Yehuda B. Band

Four-wave mixing with matter waves

The advent of the laser as an intense source of coherent light gave rise to nonlinear optics, which now plays an important role in many areas of science and technology. One of the first applications of nonlinear optics was the multi-wave mixing, of several optical fields in a nonlinear medium (one in which the refractive index depends on the intensity of the field) to produce coherent light of a new frequency. The recent experimental realization of the matter-wave ‘laser’,—based on the extraction of coherent atoms from a Bose–Einstein condensate—opens the way for analogous experiments with intense sources of matter waves: nonlinear atom optics. Here we report coherent four-wave mixing in which three sodium matter waves of differing momenta mix to produce, by means of nonlinear atom–atom interactions, a fourth wave with new momentum. We find a clear signature of a four-wave mixing process in the dependence of the generated matter wave on the densities of the input waves. Our results may ultimately facilitate the production and investigation of quantum correlations between matter waves.

Dissociation processes of polyatomic molecules

A general quantum mechanical theory is considered for the diverse dissociation processes of polyatomic molecules. The theory emphasizes the use of the proper normal vibrational coordinates for both the initial state of the polyatomic molecule and the final state of the dissociation fragments. The present theory provides a significant advance over all previous ones that invoke the quasidiatomic hypothesis, wherein the reaction coordinate is taken to be an initial normal mode, the remaining fragment normal modes are assumed to be identical to initial state normal modes, and the dissociation into vibrationally excited fragments is assumed to arise from the final state interactions occurring during the recoil of the fragments. Our more general theory of the vibrational and translational energy distributions in the fragments leads to a generalized Franck–Condon description of dissociation processes in terms of multidimensional bound‐continuum matrix elements which can be reduced to one‐dimensional ones that ar...

Theory of diatomic molecule photodissociation: Electronic angular momentum influence on fragment and fluorescence cross sections

We present a general theory of the photodissociation of diatomic molecules in the presence of nonadiabatic interactions between dissociative electronic states. Nonadiabatic couplings exert a profound influence on the photodissociation process when the molecule dissociates to atoms with nonvanishing electronic angular momentum, even if there are no ordinary curve crossings. Nonadiabatic interactions in this latter situation couple adiabatic molecular states which would otherwise be degenerate at infinite internuclear separation. Methods are developed for properly including nonadiabatic interactions in an exact or approximate calculation of photodissociation transition amplitudes for the production of the atomic fragments in particular fine structure levels. We derive differential cross sections for photofragment production and general expressions describing the detection of fragments by any secondary process, such as spontaneous emission, occurring during or after the breakup of the diatom. These expressio...

Half‐collision description of final state distributions of the photodissociation of polyatomic molecules

The full three‐dimensional quantum mechanical scattering equations, describing direct photodissociation and weak predissociation from initially selected levels, are analyzed within a formulation which permits the use of the different nuclear coordinate systems appropriate to the bound and dissociative surfaces. The coupled two surface scattering equations satisfy the physical boundary conditions of regularity at the origin and purely outgoing flux on the dissociative surface (with incoming photon flux.) These equations are transformed, both in integral and differential equation forms, into single surface half‐collision equations wherein the initial bound state wave function, multiplied by the appropriate coupling operator, is propagated on the dissociative surface with the physical boundary conditions. These driven equations are shown to yield transition amplitudes which are equivalent to the transition amplitudes obtained from the Gell‐Mann and Goldberger (GMG) scattering formulation which employs plane ...

On the use of graph invariants for efficiently generating hydrogen bond topologies and predicting physical properties of water clusters and ice

Water clusters and some phases of ice are characterized by many isomers with similar oxygen positions, but which differ in direction of hydrogen bonds. A relationship between physical properties, like energy or magnitude of the dipole moment, and hydrogen bond arrangements has long been conjectured. The topology of the hydrogen bond network can be summarized by oriented graphs. Since scalar physical properties like the energy are invariant to symmetry operations, graphical invariants are the proper features of the hydrogen bond network which can be used to discover the correlation with physical properties. We demonstrate how graph invariants are generated and illustrate some of their formal properties. It is shown that invariants can be used to change the enumeration of symmetry-distinct hydrogen bond topologies, nominally a task whose computational cost scales like N2, where N is the number of configurations, into an N ln N process. The utility of graph invariants is confirmed by considering two water clusters, the (H2O)6 cage and (H2O)20 dodecahedron, which, respectively, possess 27 and 30 026 symmetry-distinct hydrogen bond topologies associated with roughly the same oxygen atom arrangements. Physical properties of these clusters are successfully fit to a handful of graph invariants. Using a small number of isomers as a training set, the energy of other isomers of the (H2O)20 dodecahedron can even be estimated well enough to locate phase transitions. Some preliminary results for unit cells of ice-Ih are given to illustrate the application of our results to periodic systems.

Rotational distributions from photodissociations. I. Linear triatomic molecules

The generalized Franck–Codon theory of the collinear dissociation of linear triatomic molecules is presented, including a proper description of the bending vibrations in the initial bound electronic state and of the rotational motions on both the initial and the final repulsive electronic surface. The nonseparable multidimensional bound–continuum Franck–Condon integrals are reduced to a rapidly convergent series of products of one dimensional integrals. Analytical expressions are derived for rotational and orbital angular momentum distributions of the products, for scalar coupling (as in predissociations), as well as parallel and perpendicular transitions (as in direct photodissociation). This fully quantum mechanical theory makes explicit the separate and interrelated roles played by angular momentum and energy conservation. The present work is applied in a separate paper to the photodissociation of ICN, and qualitative agrement with experiment is obtained.

The generalized Carnot cycle: A working fluid operating in finite time between finite heat sources and sinks

The production of work in finite time from a reservoir with finite heat capacity is studied. A model system, for which the only irreversibilities result from finite rates of heat conduction, is adopted. The maximum work obtainable in finite time from such a system is derived, and is found to be strongly dependent upon the reservoir heat capacity. The cycle producing the maximum work is derived for an arbitrary one‐component working fluid; no equation of state is assumed. In the optimum cycle, when the working substance is in contact with a finite reservoir, then the temperature of the working fluid is an exponential function of time and the entropy of the working substance is a linear function of time. While the maximum work obtainable in a single fixed‐time cycle is a strictly increasing function of the reservoir heat capacity, the efficiency (work produced/heat put in) is a strictly decreasing function of the reservoir heat capacity, for the model system with a finite hot reservoir and an infinite cold ...

Finite time thermodynamics: Optimal expansion of a heated working fluid

We determine the solution to the prototype problem: Given a finite amount of time, what is the optimal motion of a piston fitted to a cylinder containing a gas pumped with a given heating rate and coupled to a heat bath? The optimal motion is such as to maximize the work obtained via the piston in a specified period of time. This problem is solved for various end‐point constraints, including constraints on final volume, final energy, or final volume and energy. We consider several associated problems including constraints on the rate of change of volume, piston friction, piston mass, and inertial effects of the gas. Explicit thermodynamic analyses of the solutions are carried out for various examples. The efficiency and the gain over nonoptimal paths are studied. Significant improvement over the bound on the efficiency is obtained as calculated by (infinite time, reversible) thermodynamics. The nature of the limit of the optimal solution as the time approaches infinity is determined. For a finite heating ...

Rotational distributions from photodissociation. II. Results for ICN+hν→l+CN(X 2Σ+)

The quantum theory of rotational, vibrational, translational and electronic energy distributions in photodissociation is applied to the A continuum photodissociation of ICN. Excited state potential energy surfaces are fitted to the available experimental data, and predictions are made of the product energy distributions. General results are discussed which are applicable to other photodissociations and predissociations. In particular, the calculated rotational energy distributions display a strong sensitivity to the details of the unbound potential surface. The results of the collinear approximation for vibrational distributions in photodissociation of linear molecules are shown to be considerably modified by including rotational degrees of freedom, especially at high photon energies.

Power/energy limiter using reverse saturable absorption

In materials with an excited‐state absorption cross section larger than the ground‐state absorption cross section, increasing the incident light intensity (thus populating the excited state) increases the absorption. We show that such a reverse saturable absorber can function as a power limiter and pulse smoother for long pulses and as an energy limiter and pulse shortener for short pulses. The necessary properties for such a material are described. Reverse saturable absorption is demonstrated at 488 nm in alexandrite. A simple model describing these effects is presented.