We study the time evolution of quantum systems with a time-dependent Hamiltonian given by a linear combination of SU(1,1) and SU(2) generators. The invariant Hermitian operator is constructed in the same manner as for both the SU(1,1) and SU(2) systems. With the help of the invariant Hermitian operator we obtain not only the exact solutions of the Schrödinger equation but also the time-evolution operator. The adiabatic and nonadiabatic Berry phases are calculated with the exact solutions. © 1996 The American Physical Society.

Squeezing the signal field or the local oscillator can improve the accuracy of homodyne detection. We show that an equivalence exists between antisqueezing the signal field and squeezing the local oscillator state. The importance of this result is illustrated in two contexts: a homodyne measurement of squeezing and the reconstruction of the wave function. © 1996 The American Physical Society.

A scheme for the "protective measurement" [Phys. Rev. A 47, 4616 (1993)] of the wave function of a squeezed harmonic-oscillator state is described. This protective measurement is shown to be equivalent to a measurement of an ensemble of states. The protective measurement, therefore, allows for a definition of the quantum wave function on a single system. Yet, this equivalency also suggests that both measurement schemes account for the epistemological meaning of the wave function only. The protective measurement requires a full a priori knowledge of the measured state. The intermediate cases, in which only partial a priori information is given, are also discussed.

The exact electronic ground-state density and external potential are used to improve the accuracy of approximate density functionals. Our approach combines the advantages that the exact exchange-correlation energy functional is more local for full-coupling strength than for the coupling-constant average, and that knowledge of the exact virial can be used to reduce the exchange energy error by a factor of 2.

The exchange-correlation energy is calculated from expressions for $\frac{(E_{\mathrm{xc}}+T_c)}{2}$ and $\frac{(E_{\mathrm{xc}}-T_c)}{2}$. The expression for $E_{\mathrm{xc}}+T_c$ is known exactly. The expression for $E_{\mathrm{xc}}-T_c$ is not known exactly and we approximate $G_{\mathrm{xc}}-T_c$, where $G_{\mathrm{xc}}=E_{\mathrm{xc}}+\frac{J}{N}$, by assuming that it is a functional that is homogeneous of degree 1 in the electron density and that $T_c$ is homogeneous of degree 0 in the electron density. The resulting formula for the total energy reduces the average of the errors in the Parr and Ghosh [Phys. Rev. A 51, 3564 (1995)] approximation by about one-half.

The time evolution of the rotational alignment of $\mathrm{NO}\left[A{}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}\right(v^{\prime }=0\left)\right]$ and C${\mathrm{O}}_2$ as quench gas is measured by picosecond laser spectroscopy. The rates for alignment destroying collisions are obtained to be $J$ and pressure dependent. For a C${\mathrm{O}}_2$ pressure of about 80 mbar the relaxation time for laser-induced alignment is found to be ${\tau }_2=155\mathrm{}$ ps for $J^{\prime }=3.5\mathrm{}$, while it is ${\tau }_2=330\mathrm{}$ ps for $J^{\prime }=10.5\mathrm{}$. High rotational $J$ levels are shown to have an enhanced propensity to preserve anisotropic distributions of $m_J$ states. These results give important insights into the mechanisms for the destruction of rotational alignment.

The interaction of ${\mathrm{Ar}}^{\mathrm{}(17,18)+}$ ions with ${\mathrm{C}}_{60}$ has been studied by observing coincidences between Ar $K$ x rays and the fullerene ions and fragments. At large distances the capture of electrons from ${\mathrm{C}}_{60}$ into excited states of the ion has been observed and compared to the interaction of the same ions with surfaces. Most of the observed events correspond to the capture of many electrons by the ion and the loss of all but one. These results show clearly the characteristic behavior of ions flying over a surface without any contact.

The ionization of potassium Rydberg atoms with $n\sim 388$ and $n\sim 520$ by pulsed electric fields whose durations, which range from ∼ 2 to ∼ 110 ns, span the transition from the short-pulse to the long-pulse regime is investigated experimentally and the data compared with the results of classical trajectory Monte Carlo calculations. We observe excellent agreement between theory and experiment providing a benchmark test for the validity of the classical limit of ionization. Very-high-$n$ atoms provide an excellent tool with which to probe the response of atoms to pulsed electric fields in the short-pulse regime.

We investigate quantum-mechanical effects in the recollision picture of high-harmonic generation, relate these to its classical counterpart, and discuss the generation of attosecond pulses from recollision bremsstrahlung.

The expression for the azimuthal force on an atom in a circularly polarized Laguerre-Gaussian beam is shown to contain a term that depends upon the coupling of the intrinsic spin and orbital angular momenta of the light. Consequently, the state of polarization of the light affects the gross motion of the atom and not simply its internal dynamics. The effect arises from the spin-orbit coupling exhibited in the linear momentum density of the free-space mode.

We apply optimal control techniques to maximize the absorptionless index of refraction, the density-dependent piezophotonic switching between absorption and amplification, and the ground-state energy-level-spacing-dependent magnetophotonic switching of susceptibility in a dense medium of coherently prepared three-level systems.

Uncertainty relations between a bounded coordinate operator and a conjugate momentum operator frequently appear in quantum mechanics. We prove that physically reasonable minimum-uncertainty solutions to such relations have quantized expectation values of the conjugate momentum. This implies, for example, that the mean angular momentum is quantized for any minimum-uncertainty state obtained from any uncertainty relation involving the angular-momentum operator and a conjugate coordinate. Experiments specifically seeking to create minimum-uncertainty states localized in angular coordinates therefore must produce packets with integer angular momentum. © 1996 The American Physical Society.

A quantum-mechanical description of the continuous Stern-Gerlach effect is developed in which environmental effects, as well as effects arising from the continuous measurement of the electronic z motion, are taken into account. Master equations are presented that describe the behavior of a quantum statistical ensemble of continuous measurement processes. On the basis of these master equations and with the help of the quantum-state diffusion model a theoretical description of individual continuous measurement processes is developed. © 1996 The American Physical Society.

We investigate the Dirac Hamiltonian for an atomic electron coupled to a classical radiation field. Our starting point is the exact retardation expansion of the electromagnetic potentials in the Poincaré gauge. Specific prescriptions, which are the same for the Dirac and Pauli equations, are stated for obtaining, to any order of retardation, the genuine electric, magnetic, and displacement-current multipole contributions to the Hamiltonian. Accordingly, one has to carry out an appropriate phase-factor transformation of the wave function for every retardation correction that is linear in the field except for the first-order one. Along with the electric multipole interactions, the corresponding phase factors have the same functional dependence on coordinates and time in relativistic as well as in nonrelativistic quantum mechanics. We have derived and written explicitly the three different kinds of multipole terms in both the Dirac and Pauli Hamiltonians, within a fourth-order retardation approach. In the nonrelativistic limit, the Dirac magnetic and displacement-current multipole corrections split termwise into linear orbital contributions and their spin counterparts. Moreover, they combine to yield the quadratic orbital terms of the Pauli Hamiltonian. © 1996 The American Physical Society.

Semiclassical theories similar to stochastic electrodynamics are widely used in optics. The distinguishing feature of such theories is that the quantum uncertainty is represented by random statistical fluctuations. They can successfully predict some quantum-mechanical phenomena; for example, the squeezing of the quantum uncertainty in the parametric oscillator. However, since such theories are not equivalent to quantum mechanics, they will not always be useful. Complex number representations can be used to exactly model the quantum uncertainty, but care has to be taken that approximations do not reduce the description to a hidden variable one. This paper helps show the limitations of ‘‘semiclassical theories,’’ and helps show where a true quantum-mechanical treatment needs to be used. Third-order correlations are a test that provides a clear distinction between quantum and hidden variable theories in a way analogous to that provided by the ‘‘all or nothing’’ Greenberger-Horne-Zeilinger test of local hidden variable theories. © 1996 The American Physical Society.

A method for calculating the analytical solutions of the one-dimensional Schrödinger equation is suggested. A general discussion of the possible forms of the potentials and wave functions that are necessary to get the analytical solution is presented. In general, the analytical solutions appear in multiplets corresponding to the quantum number n of the harmonic oscillator. As an application, known solutions for the anharmonic oscillators are critically recalculated and a few additional results are found. Analytical solutions are also found for the generalized Morse oscillators. © 1996 The American Physical Society.

The consistent histories formalism is discussed using path-projected states. These are used to analyze various criteria for approximate consistency. The connection between the Dowker-Halliwell criterion and sphere packing problems is shown and used to prove several bounds on the violation of probability sum rules. The quantum Zeno effect is also analyzed within the consistent histories formalism and used to demonstrate some of the difficulties involved in discussing approximate consistency. The complications associated with null histories and infinite sets are briefly discussed. © 1996 The American Physical Society.

We analyze the quantum Langevin equation obtained for the Ford-Kac-Mazur and related models. We study an explicit expression for the correlation function of the noise, obtained by making use of the normal-ordered product of operators. Such an expression is divergence-free, does not require any frequency cutoff, and yields the classical (Markoffian) case in the limit of vanishing ħ. We also bring to light and discuss two different regimes for the momentum autocorrelation. The high-temperature and weak-coupling limits are considered, and the latter is shown to be related to van Hove’s ‘‘${\lambda }^2$T’’ limit. © 1996 The American Physical Society.

When an observer wants to identify a quantum state, which is known to be one of a given set of nonorthogonal states, the act of observation causes a disturbance to that state. We investigate the trade-off between the information gain and that disturbance. This issue has important applications in quantum cryptography. The optimal detection method, for a given tolerated disturbance, is explicitly found in the case of two equiprobable nonorthogonal pure states. © 1996 The American Physical Society.

If two separated observers are supplied with entanglement, in the form of n pairs of particles in identical partly entangled pure states, one member of each pair being given to each observer, they can, by local actions of each observer, concentrate this entanglement into a smaller number of maximally entangled pairs of particles, for example, Einstein-Podolsky-Rosen singlets, similarly shared between the two observers. The concentration process asymptotically conserves entropy of entanglement—the von Neumann entropy of the partial density matrix seen by either observer—with the yield of singlets approaching, for large n, the base-2 entropy of entanglement of the initial partly entangled pure state. Conversely, any pure or mixed entangled state of two systems can be produced by two classically communicating separated observers, drawing on a supply of singlets as their sole source of entanglement. © 1996 The American Physical Society.