Novel Properties of Coherent Matter

Sonja Franke‐Arnold, Stephen Mark Barnett, G. Huyet

Summary form only given. We introduce the concept and mathematical description of a coherence length and a coherence momentum for matter states, and explain their significance via the example of the motional states of a single cold trapped ion. These parameters describe the coherence properties of matter waves analogously to the way in which optical coherence determines the coherence time and spectral width. They become apparent in the interference pattern of a matter or light wave interferometer, respectively. While the coherence length is a characteristic length by which two parts of a matter wave packet can be separated so that they still interfere, the coherence momentum describes the time interval of this overlap.

Board on Physics and Astronomy, Division on Engineering and Physical Sciences, National Academies of Sciences, Engineering, and Medicine

P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-González

Mikio Kozuma, Yoichi Suzuki, Yoshio Torii +4 more

Phase-coherent matter-wave amplification was demonstrated using Bose- Einstein-condensed rubidium-87 atoms. A small seed matter wave was created with coherent optical Bragg diffraction. Amplification of this seed matter wave was achieved by using the initial condensate as a gain medium through the superradiance effect. The coherence properties of the amplified matter wave, studied with a matter-wave interferometer, were shown to be locked to those of the initial seed wave. The active matter-wave device demonstrated here has great potential in the fields of atom optics, atom lithography, and precision measurements.

Nicholas K Whitlock, Stephen Mark Barnett, John Jeffers

PACS number: 03.75.-b Abstract. Electromagnetic waves and fluids have locally conserved mechanical properties associated with them and we may expect these to exist for matter waves. We present a semiclassical description of the continuity equations relating to these conserved properties of matter-waves and derive a general expression for their respective fluxes. It has long been known that electromagnetic waves have associated mechanical properties. Maxwell described the radiation pressure exerted by light [1] and Poynting identified the momentum carried by light [2] and that angular momentum was associated with circular polarisation [3]. The energy, momentum and angular momentum of electromagnetic waves are particularly important as these quantities are all conserved. Associated with the density of each of these quantities is a flux density (or current density) which is related to the density via continuity equations [4]. The creation of the first Bose-Einstein condensates (BECs) in dilute atomic gases in 1995 [5, 6, 7] brought about the possibility of creating coherent matter waves. A BEC in a trap is analogous to an electromagnetic field in a laser cavity, in that macroscopic occupation of a single quantum state occurs. Just as a laser cavity is a source of coherent light, a BEC can be a source of coherent matter waves. To continue this analogy we assert that matter waves will have associated mechanical properties and present a general theory of the local mechanical properties of matter waves. We give, as examples, the densities and flux densities of the matter wave particle number and energy. The same theory applies to their momentum and angular momentum. The local conservation of particles is a well established concept in fluid mechanics. It states that in any volume element of a fluid, no matter how small, the rate of change of particles in an element of fluid is equal to the rate at which the particles flow into the surface of the element. This principle is made quantitative in the following equation [8];

Zoltan Fried, Lloyd C. Kannenberg