We report the reflection and focusing of a Bose-Einstein condensate by a pulsed magnetic mirror. The mirror is adaptive, inelastic, and has extremely high optical quality. Deviations from specularity are below 1 mrad rms — almost an order of magnitude better than other atomic mirrors. The mirror has been used to realize the atom-optical analog of a beam expander, producing an ultracold collimated fountain of matter waves. The results of these experiments are in good agreement with simple theoretical models.

Wave functions for the Coulomb, Morse, Rosen-Morse, and Eckart systems are expressed exactly and explicitly in terms of the corresponding classical trajectories. This is accomplished by a technique that maps previously obtained classical representations for wave functions of the three-dimensional isotropic harmonic oscillator to the wave functions for the present systems. By design, the classical behavior enters these expressions in a manner that allows them to be used as uniform semiclassical approximations for other systems. The construction of a hydrogen orbital from the corresponding classical orbits is illustrated for a particular case. The classical representation of the Eckart wave function is analyzed to understand how ordinary, real, classical trajectories that are confined to one side of a barrier are able to describe tunneling through the barrier.

A locally real representation is derived from projections in Hilbert space without arbitrary constants. The inherent enhancement property of the resultant states removes restriction by Bell’s theorem. Exact agreement with quantum mechanics is demonstrated by explicit calculations of photon transmission in Malus’s law, joint detection probability for correlated photons, spin $\frac{1}{2}$ particle transmission through successive Stern-Gerlach analyzers, and joint detection probability for correlated spin $\frac{1}{2}$ particles. The representation is experimentally testable with respect to quantum mechanics.

A derivation has been performed of some central potentials with no quantum correction to the Hamilton-Jacobi equation. In this exact limit of quantum mechanics, quantum trajectories identical to the classical ones are obtained. Interestingly, some of them are closed orbits. Applications of the found potentials in many areas of physics are also discussed.

Using the q-deformed commutator formalism (“q mutators”), we have calculated the two-photon transition amplitude connecting a $J=0\mathrm{}$ atomic ground state to a $J=1\mathrm{}$ atomic excited state of the same parity. We find, in agreement with a semiclassical calculation, that this transition amplitude vanishes for two equal-frequency photons if the photons are traditional bosons with $q=1.\mathrm{}$ If $q<\mathrm{}1\mathrm{}$ (i.e., if the spin-statistics connection is violated for photons), then the amplitude is nonzero and is proportional to $\left(1\mathrm{}-q\right).\mathrm{}$ Thus such an experiment, originally proposed by Budker and DeMille, provides a sensitive test of the spin-statistics connection for photons within the q-mutator formalism.

Radio-frequency pulses are used in nuclear-magnetic-resonance spectroscopy to produce unitary transfer of states. Pulse sequences that accomplish a desired transfer should be as short as possible in order to minimize the effects of relaxation, and to optimize the sensitivity of the experiments. Many coherence-transfer experiments in NMR, involving a network of coupled spins, use temporary spin decoupling to produce desired effective Hamiltonians. In this paper, we demonstrate that significant time can be saved in producing an effective Hamiltonian if spin decoupling is avoided. We provide time-optimal pulse sequences for producing an important class of effective Hamiltonians in three-spin networks. These effective Hamiltonians are useful for coherence-transfer experiments in three-spin systems and implementation of indirect swap and ${\Lambda }_2\mathrm{}\left(U\right)\mathrm{}$ gates in the context of NMR quantum computing. It is shown that computing these time-optimal pulses can be reduced to geometric problems that involve computing sub-Riemannian geodesics. Using these geometric ideas, explicit expressions for the minimum time required for producing these effective Hamiltonians, transfer of coherence, and implementation of indirect swap gates, in a three-spin network are derived (Theorems 1 and 2). It is demonstrated that geometric control techniques provide a systematic way of finding time-optimal pulse sequences for transferring coherence and synthesizing unitary transformations in quantum networks, with considerable time savings (e.g., 42.3% for constructing indirect swap gates).

The electron-helium scattering system is studied within the S-wave framework with a particular emphasis on one-electron ionization processes. Total ionization and the singly differential cross section for the equal-energy-sharing point are given for three initial states. In addition, discrete excitation cross sections are also given. Whereas generally there is no a priori relationship between cross sections for excitation of corresponding singlet and triplet states, we find that for the case of ionization with equal-energy outgoing electrons the triplet cross section is approximately three times bigger than the corresponding singlet one, irrespective of the initial state or energy.

We consider two large ideal parallel plates, each $l_1$ by $l_2,$ at a temperature T. The plates are a distance $l_3$ apart, where $l_3\ll l_1$ and $l_3\ll l_2,$ with a vacuum between them. The free energy per unit area, $A^T{/l}_1{l}_2,$ of such a system has long been known. The derivation was a quantum field-theoretic one. It was found that, for $k_{B}T\gg ħ{c/l}_3,$ $A^T{/l}_1{l}_2$ becomes ħ independent, that is, classical. The classical result is given by $A_{\mathrm{Cl}}^T{/l}_1{l}_2{=A}^{T\sim \infty }{/l}_1{l}_2=-\zeta {\mathrm{}\left(3\right)k}_{B}T/8\mathrm{}\pi l_3^2,$ where $\zeta \mathrm{}\left(3\right)=1.20\mathrm{}\dots .$ We show that the classical limit can be obtained within the framework of renormalized classical theory, the ultraviolet catastrophe having been eliminated on taking the difference between the electromagnetic fields in the presence and absence of the walls; a Casimir effect could have been obtained before the advent of quantum field theory, or even of quantum mechanics. The domain of validity of the result could not have been obtained, nor would the experimental verification of the theory have been remotely possible.

By means of an electrostatic analogy, an electron density is proposed that is related to the exchange-correlation potential $V_{\mathrm{xc}}\mathrm{}\left(r\right)\mathrm{}$ in atoms. More precisely, such an electron density is best characterized by the amount of electronic charge $Q_{\mathrm{xc}}\mathrm{}\left(r\right),$ say, enclosed within a sphere of radius r centered on the atomic nucleus. Then $Q_{\mathrm{xc}}\mathrm{}\left(r\right)\mathrm{}$ is related to the radial derivative of $V_{\mathrm{xc}}\mathrm{}\left(r\right)\mathrm{}$ by $Q_{\mathrm{xc}}\mathrm{}\left(r\right)=-r^2\partial V_{\mathrm{xc}}/\partial r.\mathrm{}$ $|Q_{\mathrm{xc}}\mathrm{}\left(r\right)\mathrm{}|$ tends to unity as $\overrightarrow{r}\infty$ and becomes zero in the limit $\overrightarrow{r}0.$ However, it increases at first as one comes away from the point at infinity, having the form at large r $|Q_{\mathrm{xc}}\mathrm{}\left(r\right)\mathrm{}\overrightarrow{|}1+2\alpha {/r}^3{+O(1/r}^4),$ where α is the dipole polarizability of the singly charged positive ion. This means that $|Q_{\mathrm{xc}}\mathrm{}\left(r\right)\mathrm{}|$ must have at least one maximum, its height $Q_{\mathrm{xc}}{(r}_m)$ and its position $r_m$ then being important parameters characterizing the shape of $Q_{\mathrm{xc}}\mathrm{}\left(r\right).$ The intersection(s) with the line $|Q_{\mathrm{xc}}|=1\mathrm{}$ are also plainly of importance in this same context. The exact form of $Q_{\mathrm{xc}}\mathrm{}\left(r\right)\mathrm{}$ involves both fully interacting one- and two-particle fermion density matrices, as well as the orbitals of the Slater-Kohn-Sham (SKS) reference system. However, the example of Be is worked out, where it is shown that, if the ground-state density $\rho \mathrm{}\left(r\right)={\rho }_{\mathrm{SKS}}\mathrm{}\left(r\right)\mathrm{}$ is known from either x-ray or electron diffraction experiments or from quantal computer simulation studies, then $Q_{\mathrm{xc}}\mathrm{}\left(r\right)\mathrm{}$ can be derived for this light atom.

We present a simple explanation that Ericson fluctuations in nuclear, atomic, molecular, and mesoscopic systems originate from the interference between random-partial-width amplitudes in regime of strongly overlapping resonances.

We present an analytical approximation for nonlinear dynamics of trapped Bose-Einstein condensates. The approximation is a substantial improvement over the Thomas-Fermi approximation and is shown to be applicable for systems with a rather small number of atoms N. The calculated aspect ratios after ballistic expansion are found to be in good agreement with those observed in recent experiments. The approximation is useful in providing a simple and easy quantitative computational tool for the analysis of experimental data.

The general form of the molecular frame photoelectron angular distributions (MFPADs) for linear ground-state molecules ionized by linearly polarized light $\left(\mathrm{n̂}\right)$ is reported. A comparison between computed and measured MFPADs as a function of the polar and azimuthal emission angles is presented for photoionization of NO leading to the $c{}^3\Pi$ state of ${\mathrm{NO}}^{+}.$ The importance of the azimuthal dependence of the MFPADs for the determination of the symmetry of the states involved in the excitation and of the underlying photoionization dipole matrix elements is demonstrated.

We show that the amount of entanglement needed as an initial resource to set up a certain final amount of entanglement between two ends of a noisy channel can be reduced in certain cases by using quantum repeaters. Our investigation (for various channels) considers cases in which a large number of entangled pairs are transmitted through the channel using known asymptotic results and conjectured bounds on distillable entanglement.

High-resolution measurements of the photoinduced dipole-forbidden $L_1{-M}_{4,5}$ x-ray emission lines were performed with a reflection-type and a transmission-type bent-crystal spectrometer for ${}_{62}\mathrm{Sm},$ ${}_{67}\mathrm{Ho},$ ${}_{70}\mathrm{Yb},$ ${}_{74}\mathrm{W},$ ${}_{78}\mathrm{Pt},$ ${}_{80}\mathrm{Hg},$ and ${}_{83}\mathrm{Bi}.$ From the observed linewidths of the $L_1{-M}_{4,5}$ x-ray transitions, the level widths of the subshell $L_1$ were determined assuming for the $M_{4,5}$ level widths the values reported recently by Campbell and Papp [X-ray Spectrom. 24, 307 (1995); At. Data Nucl. Data Tables 77, 1 (2001)].

We study two aspects of measurement theory in spinor Bose-Einstein condensates of $F=1\mathrm{}$ atoms: the probability of obtaining a certain outcome of the measurement and the evolution of the state of the condensate due to the measurement. We also study the interference patterns arising from the spatial overlap of two spinor condensates. We show that neither a measurement on a small number of escaping atoms nor an interference experiment can distinguish between an antiferromagnetic coherent state condensate, i.e., a condensate in which all the atoms have $S_z=0\mathrm{}$ along an a priori unknown direction, and a spin-singlet condensate, i.e., a condensate with $S_{\mathrm{total}}=0.\mathrm{}$ We also show that a singlet-state condensate evolves into a coherent state as a result of the measurement.

We study two-photon excitation using biphotons generated via the process of spontaneous parametric down conversion in a nonlinear crystal. We show that the focusing of these biphotons yields an excitation distribution that is the same as the distribution of one-photon excitation at the pump wavelength. We also demonstrate that biphoton excitation in the image region yields a distribution whose axial width is approximately that of the crystal thickness and whose transverse width is that of the pump at the input to the crystal.

A type of beat in nonlinear optical spectroscopy that is distinct from quantum beats (QB’s) and polarization beats, is described. Like a quantum beat, this beat, which we refer to as an accidental degeneracy beat (ADB), can only be seen in multilevel systems. However, unlike quantum beats, which are the result of intramolecular interferences, ADB’s are interferences between different subensembles of molecules in the sample. They require multilevel systems with spectral overlap. ADB’s can appear as separate frequencies or as phase and amplitude contributions with the same frequency as that of quantum beats. A procedure for distinguishing between quantum beats and ADB’s is outlined, and criteria under which ADB’s are expected to be observed are delineated. Calculations of the spectrally resolved stimulated vibrational echo signal from an inhomogeneously broadened coupled anharmonic oscillator system are presented to illustrate the differences between the two types of beats. ADB’s carry information about the anharmonicity of a system, while QB’s carry information about intramolecular correspondence of transition frequencies in a multilevel system.

We have used momentum spectroscopy to examine the production of deuteron pairs in the double ionization of ${\mathrm{D}}_2$ molecules by a fast $(<\mathrm{}200\mathrm{}\hspace{0.5em}\mathrm{fs}),$ moderately intense $\left[\right(0.65\mathrm{}–8.0)\times {10}^{14}\hspace{0.5em}\mathrm{W}/{\mathrm{cm}}^2]$ laser pulse. By measuring in coincidence the momentum vectors of both deuterons, we have isolated, at the lowest laser power density, a weak ionization channel characterized by Coulomb-explosion deuterons with a sum energy near 10 eV. This is much higher than has been seen in previous studies. The angular distribution of these deuterons is nearly isotropic, in contrast to previous observations that the deuterons are strongly peaked along the laser polarization. These new observations suggest a previously unobserved ionization mechanism.