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Physical Review A

Negative refraction for incoherent atomic matter waves

Thibault Vogt, Wenhui Li

Published Mar 30, 2015• 3 citations
Publisher

Abstract

In a recent paper [Phys. Rev. Lett. 102, 140403 (2009)], Baudon et al. reported that a comoving potential acting on atoms could mimic negative-index-refraction properties of left-handed photonic metamaterials. We show in this article that a better approximation is necessary in order to describe the real physical system proposed by Baudon et al. We derive analytical formulas and compare their solutions with numerical simulations. It turns out that instead of negative refraction, it is simply atomic reflection that occurs in the above-mentioned comoving potential. Furthermore, we find that the wave packet of the reflected atomic beam by comoving potentials can be narrowed by negative dispersion. Finally, we identify a potential configuration, near the interface with a cubic-type potential barrier, that may lead to the observation of negative refraction with incoherent matter waves.

DOI
10.1103/physreva.91.033634

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In a recent paper [Phys. Rev. Lett. 102, 140403 (2009)], Baudon et al. reported that a comoving potential acting on atoms could mimic negative-index-refraction properties of left-handed photonic metamaterials. We show in this article that a better approximation is necessary in order to describe the real physical system proposed by Baudon et al. We derive analytical formulas and compare their solutions with numerical simulations. It turns out that instead of negative refraction, it is simply atomic reflection that occurs in the above-mentioned comoving potential. Furthermore, we find that the wave packet of the reflected atomic beam by comoving potentials can be narrowed by negative dispersion. Finally, we identify a potential configuration, near the interface with a cubic-type potential barrier, that may lead to the observation of negative refraction with incoherent matter waves.
Evanescent matter-waves produced by an atom wave packet incident onto a repulsive barrier edge can be back-refracted and reconstructed by the application of negative-index "comoving" potential pulses. One shows that those collapses and revivals of evanescent matter waves give rise to surface matter waves and should be observable via atom reflection echoes issued from the barrier interface. This property, together with the property of inducing negative refraction, makes such potentials the matter-wave counterpart of negative-index materials in light optics.
Abstract\nnumbers: 03.75.-b Matter Waves 03.75.Be Atom and Neutron Optics 37.10.Gh Atom Traps and Guides 42.25.-p Wave Optics ABSTRACT Semi-evanescent and evanescent matter-waves produced by an atom wave packet impinging a repulsive barrier can be back-refracted and reconstructed by the application of negative-index " comoving " potential pulses. One shows that those collapses and revivals generate a matter wave confined on both sides of the barrier border (" surface matter wave ") and should be observable via the retardation of atom reflection from the barrier interface. This property, joined to the possibility recently demonstrated of inducing negative refraction of atom waves, makes such potentials a matter-wave counterpart of negative-index materials or " meta materials " well-known in light optics.
We consider the extension of optical metamaterials to matter waves and then the down scaling of metaoptics to nanometric wavelengths. We show that the generic property of pulsed comoving magnetic fields allows us to fashion the wave-number dependence of the atomic phase shift. It can be used to produce a transient negative group velocity of an atomic wave packet, which results into a negative refraction of the matter wave. Application to slow metastable argon atoms Ar(3P2) shows that the device is able to operate either as an efficient beam splitter or an atomic metalens.
A scenario for realizing simultaneously negative permittivity and permeability of a two-photon quantum-coherent atomic vapor is suggested in order to achieve a left-handed atomic medium with a negative refractive index. One of the remarkable features of the present scheme is that it can lead to a controllable manipulation of the negative refractive index of the atomic vapor. Since the electric- and magnetic-dipole allowed transitions of atoms can be excited by visible and infrared lightwaves, the refractive index of the atomic vapor can exhibit its negative refractive index at optical and near-optical frequency bands. This may be a new scheme to fabricate a negatively refracting material based on the quantum optical approach. Such a three-dimensionally isotropic negative refractive index at visible and infrared wavelengths induced by the two-photon-resonant quantum coherence would find a potential application in fabrication of superlenses for perfect imaging and subwavelength focusing.
A new scheme for overcoming losses with incoherent optical gain in a quantum-coherent left-handed atomic vapor is suggested. In order to obtain low-loss, lossless or active left-handed media (LHM), a pump fleld, which aims at realizing population inversion of atomic levels, is introduced into a four-level atomic system. Both analytical and numerical results are given to illustrate that such an atomic vapor can exhibit intriguing electric and magnetic responses required for achieving simultaneously negative permittivity and permeability (and hence a gain-assisted quantum-coherent negative refractive index would emerge). The quantum-coherent left-handed atomic vapor presented here could have four fascinating characteristics: i) three-dimensionally isotropic negative refractive index, ii) double- negative atomic medium at visible and infrared wavelengths, iii) high-gain optical ampliflcation, and iv) tunable negative refractive index based on quantum coherent control. Such a three-dimensionally isotropic gain medium with negative refractive index at visible and infrared frequencies would have a potential application in design of new quantum optical and photonic devices, including superlenses for perfect imaging and subwavelength focusing.