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arXiv:quant-ph/0607121 · Journal of Physics B Atomic Molecular and Optical Physics

Scattering of two-level atoms by delta lasers: exactly solvable models in atom optics

D Seidel, J G Muga, Gerhard C. Hegerfeldt

Published Nov 1, 2006• 3 citations
arXivHTMLPDF

Abstract

We study the scattering of two-level atoms at narrow laser fields, modelled 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 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 in Ramsey interferometry.

DOI
10.1088/0953-4075/39/22/011

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We study the scattering of two-level atoms at narrow laser fields, modelled 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 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 in Ramsey interferometry.
We study the scattering of two-level atoms at narrow laser fields, modeled by a delta\\deltadelta-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 delta\\deltadelta-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 delta\\deltadelta-lasers are used to investigate quantized-motion effects on Ramsey interferometry.
Quantum stochastic differential equations have been used to describe the dynamics of an atom interacting with the electromagnetic field via absorption/emission processes. Here, by using the full quantum stochastic Schrödinger equation proposed by Hudson and Parthasarathy, we show that such models can be generalized to include other processes into the interaction. In the case of a two-level atom we construct a model on the basis of some physical requirements, the main being a balance equation on the fluxes of the ingoing and outgoing photons; in this model the atom-field interaction turns out to be due either to absorption/emission processes either to direct scattering processes, which simulate the interaction due to virtual transitions to the levels which have been eliminated from the description. To see the effects of the new terms, we consider both direct and heterodyne detection of the fluorescence light emitted by an atom stimulated by a monochromatic coherent laser and we deduce from these two detection schemes the expressions of the total, elastic and inelastic electromagnetic cross sections and the spectral distribution of the fluorescence light. The total cross section, as a function of the frequency of the stimulating laser, can present not only a Lorentzian shape, but the full variety of Fano profiles; intensity dependent widths and shifts are obtained. The fluorescence spectrum can present complicated shapes, according to the values of the various parameters; when the direct scattering is not important the usual symmetric triplet structure of the Mollow spectrum appears (for high intensity of the stimulating laser), while a strong contribution of the direct scattering process can distort such a triplet structure or can even make it to disappear.
The beam splitting process of an atomic beam is described by an exactly solvable theory. We use exact plane wave solutions of an atomic two-level system interacting with laser beams and employ appropriate jump conditions between regions with and without laser beam. The transmission matrix as well as the reflection matrix are given explicitely. Also, the conditions for atom optical analogues of the Borrmann effect and of the pendellösung effect are treated exactly. The high-energy limit of these phenomena is discussed which is sufficient for many practical purposes.
Atom-laser interaction is at the heart of the vibrant field of quantum optics. The dynamical properties of a moving atom submitted to a laser radiation are strongly \ninfluenced by the position- and time-dependence of the latter. The full physical state of the atom must include information about the centre-of-mass motion and the internal structure of the atom. It is challenging to obtain a complete description of the full state of the atom. However, there exists an alternative approach to the dynamics of an atom in the presence of a laser, which is based on the concept of matter-wave absorption. \n \nIn this thesis, we theoretically study the nonrelativistic one-dimensional motion of an electrically neutral quantum particle in the presence of a thin time-dependent absorber, representing the laser radiation. Our aim is to better understand the precise connection between time-dependent matter-wave absorption and the interaction between an atom and a localised time-dependent laser. \n \nOur analysis is based on two different approaches to the problem. The first one describes the moving atom by a two-level system, and represents the laser radiation \nby an off-diagonal δ-potential. The second model treats the atom as a structureless particle, and describes the laser by a time-dependent absorbing barrier. While the \nformer model can be derived from first principles, the treatment of the absorbing barrier in the latter model lacks a rigorous quantum mechanical justification. The \nmain outcome of our work is to provide a solid physical ground for the absorber model, by explicitly connecting it to the δ-potential model. We have thus extended \nthe range of theoretical tools useful for investigating the effects of time-dependent laser radiation on quantum matter.
The theoretical analysis of time observables in quantum mechanics has been controversial and is still subject to debate. In the present work, a measurement-based approach to quantum arrival times is studied in detail. It is based on the emission time of the first spontaneous photon from a a two-level atom moving into a laser-illuminated region. This quantum-optical model is shown to give an operational understanding of various ideal proposals for quantum arrival-time distributions as well as for local kinetic energy densities. As a main result, a first measurement-based procedure to Kijowski`s arrival-time distribution is given and the approach is used to generalize this distribution to the case of particles interacting with an external potential.
We formulate a quantum arrival time measurement process for a Bosonic many-particle system, with the aim of extracting statistical information on single-particle properties. The arrival time is based on a dynamical multi-particle absorption model in the Fock space, and we consider systems in coherent and incoherent mixtures of NNN-particle states. We find the resulting probability distributions for arrival time sequences, which we consider as parametric models for the statistical inference of single-particle parameters, and derive a tractable expression for the associated (classical) Fisher information. Subsequently focusing on the concrete case of the momentum parameter of a 1D particle, we consider the idealized limits of a point (Dirac delta) detector and an infinite particle system forming a spatially uniform ``beam''. We observe that even though no information remains in the spatial distribution, the single-particle momentum is indeed identifiable from the arrival time data, even in the limit of ``sparse beams'' of vanishing particle density, where we obtain simple analytical form for the Fisher information, which, interestingly, coincides with the one obtained from a hypothetical time-stationary detection model. Our results contribute to the fundamental understanding of temporal measurement data arising from quantum systems consisting of freely evolving particles.