Time reversal in matter-wave optics (original) (raw)

Negative-Index Media for Matter Waves

Laser Spectroscopy - Proceedings of the XIX International Conference, 2010

One reviews the recently introduced field of matter-wave "meta-optics", i.e. the extension of optical negative-index media (NIM) to atom optics. After emphasizing the differences with light meta-optics and particularly the necessary transient character of NIM's in atom optics, we present the way of generating matter-wave NIM's and their general properties: negative refraction, atom meta-lenses. Finally their specific features are reviewed: longitudinal wave packet narrowing associated to a time-reversal effect, transient revivals of evanescent matter waves and atom reflection echoes at a potential barrier.

Negative-Index Media for Matter-Wave Optics

Physical Review Letters, 2009

We consider the extension of optical meta-materials to matter waves and then the down scaling of meta-optics 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*( 3 P2) shows that the device is able to operate either as an efficient beam splitter or an atomic meta-lens. 03.75.Be, 37.10.Gh, Since the pioneering work of H. Lamb [1] and V.G. Veselago's seminal paper [2] about so-called "lefthanded" or "meta" media for light optics, a number of studies have been devoted to these new media and their applications (negative refraction, reversed Doppler effect, perfect lens, van der Waals atom-surface interaction, etc.) , in various spectral domains , some of them being even extended to acoustic waves . Such media are essentially characterised by a negative value of the optical index, which results into opposite directions of the wave vector k and the Poynting vector R. Our goal here is to extend this concept to matter waves, and the first arising question is the following: what should be the "de-Broglie optics" equivalent of those meta-materials? To the energy flux in electromagnetism (R vector) corresponds the atomic probability flux, namely the current density of probability J, or equivalently the group velocity v g = |ψ| −2 J, where ψ is the wave-function. Therefore, here also, one has to reverse v g with respect to the wave vector k or the phase velocity. However, as discussed below, contrarily to what occurs in light optics where R remains directed outwards whereas k is directed towards the light source [10], for matter waves the direction of the phase velocity (k) remains unchanged, whereas v g is now directed towards the source. Obviously, because of the conservation of probability, such an effect is necessarily a transient effect.

Diffractive matter wave optics in time

Journal of the Optical Society of America B, 1998

We demonstrate a programmable sideband modulator for atoms. A controlled phase modulation is engraved on an atomic matter wave by interaction with a frequency-modulated light potential. The principle allows for tailoring atomic optical elements, e.g., temporal lenses, adjustable beam splitters, and holograms, in the time domain. As an illustration we present the time analog of a blazed grating that is generating asymmetric sidebands of atomic matter waves.

Atom reflection echoes and surface matter waves in atom meta-optics

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. Comment: 4 pages, 3 figs

Wave Refraction in Negative-Index Media: Always Positive and Very Inhomogeneous

Physical Review Letters, 2002

We present the first treatment of the refraction of physical electromagnetic waves in newly developed negative index media (NIM), also known as left-handed media (LHM). The NIM dispersion relation implies that group fronts refract positively even when phase fronts refract negatively. This difference results in rapidly dispersing, very inhomogeneous waves. In fact, causality and finite signal speed always prevent negative wave signal (not phase) refraction. Earlier interpretations of phase refraction as "negative light refraction" and "light focusing by plane slabs" are therefore incorrect, and published NIM experiments can be explained without invoking negative signal refraction.

A plethora of negative-refraction phenomenons in relativistic and non-relativistic scenarios

2010 URSI International Symposium on Electromagnetic Theory, 2010

In accordance with Snel's law of refraction, whether a plane wave is refracted in the negative sense or positive sense at a planar boundary between two homogenous mediums is determined solely by the orientation of the real parts of the wavevectors involved. Thus, negative refraction should be distinguished from the associated but independent phenomenons of negative phase velocity, counterposition and negative deflection of energy flux. None of these phenomenons is Lorentz covariant.

Negative refraction of ultra-short electromagnetic pulses

Applied Physics B, 2005

We study pulse propagation across a boundary that separates an ordinary medium from a medium with simultaneously negative dielectric permittivity and magnetic permeability. Solving Maxwell's equations with two spatial coordinates (one longitudinal, one transverse) and time we find negative refraction as the wave packet undergoes significant and unusual shape distortions. The pulse acquires and maintains a chirp as it traverses the interface, as expected, but with a sign that is opposite to the chirp attained upon traversal into a positive-index material. Both a direct calculation of the spatial derivative of the instantaneous, local phase of the pulse and a Fourier analysis of the signal reveal the same inescapable fact: that inside a negative-index material, a transmitted, forward-moving wave packet is indeed a superposition of purely negative wave vectors. The central findings of this paper are a confirmation that causality is not violated in the short-pulse regime, and that energy and group velocities never exceed the speed of light in vacuum.

Negative phase time for scattering at quantum wells: A microwave analogy experiment

Physical Review E, 2001

If a quantum mechanical particle is scattered by a potential well, the wave function of the particle can propagate with negative phase time. Due to the analogy of the Schrödinger and the Helmholtz equation this phenomenon is expected to be observable for electromagnetic wave propagation. Experimental data of electromagnetic wells realized by wave guides filled with different dielectrics confirm this conjecture now. The propagation of a wave packet is determined by the dispersion relation of the medium. E.g. in vacuum a plane wave propagates with a constant amplitude and a phase shift proportional to frequency. In the case of tunnelling through a barrier, the constant phase leads to propagation speeds faster than light, calculated by [1] and measured for microwaves, single photons and infrared light [2, 3, 4]. In the contrary case of particles scattered by a potential well instead of a barrier, Li and Wang predicted a non-evanescent propagation but also with negative phase shifts [5]. We present here an experimental simulation of the quantum well by a microwave setup performing the analogy between the Schrödinger and the Helmholtz equation. Applying the stationary phase approximation, the peak value of a quantum mechanical wave packet with a mean impulse p 0 =hk 0 propagates with the group velocity v gr =