We introduce a method for quantum-state tomography for a pair of optical modes, which we call generalized rotations in phase space. Rather than using a dual-mode local oscillator field for implementing balanced-homodyne detection, as in previous methods, a single-mode local oscillator field can be used in our method, greatly simplifying certain aspects of experiments. The signal field is put through a series of general transformations before entering the detection system where quantum statistics are measured.

We propose a method to reconstruct the vibrational quantum state of atoms bound in arbitrary periodic potentials created by an optical lattice. The vibrational density matrix is determined from vibrational populations that are measured after translations of the optical-lattice potential. These translations are realized by phase shifts of the lattice laser fields. The feasibility of the reconstruction method is shown for a typical situation realized in recent experiments.

We reappraise and clarify the contradictory statements found in the literature concerning the time-of-arrival operator introduced by Aharonov and Bohm in Phys. Rev. 122, 1649 (1961). We use Naimark’s dilation theorem to reproduce the generalized decomposition of unity (or positive-operator-valued measures) from any self-adjoint extension of the operator, emphasizing a natural one, which arises from the analogy with the momentum operator on the half-line. General time operators are set within a unifying perspective. It is shown that they are not in general related to the time of arrival, even though they may have the same form.

The results of two-photon interferometer experiments are nonclassical and have been interpreted as providing evidence against local realistic theories. But half of the events must be discarded, and it has been suggested that there may be local realistic theories that are consistent with the experimental results as a consequence. It is shown here that the predicted results of two-photon interferometer experiments, including the discarded events, are inconsistent with any local realistic theory in the limit of high detector efficiency if suitable shutters and randomly chosen phase shifts are included. The shutters and randomly chosen phase shifts are unnecessary for any theory in which it is assumed that the photons and their associated hidden variables must propagate away from the source at the speed of light.

It is commonly assumed that exact Kohn-Sham theory implies a local exchange-correlation potential for ground states. Here we show that this is not true for the exchange potential in a Hartree-Fock model of density-functional theory, although Hohenberg-Kohn theorems can be proved for this model. It may not be possible to express exact Kohn-Sham equations in general in terms of density-functional derivatives that are equivalent to local potential functions.

Electron-impact excitation of $\mathrm{Ar}\mathrm{}\mathrm{I}$ from the ground ${3p}^6{}^1{S}_0$ as well as the two metastable levels of the ${3p}^{5}4s$ ${(}^3{P}_2$ and ${}^3{P}_0)$ configuration to all ten levels of the ${3p}^{5}4p$ excited configuration are calculated in the distorted-wave approximation. Polarization of the ground state is explicitly included by adding a polarization potential in the calculation. Unitarization of the scattering matrix $\mathbf{S}$ is carried out by including the elastic terms, and effects of unitarization in the $\mathrm{LS}$ as well as $\mathrm{jj}$ formalisms are investigated. The excitation cross sections are calculated from threshold to $\sim 100$ eV. The calculations are compared and contrasted with recent experimental data and other theoretical work. The study shows that the effect of the polarization potential is not very significant but unitarization of the $\mathbf{S}$ matrix reduces the cross sections considerably and the cross sections obtained using the two different methods of unitarization are significantly different for some excitation transitions. The results are useful for analyzing low-pressure plasmas used in processing applications as well as electron beam excitation, as in excimer lasers.

Interaction between collective monopole oscillations of a trapped Bose-Einstein condensate and thermal excitations is investigated by means of perturbation theory. We assume spherical symmetry to calculate the matrix elements by solving the linearized Gross-Pitaevskii equations. We use them to study the resonances of the condensate induced by temperature when an external perturbation of the trapping frequency is applied and to calculate the Landau damping of the oscillations.

We analyze the possibilities of approaching atom-surface interactions through their contribution to the atomic matter de Broglie wave phase, in an interferometer based on an evanescent light atomic mirror. The surface interactions produce an additional phase shift that is evaluated to a few times π for a neon atom in a metastable state. We propose and investigate an experimental procedure that uses the principles of polarization (for instance, Stern-Gerlach) interferometers in order to monitor these long-range interactions (van der Waals, Casimir-Polder, etc.) between a ground-state or metastable-state atom and either a metallic or a dielectric surface. Our approach gives access to the differential phase shift between Zeeman sublevels, and should then be sensitive to an eventual anisotropy of the atom-surface interaction.

Entanglement of quantum variables is usually thought to be a prerequisite for obtaining quantum speedups of information processing tasks such as searching databases. This paper presents methods for quantum search that give a speedup over classical methods, but that do not require entanglement. These methods rely instead on interference to provide a speedup. Search without entanglement comes at a cost: although they outperform analogous classical devices, the quantum devices that perform the search are not universal quantum computers and require exponentially greater overhead than a quantum computer that operates using entanglement. Quantum search without entanglement is compared to classical search using waves.

We give a protocol and criteria for demonstrating unconditional teleportation of continuous-variable entanglement (i.e., entanglement swapping). The initial entangled states are produced with squeezed light and linear optics. We show that any nonzero entanglement (any nonzero squeezing) in both of two entanglement sources is sufficient for entanglement swapping to occur. In fact, realization of continuous-variable entanglement swapping is possible using only two single-mode squeezed states.

We propose a quantum cryptographic scheme in which small phase and amplitude modulations of cw light beams carry the key information. The presence of Einstein-Podolsky-Rosen type correlations provides the quantum protection.

We present a universal technique for quantum-state estimation based on the maximum-likelihood method. This approach provides a positive-definite estimate for the density matrix from a sequence of measurements performed on identically prepared copies of the system. The method is versatile and can be applied to multimode radiation fields as well as to spin systems. The incorporation of physical constraints, which is natural in the maximum-likelihood strategy, leads to a substantial reduction of statistical errors. Numerical implementation of the method is based on a particular form of the Gauss decomposition for positive-definite Hermitian matrices.

Using Doppler-tuned fast-beam laser spectroscopy, the $1s2p{}^3{P}_0–{}^3{P}_1$ fine-structure interval in ${}^{24}{\mathrm{Mg}}^{10+}$ has been measured to be $833.133\left(15\right)\mathrm{}\hspace{0.5em}{\mathrm{cm}}^{-1}.$ The calibration procedure used the intercombination $1s2s{}^1{S}_0–1s2p{}^3{P}_1$ transition in ${}^{14}{\mathrm{N}}^{5+}.$ The result tests quantum-electrodynamic and relativistic corrections to high precision calculations, which will be used to obtain a new value for the fine-structure constant from the fine structure of helium.

The spectrum of two-photon transitions presents destructive interferences (dark resonances) that can be used to achieve continuous-wave Raman sub-recoil cooling, as shown in the present paper. A simple one-dimensional model is developed and used to show the ability of the method to perform subrecoil cooling.

We show that an ensemble of two-level atoms commonly coupled to a single, driven, damped high-$Q$ cavity mode could be cooled and trapped via the correlated dynamics of cavity field and the atomic motion. For sufficiently large detuning between the atoms and the field, spontaneous emission plays no role in the dynamics, and the cooling scheme can be applied to all particles with a sufficient optical dipole moment. The time scale of this collective cooling process increases with the particle number and can be optimized by suitably tailoring the pump field amplitude and frequency. The key properties of the underlying mechanism are discussed using a linearized model, where one can derive a closed set of equations for certain ensemble averages and the field. The results are then compared with N-particle dynamical simulations of the full equations.

We confine $4\times {10}^8$ fermionic ${}^6\mathrm{Li}$ atoms simultaneously with $9\times {10}^9$ bosonic ${}^7\mathrm{Li}$ atoms in a magneto-optical trap based on an all-semiconductor laser system. We optimize the two-isotope sample for sympathetic evaporative cooling. This is an essential step towards the production of a quantum-degenerate gas of fermionic lithium atoms.

We present precise near-dissociation limit measurements of ultracold collision rate constants (trap loss, fine-structure changing, and photoassociative ionization) as a function of trap intensity from $I_{\mathrm{sat}}$ to $I\approx {40I}_{\mathrm{sat}}$ for Cs and Na atoms cooled and confined in a magneto-optical trap. We find strong saturation for all processes at intensities approximately 10 times the free atom saturation level $I_{\mathrm{sat}}.$ Our results provide a precise reference point for testing and comparing different theoretical models used to analyze ultracold collisions.

The nucleation of vortices and the resulting structures of vortex arrays in dilute, trapped, zero-temperature Bose-Einstein condensates are investigated numerically. Vortices are generated by rotating a three-dimensional, anisotropic harmonic atom trap. The condensate ground state is obtained by propagating the Gross-Pitaevskii equation in imaginary time. Vortices first appear at a rotation frequency significantly larger than the critical frequency for vortex stabilization, consistent with a critical velocity mechanism for vortex nucleation. At higher frequencies, the structures of the vortex arrays are strongly influenced by trap geometry.

Dissipation-free photon-photon interaction at the single-photon level is studied in the context of cavity electromagnetically induced transparency (EIT). For a single multilevel atom exhibiting EIT in the strong cavity-coupling regime, the anharmonicity of the atom-cavity system has an upper bound determined by single atom-photon coupling strength. A photon blockade effect is inferred to occur for both single- and multiatom cases from the behavior of transition rates between dressed states of the system. Numerical calculations of the second-order coherence function indicate that photon antibunching in both single- and two-atom cases are strong and comparable.

A simple theoretical model describing the positive sign of subnatural-width absorption resonances in the recent experiment of Akulshin and co-workers [Phys. Rev. A 57, 2996 (1998)] is proposed. An analytical expression for the linear response to the weak probe field is found in the low-saturation limit with respect to the control field. It is shown that the positive sign of subnatural resonance is caused by the spontaneous transfer of the light-induced coherence from the excited level to the ground one.