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arXiv:1411.3594

Localization of a quantum particle by a perfect lens

Florian Pinsker

Published Nov 13, 2014• 0 citations
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Abstract

In this work I transfer the concept of a perfect lens (superlens) for light to matter waves satisfying Schroedinger equation. I argue that in the focus of the perfect lens highly localized quantum states appear in principle on a single spot within the 2D plane orthogonal to the axis of the lens. Using the concept of the superlens implies that the limit of the quantum particle's spatial localization (in the plane) is set only by imperfections of the aperture rather than of theoretical nature.

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In this work I transfer the concept of a perfect lens (superlens) for light to matter waves satisfying Schroedinger equation. I argue that in the focus of the perfect lens highly localized quantum states appear in principle on a single spot within the 2D plane orthogonal to the axis of the lens. Using the concept of the superlens implies that the limit of the quantum particle's spatial localization (in the plane) is set only by imperfections of the aperture rather than of theoretical nature.
This paper examines the focusing of an atomic beam by the near field of laser radiation diffracted by a small aperture. The wave properties of the atom are taken into consideration within the framework of an approximate Schrödinger equation. The possibility is demonstrated of focusing an atomic beam into a spot some 3 nm across, the atomic and laser beam characteristics being quite acceptable. The main contribution to the spot size is shown to be from spherical aberrations and diffraction effects, the chromatic aberrations of the atomic beam with a 5% velocity distribution broadening having a lesser effect.
Abstract. We investigate the interaction between a single atom and a light field in the strong focusing regime. Such a configuration is subject to recent experimental work not only with atoms but also molecules and other atom-like systems as quantum dots. We derive the scattering probability for a photon from such a microscopic object modeled by a two-level system, starting with a Gaussian beam as the spatial mode of the light field. The focusing by an ideal lens is modeled using spherical wave fronts of a field compatible with Maxwell equations. Using a semi-classical approach for the atom-field interaction, we predict scattering probability of photons by a single atom of up to 98% for realistic focusing parameters. Experimental results for different focusing strengths are compared with our theoretical model. PACS numbers: 42.50Ct, 42.50Ex, 42.25BsInterfacing light and single atoms with a lens 2 1.
Summary form only given. To achieve super-resolution one must take into account a priori information about localization of the object. Such an a priori information exists in the case of an object of finite size. Its Fourier transform located in the focal plane of the lens is an entire analytic function, and analytic continuation of the object spectrum outside the spatial-frequency band allows for unlimited resolution. However such a super-resolution is extremely sensitive to the noise in the detected image. The ultimate limit of super-resolution is determined by the quantum fluctuations of light in the detection plane. We present the quantum theory of super-resolution for a one-dimensional coherent optical imaging scheme and discuss possibilities of improving the resolution limit by using multimode squeezed light. For quantum-mechanical description of this scheme we take into account the vacuum fluctuations of the electromagnetic field in the input plane outside the object. Interference of these vacuum fluctuations with the field amplitude of the object in the detection plane is the origin of the standard quantum limit or shot noise of photodetection in the image. To go beyond this limit we suggest to illuminate the object with multimode squeezed light having the spot size much larger than the object area. Then the vacuum fluctuations outside the object can be effectively suppressed resulting in sub-shot-noise detection of the image.
We consider the focusing and deflection of a nonresonant atomic beam propagating through a spatially inhomogeneous quantized electromagnetic field. Different Fock states of the field deflect the atoms in different angles and focus them at different points. We find a regime in which individual foci corresponding to neighboring Fock states can be reoslved even for large average number of photons. In this sense this quantum lens for atomic waves leaves intact the discreteness of the photons even in the classical limit.