We have calculated the two-photon above-threshold-ionization cross sections of rare-gas atoms by extreme ultraviolet (xuv) photons in the extended framework of multichannel quantum defect theory. Since free-free dipole moments do not converge in the length gauge, we have made the combined use of the length gauge for small $r$ and the acceleration gauge for large $r$. The two-photon above-threshold ionization cross sections for Xe and Ar associated with the $p^5\left[{}^{2}P_{3∕2}\right]$ and $p^5\left[{}^{2}P_{1∕2}\right]$ ionic core states are calculated to be $1.0\times {10}^{-51}{\mathrm{cm}}^4\mathrm{s}$ and $2.0\times {10}^{-51}{\mathrm{cm}}^4\mathrm{s}$, respectively, for $25\text{‐}\mathrm{eV}$ photons.

A method is proposed for a self-consistent evaluation of the coupling constant in the Gross-Pitaevskii equation without involving a pseudopotential replacement. A renormalization of the coupling constant occurs due to medium effects and the trapping potential, e.g., in quasi-1D or quasi-2D systems. It is shown that a simplified version of the Hartree-Fock-Bogoliubov approximation leads to a variational problem for both the condensate and a two-body wave function describing the behavior of a pair of bosons in the Bose-Einstein condensate. The resulting coupled equations are free of unphysical divergences. Particular cases of this scheme that admit analytical estimations are considered and compared to the literature. In addition to the well-known cases of low-dimensional trapping, crossover regimes can be studied. The values of the kinetic, interaction, external, and release energies in low dimensions are also evaluated and contributions due to short-range correlations are found to be substantial.

We present a theoretical study of the dynamical behavior of a gas made of ultracold fermionic atoms, which during their motions can collide with a much smaller number of thermal bosonic impurities. The atoms are confined inside harmonic traps and the interactions between the two species are treated as due to $s$-wave scattering with a negative scattering length modeling the ${}^{40}\mathrm{K}‐{}^{87}\mathrm{Rb}$ fermion-boson system. We set the fermions into motion by giving a small shift to their trap center and examine two alternative types of initial conditions, referring to (i) a close-to-equilibrium situation in which the two species are at the same temperature (well below the Fermi temperature and well above the Bose-Einstein condensation temperature); and (ii) a far-from-equilibrium case in which the impurities are given a Boltzmann distribution of momenta while the fermions are at very low temperatures. The dynamics of the gas is evaluated by the numerical solution of the Vlasov-Landau equations for the one-body distribution functions, supported by some analytical results on the collisional properties of a fermion gas. We find that the trapped gaseous mixture is close to the collisionless regime for values of the parameters corresponding to current experiments, but can be driven towards a collisional regime even without increasing the strength of the interactions, either by going over to heavier impurity masses or by matching the width of the momentum distribution of the impurities to the Fermi momentum of the fermion gas.

We predict the occurrence of electromagnetically induced absorption (EIA) in cycling degenerate two-level transitions where $F_e=F_g+1$ and $F_g>0$, interacting with pump and probe lasers with the same polarization. The EIA is due to transfer of population (TOP) between the Zeeman levels of the ground hyperfine state, rather than transfer of coherence (TOC) which occurs for perpendicularly polarized lasers. We model EIA-TOP using a double two-level system (TLS) which we compare with the four-level $N$ system, which models EIA-TOC. When the pump intensity is low, both models give an EIA peak at line center. The effect of introducing phase-changing collisions is studied, in the presence and absence of Doppler broadening, for both the double TLS and $N$ systems. In the presence of phase-changing collisions, the central EIA peaks are narrowed in both models and persist to higher pump Rabi frequencies than in the absence of collisions. In the double TLS, in the presence of Doppler broadening, the central EIA-TOP peak becomes narrower and does not develop a dip in its center, in contrast to the $N$ system. The central dip that appears in the Doppler-broadened EIA-TOC spectrum can be wiped out by adding phase-changing collisions. We demonstrate that EIA-TOP can be obtained for realistic atomic transitions interacting with lasers that have the same polarization.

We perform a quantum-mechanical analysis of the pendular cavity, using the positive-$P$ representation, showing that the quantum state of the moving mirror, a macroscopic object, has noticeable effects on the dynamics. This system has previously been proposed as a candidate for the quantum-limited measurement of small displacements of the mirror due to radiation pressure, for the production of states with entanglement between the mirror and the field, and even for superposition states of the mirror. However, when we treat the oscillating mirror quantum mechanically, we find that it always oscillates, has no stationary steady state, and exhibits uncertainties in position and momentum which are typically larger than the mean values. This means that previous linearized fluctuation analyses which have been used to predict these highly quantum states are of limited use. We find that the achievable accuracy in measurement is far worse than the standard quantum limit due to thermal noise, which, for typical experimental parameters, is overwhelming even at $2\mathrm{mK}$

The optical parametric process occurring in a photonic-band-gap planar waveguide is studied from the point of view of nonclassical-light generation. The nonlinearly interacting optical fields are described by the generalized superposition of coherent signals and noise using the method of operator linear corrections to a classical strong solution. Scattered backward-propagating fields are taken into account. Squeezed light as well as light with sub-Poissonian statistics can be obtained in two-mode fields under the specified conditions.

We put forward an approach for manipulating the spectral profile of entangled photon pairs. Such spectral properties are mediated by the geometry of noncollinear spontaneous parametric down-conversion and by selecting the appropriate spatial profile of the pump laser radiation. We show that one can translate spatial features imprinted in the pump beam into desired spectral profiles of the generated entangled-photon state. Particular configurations suitable for generating entangled pairs with ultranarrow spectral width and with multiple-peaked spectra are demonstrated.

A modified time-dependent perturbation theory for single-photon emission is proposed, which yields the exact photon energy for a relativistically recoiling atom. The relevant unperturbed “Hamiltonian” has stationary eigenvalues $E^2$. Its form is generalized here to hydrogenic atoms of arbitrary nuclear spins.

We propose an experimental setup for the implementation of weak measurements in the context of the gedanken experiment known as Hardy’s paradox. As Aharonov et al. [Y. Aharonov, A. Botero, S. Popescu, B. Reznik, and J. Tollaksen, Phys. Lett. A301, 130 (2002)] showed, these weak values form a language with which the paradox can be resolved. Our analysis shows that this language is indeed consistent and experimentally testable. It also reveals exactly how a combination of weak values can give rise to an apparently paradoxical result.

We use time-correlated single-photon counting techniques on a sample of ${}^{210}\mathrm{Fr}$ atoms confined and cooled in a magneto-optical trap to measure the lifetimes of the $9S_{1∕2},8P_{3∕2}$, and $8P_{1∕2}$ excited levels. We populate the $9S_{1∕2}$ level by two-photon resonant excitation through the $7P_{1∕2}$ level. The direct measurement of the $9S_{1∕2}$ decay through the $7P_{3∕2}$ level at 851 nm gives a lifetime of $107.53\pm 0.90\mathrm{ns}$. We observe the decay of the $9S_{1∕2}$ level through the $8P_{3∕2}$ level at 423 nm and the $8P_{1∕2}$ level at 433 nm down to the $7S_{1∕2}$ ground level, and indirectly determine the lifetimes of these to be $83.5\pm 1.5\mathrm{ns}$ and $149.3\pm 3.5\mathrm{ns}$, respectively.

Optical frequencies of the hyperfine components of the $D_2$ line in ${}^{133}\mathrm{Cs}$ are determined using high-resolution spectroscopy and a femtosecond laser frequency comb. A narrow-linewidth probe laser excites the $6s{}^{2}S_{1∕2}(F=3,4)\to 6p{}^{2}P_{3∕2}(F=2,3,4,5)$ transition in a highly collimated atomic beam. Fluorescence spectra are taken by scanning the laser frequency over the excited-state hyperfine structure. The laser optical frequency is referenced to a Cs fountain clock via a reference laser and a femtosecond laser frequency comb. A retroreflected laser beam is used to estimate and minimize the Doppler shift due to misalignment between the probe laser and the atomic beam. We achieve an angular resolution on the order of $5\times {10}^{-6}\mathrm{rad}$. The final uncertainties $(\sim \pm 5\mathrm{kHz})$ in the frequencies of the optical transitions are a factor of 20 better than previous results [T. Udem et al., Phys. Rev. A 62, 031801 (2000).]. We find the centroid of the $6s{}^{2}S_{1∕2}\to 6p{}^{2}P_{3∕2}$ transition to be $f_{D2}=351725718.4744\left(51\right)\mathrm{MHz}$.

We measured a spin relaxation of polarized xenon atoms in deuterated ethanol. The decay behavior depends on the magnetic dipole interaction and the electric quadrupole relaxation of deuterons. Though the cross-relaxation rate of deuteron with xenon was much less than that of proton, the enhancement of deuteron signal could be observed since the detection was performed at low magnetic fields. We define the figure of merit for a spin reservoir of solvent as the result of intensive investigation of the temperature dependence of decay rates and the solubility of xenon atoms in ethanol. For the long-term storage of a large number of polarized xenon atoms, it is important to take into account the viscosity of solvent which affects the translational motion as well as the decay time. By a time-resolved chemical-shift imaging, we observed the xenon atom acquiring its homogeneous distribution in viscous ethanol at low temperatures.

A dynamical many-body theory of single color photoassociation in a Bose-Einstein condensate is presented. The theory describes the time evolution of a condensed atomic ensemble under the influence of an arbitrarily varying near-resonant laser pulse, which strongly modifies the binary scattering properties. In particular, when considering situations with rapid variations and high light intensities the approach described in this article leads, in a consistent way, beyond standard mean-field techniques. This allows one to address the question of limits to the photoassociation rate due to many-body effects which has caused extensive discussions in the recent past. Both the possible loss rate of condensate atoms and the amount of stable ground-state molecules achievable within a certain time are found to be stronger limited than according to mean-field theory. By systematically treating the dynamics of the connected Green’s function for pair correlations the resonantly driven population of the excited molecular state as well as scattering into the continuum of noncondensed atomic states are taken into account. A detailed analysis of the low-energy stationary scattering properties of two atoms modified by the near resonant photoassociation laser, in particular of the dressed state spectrum of the relative motion prepares for the analysis of the many-body dynamics. The consequences of the finite lifetime of the resonantly coupled bound state are discussed in the two-body as well as in the many-body context. Extending the two body description to scattering in a tight trap reveals the modifications to the near resonant adiabatic dressed levels caused by the decay of the excited molecular state.

We calculate the angular momentum and energy of a vortex dipole in a trapped atomic Bose-Einstein condensate. Fully analytic expressions are obtained. We apply the results to understand an interesting phenomenon in the MIT group experiment [Raman et al., Phys. Rev. Lett. 87, 210402 (2001)], an excellent agreement is achieved, and further experimental investigation is proposed to confirm this vortex dipole mechanism. We then suggest an effective generation and detection of vortex dipole for experimental realization. Application of the sum rule to calculate collective mode frequency splitting is also discussed.

For spinor Bose-Einstein condensates both the total spin $S$ and its $Z$ component $S_Z$ should be conserved. However, in existing theories, only the conservation of $S_Z$ has been taken into account. To remedy this, here we attempt to take the conservation of both $S$ and $S_Z$ into account. For this purpose, a total spin state with the good quantum numbers $S$ and $S_Z$ is introduced in the trial wave function; thereby a generalized Gross-Pitaevskii equation has been derived. With this equation, the ground bands of the ${}^{23}\mathrm{Na}$ and ${}^{87}\mathrm{Rb}$ condensates have been studied, where the levels that are distinct in $S$ split. It was found that the level density is extremely dense in the bottom of the ground band of ${}^{23}\mathrm{Na}$, i.e., in the vicinity of the ground state. On the contrary, for ${}^{87}\mathrm{Rb}$, the levels are extremely dense in the top of the ground band.

For an $\mathrm{O}\left(N\right)$-symmetric scalar field theory with Euclidean action $\int d^{3}x\left[\frac{1}{2}\mid \nabla \varphi {\mid }^2+\frac{1}{2}r{\varphi }^2+\frac{1}{4!}u{\varphi }^4\right]$, where $\varphi =({\varphi }_1,\dots ,{\varphi }_N)$ is a vector of $N$ real-field components, variational perturbation theory through seven loops is employed for $N=0,1,2,3,4$ to compute the renormalized value of $r∕(N+2)u^2$ at the phase transition. Its exact large-$N$ limit is determined as well. We also extend an earlier computation of the interaction-induced shift $\Delta ⟨{\varphi }^2⟩∕Nu$ from $N=1,2,4$ to $N=0,3$. For $N=2$, the results for the two quantities are used to compute the second-order shift of the condensation temperature of a dilute Bose gas, both in the homogenous case and for the wide limit of a harmonic trap. Our results are in agreement with earlier Monte Carlo simulations for $N=1,2,4$. The Appendix contains previously unpublished numerical seven-loop data.

We consider the problem of searching a $d$-dimensional lattice of $N$ sites for a single marked location. We present a Hamiltonian that solves this problem in time of order $\sqrt{N}$ for $d>2$ and of order $\sqrt{N}\log N$ in the critical dimension $d=2$. This improves upon the performance of our previous quantum walk search algorithm (which has a critical dimension of $d=4$), and matches the performance of a corresponding discrete-time quantum walk algorithm. The improvement uses a lattice version of the Dirac Hamiltonian, and thus requires the introduction of spin (or coin) degrees of freedom.

A special class of molecules that are important to many subfields in molecular dynamics and chemical physics, namely free-radical molecules, now enjoy a significant degree of center-of-mass motion control in the laboratory frame. The example reported in this paper concerns the hydroxyl radical $\left(\mathrm{OH}\right)$, which, after the internal degrees of freedom are cooled in a supersonic expansion, has been bunched, accelerated, and slowed using time-varying inhomogeneous electric fields. In situ observations of laser-induced fluorescence along the beam propagation path allows for detailed characterization of the longitudinal phase-space manipulation of $\mathrm{OH}$ molecules by the electric fields. The creation of a pulse containing ${10}^3–{10}^6$ molecules possessing a longitudinal velocity spread from 2 to $80\mathrm{m}∕\mathrm{s}$ around a mean laboratory velocity variable from $550\mathrm{m}∕\mathrm{s}$ to rest with only a few mm spatial extent represents an exciting and useful experimental capability for exploring free-radical dynamics.

We suggest a time-dependent dynamical mean-field-hydrodynamic model for the collapse of a trapped boson-fermion condensate and perform numerical simulation based on it to understand some aspects of the experiment by Modugno et al. [Science 297, 2240 (2002)] on the collapse of the fermionic condensate in the ${}^{40}\mathrm{K}$- ${}^{87}\mathrm{R}\mathrm{b}$ mixture. We show that the mean-field model explains the formation of a stationary boson-fermion condensate at zero temperature with relative sizes compatible with experiment. This model is also found to yield a faithful representation of the collapse dynamics in qualitative agreement with experiment. In particular we consider the collapse of the fermionic condensate associated with (a) an increase of the number of bosonic atoms as in the experiment and (b) an increase of the attractive boson-fermion interaction using a Feshbach resonance. Suggestion for experiments of fermionic collapse using a Feshbach resonance is made.

We analyze the system of rate equations that, according to our previous studies, adequately describes the behavior of neodymium random lasers. We show that random lasers, in which a noticeable fraction of spontaneous emission goes to lasing modes, have different threshold behavior than regular lasers. We also demonstrate that although the dynamics of stimulated emission in random lasers is strongly dissimilar in different pumping regimes, the threshold energy remains constant, equal to the product of the cw threshold power and the spontaneous emission lifetime $\tau$, if the pumping pulse is much shorter than $\tau$. The results of the study suggest that one can compare the performance of random lasers in different operation regimes and use a cw approximation (with some restrictions) in an analysis of thresholds of pulsed random lasers.