^2$ shell) by the magnetic field of the external electron. This mechanism is similar to the polarization of vacuum considered by Karplus and Klein [Phys. Rev. 85, 972 (1952)] long time ago. The similarity is the reason why in both cases (Dirac sea polarization and internal atomic shells polarization) the corrections have the same dependence on the nuclear charge and fine-structure constant. In conclusion we also discuss $Z{\alpha }^2$ corrections to the parity violation effects in atoms.

The vibrational structure of the $\mathrm{O}\hspace{0.5em}{1s}^{-1}{2b}_2$ core-excited state of ${\mathrm{H}}_2\mathrm{O}$ is observed and ascribed to the mixture of symmetric stretching and bending motions with $a_1$ symmetry. The formation of ${\mathrm{H}}_2^{+}$ is found to increase linearly with an increase in energy stored in the nuclear motion of the $\mathrm{O}\hspace{0.5em}{1s}^{-1}{2b}_2$ state, demonstrating that this dissociation channel is mediated by the nuclear motion in the core-excited state. The reaction pathway to the ${\mathrm{H}}_2^{+}$ formation along the Auger final state of ${\mathrm{H}}_2{\mathrm{O}}^{+},$ mediated by the nuclear motion before the Auger decay, is discussed with the help of ab initio potential surfaces of the Auger final states.

We present an optimal control approach to the process of molecular isotope separation by exciting vibrational wave packets with femtosecond laser pulses. In the weak-field limit, we developed an optimization procedure for designing shaped laser pulses leading to the best selectivity in the two-photon ionization processes. Several control scenarios are identified, which mainly belong to two groups. The first takes advantage of the revival phenomenon, which allows one to find times at which excited wave packets of different isotopes are well localized and spatially separated in the intramolecular space. The second is based on isotopically selective quantum interference between several wave packets excited in the same molecular potential by a designed sequence of laser pulses. Simulations have been done for the isotopic mixture of ${}^{79}{\mathrm{Br}}_2$ and ${}^{81}{\mathrm{Br}}_2$ molecules, which was used in the first experiments on wave-packet isotope separation.

The level population of the hydrogen molecule is dramatically altered due to quantum interference, when the molecules are illuminated by two fields (coherent and squeezed) simultaneously. The molecules from the $B{}^1{\Sigma }_u\mathrm{}(v=0,j=1\mathrm{})\mathrm{}$ is excited stepwise to the level of same symmetry, $B{}^1{\Sigma }_u\mathrm{}(v=20,j=1\mathrm{})\mathrm{}$ by nondegenerate optical oscillator via an intermediate $E,F{}^1{\Sigma }_g\mathrm{}(v=8,j=0\mathrm{}),$ and directly by a two-photon transition by a ${\mathrm{CO}}_2$ laser. The population of the states are also affected by the correlation developed between the two modes of the squeezed field. The correlation and the quantum interference jointly affect the molecules in such a way that the inversion of population occurs periodically. This feature can further be used for studying lasing and other important optical activities.

In this Brief Report we discuss entanglement of multiparticle quantum systems. We propose a potential measure of a type of entanglement of pure states of $n$ qubits, the $n-\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}.$ For a system of two qubits the $n-\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}$ is equal to the square of the concurrence, and for systems of three qubits it is equal to the “residual entanglement.” We show that the $n-\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}$ is also equal to a generalization of the concurrence squared for even $n,$ and use this fact to prove that the $n-\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}$ is an entanglement monotone. However, the $n-\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}$ is undefined for odd $n>\mathrm{}3.\mathrm{}$ Finally, we propose a measure related to the $n-\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}$ for mixed-state systems of $n$ qubits, and find an analytical formula for this measure for even $n.\mathrm{}$

The close-coupling theory of electron-impact ionization of helium is studied. It is found that the “raw” convergent close-coupling equal-energy-sharing amplitudes converge to half the required amplitudes. As in the $e-\mathrm{H}$ case, solving the close-coupling equations yields amplitudes that behave as results of a finite Fourier expansion of a step function. We argue that the close-coupling formalism readily solves the $e-\mathrm{He}$ ionization problem with equal-energy outgoing electrons at all practical incident energies, and demonstrate it at the most difficult kinematic case of 2 eV above threshold.

We study the near-threshold $\left(\overrightarrow{E}0\right)$ behavior of quantum systems described by an attractive or repulsive ${1/r}^2$ potential in conjunction with a shorter-ranged ${1/r}^m$ $\mathrm{}(m>\mathrm{}2\mathrm{})\mathrm{}$ term in the potential tail. For an attractive ${1/r}^2$ potential supporting an infinite dipole series of bound states, we derive an explicit expression for the threshold value of the pre-exponential factor determining the absolute positions of the bound-state energies. For potentials consisting entirely of the attractive ${1/r}^2$ term and a repulsive ${1/r}^m$ term, the exact expression for this prefactor is given analytically. For a potential barrier formed by a repulsive ${1/r}^2$ term (e.g., the centrifugal potential) and an attractive ${1/r}^m$ term, we derive the leading near-threshold behavior of the transmission probability through the barrier analytically. The conventional treatment based on the WKB formula for the tunneling probability and the Langer modification of the potential yields the right energy dependence, but the absolute values of the near-threshold transmission probabilities are overestimated by a factor which depends on the strength of the ${1/r}^2$ term (i.e., on the angular momentum quantum number $l)$ and on the power m of the shorter ranged ${1/r}^m$ term. We derive a lower bound for this factor. It approaches unity for large l, but it can become arbitrarily large for fixed l and large values of m. For the realistic example $l=1\mathrm{}$ and $m=6\mathrm{}$, the conventional WKB treatment overestimates the exact near-threshold transmission probabilities by at least 38%.

In this paper, we present the experimental realization of multiqubit gates ${\Lambda }_n($NOT) in macroscopic ensemble of three-qubit and four-qubit molecules. Instead of depending heavily on the two-bit universal gate, which served as the basic quantum operation in quantum computing, we use pulses of well-defined frequency and length that simultaneously apply to all qubits in a quantum register. It appears that this method is experimentally convenient when this procedure is extended to more qubits on some quantum computation, and it can also be used in other physical systems.

The collisional system ${\mathrm{Si}}^{4+}+\mathrm{He}$ has been studied over a range of mean relative ion kinetic energy going from ${10}^{-2}$ to ${10}^2\mathrm{e}\mathrm{V}/\mathrm{a}\mathrm{m}\mathrm{u}.$ In the low-energy range, a time-dependent wave-packet approach is used both in the diabatic and the adiabatic representation using two different propagator techniques. The agreement between the two sets of results assess the accuracy of the present numerical approach. Above 2.5 eV/amu., a semiclassical eikonal calculation is performed, which includes the Coriolis couplings. Finally, the rate constant is calculated and compared with the other theoretical data as well as with the experimental value of [Fang and Kwong, Phys. Rev. A 59, 342 (1999)]. The present results confirm the order of magnitude of previous theoretical values.

We investigate the conversion of a Bose-Einstein condensate (BEC) of a weakly interacting gas into a molecular BEC (MBEC) by Bose-stimulated Raman adiabatic passage (STIRAP). This method of producing an MBEC does not experience large spontaneous losses while the condensate is in an excited electronic state, and it is robust with respect to small changes in the physical parameters. We show that the atomic interactions affect the quantum statistics of the resulting field, although they do not interfere with the production of the MBEC. We demonstrate that STIRAP is still feasible when we include the spatial degrees of freedom that cause the Bose-enhanced coupling rate to vary across the condensate. The complete conversion is destroyed by spatial effects unless the time scale of the coupling is much faster than the propagation time, which in practice requires submillisecond conversion.

In three-dimensional trapped Bose-Einstein condensate (BEC), described by the time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of initial conditions on stability using a Gaussian variational approach and exact numerical simulations. We also discuss the validity of the criterion for stability suggested by Vakhitov and Kolokolov. The maximum initial chirp (initial focusing defocusing of cloud) that can lead a stable condensate to collapse even before the number of atoms reaches its critical limit is obtained for several specific cases. When we consider two- and three-body nonlinear terms, with negative cubic and positive quintic terms, we have the conditions for the existence of two phases in the condensate. In this case, the magnitude of the oscillations between the two phases are studied considering sufficient large initial chirps. The occurrence of collapse in a BEC with repulsive two-body interaction is also shown to be possible.

The presence of undamped harmonic center-of-mass oscillations of a weakly interacting Bose gas in a harmonic trap is demonstrated within the dielectric formalism for a previously introduced finite-temperature approximation, including exchange. The consistency of the approximation with the Kohn theorem is thereby demonstrated. The Kohn modes are found explicitly, generalizing an earlier zero-temperature result found in the literature. It is shown how the Kohn mode disappears from the single-particle spectrum, while remaining in the density oscillation spectrum, when the temperature increases from below to above the condensation temperature.

We show that radiative coupling between two multilevel atoms having near-degenerate states can produce new interference effects in spontaneous emission. We explicitly demonstrate this possibility by considering two identical V systems each having a pair of transition dipole matrix elements that are orthogonal to each other. We discuss in detail the origin of the new interference terms and their consequences. Such terms lead to the evolution of certain coherences and excitations that would not occur otherwise. The special choice of the orientation of the transition dipole matrix elements enables us to illustrate the significance of vacuum-induced coherence in multiatom multilevel systems. These coherences can be significant in energy transfer studies.