Determination of the bond length and binding energy of the helium dimer by diffraction from a transmission grating

A molecular beam consisting of small helium clusters is diffracted from a 100 nm period transmission grating. The relative dimer intensities have been measured out to the 7th order and are used to determine the reduction of the effective slit width resulting from the finite size of the dimer. From a theoretical analysis of the data which also takes into account the van der Waals interaction with the grating bars, the bond length (mean internuclear distance) and the binding energy are found to be = 52+/-4 A and |E(b)| = 1. 1+0.3/-0.2 mK.     

How to study the elusive efimov state of the 4He3 molecule through a new atom-optical state-selection technique

Excited states and excitation energies of weakly bound systems, e.g., atomic few-body systems and clusters, are difficult to study experimentally. For this purpose we propose a new and very general atom-optical method which is based on inelastic diffraction from transmission gratings. The technique is applicable to the recently found helium trimer molecule 4He3, allowing for the first time an investigation of the possible existence of an excited trimer state and determination of its excitation energy. This would be of fundamental importance for the famous Efimov effect.     

The structure of space-time transformations

LetT be a one-to-one mapping ofn-dimensional space-timeM onto itself. IfT maps light cones onto light cones and dimM3, it is shown thatT is, up to a scale factor, an inhomogeneous Lorentz transformation. Thus constancy of light velocity alone implies the Lorentz group (up to dilatations). The same holds ifT andT ^–1 preserve (x–y)²>0. This generalizes Zeeman's Theorem. It is then shown that ifT maps lightlike lines onto (arbitrary) straight lines and if dimM3, thenT is linear. The last result can be applied to transformations connecting different reference frames in a relativistic or non-relativistic theory.     

The form of representations of the canonical commutation relations for Bose fields and connection with finitely many degrees of freedom

Given a representation of the canonical commutation relations (CCR) for Bose fields in a separable (or, under an additional assumption, nonseparable) Hilbert space it is shown that there exists a decreasing sequence of finite and quasi-invariant measures _n on the space of all linear functionals on the test function space, such that can be realized as the direct sum of the , the space of all _n -square-integrable functions on. In this realizationU(f) becomes multiplication by. The action ofV(g) is similar as in the case of cyclicU(f) which has been treated byAraki andGelfand. But different can be mixed now. Simply transcribing the results in terms of direct integrals one obtains a form of the representations which turns out to be essentially the direct integral form ofLew. All results are independent of the dimensionality of and hold in particular for dim. Thus one has obtained a form of the CCR which is the same for a finite and an infinite number of degrees of freedom. From this form it is in no way obvious why there is such a great distinction between the finite and infinite case. In order to explore this question we derive von Neumanns theorem about the uniqueness of the Schrödinger operators in a constructive way from this dimensionally independent form and show explicitly at which point the same procedure fails for the infinite case.Part of this paper is contained in Section IV of theHabilitationsschrift Aspekte der kanonischen Vertauschungsrelationen für Quantenfelder byG. C. Hegerfeldt, University of Marburg 1968.     

Quantum shot noise: Expansions in powers of the pulse density

Quantum shot noise consists of individual pulses which contribute time-dependent (operator) potentials toward a total potentialV(t). The averaged quantity T exp _t0 ^t dtV(t) in general can no longer be calculated explicitly, in contrast to the classical case, and expansions are of interest. Noncommutative cumulant expansions are not directly applicable if the correlation functions ofV(t) have singularities, as happens in applications. It is shown here that these expansions, when applied to quantum shot noise, can be partially summed to give expansions in powers of the pulse density. Three types of such expansions are established explicitly, and for two of them the derivation is direct. For one of them the first-order approximation is closely connected to the so-called unified theory of spectral-line broadening.     

Noncommutative cumulants for stochastic differential equations and for generalized Dyson series

For the stochastic equationU=VU, Kubo's ansalze for U in the form of differential and integrodifferential equations is investigated and a newansatz as an integral equation is added. Unique solutions in terms of noncommutative W- and K-cumulants are found by elementary functional differentiation, and expressions of van Kämpen and Terwiel are recovered. For the cumulants we find simple recursion relations and prove the important cluster property. Surprisingly, it is found that the Gaussian approximation in the differential equationansatz leads to positivity problems, while this is not the case with the integral and integrodifferential equation. The cumulant expansion technique is carried over to generalized Dyson series. In a companion paper we apply our results to quantum shot noise.     

Dark periods in the resonance fluorescence of a single Λ system

We use the quantum jump method to study the photon statistics of a single laser-driven atom in the configuration where both lower levels are strongly coupled to the common upper level. Under certain conditions we show that, for almost degenerate lower levels, light and dark periods occur which are similar to those of the well-known Dehmelt V system. Analytic results for their mean lengths and other statistical properties are given. For large separation of the lower levels we prove an interesting bunching property by the photons in the resonance fluorescence near the dark resonance. We propose a realistic system for which these effects may be observed.