In a two-electron atom, autoionization from an impulsive isolated core excitation is a sensitive probe of a Rydberg electronic wave packet. This probe via the electron-electron correlation allows a quantum measurement of the wave function to be made. In addition to this capability, the measurement process has the advantage that it is independent of the excitation process. An analytical formula describes this probe. This formula is used in conjunction with a nonlinear least-squares algorithm to reconstruct the wave function of this wave packet. The algorithm is relatively insensitive to noise. With 20% added Gaussian noise, the algorithm can still reproduce the amplitudes and phases of the wave function.

We present experimental and numerical studies of the atomic motion in an optical lattice displaying a fivefold rotational symmetry. The atomic transport has been investigated by measuring the time evolution of the size of the atomic cloud. The experimental results are compared to those of a semiclassical Monte Carlo simulation of the atomic motion in a three-dimensional optical quasicrystal. A good agreement has been obtained on the anisotropy of the diffusive expansion of the cloud.

We propose the use of Stark chirped rapid-adiabatic-passage method, a technique in which the energy of a target state is swept through resonance by a slowly varying dynamic Stark shift to induce complete population transfer from the ground $1s$ state to the metastable $2s$ state of the hydrogen atom. Parasitic ionization processes are strongly reduced by using a two-color excitation scheme. Our detailed numerical calculations show that under judicious choice of pulse parameters, up to 98% of the population can be found in the $2s$ state at the end of the process.

By the moving molasses technique we have extracted laser-cooled cesium atoms in a continuous way directly from an optical molasses. The mean launching velocity is precisely tunable from 1 to 12 m/s. The atomic beam has a flux of $1.3\times {10}^8\hspace{0.5em}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}/\mathrm{s}$ at 7 m/s and a longitudinal temperature of $70\hspace{0.5em}\mu \mathrm{K},$ which represents the highest flux and lowest velocity spread obtained so far in a continuous beam of cold atoms. These features makes it well suited for atomic fountains. The atomic flux can be slightly increased in a two-dimensional magneto-optical trap operation $\mathrm{}(+40\%).$ A simple model accounts for the observed dependence of the flux with the magnetic-field gradient.

We show that a dynamical suppression of spontaneous emission, predicted for a three-level atom [S.-Y. Zhu and M. O. Scully, Phys. Rev. Lett. 76, 388 (1996)] can occur in a two-level atom driven by a polychromatic field. We find that the quantum interference, responsible for the cancellation of spontaneous emission, appears between different channels of transitions among the dressed states of the driven atom. We discuss the effect for bichromatic and trichromatic (amplitude-modulated) fields and find that these two cases lead to the cancellation of spontaneous emission in different parts of the fluorescence spectrum. Our system has the advantage of being easily accessible by current experiments.

We observe and analyze a two-photon continuous-wave optical gain mechanism designed for building a two-photon laser. The two-photon stimulated emission is spectrally isolated and resonantly enhanced using the multilevel structure of ${}^{39}\mathrm{K},$ in conjunction with an alternative interaction geometry involving orthogonal beams and polarizations. The observed two-photon laser beam amplification increases linearly with low input laser beam intensity, as expected, and saturates at a gain of $2\times {10}^{-4}$ at high intensity. A theoretical analysis of the observations is outlined.

We develop the broadest possible generalization of the well known connection between quantum-mechanical Bargmann invariants and geometric phases. The key concept is that of null phase curves in quantum-mechanical ray and Hilbert spaces. Examples of such curves are developed. Our generalization is shown to be essential for properly understanding geometric phase results in the cases of coherent states and of Gaussian states. Differential geometric aspects of null phase curves are also briefly explored.

The electromagnetic field is quantized using the Green’s-function method for the geometry of a Fabry-Perot cavity, made up of two identical lossy dispersive slabs of finite thickness. The dielectric functions of the slabs are assumed to be an arbitrary complex function of frequency obeying causality requirements. The attractive Casimir force between the two slabs is calculated by the help of the latter field operators, via evaluating the difference between the vacuum pressures on both sides of each slab. Special attention is paid to the limiting case of the Casimir effect for two conducting plates. The Lorentz model of the dielectric function is used to demonstrate the variation of the force in terms of plasma frequency. The Casimir force expression is also related to the imaginary part of the response function. The latter expression is used to introduce the repulsive Casimir force between two conducting plates located inside a Fabry-Perot cavity.

The Maxwell stress tensor is used to introduce the radiation pressure force of the electromagnetic field on a conducting surface. This expression is related to the imaginary part of the vector potential Green function for the fluctuating fields of the vacuum via the fluctuation dissipation theorem and Kubo’s formula. The formalism allows one to evaluate the vacuum radiation pressure on a conducting surface without resorting to the process of field quantization. The latter formula is used to calculate the attractive and repulsive Casimir force between two conducting plates. What is more, in this formalism, there is no need to apply any regularization procedure to recover the final result.

We develop a convergent variational perturbation theory for quantum-statistical density matrices which is applicable to polynomial as well as nonpolynomial interactions. We illustrate the power of the theory by calculating the temperature-dependent density of a particle in the double-well potential to second order, and of the electron in the hydrogen atom to first order.

We show that it is, in principle, possible to perform local-realism violating experiments of the Hardy type in which only position and momentum measurements are made on two particles emanating from a common source. In the optical domain, homodyne detection of the in-phase and out-of-phase amplitude components of an electromagnetic field is analogous to position and momentum measurement. Hence, local realism violations of the Hardy type are possible in optical systems employing only homodyne detection.

The dynamics of a quantum system undergoing frequent “measurements,” leading to the so-called quantum Zeno effect, is examined on the basis of a neutron-spin experiment recently proposed for its demonstration. Unlike in all previous studies, the spatial degrees of freedom of the neutron are duly taken into account. Their inclusion in the analysis is important for two reasons: first, neutron-reflection effects are shown to be very important; second, the evolution may turn out to be totally different from the ideal case. Our results can be interpreted in terms of a rigorous theorem due to Misra and Sudarshan: indeed we clarify that, in contrast with a widespread belief, a quantum Zeno effect does not halt the evolution of a quantum system; it rather modifies it, by forcing the system to remain in a certain subspace, defined by the very measurement performed.

The problem of quantum-state inference and the concept of quantum entanglement are studied using a nonadditive measure in the form of the Tsallis entropy indexed by the positive parameter q. The maximum entropy principle associated with this entropy along with its thermodynamic interpretation are discussed in detail for the Einstein-Podolsky-Rosen pair of two spin-$\frac{1}{2}$ particles. Given the data on the Bell-Clauser-Horne-Shimony-Holt observable, the analytic expression is presented for the inferred quantum entangled state. It is shown that for $q>\mathrm{}1,$ indicating the subadditive feature of the Tsallis entropy, the entangled region is small and enlarges as one goes into the superadditive regime where $q<\mathrm{}1.\mathrm{}$ It is also shown that quantum entanglement can be quantified by the generalized (Kullback-Leibler) relative entropy.

Fractional Fourier operators are introduced, and their properties are studied. Products of these operators with the displacement operators are also considered and used to define generalized Wigner functions which in special cases give the known Wigner functions and Weyl functions. The properties of these generalized Wigner functions are explored. Complex fractional Fourier operators are also studied.

A new type of procedures, called protective measurements, was proposed by Aharonov, Anandan, and Vaidman [Phys. Rev. A 97, 4616 (1993); Found. Phys. 26, 117 (1996)]. These authors argued that a protective measurement allows the determination of arbitrary observables of a single quantum system, and claimed that this favors a realistic interpretation of the quantum state. This paper proves that only observables that commute with the system’s Hamiltonian can be measured protectively. It is argued that this restriction saves the coherence of alternative interpretations.

Differential realizations in coordinate space for deformed Lie algebras with three generators are obtained using bosonic creation and annihilation operators satisfying Heisenberg commutation relations. The unified treatment presented here contains as special cases all previously given coordinate realizations of so(2,1), so(3), and their deformations. Applications to physical problems involving eigenvalue determination in nonrelativistic quantum mechanics are discussed.

We consider detailed roughness and conductivity corrections to the Casimir force in the recent Casimir force measurement employing an atomic force microscope. The roughness of the test bodies—a metal plate and a sphere—was investigated with the atomic force microscope and the scanning electron microscope, respectively. It consists of separate crystals of different heights and a stochastic background. The amplitude of roughness relative to the zero roughness level was determined and the corrections to the Casimir force were calculated up to the fourth order in a small parameter (which is this amplitude divided by the distance between the two test bodies). Also the corrections due to finite conductivity were found up to fourth order in relative penetration depths of electromagnetic zero-point oscillations into the metal. The theoretical result for the configuration of a sphere above a plate taking into account both corrections is in excellent agreement with the measured Casimir force.

The problem of how many entangled or, respectively, separable states there are in the set of all quantum states is investigated. We study to what extent the choice of a measure in the space of density matrices $\varrho$ describing N-dimensional quantum systems affects the results obtained. We demonstrate that the link between the purity of the mixed states and the probability of entanglement is not sensitive to the measure chosen. Since the criterion of partial transposition is not sufficient to distinguish all separable states for $N>~8$, we develop an efficient algorithm to calculate numerically the entanglement of formation of a given mixed quantum state, which allows us to compute the volume of separable states for $N=8\mathrm{}$ and to estimate the volume of the bound entangled states in this case.

A quantum computer is proposed in which information is stored in the two lowest electronic states of doped quantum dots (QD’s). Many QD’s are located in a microcavity. A pair of gates controls the energy levels in each QD. A controlled-NOT (C-NOT) operation involving any pair of QD’s can be effected by a sequence of gate-voltage pulses which tune the QD energy levels into resonance with frequencies of the cavity or a laser. The duration of a C-NOT operation is estimated to be much shorter than the time for an electron to decohere by emitting an acoustic phonon.

Recent calculations of the electron-detachment energies of the alkaline-earth-metal tetrahalides and alkali-metal trihalides yield values between 1.5 and 3.3 eV. If these values are correct, these molecular ions would be the most stable small dianions of any considered so far, and it should be easy to produce them in negative-ion sources. Using a cesium sputter source and accelerator mass spectrometry (AMS), we have detected and identified two multiply charged alkaline-earth-metal molecular-cluster ions, ${\mathrm{BeF}}_4^{2\mathrm{-}}$ and ${\mathrm{MgF}}_4^{2\mathrm{-}}.$ Using the techniques that we developed earlier to study ${\mathrm{C}}_n^{2-},$ we have been able to use AMS to unambiguously identify these dianions. We provide further evidence for their existence in the form of Coulomb explosion images that we produced in the terminal of our tandem accelerator. An unsuccessful search for alkali-metal dianions of the form ${\mathrm{MX}}_3^{2-}$ and $M_2{X}_4^{2-}$ $({\mathrm{LiF}}_3^{2\mathrm{-}}$ and ${\mathrm{Li}}_2{\mathrm{F}}_4^{2\mathrm{-}})$ allows us to set an upper limit of ${10}^{-17}$ relative to ${\mathrm{F}}^{\mathrm{-}}$ for their production in a Cs sputter source assuming their lifetimes are greater than 10 μs. It seems likely that they are either not formed at all in the sputter source or their lifetimes are considerably shorter than 10 μs.