We present a method, using adiabatic passage, for creating a maximally coherent superposition in a two-state atom. The method exploits the analogy between the two-state Bloch equations and the three-state stimulated Raman adiabatic passage (STIRAP) equations, and uses two sequential but overlapping pulsed fields, a driving pump pulse and a delayed but overlapped detuning pulse. Like STIRAP, this method is robustly insensitive to small changes in pulse properties.

The process of electron scattering from heavy target atoms is of considerable interest due to the enhanced role of relativistic effects and distortion of the electron trajectories resulting from the large value of nuclear charge. Here we present (e,2e) ionization measurements and distorted-wave Born approximation calculations for the scattering of spin-polarized electrons from xenon atoms in which the fine-structure levels of the residual ion are resolved. Comparison of measurements performed using a high-sensitivity toroidal analyzer spectrometer with the predictions of sophisticated calculations provide an improved understanding of the ionization dynamics of heavy target atoms and the treatment of electron exchange processes.

A quantum control landscape is defined by the value of a physical observable as a functional of the time-dependent control field $E\left(t\right)$ for a given quantum-mechanical system. Level sets through this landscape are prescribed by a particular value of the target observable at the final dynamical time $T$, regardless of the intervening dynamics. We present a technique for exploring a landscape level set, where a scalar variable $s$ is introduced to characterize trajectories along these level sets. The control fields $E(s,t)$ accomplishing this exploration (i.e., that produce the same value of the target observable for a given system) are determined by solving a differential equation over $s$ in conjunction with the time-dependent Schrödinger equation. There is full freedom to traverse a level set, and a particular trajectory is realized by making an a priori choice for a continuous function $f(s,t)$ that appears in the differential equation for the control field. The continuous function $f(s,t)$ can assume an arbitrary form, and thus a level set generally contains a family of controls, where each control takes the quantum system to the same final target value, but produces a distinct control mechanism. In addition, although the observable value remains invariant over the level set, other dynamical properties (e.g., the degree of robustness to control noise) are not specifically preserved and can vary greatly. Examples are presented to illustrate the continuous nature of level-set controls and their associated induced dynamical features, including continuously morphing mechanisms for population control in model quantum systems.

We investigate the color-locked twin-noisy-field correlation effects in third-order nonlinear absorption and dispersion of ultrafast polarization beats. We demonstrate a phase-sensitive method for studying the two-photon nondegenerate four-wave mixing (NDFWM) due to atomic coherence in a multilevel system. The reference signal is another one-photon degenerate four-wave-mixing signal, which propagates along the same optical path as the NDFWM signal. This method is used for studying the phase dispersion of the third-order susceptibility and for the optical heterodyne detection of the NDFWM signal. The third-order nonlinear response can be controlled and modified through the color-locked correlation of twin noisy fields.

We consider an open quantum system which contains unstable states. The time evolution of the system can be described by an effective non-Hermitian Hamiltonian $H_{\mathrm{eff}}$, in accord with the Wigner-Weisskopf approximation, and an additional term of the Lindblad form, the so-called dissipator. We show that, after enlarging the original Hilbert space by states which represent the decay products of the unstable states, the non-Hermitian part of $H_{\mathrm{eff}}$—the “particle decay”—can be incorporated into the dissipator of the enlarged space via a specific Lindblad operator. Thus the formulation of the time evolution on the enlarged space has a Hermitian Hamiltonian and is probability conserving. The equivalence of the formulation with the original one demonstrates that the time evolution which is governed by a non-Hermitian Hamiltonian and a dissipator of the Lindblad form is nevertheless completely positive, just as systems with Hermitian Hamiltonians.

Highly efficient, nearly deterministic, and isotope selective generation of ${\mathrm{Yb}}^{+}$ ions by one- and two-color photoionization is demonstrated. State preparation and state selective detection of hyperfine states in ${}^{171}\mathrm{Yb}^{+}$ is investigated in order to optimize the purity of the prepared state and to time-optimize the detection process. Linear laser-cooled ${\mathrm{Yb}}^{+}$ ion crystals confined in a Paul trap are demonstrated. Advantageous features of different previous ion trap experiments are combined, while at the same time the number of possible error sources is reduced by using a comparatively simple experimental apparatus. This opens a new path toward quantum state manipulation of individual trapped ions, and in particular, to scalable quantum computing.

Cold-atom optical lattices allow for the study of quantum localization and mobility edges in a disorder-free environment. We predict the existence of an Anderson-like insulator with sharp mobility edges in a one-dimensional nearly periodic optical lattice. We show that the mobility edge manifests itself as the early onset of pinning in center of mass dipole oscillations in the presence of a magnetic trap, which should be observable in optical lattices.

This paper addresses a very fundamental and important problem in the numerical analysis of atomic and molecular systems: How to discretize Hamiltonians with divergent potential terms, such as Coulomb singularities. At the point of a Coulomb singularity, the wave function cannot be described by a Taylor series expansion, which results in problems when standard discretization schemes are used. We propose using the known asymptotic form of the wave function near the singularity instead of the (nonexistent) Taylor series. This principle, namely discretization by asymptotic behavior correspondence (ABC), is employed in this paper for obtaining grid-discretizations for the Coulomb potential in Cartesian, cylindrical and spherical coordinate systems. We show that computations with the ABC discretization are faster and more precise than with a naive discretization by orders of magnitude. The ABC discretization is well suited for the standard numerical time propagators, such as the Crank-Nicholson, Peaceman-Rachford, and leapfrog schemes. We use the latter, since it is faster and has the same order of accuracy. The leapfrog scheme is generalized to allow absorbing potentials at the grid boundaries.

We describe an assembly of $N$ superconducting qubits contained in a single-mode cavity. In the dispersive regime, the correlation between the cavity field and each qubit results in an effective interaction between qubits that can be used to dynamically generate maximally entangled states. With only collective manipulations, we show how to create maximally entangled quantum states and how to use these states to reach the Heisenberg limit in the determination of the qubit bias control parameter (gate charge for charge qubits, external magnetic flux for rf-superconducting quantum interference devices).

We propose a method for directly probing the dynamics of disentanglement of an initial two-qubit entangled state under the action of a reservoir. We show that it is possible to detect disentanglement, for experimentally realizable examples of decaying systems, through the measurement of a single observable, which is invariant throughout the decay. The systems under consideration may lead to either finite-time or asymptotic disentanglement. A general prescription for measuring this observable, which yields an operational meaning to entanglement measures, is proposed, and exemplified for cavity quantum electrodynamics and trapped ions.

Double ionization channels of ${\mathrm{H}}_2$ are separated in the time domain using ultrashort $10\text{−}\mathrm{fs}$ laser pulses in the ${10}^{13}–{10}^{15}\mathrm{W}{\mathrm{cm}}^{-2}$ intensity range. Charge resonance enhanced ionization does not contribute anymore to double ionization because the ${\mathrm{H}}_2^{+}$ ion does not have enough time to stretch up to the critical internuclear distance. Using a pump-probe excitation scheme, this process is shown to be very sensitive for the detection of pre- and post-pulses situated at a few tens of femtoseconds from the maximum pulse envelope.

We propose a fast scheme involving atoms fixed in an optical cavity to directly implement the universal controlled-unitary gate. The present technique based on adiabatic passage uses dark states well suited for the controlled-rotation operation. We show that these dark states allow the robust implementation of a gate that is a generalization of the controlled-unitary gate to the case where the control qubit can be selected to be an arbitrary state. This gate has potential applications to the rapid implementation of quantum algorithms such as the projective measurement algorithm. This process is decoherence-free since excited atomic states and cavity modes are not populated during the dynamics.

A general model using a multiconfiguration Dirac-Fock program with Breit interaction and QED corrections is established to calculate the $4f$ core-level transitions in the rare earths. This model is tested by comparing the calculated spectra to the experimental spectra of all the elements of the rare-earth series obtained by electron-induced x-ray emission spectroscopy. Agreement between the ab initio energies calculated in the free-ion model and the energies measured for the solid rare-earth spectra is of the order of $1\text{to}2\mathrm{eV}$, i.e., better than 0.2%. Each observed structure is interpreted. Variation of the intensity ratios of the various emissions along the lanthanide series is explained. These results prove the validity of our theoretical model to describe the $4f\text{−}3d$ transitions in the solids. This general model can be used to interpret the $4f$ core-level transitions observed from other spectroscopies.

We propose a technique to prepare coherent superpositions of two nondegenerate quantum states in a three-state ladder system, driven by two simultaneous fields near resonance with an intermediate state. The technique, of potential application to the enhancement of nonlinear processes, uses an adiabatic passage assisted by dynamic Stark shifts induced by a third laser field. The method offers significant advantages over alternative techniques: (i) it does not require laser pulses of specific shape and duration and (ii) it requires less intense fields than schemes based on two-photon excitation with nonresonant intermediate states. We discuss possible experimental implementation for enhancement of frequency conversion in mercury atoms.

We report on an experimental and theoretical study of the dynamic (ac) Stark effect on a forbidden transition. A general framework for parametrizing and describing off-resonant ac-Stark shifts is presented. A model is developed to calculate spectral line shapes resulting from resonant excitation of atoms in an intense standing light wave in the presence of off-resonant ac-Stark shifts. The model is used in the analysis and interpretation of a measurement of the ac-Stark shifts of the static-electric-field-induced $6s^2{}^{1}S_0\to 5d6s{}^{3}D_1$ transition at $408\mathrm{nm}$ in atomic Yb. The results are in agreement with estimates of the ac-Stark shift of the transition under the assumption that the shift is dominated by that of the $6s^2{}^{1}S_0$ ground state. A detailed description of the experiment and analysis is presented. A biproduct of this work is an independent determination (from the saturation behavior of the 408-nm transition) of the Stark transition polarizability, which is found to be in agreement with our earlier measurement. This work is part of the ongoing effort aimed at a precision measurement of atomic parity-violation effects in Yb.

Direct ionization to dissociative potential curves is the dominant explanation for intense-field dissociative ionization of ${\mathrm{N}}_2$. In this article we contradict this notion by showing that the dissociation of $\mathrm{N}_2{}^{2+}$ adiabatically follows the avoided crossing formed by the $\mid X{}^3\Pi _u,n⟩$ and $\mid D{}^3\Pi _g,n-1⟩$ dressed curves. Dissociation along this light-induced molecular potential implies that one photon is absorbed and adds to the kinetic release of the fragments. We compare the fragmentation energies for three different laser wavelengths and find that nitrogen shows photon absorption whereas iodine does not. From this we conclude that one must account for the absorbed photon when interpreting the time-of-flight spectra for molecules with appreciable nuclear motion during the laser pulse. In nitrogen, doing so allows us to identify enhanced ionization of the dication at $2.2\mathrm{\AA }$ independent of laser wavelength.

We present a unified overview, from the mean-field to the unitarity regime, of the stability of a trapped Fermi gas with short range attractive interactions. Unlike in a system of bosons, a Fermi gas is always stable in these regimes, no matter how large the particle number. However, when the interparticle spacing becomes comparable to the range of the interatomic interactions, instability is not precluded.

We investigate numerically simulated collisions between experimentally realistic Bose-Einstein condensate wave packets, within a regime where highly populated scattering haloes are formed. The theoretical basis for this work is the truncated Wigner method, for which we present a detailed derivation, paying particular attention to its validity regime for colliding condensates. This paper is an extension of our previous Letter [A. A. Norrie, R. J. Ballagh, and C. W. Gardiner, Phys. Rev. Lett. 94, 040401 (2005)], and we investigate both single-trajectory solutions, which reveal the presence of quantum turbulence in the scattering halo, and ensembles of trajectories, which we use to calculate quantum-mechanical correlation functions of the field.