arXiv subjects
Publications and source records attributed to G. C. Hegerfeldt.
Given an ensemble of systems in an unknown state, as well as an observable $\hat A$ and a physical apparatus which performs a measurement of $\hat A$ on the ensemble, whose detailed working is unknown ('black box'), how can one test whether the Lüders or von Neumann reduction rule applies?
All covariant time operators with normalized probability distribution are derived. Symmetry criteria are invoked to arrive at a unique expression for a given Hamiltonian. As an application, a well known result for the arrival time distribution of a free particle is generalized and extended. Interestingly, the resulting arrival time distribution operator is connected to a particular, positive, quantization of the classical current. For particles in a potential we also introduce and study the notion of conditional arrival-time distribution.
We provide the most general forms of covariant and normalized time operators and their probability densities, with applications to quantum clocks, the time of arrival, and Lyapunov quantum operators. Examples are discussed of the profusion of possible operators and their physical meaning. Criteria to define unique, optimal operators for specific cases are given.
Through tunneling, or barrier penetration, small wavefunction tails can enter a finitely shielded cylinder with a magnetic field inside. When the shielding increases to infinity the Lorentz force goes to zero together with these tails. However, it is shown, by considering the radial derivative of the wavefunction on the cylinder surface, that a flux dependent force remains. This force explains in a natural way the Aharonov-Bohm effect in the idealized case of infinite shielding.
We study the scattering of two-level atoms at narrow laser fields, modeled by a $δ$-shape intensity profile. The unique properties of these potentials allow us to give simple analytic solutions for one or two field zones. Several applications are studied: a single $δ$-laser may serve as a detector model for atom detection and arrival-time measurements, either by means of fluorescence or variations in occupation probabilities. We show that, in principle, this ideal detector can measure the particle density, the quantum mechanical flux, arrival time distributions or local kinetic energy densities. Moreover, two spatially separated $δ$-lasers are used to investigate quantized-motion effects on Ramsey interferometry.
We propose and investigate a procedure to measure, at least in principle, a positive quantum version of the local kinetic energy density. This procedure is based, under certain idealized limits, on the detection rate of photons emitted by moving atoms which are excited by a localized laser beam. The same type of experiment, but in different limits, can also provide other non positive-definite versions of the kinetic energy density. A connection with quantum arrival time distributions is discussed.
The size of the helium trimer is determined by diffracting a beam of He-4 clusters from a 100 nm grating inclined by 21 degree. Due to the bar thickness the projected slit width is roughly halved to 27 nm, increasing the sensitivity to the trimer size. The peak intensities measured out to the 8th order are evaluated via a few-body scattering theory. The trimer pair distance is found to be 1.1+0.4/-0.5 nm in agreement with predictions for the ground state. No evidence for a significant amount of Efimov trimers is found. Their concentration is estimated to be less than 6%.
We investigate the three-dimensional formulation of a recently proposed operational arrival-time model. It is shown that within typical conditions for optical transitions the results of the simple one-dimensional version are generally valid. Differences that may occur are consequences of Doppler and momentum-transfer effects. Ways to minimize these are discussed.
A recent approach to arrival times used the fluorescence of an atom entering a laser illuminated region and the resulting arrival-time distribution was close to the axiomatic distribution of Kijowski, but not exactly equal, neither in limiting cases nor after compensation of reflection losses by normalization on the level of expectation values. In this paper we employ a normalization on the level of operators, recently proposed in a slightly different context. We show that in this case the axiomatic arrival time distribution of Kijowski is recovered as a limiting case. In addition, it is shown that Allcock's complex potential model is also a limit of the physically motivated fluorescence approach and connected to Kijowski's distribution through operator normalization.
We model ideal arrival-time measurements for free quantum particles and for particles subject to an external interaction by means of a narrow and weak absorbing potential. This approach is related to the operational approach of measuring the first photon emitted from a two-level atom illuminated by a laser. By operator-normalizing the resulting time-of-arrival distribution, a distribution is obtained which for freely moving particles not only recovers the axiomatically derived distribution of Kijowski for states with purely positive momenta but is also applicable to general momentum components. For particles interacting with a square barrier the mean arrival time and corresponding ``tunneling time'' obtained at the transmission side of the barrier becomes independent of the barrier width (Hartman effect) for arbitrarily wide barriers, i.e., without the transition to the ultra-opaque, classical-like regime dominated by wave packet components above the barrier.
Atomic detection by fluorescence may fail because of reflection from the laser or transmission without excitation. The detection probability for a given velocity range may be improved by controlling the detuning and the spatial dependence of the laser intensity. A simple optimization method is discussed and exemplified.
A natural approach to measure the time of arrival of an atom at a spatial region is to illuminate this region with a laser and detect the first fluorescence photons produced by the excitation of the atom and subsequent decay. We investigate the actual physical content of such a measurement in terms of atomic dynamical variables, taking into account the finite width of the laser beam. Different operation regimes are identified, in particular the ones in which the quantum current density may be obtained.
The well-known laser-induced Rabi oscillations of a two-level atom are shown to be suppressed under certain conditions when the atom is entering a laser-illuminated region. For temporal Rabi oscillations the effect has two regimes: classical-like, at intermediate atomic velocities, and quantum at low velocities, associated respectively with the formation of incoherent or coherent internal states of the atom in the laser region. In the low velocity regime the laser projects the atom onto a pure internal state that can be controlled by detuning. Spatial Rabi oscillations are only suppressed in this low velocity, quantum regime.
For a quantum-mechanically spread-out particle we investigate a method for determining its arrival time at a specific location. The procedure is based on the emission of a first photon from a two-level system moving into a laser-illuminated region. The resulting temporal distribution is explicitly calculated for the one-dimensional case and compared with axiomatically proposed expressions. As a main result we show that by means of a deconvolution one obtains the well known quantum mechanical probability flux of the particle at the location as a limiting distribution.
Molecular beams of rare gas atoms and D_2 have been diffracted from 100 nm period SiN_x transmission gratings. The relative intensities of the diffraction peaks out to the 8th order depend on the diffracting particle and are interpreted in terms of effective slit widths. These differences have been analyzed by a new theory which accounts for the long-range van der Waals -C_3/l^3 interaction of the particles with the walls of the grating bars. The values of the C_3 constant for two different gratings are in good agreement and the results exhibit the expected linear dependence on the dipole polarizability.
We investigate the interaction of an atom with a multi-channel squeezed vacuum. It turns out that the light coming out in a particular channel can have anomalous spectral properties, among them asymmetry of the spectrum, absence of the central peak as well as central hole burning for particular parameters. As an example plane-wave squeezing is considered. In this case the above phenomena can occur for the light spectra in certain directions. In the total spectrum these phenomena are washed out.