We propose a phenomenological Hamiltonian for the analysis of photoassociation of a Bose-Einstein condensate. We find that, by adiabatically sweeping the frequency of the driving laser, a condensate of atoms may be converted rapidly to a condensate of molecules.

We describe a method and present experimental results for obtaining electromagnetically induced transparency by adjusting the frequencies of two lasers so that they coincide with the centers of gravity of two hyperfine split transitions. No hyperfine states are in Raman resonance and the zero of the dipole moment results from the interference of the manifold of cooperating m states.

The recently proposed idea of “protective” measurement of a quantum state is critically examined, and generalized. Earlier criticisms of the idea are discussed, and their relevance to the proposal assessed. Several constraints on measuring apparatus required by “protective” measurements are discussed, with emphasis on how they may restrict their experimental feasibility. Though “protective” measurements result in an unchanged system state and a shift of the pointer proportional to the expectation value of the measured observable in the system state, the actual reading of the pointer position gives rise to several subtleties. We propose several schemes for reading the pointer position, both when the apparatus is treated as a classical system as well as when its quantum aspects are taken into account, that address these issues. The tiny entanglement which is always present due to deviation from extreme adiabaticity in realistic situations is argued to be the weakest aspect of the proposal. Because of this, one can never perform a protective measurement on a single quantum system with absolute certainty. This clearly precludes an ontological status for the wave function. Several other conceptual issues are also discussed.

It is shown that a unique measure of volume is associated with any statistical ensemble, which directly quantifies the inherent spread or localization of the ensemble. It is applicable whether the ensemble is classical or quantum, continuous or discrete, and may be derived from a small number of theory-independent geometric postulates. Remarkably, this unique ensemble volume is proportional to the exponential of the ensemble entropy, and hence provides an interesting geometric characterization of the latter quantity. Applications include unified volume-based derivations of results in quantum and classical information theory, a precise geometric interpretation of thermodynamic entropy for equilibrium ensembles, a geometric derivation of semiclassical uncertainty relations, a means for defining classical and quantum localization for arbitrary evolution processes, and a proposed definition for the spot size of an optical beam. Advantages of ensemble volume over other measures of localization (root-mean-square deviation, Renyi entropies, and inverse participation ratio) are discussed.

A generalization of a driven harmonic oscillator with time-dependent mass and frequency, by adding total time-derivative terms to the Lagrangian, is considered. The generalization, which gives a general quadratic Hamiltonian system, does not change the classical equation of motion. Based on the observation by Feynman and Hibbs, the propagators (kernels) of the systems are calculated from the classical action, in terms of solutions of the classical equation of motion: two homogeneous solutions and one particular solution. The kernels are then used to find wave functions that satisfy the Schrödinger equation. One of the wave functions is shown to be that of a Gaussian pure state. In every case considered, we prove that the kernel does not depend on the way of choosing the classical solutions, while the wave functions depend on the choice. The generalization, which gives a rather complicated quadratic Hamiltonian, is simply interpreted as applying unitary transformation to the driven harmonic oscillator system in the Hamiltonian formulation.

Regarding the Pauli principle in quantum field theory and in many-body quantum mechanics, Feynman advocated that Pauli’s exclusion principle can be completely ignored in intermediate states of perturbation theory. He observed that all virtual processes (of the same order) that violate the Pauli principle cancel out. Feynman accordingly introduced a prescription, which is to disregard the Pauli principle in all intermediate processes. This ingenious trick is of crucial importance in the Feynman diagram technique. We show, however, an example in which Feynman’s prescription fails. This casts doubts on the general validity of Feynman’s prescription.

We show how macroscopically distinct quantum superposition states (Schrödinger cat states) may be used as logical qubit encodings for the correction of spontaneous emission errors. Spontaneous emission causes a bit flip error, which is easily corrected by a standard error correction circuit. The method works arbitrarily well as the distance between the amplitudes of the superposed coherent states increases.

It is shown that with the use of entanglement a specific two-party communication task can be done with a systematically smaller expected error than any possible classical protocol could do. The example utilizes the very tight correlation between separate spin measurements on a singlet state for small differences in the angles of these two measurements. An extension of this example to many parties arranged in a row with only local, one-to-one communication (quantum whispering) is then considered. It is argued that in this scenario there exists no reliable classical protocol, whereas in the quantum case there does.

We derive lower bounds for the attainable fidelity of standard entanglement purification protocols when local operations and measurements are subjected to errors. We introduce an error parameter which measures the distance between the ideal completely positive map describing a purification step and the one in the presence of errors. We derive nonlinear maps for a lower bound of the fidelity at each purification step in terms of this parameter.

By numerically simulating an implementation of the quantum baker’s map on a NMR quantum computer based on the molecule trichloroethylene, we demonstrate the feasibility of quantum chaos experiments on present day quantum computers. We give detailed descriptions of proposed experiments that investigate (a) the rate of entropy increase due to decoherence and (b) the phenomenon of hypersensitivity to perturbation.

We show that quantum information may be transferred between atoms in different locations by using “phantom” or “dark” photons: the atoms are coupled through electromagnetic fields, but the corresponding field modes do not have to be fully populated. In the case where atoms are placed inside optical cavities, errors in quantum information processing due to photon absorption inside the cavity are diminished in this way. This effect persists up to intercavity distances of about a meter for the current levels of cavity losses, and may be useful for distributed quantum computing.

It is demonstrated that the eavesdropping optimization obtained recently by Slutsky et al. [Phys. Rev. A 57, 2383 (1998)] for Bennett’s two-state protocol of key distribution in quantum cryptography holds, not only for the case in which an ordinary von Neumann projective measure is implemented by the legitimate receiver, but also for the case in which a positive operator-valued measure is implemented, as in Brandt et al. [Phys. Rev. A 56, 4456 (1997)]. In both cases, identical expressions hold for both the Renyi information gained by the eavesdropper and for the error rate induced by the eavesdropper in terms of the parameters characterizing the key distribution system and the eavesdropper’s probe.

We examine the behavior of the Kohn-Sham kinetic energy $T_s\left[\rho \right]$ and the interacting kinetic energy $T\left[\rho \right]$ under homogeneous density scaling, $\rho \left(\mathbf{r}\right)\to \zeta \rho \left(\mathbf{r}\right).\mathrm{}$ Using convexity arguments, we derive simple inequalities and scaling constraints for the kinetic energy. We also demonstrate that a recently derived homogeneity relation for the kinetic energy [S. B. Liu and R. G. Parr, Chem. Phys. Lett. 278, 341 (1997)] does not hold in real systems, due to nonsmoothness of the kinetic-energy functional. We carry out a numerical study of the density scaling of $T_s\left[\rho \right]$ using ab initio densities, and find it exhibits an effective homogeneity close to 5/3. We also explore alternative reference systems for the kinetic energy which have fewer particles than the true N-particle interacting system. However, we conclude that the Kohn-Sham reference system is the only viable choice for accurate calculation, as it contains the necessary physics.

We apply a method suggested by Delos [Rev. Mod. Phys. 53, 287 (1981)] to correct the Born-Oppenheimer basis by incorporation of proper boundary conditions for bound states of molecular systems. We calculate the correct nonadiabatic coupling matrix elements for ${\mathrm{H}}_2^{+}$ and its isotopic variants and use them to determine the ${\mathrm{HD}}^{+}$ vibronic spectrum.

We have considered a perturbative approach in the WKB framework. Based on an expression for $\partial E/\partial \lambda ,$ we have calculated perturbatively the Stark energy shifts for two important systems, a particle in a one-dimensional power-law potential and the hydrogen atom. The results provide important insight into the properties of these systems.

Resonances of ${}^4{S}^e$ symmetry in ${\mathrm{He}}^{-}$ are searched for in the region below the ${\mathrm{He}}^{+}\mathrm{}(n=1\mathrm{})\mathrm{}$ threshold. The energies and widths of the resonances are calculated with an ab initio three-electron description of the ion. The complex rotation method is combined with the use of B splines in a spherical cavity to describe the ion and the decaying channels. Four resonances are found. The first three resonances agree well with experiments. The fourth resonance has not been seen in an experiment yet, due to a small photodetachment cross section and large width.

The fully correlated calculations in Hylleraas coordinates for the nonrelativistic ground-state energy and the first three S-wave resonances of positronium hydride are reported. For the resonances, the positions and widths are determined using the method of complex-coordinate rotation. Our results significantly improve previous work. For example, the ground-state energy is about five parts in ${10}^9$ in accuracy, the lowest variational upper bound reported to date. A comparison with other previous work is made.

Stimulated by recent mass spectrometric observations, we have investigated several high-spin states of ${\mathrm{CO}}^{\mathrm{-}}$ to identify the observed anionic state. We follow a general construction principle for long-lived anionic states of small molecules: A possibly long-lived anionic state possesses several “equivalent” valence electrons bound to a positively charged ion core. Applying this idea to ${\mathrm{CO}}^{\mathrm{-}},$ we have found a ${}^6\Pi$ state which is stable with respect to both single-electron emission and dissociation. Since all different decay channels are spin forbidden, this state is long-lived, and will be observable in a mass spectrometer.

The self-energy (SE) correction is evaluated for a single valence $\mathrm{ns}$ electron of heavy and superheavy atoms with n up to 8 and the nuclear charge Z up to 119. The recently developed approach based on the commutator expansion is employed. Various Dirac-Slater one-electron local potentials with extended nuclei are used. The Lamb shifts were calculated by adding the average values of the Uehling potential to the SE contributions. The results confirm the earlier estimates for the quantum electrodynamical effects on the valence energies of heavy and superheavy atoms.

The nonpenetrating approximation appears to be the simplest way to allow one to incorporate nonadiabatic effects in the polarization potential calculated by means of the polarized orbital method. Unfortunately, this approximation is not well suited for an efficient implementation in quantum chemistry codes which, nowadays, use exclusively Gaussian-type orbitals. This computational limitation is remedied by replacing the incident point charge by a spherical Gaussian charge distribution, the exponent of which is suitably chosen. In so doing, we obtain a very efficient numerical algorithm that may be used with any molecular target regardless of its complexity or geometry.