Interference pattern state detection

Consider a Fraunhofer diffraction case. At the detecting surface, there will be a maximum intensity at the center of the shadow slit, followed by concentric circles with decreasing intensity. The diffraction pattern will reproduce itself a shadow slit at 2 when slit-1 is closed. If there were no interference between states 1 and 2, one would expect a sum of each slit s diffraction intensity pattern. Thus, very little intensity will be found in between the shadow slits. 

The key is to calculate the physical quantum states as they reach DS-2. From preceding sections, the theory predicts that if sameness is there, an interference pattern will form and shall be detected. 

But now, the field quantum states are no longer orthogonal. An interference pattern can hence be detected. This result is quoted in Ref. [15]. 

The interference of microscopic particles leads to a diffraction pattern with deviations with respect to the mere sum of the individual probabilities. The two events are no longer independent. If we wish to state in advance where the next particle will appear, we are unable to do so. The best we can do is to say that the next particle is more likely to strike in one area than another. A limit to our knowledge, associated with the wave-matter duality, becomes apparent. In the double-slit experiment, we may know the momentum of each particle but we do not know an5 hing about the way the particles traverse the slits. Alternatively, we could think of an experiment that would enable us to decide through which slit the particle has passed, but then the experiment would be substantially different and the particles would arrive at the screen with different distributions. In particular, the two slits would become distinguishable and independent events would occur. No interference would be detected, that is, the wave nature of the particle would be absent. In such an experiment, in order to obtain information about the particle position just beyond the slits, we would change its momentum in an unknown way. Indeed, recent experiments have shown that interference can be made to disappear and reappear in a quantum eraser (ref. 6 and references therein). 

An alternative way to detect an internal state of the two atom system is to observe an interference pattern of the fluorescence field emitted in the direction R, not necessary perpendicular to the interatomic axis. The usual measure of the depth of modulation of the interference fringes is a visibility defined as... 

At metallic surfaces, STS spectra are generally not as structured as at semiconductors. This probably explains why STS has had much less impact upon metals [69]. STS has nevertheless been successfully attempted on Au(lOO), Au(lll) and Pd(lll) [70-72]. On Au(lll), imaging the surface near the surface state gives a better contrast [73]. On Ni(lOO), islands of NiO were detected by STS [2]. Very nice results have recently been obtained on Al(lll) after adsorption of various species [74]. Hasegawa and Avouris [75] have imaged on reconstructed Au(lll) the standing wave pattern formed by the electron density. Such a phenomenon, observed at steps or around adsorbates, stems from interferences between the incident and the reflected wave functions of electrons in 2-D states on this surface. 

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