We show that wave-packet interference techniques can reconstruct the quantum state of wave packets excited by strong laser pulses. The measurement may be accomplished even when the strength of the excitation is sufficient to significantly deplete the ground state. The probe of the wave packet can still remain perturbative. An inversion algorithm is also developed that is a generalization of the standard Ramsey fringe probe of a wave packet. The normalized sums and differences of the populations of two of the Rydberg states display Ramsey fringes and from these fringes the relative phase between these two states can be found. The algorithm offers advantages in efficiency over previous interferometric algorithms. The algorithm is not sensitive to the precise nature of the distribution of the phase between the pump and probe pulses.

We demonstrate a contradiction of quantum mechanics with local hidden variable theories for continuous quadrature phase amplitude (“position” and “momentum”) measurements. A contradiction is shown possible for two quantum states: a pair-coherent state, and a superpositions of two coherent states, where the superposition state has been squeezed by the action of a two-mode squeezing operator. In one case a contradiction is still possible for states of increasing photon number, though the effect becomes smaller and more difficult to observe. The high efficiency of the homodyne method of measurement of quadrature phase amplitudes may open a way for a loophole-free test of local hidden variable theories, and the effect of detection loss on the contradiction with local hidden variables is calculated.

In the scalar Aharonov-Bohm effect, a charged particle (electron) interacts with the scalar electrostatic potential U in the field-free (i.e., force-free) region inside an electrostatic cylinder (Faraday cage). Using a perfect single-crystal neutron interferometer we have performed a “dual” scalar Aharonov-Bohm experiment by subjecting polarized thermal neutrons to a pulsed magnetic field. The pulsed magnetic field was spatially uniform, precluding any force on the neutrons. Aligning the direction of the pulsed magnetic field to the neutron magnetic moment also rules out any classical torque acting to change the neutron polarization. The observed phase shift is purely quantum mechanical in origin. A detailed description of the experiment, performed at the University of Missouri Research Reactor, and its interpretation is given in this paper.

The notion of wave-particle duality may be quantified by the inequality $V^2{+K}^2<~1,$ relating interference fringe visibility V, and path knowledge K. With a single-photon interferometer in which polarization is used to label the paths, we have investigated the relation for various situations, including pure, mixed, and partially mixed input states. A quantum-eraser scheme has been realized that recovers interference fringes even when no which way information is available to erase.

Detailed analysis of the coupled Dirac-Maxwell equations and the structure of their solutions is presented. Numerical solutions of the field equations in the case of spherical symmetry with negligible gravitational self-interaction reveal the existence of families of solitons with electric-field dominance that are completely determined by the observed charge and mass of the underlying particles. A soliton is found which has the charge and mass of the electron as well as a charge radius of ${10}^{-23}\hspace{0.5em}\mathrm{m}.$ This is well within the present experimentally determined upper limit of $\simeq {10}^{-18}\hspace{0.5em}\mathrm{m}.$ Properties of these particles as well as possible extension to the work herein are discussed.

A moving dielectric appears to light as an effective gravitational field. At low flow velocities the dielectric acts on light in the same way as a magnetic field acts on a charged matter wave. We develop in detail the geometrical optics of moving dispersionless media. We derive a Hamiltonian and a Lagrangian to describe ray propagation. We elucidate how the gravitational and the magnetic models of light propagation are related to each other. Finally, we study light propagation around a vortex flow. The vortex shows an optical Aharonov-Bohm effect at large distances from the core, and, at shorter ranges, the vortex may resemble an optical black hole.

The geometric phase in Dirac relativistic quantum theory is obtained in this paper. It is slightly different from Berry’s nonrelativistic result, and satisfies the invariance of the general Lorenz transformation in the relativistic quantum theory. This relativistic geometric phase can reduce to Berry’s expression when we adopt the nonrelativistic approximation.

We consider the application of the supersymmetric quantum-mechanical formalism to the Schrödinger equation describing a particle characterized by a position-dependent effective mass $m\left(x\right).$ We show that any one-dimensional quantum system with effective mass has a supersymmetric partner system characterized by the same position dependence of the mass, but with a new potential function. The form of this supersymmetric partner potential $V_2\mathrm{}\left(x\right)\mathrm{}$ depends on both the form of the original potential $V_1\mathrm{}\left(x\right)\mathrm{}$ and the form of the mass x dependence. We also generalize the concept of shape invariance to the nonconstant mass scenario. As illustrative examples we provide, for a given form $m\left(x\right)\mathrm{}$ of the effective mass, shape-invariant potentials exhibiting (a) harmonic-oscillator-like spectra and (b) Morse-like spectra. In both cases the energy eigenvalues and eigenfunctions can be obtained in algebraic fashion.

The constraints imposed by relativistic covariance on the law of motion of fermions in the trajectory interpretation of quantum mechanics are examined. It is found that the quantum current satisfies a uniqueness property that fixes the guidance law. This in turn fixes the nonrelativistic equation which generally differs from that originally given by de Broglie and Bohm for electrons. These results extend to Bohm’s noncovariant many-body theory. The demonstration does not exclude other guidance equations and this is shown by the explicit construction of an alternative Lorentz covariant many-body theory possessing future-causal space-time paths.

Suppose an oracle is known to hold one of a given set of D two-valued functions. To successfully identify which function the oracle holds with k classical queries, it must be the case that D is at most $2^k.$ In this paper we derive a bound for how many functions can be distinguished with k quantum queries.

We present a data-processing scheme, a hybrid of existing cellular automata (CA) and gate array architectures, which is optimized for realization at the quantum scale. For classical computing, our CA-like external clocking avoids problems associated with existing ground-state relaxation schemes. For quantum computing, our architecture constitutes a paradigm whereby the algorithm is embedded in spatial, as opposed to temporal, structure; we discuss the consequences for algorithmic efficiency. Two potential physical realizations of the scheme are discussed.

We show that the Jaynes principle is indeed a proper inference scheme when applied to compound systems and will correctly produce the entangled maximum entropy states compatible with appropriate data. This is shown in a particular example considered recently by Horodecki et al. [Phys. Rev. A 59, 1799 (1999)], by including the dispersion of the entanglement along with its mean value as constraints and an application of the uncertainty principle. We also construct a “thermodynamiclike” description of the entanglement arising out of the maximum entropy principle.

We consider a disentanglement process in which local properties of an entangled state are preserved, while the entanglement between the subsystems is erased. Sufficient conditions for a perfect disentanglement (into product states and into separable states) are derived, and connections to the conditions for perfect cloning and for perfect broadcasting are observed.

The concept of entanglement splitting is introduced by asking whether it is possible for a party possessing half of a pure bipartite quantum state to transfer some of his entanglement with the other party to a third party. We describe the unitary local transformation for symmetric and isotropic splitting of a singlet into two branches that leads to the highest entanglement of the output. The capacity of the resulting quantum channels is discussed. Using the same transformation for less than maximally entangled pure states, the entanglement of the resulting states is found. We discuss whether they can be used to do teleportation and to test the Bell inequality. Finally, we generalize to entanglement splitting into more than two branches.

An exploratory approach to the possibility of analyzing nonorthogonality as a quantifiable property is presented. Three different measures for the nonorthogonality of pure states are introduced, and one of these measures is extended to single-particle density matrices using methods that are similar to recently introduced techniques for quantifying entanglement. Several interesting special cases are considered. It is pointed out that a measure of nonorthogonality can meaningfully be associated with a single mixed quantum state. It is then shown how nonorthogonality can be unlocked with classical information; this analysis reveals interesting inequalities and points to a number of connections between nonorthogonality and entanglement.

We present a classical model for bulk-ensemble NMR quantum computation: the quantum state of the NMR sample is described by a probability distribution over the orientations of classical tops, and quantum gates are described by classical transition probabilities. All NMR quantum computing experiments performed so far with three quantum bits can be accounted for in this classical model. After a few entangling gates, the classical model suffers an exponential decrease of the measured signal, whereas there is no corresponding decrease in the quantum description. We suggest that for small numbers of quantum bits, the quantum nature of NMR quantum computation lies in the ability to avoid an exponential signal decrease.

When coherent states of the electromagnetic field are used to drive the evolution of a quantum computer, a decoherence results due to the back reaction from the qubits onto the fields. We show how to calculate this effect. No assumptions about the environment are necessary, so this represents a useful model to test the fidelity of quantum error correcting codes. We examine two cases of interest. First, the decoherence from the Walsh-Hadamard transformations in Grover’s search algorithm is found [Phys. Rev. Lett. 79, 325 (1997)]. Interference effects, and decoherence-dependent phases, are present that could be useful in reducing the decoherence. Second, Shor’s fault-tolerant controlled-NOT gate is examined, utilizing frequency-selective pulses [Proceedings, 35th Annual Symposium on Foundations of Computer Science (IEEE Press, New York, 1994), pp. 56–65]. This implementation is found not to be optimal in regards to fault-tolerant quantum computation.

The radial and electron-pair density functions of two bound excited states of the helium anion have been calculated at the full configuration-interaction level with an extended basis set. It is shown that the form of the radial density in the ${\mathrm{}\left(1s2s2p\right)\mathrm{}}^{4}P$ and ${(2p}^3{)}^{4}S$ states of ${\mathrm{He}}^{-}$ is readily interpreted in terms of orbital contributions, even at the full configuration level at which level of theory the notion of an electronic configuration loses its precise meaning. The smaller radial distance of the L-shell maximum in the ${}^{4}S$ state relative to the lower-lying ${}^{4}P$ state is interpreted in terms of a higher effective nuclear charge in the ${}^{4}S$ state. The more compact electron cloud of the ${}^{4}S$ state leads to a narrower intracule density than that observed for the ${}^{4}P$ state. The ${}^{4}S$ state is shown to have a Coulomb hole with the same classic form as the ground state of helium but with a radius that is about six times larger. The depth of the Coulomb hole is substantially greater in the ${}^{4}S$ state than in the ${}^{4}P$ state, as expected from the fact that the correlation energy is greater in the former state. The Coulomb holes of both states exhibit a vanishingly small depth at small interelectronic distances due to the presence of the Fermi hole.

We have made measurements of the $7G-H,$ $7H-I,$ $9G-H,$ $9H-I,$ and the $10G-H$ intervals in helium. These measurements are in good agreement with theoretical calculations up to the level of about 1 kHz precision. This confirms the importance of retardation to the intervals with about 1% precision. At the 1 kHz level, however, systematic discrepancies are seen which cannot be accounted for by suggested additional retardation corrections.