For the models of N-body identical harmonic oscillators interacting through potentials of homogeneous degree -2, the unitary operator that transforms a system of time-dependent parameters into that of unit spring constant and unit mass of different time scale is found. If the interactions can be written in terms of the differences between positions of two particles, it is also shown that the Schrödinger equation is invariant under a unitary transformation. These unitary relations can be used not only in finding coherent states from the given stationary states in a system, but also in finding exact wave functions of the Hamiltonian systems of time-dependent parameters from those of time-independent Hamiltonian systems. Both operators are invariant under the exchange of any pair of particles. The transformations are explicitly applied for some of the Calogero-Sutherland models to find exact coherent states.

We find the optimal universal way of manipulating a single qubit, $|\psi (\vartheta ,\phi )〉,$ such that $(\vartheta ,\phi )\to (\vartheta -\alpha ,\phi -\beta ).\mathrm{}$ Such optimal transformations fall into two classes. For $0<~\alpha <~\pi /2,$ the optimal map is the identity and the fidelity varies monotonically from 1 (for $\alpha =0)$ to $\frac{1}{2}$ (for $\alpha =\pi /2).\mathrm{}$ For $\pi /2\mathrm{}<~\alpha <~\pi ,$ the optimal map is the universal-NOT gate and the fidelity varies monotonically from $\frac{1}{2}$ (for $\alpha =\pi /2)$ to $\frac{2}{3}$ (for $\alpha =\pi ).\mathrm{}$ The fidelity $\frac{2}{3}$ is equal to the fidelity of measurement. It is therefore rather surprising that for some values of $\alpha$ the fidelity is lower than $\frac{2}{3}.$ For instance, a universal square root of NOT operation is more difficult to approximate than the universal NOT gate itself.

This paper represents one approach to making explicit some of the assumptions and conditions implied in the widespread representation of numbers by composite quantum systems. Any nonempty set and associated operations is a set of natural numbers or a model of arithmetic if the set and operations satisfy the axioms of number theory or arithmetic. This paper is limited to $k-\mathrm{ary}$ representations of length L and to the axioms for arithmetic modulo $k^L.$ A model of the axioms is described based on an abstract L-fold tensor product Hilbert space ${\mathcal{H}}^{\mathrm{arith}}.$ Unitary maps of this space onto a physical parameter based product space ${\mathcal{H}}^{\mathrm{phy}}$ are then described. Each of these maps makes states in ${\mathcal{H}}^{\mathrm{phy}},$ and the induced operators, a model of the axioms. Consequences of the existence of many of these maps are discussed along with the dependence of Grover’s and Shor’s algorithms on these maps. The importance of the main physical requirement, that the basic arithmetic operations are efficiently implementable, is discussed. This condition states that there exist physically realizable Hamiltonians that can implement the basic arithmetic operations and that the space-time and thermodynamic resources required are polynomial in L.

We present a method that allows state-selective measurement of the lifetime of metastable doubly charged molecular ions. The method is based on the simultaneous measurement of kinetic-energy release upon dissociation and lifetime and relies on three-dimensional fragment imaging. The experimental determination of the energy and lifetime of a vibrational state provides a stringent test for the theory. Using this method, we have measured the lifetime of two vibrational states of ${}^{12}{\mathrm{C}}^{16}{\mathrm{O}}^{2+}.$ Explicitly, $\tau =670\mathrm{}\pm 50\hspace{0.5em}\mathrm{ns}$ and $\tau =26\mathrm{}\pm 5\hspace{0.5em}\mathrm{ns}$ were measured for the states with $E_k=5.713\mathrm{}\hspace{0.5em}\mathrm{eV}$ and $E_k=5.841\mathrm{}\hspace{0.5em}\mathrm{eV},$ respectively. The measured mean lifetimes and kinetic-energy releases are consistent with previous measurements, and the results indicate that further theoretical work is required.

In the present work, the method of continued fractions at a five-channel close-coupling level of approximation is applied to study the low-energy electron-impact excitation in linear molecules. Particularly, cross sections for the $X^1{\Sigma }_g^{+}\to b^3{\Sigma }_u^{+},$ $X^1{\Sigma }_g^{+}\to a^3{\Sigma }_g^{+},$ and $X^1{\Sigma }_g^{+}\to c^3{\Pi }_u$ transitions in ${\mathrm{H}}_2$ in the (15–40)-eV energy range are reported. As in our early two-state studies, no orthogonality constraint between the bound and continuum orbitals is imposed and the one-electron exchange terms are considered explicitly. In general, our calculated cross sections are in good agreement with the results obtained by the four-state Kohn variational method. Comparison between our calculated results with available experimental data is encouraging.

The development of integrated, waveguide-based atom optical devices requires a thorough understanding of nonlinear matter-wave mixing processes in confined geometries. This paper analyzes the stability of counterpropagating two-component Bose-Einstein condensates in such a geometry. The steady-state field equations of this system are solved analytically, predicting a multivalued relation between the input and output field intensities. The spatiotemporal linear stability of these solutions is investigated numerically, leading to the prediction of a self-oscillation threshold that can be expressed in terms of a matter-wave analog of the Fresnel number in optics.

We investigate the properties of a degenerate dilute gas of neutral fermionic particles in a harmonic trap that interact via dipole-dipole forces. We employ the semiclassical Thomas-Fermi method and discuss the Dirac correction to the interaction energy. A nearly analytic as well as an exact numerical minimization of the Thomas-Fermi-Dirac energy functional are performed in order to obtain the density distribution. We determine the stability of the system as a function of the interaction strength, the particle number, and the trap geometry. We find that there are interaction strengths and particle numbers for which the gas cannot be trapped stably in a spherically symmetric trap, but both prolate and oblate traps will work successfully.

We consider multimode homodyne tomography with a single local oscillator and derive sampling functions for multimode s-parametrized quasidistributions and s-ordered moments of creation and annihilation operators. In both cases, loss-compensating sampling functions, applicable to realistic measurement with imperfect detection, are provided. Results of Monte Carlo simulations for a squeezed three-mode state are reported and the feasibility of reconstruction of the three-mode Q function from ${10}^7$ sampled data points is demonstrated.

We solve the problem of a neutral atom interacting with a charged wire, giving rise to an attractive ${1/r}^2$ potential in two dimensions. We show how a suitable average over all possible self-adjoint extensions of the radial Schrödinger Hamiltonian eventually leads to the classical formula for absorption of the atom, a formula shown to be in agreement with a recent experiment.

A direct experimental evidence of non-Coulombic states of ${\mathrm{N}}_2{}^{4+}$ and ${\mathrm{O}}_2{}^{4+}$ transient multicharged ions is presented using laser-induced Coulomb explosion and kinetic-energy spectra measurements of, respectively, the ${\mathrm{N}}^{2+}+{\mathrm{N}}^{2+}$ and ${\mathrm{O}}^{2+}+{\mathrm{O}}^{2+}$ fragmentation channels. The substructure patterns of the energy spectra provide an unambiguous identification of several fragmentation channels within the same final charge states of the fragments. Higher laser intensities favor higher energetic channels. This experimental fact and ab initio calculations from the literature indicate that the molecule explodes at an internuclear distance range close to the equilibrium internuclear distance for these high energetic channels.

Spatial soliton-induced cloning, which achieves and maintains perfect spatial overlap of interacting beams, is proposed as a tool for amplification of nonlinear optical effects on propagation. This is illustrated by the enhancement of the parametric amplification, obtained through pump-induced cloning of the transverse profiles of the copropagating probe and generated four-wave mixing beams, in an all-optical antiwaveguiding configuration.

We study the synchronization of feedback-induced chaos in semiconductor lasers by the optical injection scheme that consists of a transmitter laser with external optical feedback and a receiver laser with optical injection from the transmitter laser. The stable synchronization condition and the effects of the frequency detuning between the transmitter and the receiver lasers are investigated using numerical simulation. The results show that positive and negative frequency detuning exert different influences on the synchronization. A time lag between the waveforms of the transmitter and the receiver lasers in the case of a large frequency detuning is found and its experimental significance is commented on.

Upon entangling a spatial binary alternative of a photon with its polarization, one can use single photons to study arbitrary 2-qubit states. Sending the photon through a Mach-Zehnder interferometer, equipped with sets of wave plates that change the polarization, amounts to performing a unitary transformation on the 2-qubit state. We show that any desired unitary gate can be realized by a judicious choice of the parameters of the setup and discuss a number of applications. They include the diagnosis of an unknown 2-qubit state, an optical Grover search, and the realization of a thought experiment invented by Vaidman, Aharonov, and Albert.

We observe transitions between Rydberg states driven by intense 500-ps-wide half-cycle electric-field pulses in a microwave transmission line. Using two identical temporally spaced pulses we can perform spectroscopic measurements. We have measured fine-structure intervals between the $d_{3/2}$ and $d_{5/2}$ states in Na and K using this technique. The frequency measurements span two orders of magnitude and are an order of magnitude more accurate than previous direct measurements of these transitions and more than a factor of 2 more accurate than previous high-precision microwave measurements.

Radiative lifetimes in the B I ${2s}^2\mathrm{ns}{}^{2}S$ $(n<~7)$ and ${2s}^2\mathrm{nd}{}^{2}D$ $(n<~6)$ sequences have been measured employing selective laser excitation at vacuum ultraviolet wavelengths. Theoretical calculations were performed using the multiconfiguration Hartree-Fock method. In particular the effect of configuration interaction with the sequence perturbers ${2s2p}^2{}^{2}S$ and ${}^{2}D$ was studied.

Uncertainties involving the distribution of nuclear magnetism that affect the interpretation of ground-state hyperfine splitting (hfs) in hydrogenlike ions can be avoided by also measuring hyperfine splitting in lithiumlike ions. Because a recent experiment looking for hfs in lithiumlike bismuth at the predicted value of 0.7971(2) eV had negative results, we have repeated the calculation using a QED approach based on both screened potentials and the Coulomb potential. We find 0.797 15(13) eV, in good agreement with the previous calculation.

We discuss spectral profiles from the point of view of a Boltzmann transport relaxation equation. We present an exact solution to the Fokker-Planck-type equation in the soft collision limit for the special case of a quadratic speed-dependent collisional width and shift of the line. The resultant spectral profile is compared to several related, more approximate expressions reported previously.

The hyperfine structure of ground-state muonic helium is calculated numerically using the variational approach. Comparison to former theoretical and experimental results is made and prospects for the high-precision determination of related physical constants are drawn.

The interaction of a high-intensity 60-fs laser pulse with argon clusters is investigated experimentally using methods of x-ray spectroscopy. It is shown that the plasma emission in the vicinity of He-like Ar XVII resonance line contains intense satellites caused by transitions in Li-like, Be-like, and other argon ions. It is shown that observed spectra could be explained by the presence of hot electrons in moderately ionized plasma. A simple physical model of plasma creation is proposed involving the incident picosecond prepulse followed by the main laser femtosecond pulse. Atomic kinetic calculations based on the proposed model give a good description of the experimental data.