Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1805.11739 · Physical Review A

Quantum optics in Maxwell's fish eye lens with single atoms and photons

J. Perczel, P. Kómár, Mikhail D. Lukin

Published Sep 5, 2018• 12 citations
arXivHTMLPDF

Abstract

The imaging properties of a lens that may perfectly focus electromagnetic waves is investigated at the quantum level. The lens is shown to be diffraction limited, and its role in entangling operations based on dipole-dipole interactions is discussed.
DOI
10.1103/physreva.98.033803

Related papers

Quantum lens for atomic waves

Ilya Sh. Averbukh, V. M. Akulin, W. P. Schleich

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.

Physical Review Letters•Jan 24, 1994•40 citations

Interfacing light and single atoms with a lens

Meng Khoon Tey, Syed Abdullah Aljunid, Florian Huber +4 more

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.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Dec 2, 2008•7 citations

Two-Photon Optics: Imaging below the diffraction limit

Daniel Schlenk, Harald Weinfurter

Imaging properties of an optical system are limited by the wave nature of light. Entangled photons allow an improvement in resolution [1]. We show an experimental realisation using entangled photons from a Spontaneous Parametric Downconversion source.

Frontiers in Optics•Jan 1, 2006•0 citations

Strongly focused light beams interacting with single atoms in free space

S. J. van Enk, Harry J. Kimble

We construct three-dimensional solutions of Maxwell's equations that describe Gaussian light beams focused by a strong lens. We investigate the interaction of such beams with single atoms in free space and the interplay between angular and quantum properties of the scattered radiation. We compare the exact results with those obtained with paraxial light beams and from a standard input-output formalism. We put our results in the context of quantum information processing with single atoms.

arXiv:quant-ph/0006002•Physical Review A•Jan 12, 2001•79 citations

Wide optical lenses for atomic beams

Ole Steuernagel

The field of atom-optics offers considerable potential in fundamental and applied physics, both for imaging atoms and their deposition (to create nano-structures). Here we work in the paraxial approximation throughout and can therefore assume that the scalar modes represent (e. g., linearly polarized) electro-magnetic laser-field modes. For atomic lens design, based on the optical dipole force, it is necessary to coherently superpose suitable laser modes in order to create wide thin parabolic lenses with large numerical apertures. Only in this manner can the tiny diffraction limits promised by the extraordinary smallness of the de Broglie wavelengths of atomic beams be realized.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2009•0 citations

A Maxwell Fish-Eye Lens in a Bose-Einstein Condensate

Jelte Duchêne, Elinor Kath, Floriane Arrouas +7 more

We experimentally realize an analogue of the optical Maxwell fish-eye lens (MFEL) using phononic excitations in a Bose-Einstein condensate (BEC). A MFEL is characterized by a radially symmetric, spatially varying refractive index with the remarkable property that rays emitted from any point within the lens are perfectly focused at their antipodal points. While the implementation of such gradient-index lenses is challenging in conventional optical systems, BECs offer a highly tunable platform in which the spatially varying speed of sound of collective excitations -- phonons, the acoustic analogues of photons -- can be engineered and their dynamics observed in real time. Time-resolved measurements of phonon wavefronts reveal focusing behavior that shows good agreement with analytical theory and numerical simulations. This work provides both a geometric and physical framework for engineering effective refractive indices using ultracold atoms, and simulating wave propagation on effective spherical geometries.

cond-mat.quant-gasCross-listedarXiv:2602.23125•New Journal of Physics•Feb 27, 2026•0 citations
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.
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.
The field of atom-optics offers considerable potential in fundamental and applied physics, both for imaging atoms and their deposition (to create nano-structures). Here we work in the paraxial approximation throughout and can therefore assume that the scalar modes represent (e. g., linearly polarized) electro-magnetic laser-field modes. For atomic lens design, based on the optical dipole force, it is necessary to coherently superpose suitable laser modes in order to create wide thin parabolic lenses with large numerical apertures. Only in this manner can the tiny diffraction limits promised by the extraordinary smallness of the de Broglie wavelengths of atomic beams be realized.
We experimentally realize an analogue of the optical Maxwell fish-eye lens (MFEL) using phononic excitations in a Bose-Einstein condensate (BEC). A MFEL is characterized by a radially symmetric, spatially varying refractive index with the remarkable property that rays emitted from any point within the lens are perfectly focused at their antipodal points. While the implementation of such gradient-index lenses is challenging in conventional optical systems, BECs offer a highly tunable platform in which the spatially varying speed of sound of collective excitations -- phonons, the acoustic analogues of photons -- can be engineered and their dynamics observed in real time. Time-resolved measurements of phonon wavefronts reveal focusing behavior that shows good agreement with analytical theory and numerical simulations. This work provides both a geometric and physical framework for engineering effective refractive indices using ultracold atoms, and simulating wave propagation on effective spherical geometries.