States near the vacuum having 〈n^〉≪1 are used for the precision determination of a phase shift. When this phase shift is sampled by enough of these near-vacuum states, its size may be extracted via data analysis. We calculate the achievable sensitivity of such schemes when we are limited in our resources to a mean total number of quanta ${\mathit{N}}_{\mathrm{tot}}$. We study in detail some examples of these near-vacuum schemes and show that in the absence of loss or noise their sensitivity approaches that of squeezed-state interferometry.

From the very beginning quantum statistical mechanics can be formulated in terms of a thermodynamic potential, which has the electron density as the basic variable. By employing a well-known procedure in quantum statistical mechanics for the construction of stationarity principles [T. D. Lee and C. N. Yang, Phys. Rev. 113, 1165 (1959); 117, 22 (1960)], the variational principles of Hohenberg, Kohn [P. Hohenberg and W. Kohn, Phys. Rev. B 136, 864 (1964)], and Mermin [N. D. Mermin, Phys. Rev. A 137, 1441 (1965)] are obtained as are generalizations thereof.

In this paper, momentum-space wave functions are obtained for unbounded relativistic motion of single electrons in a Coulomb potential. The waves are expressed in terms of a simple contour integral which is easily evaluated numerically. Various examples for motion around a bare uranium nucleus are displayed including negative-energy solutions and dependence on partial-wave angular momentum.

We consider systems coupled to a heat reservoir that has a Debye density of states. In particular, starting from master equations derived in the secular (or rotating-wave) approximation, we derive expressions for the decoherence rates and energy-jump moments for systems and couplings of varying degrees of generality. We also furnish the semiclassical analogs of these expressions. Finally, using the jump moments, we examine various aspects of the energy relaxation to thermal equilibrium.

We perform convergent close-coupling (CCC) calculations of electrons scattering on atomic sodium. We show that the results are in excellent quantitative agreement with the measurements of spin asymmetries and singlet and triplet ${\mathit{L}}_{\mathrm{\perp }}$ at the two projectile energies considered of 10 and 20 eV. The CCC method is the only one that is able to achieve this to date, and demonstrates that the very large effects of the target continuum are very accurately treated using square-integrable states. The method is applicable to all hydrogenlike atoms or ions and all projectile energies.

We describe the results of our quasiclassical calculations of the ionization probabilities of a helium atom, exposed to a short pulse of linearly polarized laser radiation. The technique known as Fermi molecular dynamics was applied. Of particular interest was our observation of the signature of a new process of double ionization, at relatively low laser irradiances. We interpret this as a signature of the simultaneous double ionization of helium. This new process was found to proceed in competition with sequential double ionization. The simultaneous double ionization of helium, as a distinct process at relatively long wavelengths, has just been discovered experimentally [D. Fittinghoff, P. Bolton, B. Chang, and K. Kulander, Phys. Rev. Lett. 69, 2642 (1993)].

We report on the observation of velocity-tuned (doppleron) resonances in the grazing-incidence reflection of thermal sodium atoms from a moving evanescent light grating created by interference between two counterpropagating laser beams. The relative velocity between the atoms and the grating can be varied continuously by adjusting the frequency of one laser. We observe an exchange of photons between copropagating and counterpropagating fields in an evanescent light grating. The results are in general agreement with a dressed-state model for the diffraction of atoms from such a grating.

It is shown that the field in a cavity, periodically kicked with classical pulses and containing a nonlinear Kerr medium, can reach the one-photon quantum state if the amplitude of the kicks and the time between the kicks are appropriately chosen.

We report the observation and characterization of chaos in stimulated Brillouin scattering (SBS) generated in a single-mode fiber in the presence of weak external feedback. We establish that the noise, which initiates this process and dominates the emission near the SBS threshold, is dramatically suppressed from the onset of strong SBS emission, giving rise to various highly deterministic dynamical features.

We report the observation of harmonics up to the 119th in helium, generated using a 1.053-μm, 1-ps chirped-pulse-amplification laser at intensities up to 3×${10}^{14}$ W/${\mathrm{cm}}^2$, and the measurement of their far-field spatial distribution. Complex spatial distributions are found for harmonics in the plateau region and near the cutoff; their angular distribution narrows to approximately that predicted by lowest-order perturbation theory.

Doubly differential ionization cross sections for positron impact on argon atoms were determined by energy- and angle-resolved measurements of ejected electrons in time correlation with the produced ions. Corresponding measurements with incident electrons were made for comparison. With primary particles (positrons or electrons) of 100 eV and ejected electrons of 15 eV, measurements were extended over electron-emission angles from 0° to 90°. Lacking theoretical predictions for the ionization of argon we compared our data with the doubly differential ionization cross sections of Klar and Berakdar computed for positron and electron impact on hydrogen. The measured angular dependence of positron and electron cross sections for Ar agrees well with the theory for H. In particular, we find that at small angles of electron ejection the cross section for positron impact exceeds that for electron impact by an order of magnitude in accordance with the calculations of Klar and Berakdar (unpublished).

A laser-induced vibrational trapping mechanism is proposed for isotope separation in the ${\mathrm{D}}_2^{+\mathrm{-}}$${\mathrm{H}}_2^{+}$ system interacting with an intense field. The theory is based on laser-induced quasibound states that can suppress the photodissociation of one of the isotopes, whereas the other still has a large dissociation rate. Such states, the existence of which has previously been evidenced, can be reached by appropriately adjusting laser parameters (wavelength and intensity). Great efficiency is expected for conveniently prepared initial vibrational states of a rotationless isotope and using a continuous-wave laser.

The quantum-mechanical double harmonic oscillator is proposed as a model for the generation of Schrödinger-cat states. To demonstrate this the quantum-statistical properties of the double oscillator in its ground state are examined. The nonclassical nature of this state and interference effects are analyzed. The squeezing properties of the double harmonic oscillator are calculated and compared with those of the ‘‘idealized’’ cat state. The behavior of the quasiprobability distribution function is also discussed.

We discuss the canonical quantization of an interacting massless U(1) gauge field using a bosonic gauge-fixing method. We present a way to make the transformation between the Lorentz and the Coulomb gauge of such theories, without using an explicit representation of the fields in terms of creation-annihilation operators. We demonstrate this method in the case of Maxwell photons interacting with Schrödinger electrons and then we treat, with the same methods, a system of higher-dimensional equations appearing in the framework of a manifestly covariant relativistic quantum theory. The nonrelativistic limit of the Coulomb term for such a theory is discussed and compared to the Fokker action appearing in the Wheeler-Feynman action-at-a-distance theory for electromagnetic interactions.

A rigorous expression for the partition function of N identical fermions with spin 1/2 is obtained in a form suitable for a path-integral Monte Carlo (PIMC) simulation of a many-electron system at a finite temperature. A sum over permutations is reduced to a sum over classes with readily determinable factors. A distribution over projections and values of the total spin is also obtained, enabling PIMC calculations of spin-dependent quantities. An MC algorithm is proposed which accounts simultaneously for all types of trajectory linkages. A test calculation, four electrons in a spherical cavity with a radius of 1 nm at a temperature of 300–2000 K, is performed.

An analaysis of errors in measurement yields insight into the penetration of quantum particles into classically forbidden regions. In addition to physical values, realistic measurements yield ‘‘unphysical’’ values which, we show, can form a consistent pattern. An experiment to isolate a particle in a classically forbidden region obtains negative values for its kinetic energy. These values realize the concept of a weak value, discussed in previous works.

It is argued that quantum-mechanical β functions can be derived consistently by using renormalization length scales implied by the quasiclassical minimization of Hamiltonian forms. Our renormalization-group results for the Dirac-Coulomb system can then be related analytically to ones obtained in ladder quantum electrodynamics in four space-time dimensions. Involving spinless relativistic two-body Hamiltonians, one can present exact energy- and β-function solutions for the Lorentz scalar linear potential. Inverse-square, other linear, and mixed linear plus Coulomb potentials can also be treated. The exact energy of this last potential has been discussed in conjunction with an alternative β function.

Orthogonal trigonometric basis functions in (-π,π) are considered and the suitability of Fourier-like expansions involving odd harmonics of the semifundamental frequency is noted. Comparison with the conventional representation is made, pointing out the advantages of employing non-Fourier bases. As a practical application, near-exact results of variational calculations for the ground state of the quartic-anharmonic-oscillator problem are presented both for small and large coupling strengths.

The geometric structure of the law of quantum-state evolution is studied. The Fubini-Study metric induced on the quantum evolution submanifold of the projective Hilbert space is shown to be completely expressed by the uncertainties and correlations of various generators of evolutions. The Riemannian connection is expressed as a quantum-mechanical expectation value of a certain Hermitian operator. It is discussed that the metric carries some of quantum numbers contained in a given reference state, in general, and consequently the geometry is inherently quantized. These results are demonstrated by the simple examples of the squeezed coherent state, displaced number state, squeezed number state, and generalized coherent spin state.