The behavior of $\mathrm{Rb}\mathrm{}\left(390p\right)\mathrm{}$ atoms subject to a train of up to 50 half-cycle pulses (HCPs) with duration $T_p\ll T_n,$ where $T_n$ is the classical electron orbital period, is investigated. In this limit, each HCP simply delivers an impulsive momentum transfer or “kick” to the electron. The response of atoms to a series of unidirectional kicks and to a series of kicks that alternate in direction is compared. For unidirectional kicks, the Rydberg atom survival probability has a pronounced maximum when the pulse repetition frequency $v_p$ is ∼1.3 times the classical orbital frequency $v_n.$ Classical simulations show this behavior provides a signature of dynamical stabilization. Evidence of dynamical stabilization and chaotic diffusion is also found in the distribution of final bound states. Very different behavior is observed for alternating kicks. The survival probability generally increases with $v_p,$ although a small local maximum is evident when $v_p\sim v_n.$ Little evidence of dynamical stabilization is observed in either the calculated dependence of the survival probability on the number of applied kicks, in the measured final bound-state distribution, or in the classical phase space of the kicked atom. Model calculations for a one-dimensional “atom” reveal islands of stability, but their three-dimensional counterparts are found to be unstable.

Application of nonlinear magneto-optical (Faraday) rotation to magnetometry is investigated. Our experimental setup consists of a modulation polarimeter that measures rotation of the polarization plane of a laser beam resonant with transitions in Rb. Rb vapor is contained in an evacuated cell with antirelaxation coating that enables atomic ground-state polarization to survive many thousand wall collisions. This leads to ultranarrow features $\left(\sim {10}^{-6}\hspace{0.5em}\mathrm{G}\right)$ in the magnetic-field dependence of optical rotation. The potential sensitivity of this scheme to sub-$\mu \mathrm{G}$ magnetic fields as a function of atomic density, light intensity, and light frequency is investigated near the $D1\mathrm{}$ and $D2\mathrm{}$ lines of ${}^{85}\mathrm{Rb}.$ It is shown that through an appropriate choice of parameters the shot-noise-limited sensitivity to small magnetic fields can reach $3\times {10}^{-12}\hspace{0.5em}\mathrm{G}/\sqrt{\mathrm{Hz}}.$

We consider the evolution of an interacting dilute Bose-Einstein condensate transferred from a harmonic trap to a perfect box of finite size. We study numerically the influence of the nonlinearities in the system on its dynamics. The parallelism between this problem and the Fermi-Pasta-Ulam problem in the context of matter waves is established. Criteria for the appearance of statistical behavior are discussed. We show that by increasing the nonlinearity we pass from a regime of collapses and revivals for the wave function to a regime of collapses and revivals of regular motion.

We use a Fano diagonalization technique to find the eigenmodes of an atom laser consisting of a single-mode atomic cavity that is coherently coupled to the continuum of free space modes. Under very general conditions the system exhibits a single, stationary bound mode. We discuss the properties of this bound mode depending on the system parameters and investigate its effect on the output beam of the atom laser.

Dielectric four-port devices play an important role in optical quantum information processing. Since for causality reasons the permittivity is a complex function of frequency, dielectrics are typical examples of noisy quantum channels, which cannot preserve quantum coherence. To study the effects of quantum decoherence, we start from the quantized electromagnetic field in an arbitrary Kramers-Kronig dielectric of given complex permittivity and construct the transformation relating the output quantum state to the input quantum state, without placing restrictions on the frequency. We apply the formalism to some typical examples in quantum communication. In particular we show that for Fock-entangled qubits the Bell-basis states $|{\Psi }^{\pm }〉$ are more robust against decoherence than the states $|{\Phi }^{\pm }〉.$

The spontaneous-emission rate is evaluated for dipole emitters situated in the thin slab region between two semi-infinite one-dimensionally periodic photonic crystals, a situation reminiscent of planar cavity laser structures. It is pointed out that the long-wavelength electromagnetic fields supported by such complex structures can be directly quantized provided that the pair of semi-infinite photonic crystals are treated within the effective-medium approach, in which each photonic crystal is represented by a truncated uniaxial medium whose dielectric tensor components are determinable in terms of layer thicknesses and dielectric functions of the individual photonic crystal components. The spontaneous-emission rate is evaluated for a dipole emitter situated in the slab region, and oscillating at a frequency resonant with one of the modes that are localized within the slab and exponentially decaying within the photonic crystals. Both symmetric and asymmetric structures are discussed. Interesting features are predicted when the variations of the adjustable parameters are examined, including suppression and enhancement of the spontaneous rate.

It is shown that quantum mechanics allows a qubit to be transferred so that it can be accessed symmetrically by two observers. These can then decide later which one is to take possession of the quantum information. The process is not fully successful, but a failed experiment may allow the retention of the quantum information for use in a subsequent operation.

We present the single-particle stability diagram for the radial motion in a linear Paul trap in a situation where the applied axial dc potential gives rise to a harmonic defocusing radial potential. Although most linear Paul trap experiments have been conducted in a regime where this approximation is reasonably valid, the effect of the axial confinement on the stability of the radial motion has not previously been analyzed. The defocusing effect in both radial directions leads to a stability diagram different from that of the two-dimensional quadrupole mass filter, and hence points toward new studies of few ion dynamics. Expressions for the effective or pseudopotentials for one and two charged particles are presented and discussed.

While it is known that copying a quantum system does not increase the amount of information obtainable about the originals, it may increase the amount available in practice, when one is restricted to imperfect measurements. We present a detection scheme which, using imperfect detectors and possibly noisy quantum copying machines (that entangle the copies), allows one to extract more information from an incoming signal than with the imperfect detectors alone. The case of single-photon detection with noisy, inefficient detectors and copiers (single controlled-NOT gates in this case) is investigated in detail. The improvement in distinguishability between a photon and vacuum is found to occur for a wide range of parameters, and to be quite robust to random noise. The properties that a quantum-copying device must have to be useful in this scheme are investigated.

We study ionization of atomic hydrogen by fast electrons using asymptotically correct two-center wave functions to describe the scattering system both initially and finally. For the final state, we employ the well-known product wave function of Redmond, which treats all three two-body Coulomb interactions exactly, albeit independently. This “3C” wave function is the leading term of the exact scattering wave function, regardless of how slow the three particles are, if any two particles have large relative separation [Y.E. Kim and A.L. Zubarev, Phys. Rev. A 56, 521 (1997)]. Here we extend the analysis of Qiu et al. [Phys. Rev. A 57, R1489 (1998)] to show that the 3C wave function is the leading term of the exact scattering wave function, regardless of how close the three particles are, if any two particles have large relative speed. Whereas Brauner, Briggs, and Klar [J. Phys. B 22, 2265 (1989)], using the above wave function, demonstrated the importance of final-state two-center effects, we have shown that initial-state two-center effects must also be included to obtain accurate results at lower energies [S. Jones and D.H. Madison, Phys. Rev. Lett. 81, 2886, (1998)]. Here we consider three different two-center approximations for the initial state, which yield nearly identical results for impact energies above 250 eV. For lower energies, the model that uses the eikonal approximation for the initial state emerges as the most accurate one, just as is observed in the case of ion impact.

A method is proposed for searching the formal solution of the Hylleraas equation for the helium atom. A mathematically rigorous study confirms, in a unified and simpler manner, several results obtained earlier in the literature but not necessarily in the same contexts. We use an adequate transformation of the Schrödinger equation to identify three asymptotic channels. Two of these are considered in detail as physical and are seen to differ from “traditional” ones. In particular, we demonstrate that there is no place for the widely used Hylleraas-type exponent. Furthermore, we show how the mathematical presence of logarithms at small hyper-radii, first suggested by Bartlett, is linked to the electron-electron interaction. Finally, the study leads to the development of simple procedures for the numerical calculations of energy levels and approximate wave functions.

This paper discusses the realization of a quantum associative memory using linear integrated optics. An associative memory produces a full pattern of bits when presented with only a partial pattern. Quantum computers have the potential to store large numbers of patterns and hence have the ability to far surpass any classical neural-network realization of an associative memory. In this work two three-qubit associative memories will be discussed using linear integrated optics. In addition, corrupted, invented and degenerate memories are discussed.

We derive a simple semiclassical representation to describe the large-scale structure of the spectrum of regular systems weighted by some arbitrary function W. Examples of weighted spectra are the width-weighted spectrum, which represents the decay rate of an unstable system, and the oscillator-strength-weighted spectrum, which represents the photoabsorption rate. Semiclassical representations of such spectra involve stationary-phase contributions, which are periodic or closed orbits, and end-point contributions, which are loops on an extremal torus. The theory provides the link between semiquantal formulas and the closed-orbit theory of atomic photoabsorption. It also allows calculation of an average decay rate without knowledge of the widths of individual quantum states.

We propose a probabilistic quantum cloning scheme using Greenberger-Horne-Zeilinger (GHZ) states, Bell-basis measurements, single-qubit unitary operations, and generalized measurements, all of which are within the reach of current technology. Compared to another possible scheme via Tele-controlled-NOT gate [D. Gottesman and I. L. Chuang, Nature (London) 402, 390 (1999)], the present scheme may be used in experiment to clone the states of one particle to those of two different particles with higher probability and less GHZ resources.

In this paper, we examine the precession of a spin in a magnetic field, treating the particle and the applied magnetic field as a single closed system whose energy is conserved. Through two simple examples, it is shown that the standard expression for spin precession emerges only indirectly, and as a first-order approximate result. For the first example, deviations from the first-order result are easy to obtain, and are familiar from Stern-Gerlach spin separation. For the second example, deviations from the first-order result are not practically possible to obtain. Beyond these two examples, it is also shown within a semiclassical approach that the standard expression for spin precession in a magnetic field is always valid to first order, irrespective of how the Hamiltonian depends on other dynamical variables of the system.

We analyze the estimation of a finite ensemble of quantum bits that have been sent through a depolarizing channel. Instead of using the depolarized qubits directly, we first apply a purification step and show that this improves the fidelity of subsequent quantum estimation. Even though we lose some qubits of our finite ensemble the information is concentrated in the remaining purified ones.

We consider continuous observation of the nonlinear dynamics of single atom trapped in an optical cavity by a standing wave with intensity modulation. The motion of the atom changes the phase of the field which is then monitored by homodyne detection of the output field. We show that the conditional Hilbert space dynamics of this system, subject to measurement-induced perturbations, depends strongly on whether the corresponding classical dynamics is regular or chaotic. If the classical dynamics is chaotic, the distribution of conditional Hilbert space vectors corresponding to different observation records tends to be orthogonal. This is a characteristic feature of hypersensitivity to perturbation for quantum chaotic systems.

We study Bloch waves and Wannier functions in periodic superstructure Bragg gratings using coupled-mode theory. We formulate the procedure that leads to Wannier functions that have a high degree of symmetry and appear to fall off exponentially, away from the photonic well. These Wannier functions can be considered to be the equivalent of those found by Kohn for the one-dimensional Schrödinger equation with a periodic potential [W. Kohn, Phys. Rev. $115,$ 809 (1959)].

Resonance penetration of two coupled particles through a repulsive barrier is considered. It is shown that a local minimum of the total potential generates metastable bound states, and their spectrum determines the position of resonances in the penetration probability. It is pointed out that the probabilities of tunneling of two interacting particles from the false vacuum can be essentially higher than has been assumed earlier.