Experimental Optics. Michelson Interferometer. Contact. Last edition:

Transcription

1 Experimental Optics Contact Last edition: Michelson Interferometer

2 1 Background

3 1 Background 3

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5 Figure 1Michelson Interferometer. The source intensity is split evenly by the beam splitter into /2 and /2 which propagate along the two mirror arms of the interferometer. When the translating mirror is moved either towards or away from the beam-splitter the optical path of light L B is changed relative to the fixed mirror light path L A. This movement changes the interference conditions at the detector position. AxtE t kz I A 2kL A/B L P = cos( 2 ) = cos ( 2 ) 5

6 L A/B L P I p I cos kl A L B k = : L = = = 0,1,2,. Minimum: L = = ( ) = 0,1,2,. d d N He:Ne Interference and Coherence: 6

7 Figure 2Creation of interference fringes by an optical flat on a reflective surface. Light rays from a monochromatic source pass through the glass and are reflected off from the bottom surface of the flat and the supporting surface. The tiny gap between the surfaces means the two reflected rays have different path lengths and interfere when they combine. At locations (b) where the path difference is an he waves reinforce. At locations (a) where the path difference is an odd multiple series of alternating bright and dark bands are seen ( Temporal Coherence: Figure 3The amplitude of a single frequency wave as a function of time t (red) and a copy of the same wave delayed by (green). The coherence time of the single frequency wave is infinite since it is ( 7

8 Figure 4The amplitudes of two waves with slightly different frequency. Twice the correlation time corresponds to the relative phase drift of 180. At any particular time t the two waves can interfere perfectly with each other. But, since half the time the red and green waves are in phase and half the time out of phase, when averaged over t, any interference disappears at this delay ( Spatial Coherence: Figure 5Young s Double Slit Experiment ( Figure 6 Examples for spatial coherence, a) plane wave with infinite coherence length, b) wave with varying wavefront and infinite coherence length, c)wave with varying wavefront and finite coherence s in the extent of a wave to interfere, when averaged over time ( 8

9 The next session describe quantum optical test and is supposed to be considered as an advanced topic. It means, that students are not obligated, but encouraged to learn an introductory to the quantum optic topic material, given in this section. Knowledge of this topic improves your grade, but absence of this knowledge does not make your grade lower. Knaller (Bomb) test Which-way experiments: Where classical physics fails We first consider what happens, when we e.g. launch 4 photons from the laser into the measurement setup of Michelson interferometer. We can symbolize the photon as one cent coin and send iton the way from the Laser to the beam splitter.what happens? 9

10 Let's now do the same with a single photon, i.e. with a singlecent coin.what happens at the beam splitter? Psi two single Conclusion: - If the paths in the interferometer indistinguishable, as one photon interference both possible paths (wave functions), i.e. an interference pattern on the screenis visible. - If the paths are distinct, i.e. path information is given, then thewave function is set to one value (from the only possibility), the other disappears - there can be no more interference. Experiment on interaction-free quantum measurement: The Knaller-Test the in the Michelson interferometer What is an interaction-free quantum measurement? 10

11 Figure 7 Sketch of the Michelson interferometer - introducing the Knallers(Bombs) test. 11

12 In summary, we found that in 25% cases, a functional bomb can be detected without exploding it.in 50% cases a functional bomb explodes and in 25% no statement can be made because the photon propagates back tothe laser. Ultimately, this also means that we can prove the presence of functional Knallers/Bombs without an interaction between photons and Knallers/bombs! Radius Figure 8Knaller (Bomb) test. Destructive interference (solid line) in the center appears in case when no arm is blocked. The interference collapses when one arm of the interferometer is blocked and light appears in the center (dashed line). 12

13 Figure 9:Experimental setup of the Michelson Interferometer 13

14 4.2 Figure 10:Expanded experimental setup of the Michelson Interferometer 14

15 Figure 11:Adjustment of the laser to define the optical axis Figure 12:Adjustment of the beam splitter 15

16 Figure 13:Adjustment of the reference mirror Figure 14:Adjustment of the translation mirror 16

17 Figure 15Michelson interferometer with the alignment procedure completed = 17

18 Figure 16etup for the visibility measurement with the photodiode Figure 17Beam expansion of the collimated laser source 18

19 = cos () () () () = /2) = 45 = cos(45 ) sin(45 ) sin(45 ) cos(45 ) 0 cos(45 ) 0 sin(45 ) sin(45 ) cos(45 ) = = 1 2 [1 ] +[1+] [1 + ] +[1] 19

20 = [1 ] +[1+] [1 + ] +[1] = 1 2 [1 ] +[1+] 0 / = / = 1 4 ([1 ] + [1+] ) ([1+] + [1 ] ) 1 4 ( + 2 sin ()) sin ()) Figure 18:xperimental setup of the technical interferometer. The positions for the calculation steps are represented by the green circles. 20

21 Figure 19:Pair of interference signals detected when the translating mirror is moved 21

22 = [] [] f = vf =. 22

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