We present a three-dimensional quantum-mechanical theory of radio-frequency-outcoupled atom lasers from trapped atomic gases in the presence of the gravitational force. Predictions for the total outcoupling rate as a function of the radio frequency and for the beam wave function are given. We establish a sum rule for the energy-integrated outcoupling, which leads to a separate determination of the coupling strength between the atoms and radiation field. For a noninteracting Bose-Einstein condensate analytic solutions are derived which are subsequently extended to include the effects of atomic interactions. The interactions enhance interference effects in the beam profile and modify the outcoupling rate of the atom laser. We provide a complete quantum-mechanical solution which is in line with experimental findings and allows us to determine the validity of commonly used approximative methods. We also extend the formalism to a fermionic atom laser and analyze the effect of superfluidity on the outcoupling of atoms.

The interaction of a quantized field with three-level atoms in a $\Lambda$ configuration inside a two mode cavity is analyzed. We calculate the stationary quadrature noise spectrum of the field outside the cavity in the case where the input probe field is in a squeezed state and the atoms show electromagnetically induced transparency. If the Rabi frequencies of both dipole transitions of the atoms are different from zero, we show that the output probe field has four maxima of squeezing absorption. We show that in some cases two of these frequencies can be very close to the transition frequency of the atom, in a region where the mean value of the field entering the cavity is hardly altered. Furthermore, part of the absorbed squeezing of the probe field is transferred to the pump field. For some conditions this transfer of squeezing can be complete.

It is proven that recently introduced states with perfectly secure bits of cryptographic key (private states representing secure bit) [K. Horodecki et al., Phys. Rev. Lett. 94, 160502 (2005)] as well as its multipartite and higher dimension generalizations always represent distillable entanglement. The corresponding lower bounds on distillable entanglement are provided. We also present a simple alternative proof that for any bipartite quantum state entanglement cost is an upper bound on a distillable cryptographic key in a bipartite scenario.

We present measurements of the temperature-dependent momentum distribution of a trapped Fermi gas consisting of ${}^{40}\mathrm{K}$ in the BCS to Bose-Einstein condensation crossover regime. Accompanying theoretical results based upon a simple mean-field ground state are compared to the experimental data. Nonmonotonic effects associated with temperature $T$ arise from the competition between thermal broadening and a narrowing of the distribution induced by the decrease in the excitation gap $\Delta \left(T\right)$ with increasing $T$.

A simple analytic decomposition of the spatially entangled two-photon field allows us to generalize the earlier results of Law and Eberly [Phys. Rev. Lett. 92, 127903 (2004)] to more realistic experimental geometries of spontaneous parametric down-conversion. We quantify analytically how spatial filtering reduces the Schmidt number or dimensionality of the two-photon entanglement from a “generated” value to a generally much lower “usable or detected” value, for both collinear and noncollinear phase matching. We also discuss the intimate relation between the (two-photon) Schmidt number and the classical (one-photon) concept of etendue or geometric extent.

We examine dense coding with an arbitrary pure entangled state sharing between the sender and the receiver. Upper bounds on the average success probability in approximate dense coding and on the probability of conclusive results in unambiguous dense coding are derived. We also construct the optimal protocol which saturates the upper bound in each case.

We have measured the energy differential transition probabilities for the two-photon decay of $K$ vacancies in gold atoms (nuclear charge $Z=79$). This is the heaviest atom for which this information has been obtained, and so is most sensitive to relativistic effects. The experiment determined the shape of the continuum radiation for the transitions $2s\to 1s$, $3s\to 1s$, $3d\to 1s$, and $(4s+4d)\to 1s$ at an emission pair opening angle $\theta =\pi ∕2$. Our results for $3d\to 1s$ and $(4s+4d)\to 1s$ extend to energies above and below the region of the intermediate state resonances. No relativistic calculations exist for Au, so we compare with calculations by Mu and Crasemann and Tong et al. for $\mathrm{Ag}(Z=47)$ and $\mathrm{Xe}(Z=54)$. For equal-energy, back-to-back two-photon decay, the calculations show an increase in transition probability with $Z$ for the $2s\to 1s$ and $3d\to 1s$ transitions. In contrast, our data, at $Z=79$, corrected for the angular distribution, give a smaller transition probability than the lower-$Z$ experimental results of Ilakovac et al. and Mokler et al. for Ag and Xe. The shapes of the two-photon continua in our data are in general agreement with theory except that we find anomalously high values for the differential two-photon transition probability for the $3s\to 1s$ transition near $y=0.35$, where $y$ is the fraction of the transition energy carried by the lower-energy photon.

In the wake of successful experiments in Fermi condensates, experimental attention is broadening to study resonant interactions in degenerate Bose-Fermi mixtures. Here, we consider the properties and stability of the fermionic molecules that can be created in such a mixture near a Feshbach resonance. To do this, we consider the two-body scattering matrix in the many-body environment, and assess its complex poles. The stability properties of these molecules strongly depend on their center-of-mass motion, because they must satisfy Fermi statistics. At low center-of-mass momenta the molecules are more stable than in the absence of the environment (due to Pauli-blocking effects), while at high center-of-mass momenta nontrivial many-body effects render them somewhat less stable.

The theory of ordinary differential equations together with judicious use of boundary conditions and certain properties of higher transcendental functions is exploited to derive a useful analytical expression for the Coulomb-Yamaguchi Jost solution through an $r$-space approach to the problem. Note that the off-shell Jost solution is expressed in its maximal reduced form involving confluent and Gaussian hypergeometric functions. As an application of the Jost solution the off-shell $T$ matrix is also expressed in terms of Gaussian hypergeometric functions.

High-resolution $\mathrm{S}2p^{-1}$ photoelectron spectra and $\mathrm{S}2p^{-1}\to X{}^{1}A_1\left(2b_1^{-2}\right)$ normal Auger electron spectra (AES) of ${\mathrm{H}}_2\mathrm{S}$ were measured for various photon energies in the range from 180 to $240\mathrm{eV}$. The equilibrium geometry, vibrational energies $\hslash \omega$, and anharmonicities $x\hslash \omega$, for the $\mathrm{S}2p^{-1}$ intermediate and $X{}^{1}A_1\left(2b_1^{-2}\right)$ final states were derived from the energy splittings and the intensity distributions of the vibrational substates. The relative intensities of the various $\mathrm{S}2p^{-1}\to X{}^{1}A_1\left(2b_1^{-2}\right)$ normal Auger transitions as well as the lifetimes of the various $\mathrm{S}2p^{-1}$ core-ionized states were also derived. In addition to the $\mathrm{S}2p^{-1}\to X{}^{1}A_1\left(2b_1^{-2}\right)$ transitions, some weak structures were observed in the AES, with intensities that exhibit pronounced photon-energy dependences.

We consider the population inversion in a two-level system generated by a sub-one-cycle pulse excitation. Specifically, we explore the effect that the time derivative of the pulse envelope has on the Rabi dynamics. Our analysis is based on a combination of analytical, perturbative, and nonperturbative treatments and is complemented by numerical simulations. We find a shortening of the Rabi inversion period and show that complete inversion is unobtainable under resonant, ultrashort pulse conditions. The impact of nonresonant and carrier-envelope phase-dependent effects on the dynamics of two-level and multilevel systems is studied numerically, and conditions for complete population inversion are derived.

The possible excitation of angular degrees of freedom of pseudo-spin-1/2 $N-boson$ systems has been considered. For this purpose, the analytical forms of the fractional parentage coefficients have been introduced to deal with the symmetry problems involved. A set of equations for the Yrast band has been derived, and related numerical calculation has been performed. The yrast band is found to contain $N∕2$ subbands specified by the total spin $S$ ranging from $N∕2$ to 0 or 1/2, the one with a larger $S$ is lower. The states in a subband are further specified by the total orbital angular momentum $L$. Each state is a fragmented state (except the lowest one), where a part of particles have been excited and may form vortex. Specifically, the structure of the yrast band appears to obey the Hund's first and second rules.

The paradigm of Bose-Einstein condensation has been associated with zero momentum to which a macroscopic fraction of bosons condense. Here we propose a new quantum state where bosonic alkali-metal atoms condense at nonzero momenta, defying the paradigm. This becomes possible when the atoms are confined in the $p$-orbital Bloch band of an optical lattice rather than the usual $s$-orbital band. The new condensate simultaneously forms an order of transversely staggered orbital currents, reminiscent of orbital antiferromagnetism or $d$-density wave in correlated electronic systems but different in fundamental ways. We discuss several approaches of preparing atoms to the $p$-orbital band and propose an “energy blocking” mechanism by Feshbach resonance to protect them from decaying to the lowest $s$-orbital band. Such a model system seems very unique and novel to atomic gases. It suggests a new concept of quantum collective phenomena of no prior example from solid state materials.

We analyze the evolution of superfluidity for nonzero orbital angular momentum channels from the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein condensation (BEC) limit in three dimensions. First, we analyze the low-energy scattering properties of finite range interactions for all possible angular momentum channels. Second, we discuss ground-state $(T=0)$ superfluid properties including the order parameter, chemical potential, quasiparticle excitation spectrum, momentum distribution, atomic compressibility, ground-state energy, and low-energy collective excitations. We show that a quantum phase transition occurs for nonzero angular momentum pairing, unlike the $s$-wave case where the BCS to BEC evolution is just a crossover. Third, we present a Gaussian fluctuation theory near the critical temperature $(T=T_{\mathrm{c}})$, and we analyze the number of bound, scattering, and unbound fermions as well as the chemical potential. Finally, we derive the time-dependent Ginzburg-Landau functional near $T_{\mathrm{c}}$, and compare the Ginzburg-Landau coherence length with the zero-temperature average Cooper pair size.

The determination of the time scale for coherent and incoherent tunneling in asymmetric double-well potentials is reconsidered according to the instanton-bounce method. In particular, by making use of Feynman’s transition elements, a different, relatively simpler approach to this problem, with respect to conventional quantum-mechanical treatments, is obtained.

The absolute total cross section (TCS) for electron collisions with tetrahydrofuran ${\mathrm{C}}_4{\mathrm{H}}_8\mathrm{O}$ in the gas phase has been measured using the linear transmission technique within $1–370\mathrm{eV}$ energy range. The total cross section function for $e^{-}\text{−}{\mathrm{C}}_4{\mathrm{H}}_8\mathrm{O}$ collisions is characterized by the relatively high magnitude and the broad enhancement spanned between 4 and $12\mathrm{eV}$, with some resonantlike structures. This enhancement can be explained as a result of overlapping core-excited resonances. At higher collision energies the magnitude of the measured total cross section monotonically decreases with the energy increase. At low impact energies some additional weak resonant features are visible near 1.9 and $3.5\mathrm{eV}$. The reported TCS results are higher by 30% than recently published by Zecca et al. [J. Phys. B 38, 2079 (1995)]. They are also distinctly different from the recent $R$-matrix calculations. At intermediate energy range the present data agree well with the sum of calculated elastic and ionization cross sections.

We discuss the mechanical momentum transfer to two-level atoms by a pair of short, counterpropagating, frequency-chirped laser pulses, which partially overlap each other in the atomic medium. We show that such a pulse pair can induce a much greater change of momentum than pulses that do not overlap (interact separately with the atoms). The dispersive effect on the atomic velocity distribution is shown to be much smaller for the case of overlapping pulses. Furthermore, there are regimes where the method is not sensitive to the exact values of the pulse parameters or the initial velocity distribution. The interaction can be repeated for a cumulative effect, so a sequence of such pulse pairs can be used very effectively to manipulate the mechanical motion of atoms.

The transmissions of matter-wave solitons through linear and nonlinear inhomogeneities induced by the spatial variations of the trap and the scattering length in Bose-Einstein condensates are investigated. The enhanced transmission of a soliton through a linear trap by a modulation of the scattering length, is exhibited. The theory is based on the perturbed inverse scattering transform for solitons, and we show that radiation effects are important. Numerical simulations of the Gross-Pitaevskii equation confirm the theoretical predictions.

We study theoretically the few-body dynamics of atoms which leak out of a trap by tunneling through a thin barrier. We consider the two cases of bosons with strongly repulsive contact interactions and spinless fermions with strongly attractive contact interactions (Bose and Fermi Tonk-Girardeau gases, respectively). The tunneling is studied as a function of the number of particles $N$ and the barrier opacity. The fermionic case reproduces a nonexponential decay of a single particle, but with a signal enhanced by a factor of $N$. In the bosonic case, we find a different regime of nonexponential decay due to the contribution of different resonances of the trap. The relevant physical realization is that of atoms confined to an optical box with an end-cap laser barrier, and the prospects for future experiments are discussed.