The exact N-particle ground-state wave function for a one-dimensional condensate of hard-core bosons in a harmonic trap is employed to obtain accurate numerical results for the one-particle density matrix, occupation number distribution of the natural orbitals, and momentum distribution. Our results show that the occupation of the lowest orbital varies as $N^{0.59},$ in contrast to $N^{0.5}$ for a spatially uniform system, and N for a true Bose-Einstein condensate.

We derive an explicit relationship between the moment of inertia and the quadrupole response function of an interacting gas confined in a harmonic trap. The relationship holds for both Bose and Fermi systems and is well-suited to reveal the effects of irrotationality of the superfluid motion. Recent experimental results on the scissors mode are used to extract the value of the moment of inertia of a trapped Bose gas and to point out the deviations from the rigid value due to superfluidity.

We propose a method to reach conditions of high degeneracy in a trapped Fermi gas, based on the adiabatic transfer of a small fraction of atoms from a magnetic to a tighter optical trap. The transformation yields a large increase of the Fermi energy, without a significant change of the temperature. The large enhancement of the central density emphasizes the role of the interactions and makes the system much closer to the BCS transition. We show that, despite Pauli blocking, the thermalization processes ensuring equilibrium in the optical trap are not suppressed at low temperature.

We investigate the effects of higher-order, ${\chi }^{\mathrm{}\left(3\right)\mathrm{}},$ nonlinearities on the process of second-harmonic generation. In the traveling-wave case we find substantive differences in the macroscopic behavior of the fields when the ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ components are present. In the intracavity case, which has been investigated before using a linearized analysis, we investigate regions where these analyses may not be valid, comparing and contrasting the full quantum simulations with previous results.

We report an observation of essentially full spatial coherence in a high average power soft-x-ray laser. Rapid coherence buildup due to strong refractive antiguiding in a long plasma column is experimentally demonstrated. This allows the generation of fully coherent, milliwatt-level average power soft-x-ray radiation by a tabletop device. The peak brightness of this laser reaches $2\times {10}^{25}{\mathrm{photons}\mathrm{}\mathrm{s}}^{-1}{\mathrm{mm}}^{-2}{\mathrm{mrad}}^{\mathrm{-}2}$ within 0.01% spectral bandwidth, making it one of the brightest soft-x-ray sources available.

Recently, Schmidt and Schnack [Physica A 260, 479 (1998)], following earlier references, reiterate that the specific heat of N noninteracting bosons in a one-dimensional harmonic well equals that of N noninteracting fermions in the same potential. We show that this peculiar relationship between heat capacities results from a more dramatic equivalence between Bose and Fermi systems. Namely, we prove that the excitations of such Bose and Fermi systems are spectrally equivalent. Two complementary proofs of this equivalence are provided; one based on a combinatoric argument, the other from analysis of the underlying dynamical symmetry group.

Exact classical and quantal solutions are presented for the full array of intrashell transitions $n\mathcal{l}\to n{\mathcal{l}}^{\prime },$ between any angular momentum states, induced by slow distant collisions with a charged particle. The collisions are adiabatic with respect to the orbital frequency of the atomic electron and the transitions are induced by the weak ion-atom dipole field generated by the ion moving along a classical path. The rich symmetry of the problem allows a unified approach and is the source of the excellent agreement, beyond the usual Ehrenfest’s correspondence principle, between the classical and quantal treatments. A classical transition probability is defined. Probabilities for transition between any angular momentum states within a high Rydberg energy level are derived in exact analytic forms and are analyzed for a large number of numerical examples. The transition probabilities obtained from the three methods—quantal and classical formulations and Monte Carlo classical simulations—are directly compared to provide excellent agreement.

It is shown, that oscillators on the sphere and the pseudosphere are related, by the so-called Bohlin transformation, with the Coulomb systems on the pseudosphere. The even states of an oscillator yield the conventional Coulomb system on the pseudosphere, while the odd states yield the Coulomb system on the pseudosphere in the presence of magnetic flux tube generating spin $1/2.$ A similar relation is established for the oscillator on the (pseudo)sphere specified by the presence of constant uniform magnetic field $B_0$ and the Coulomb-like system on pseudosphere specified by the presence of the magnetic field ${(B/2r}_0\left)\right(|x_3/\mathbf{x}|-\epsilon ).\mathrm{}$ The correspondence between the oscillator and the Coulomb systems the higher dimensions is also discussed.

The saddle-point method is combined with the $L^2$ K-matrix method to investigate total as well as partial photoionization cross sections and electron-ion elastic and inelastic scattering cross sections. This approach allows us to use highly precise initial state and final target state wave functions. The results obtained are sufficiently accurate for experimental energy and cross-section calibrations. As an illustration, we present the results near the Li $2s2s2p{}^2{P}^o$ triply excited resonance. These results are used to recalibrate the recent high-resolution experimental spectra.

In a classical measurement the Shannon information is a natural measure of our ignorance about properties of a system. There, observation removes that ignorance in revealing properties of the system which can be considered to preexist prior to and independent of observation. Because of the completely different root of a quantum measurement as compared to a classical measurement, conceptual difficulties arise when we try to define the information gain in a quantum measurement using the notion of Shannon information. The reason is that, in contrast to classical measurements, quantum measurements, with very few exceptions, cannot be claimed to reveal a property of the individual quantum system existing before the measurement is performed.

What fundamental constraints characterize the relationship between a mixture $\rho ={\sum }_i{p}_i{\rho }_i$ of quantum states, the states ${\rho }_i$ being mixed, and the probabilities $p_i?$ What fundamental constraints characterize the relationship between prior and posterior states in a quantum measurement? In this paper we show that there are many surprisingly strong constraints on these mixing and measurement processes that can be expressed simply in terms of the eigenvalues of the quantum states involved. These constraints capture in a succinct fashion what it means to say that a quantum measurement acquires information about the system being measured, and considerably simplify the proofs of many results about entanglement transformation.

A relaxational approach to solving the Schrödinger equation is developed that utilizes split boundary conditions. The method solves the wave equation for the eigenvalues and eigenfunctions simultaneously. Advantages over numerical integration offered with the technique include simplification of the selection of boundary conditions and initial eigensystem estimates. The power of this technique is demonstrated by numerical solution of the radial Schrödinger equation for several important or problematic potentials, including the Saxon-Wood potential, the laser-dressed Coulombic potential, the regulated Coulombic potential, the Morse potential, and the Lennard-Jones potential. In order to demonstrate this method’s applicability to even highly nonlinear systems, the ground-state energy levels of the helium and lithium atomic systems are solved utilizing a self-consistent-field approximation. The application of the method to two- and three-dimensional systems is then briefly discussed.

A pair of coupled quantum dissipative oscillators, serving as a model for a nanosystem, is described here by the Lindblad equation. Its dynamic evolution is shown to exhibit the features of decoherence (spatial extent of quantum behavior), correlation (spatial scale over which the system localizes to its physical dimensions), and mixed-state entanglement (or inseparability, a special quantum feature in the case of pure states making its appearance first in bipartite systems) as a function of the coupling constants of the Lindblad equation. One interesting feature of this calculation is that the mixed-state separable entanglement may exhibit revivals in time. An initially inseparable entangled state need not remain so for all time and may exhibit regions of separable entanglement. Interpreting the parameters of the Lindblad theory as environmental features in certain experimental situations gives us clues as to the possible control of decoherence, correlation, and nature of entanglement.

An analysis of detector-efficiency in many-site Clauser-Horne inequalities is presented for the case of perfect visibility. It is shown that there is a violation of the presented n-site Clauser-Horne inequalities if and only if the efficiency is greater than $n/\left(2n-1\right).$ Thus, for a two-site two-setting experiment there are no quantum-mechanical predictions that violate local realism unless the efficiency is greater than $\frac{2}{3}.$ Second, there are n-site experiments for which the quantum-mechanical predictions violate local realism whenever the efficiency exceeds $\frac{1}{2}.$

Classical messages can be sent via a noisy quantum channel in various ways, corresponding to various choices of ensembles of signal states of the channel. Previous work by Holevo and by Schumacher and Westmoreland relates the capacity of the channel to the properties of the signal ensemble. Here we describe some properties characterizing the ensemble that maximizes the capacity, using the relative entropy “distance” between density operators to give the results a geometric flavor.

We prove the security of a quantum key distribution scheme based on transmission of squeezed quantum states of a harmonic oscillator. Our proof employs quantum error-correcting codes that encode a finite-dimensional quantum system in the infinite-dimensional Hilbert space of an oscillator, and protect against errors that shift the canonical variables p and q. If the noise in the quantum channel is weak, squeezing signal states by 2.51 dB (a squeeze factor $e^r=1.34)$ is sufficient in principle to ensure the security of a protocol that is suitably enhanced by classical error correction and privacy amplification. Secure key distribution can be achieved over distances comparable to the attenuation length of the quantum channel.

We adopt the view that information is the primary physical entity possessing objective meaning. Based on two postulates stating that (i) entanglement is a form of quantum information corresponding to internal energy and (ii) sending qubits corresponds to work, we show that in the closed bipartite quantum-communication systems, the information is conserved. We also discuss the entanglement-energy analogy in the context of the Gibbs-Helmholtz-like equation connecting the entanglement, of formation, distillable entanglement, and bound entanglement. Then we show that in the deterministic protocols of distillation, the information is conserved. We also discuss the objectivity of quantum information in the context of information interpretation of quantum states and algorithmic complexity.

We show a way to correct collective error through a three-qubit quantum code. The encoding and decoding (i.e., error recovery) operations for such a code, which protects one qubit of quantum information perfectly (with infinite “distance”) against collective decoherence, are presented. The code is actually a manifestation of a noiseless subsystem first reported by Knill, Laflamme, and Viola [Phys. Rev. Lett. 84, 2525 (2000)], and provides a good illustration of the relationship between noiseless subsystems and error-correcting codes already noted by these authors. We also show in detail how this code can be used to preserve an arbitrary joint state (including entangled states) of two qubits, by pairing each of them with two other qubits, even in the case in which the two resulting clusters interact in nonequivalent ways with a common environment.

A model correctly describing the asymptotic behavior of the charge density is used to derive an expression for the Shannon entropy in terms of the ionization potential of the system. A strong similarity is observed between this model entropy and the entropy obtained from correlated wave functions providing evidence that it is the asymptotic regions that are responsible for the behavior of the entropy. We also show via a model entropy that the behavior of the momentum space Shannon entropy is due to a correct description of the cusp behavior at the nucleus. The changes in the position and momentum space entropies as a function of a parameter are shown to be linearly related for these models. The expression for the entropy, derived from a density model that obeys the asymptotic behavior, is shown to be almost identical in nature to the general expression for entropy emanating in the stopping power formalism.

We report on the implementation and application of analytical energy gradients in four-component relativistic density-functional theory. Comparisons with numerical gradients for heavy diatomic molecules show good agreement. Results of geometry optimizations within the relativistic local-density approximation on heavy-element compounds are presented.