Maxwell matter waves emerge from a perspective, complementary to de Broglie's, that matter is fundamentally a wave phenomenon whose particle aspects are revealed by quantum mechanics. Their quantum mechanical description is derived through the introduction of a matter vector potential, having frequency
ω0, to Schrodinger's equation for a massive particle. Maxwell matter waves are then seen to be coherent excitations of a single-mode of the matter-wave field. In the classical regime, their mechanics is captured by a matter analog of Maxwell's equations for the electromagnetic field. As such, Maxwell matter waves enable a spectrum of systems that have useful optical analogs, such as resonant matter-wave interferometric sensors and matter-wave parametric oscillators. These waves are associated with a wavelength that is tied to the drive frequency
ω0 rather than to the massive particle's energy, as is ordinarily the case with de Broglie matter waves. As a result, simple interferometric measurements lead to different outcomes for the two types of waves. While their apparent departure from de Broglie character is surprising, Maxwell matter waves are wholly consistent with quantum mechanics.
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.
Matter waves were discovered in the early 20th century from their wavelength, predicted by DeBroglie, Planck's constant divided by the particle's momentum, that is, lmw = h/mv. But, the failure to obtain a reasonable theory for the matter wave frequency resulted somewhat in loss of further interest. It was expected that the frequency of the matter wave should correspond to the particle kinetic energy, that is, fmw = 1/2mv^2/h but the resulting velocity of the matter of the particle, v = fmw x lmw, is that the matter wave moves at one half the speed of the particle, obviously absurd as the particle and its wave must move together. If relativistic mass is used (as it should in any case) the problem remains, the same mass appearing in numerator and denominator and canceling. It is no help to hypothesize that the total energy, not just the kinetic energy, yields the matter wave. That attributes a matter wave to a particle at rest. It also gives the resulting velocity as c^2/v, the wave racing ahead of its particle. A reinterpretation of Einstein's derivation of relativistic kinetic energy (which produced his famous E = mc^2) leads to a valid matter wave frequency and a new understanding of particle kinetics and of the atom's stable orbits.