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

Seidel, D, Gerhard C. Hegerfeldt, Juan Gonzalo Muga

Published Jul 18, 2006• 3 citations
OpenAlex

Abstract

We study the scattering of two-level atoms at narrow laser fields, modeled by a $\\delta$-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 $\\delta$-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 $\\delta$-lasers are used to investigate quantized-motion effects on Ramsey interferometry.

Related papers

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

D Seidel, J G Muga, Gerhard C. Hegerfeldt

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.

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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.

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Electromagnetically induced transparency and reduced speeds for single photons in a fully quantized model

Thomas Purdy, Martin Ligare

We introduce a simple model for electromagnetically induced transparency in which all fields are treated quantum mechanically. We study a system of three separated atoms at fixed positions in a one-dimensional multimode optical cavity. The first atom serves as the source for a single spontaneously emitted photon; the photon scatters from a three-level Lambda-configuration atom which interacts with a single-mode field coupling two of the atomic levels; the third atom serves as a detector of the total transmitted field. We find an analytical solution for the quantum dynamics. From the quantum amplitude describing the excitation of the detector atom we extract information that provides exact single-photon analogs to wave delays predicted by semi-classical theories. We also find complementary information in the expectation value of the electric field intensity operator.

arXiv:quant-ph/0204173•Journal of Optics B Quantum and Semiclassical Optics•May 28, 2003•8 citations
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.
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.
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.
The interaction of light with a two-level emitter is the most fundamental process in quantum optics and key to many applications in quantum science and technology. One peculiarity is that two photons are never simultaneously detected in the light scattered by a single quantum emitter. This is commonly interpreted to mean that a single two-level quantum emitter can only absorb and emit single photons. Here we show by spectrally filtering the fluorescence of such an emitter, that the remaining light consists of a stream of photon pairs that have been simultaneously scattered by the two-level emitter [1].
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 introduce a simple model for electromagnetically induced transparency in which all fields are treated quantum mechanically. We study a system of three separated atoms at fixed positions in a one-dimensional multimode optical cavity. The first atom serves as the source for a single spontaneously emitted photon; the photon scatters from a three-level Lambda-configuration atom which interacts with a single-mode field coupling two of the atomic levels; the third atom serves as a detector of the total transmitted field. We find an analytical solution for the quantum dynamics. From the quantum amplitude describing the excitation of the detector atom we extract information that provides exact single-photon analogs to wave delays predicted by semi-classical theories. We also find complementary information in the expectation value of the electric field intensity operator.