Experimental Optics
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Michelson Interferometer
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Figure 1Michelson Interferometer. The source intensity is split evenly by the beam splitter
into ‫ܫ‬஺ /2 and ‫ܫ‬஻ /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 LB is changed relative to the fixed mirror light path LA. This movement changes
the interference conditions at the detector position.
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Interference and Coherence:
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Figure 2 Creation 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
HYHQPXOWLSOHRIȜWhe waves reinforce. At locations (a) where the path difference is an odd multiple
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series of alternating bright and dark bands are seen (www.wikipedia.com).
Temporal Coherence:
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Figure 3 The amplitude of a single frequency wave as a function of time t (red) and a copy of the
same wave delayed by IJ (green). The coherence time of the single frequency wave is infinite since it is
SHUIHFWO\FRUUHODWHGZLWKLWVHOIIRUDOOGHOD\VIJ (www.wikipedia.com).
7
Figure 4 The 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
(www.wikipedia.com).
Spatial Coherence:
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Figure 5Young’s Double Slit Experiment (www.wikipedia.com).
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
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when averaged over time (www.wikipedia.com).
8
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
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Which-way experiments: Where classical physics fails
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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?
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9
Let's now do the same with a single photon, i.e. with a singlecent coin.What happens at the
beam splitter?
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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
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Figure 7 Sketch of the Michelson interferometer - introducing the Knallers(Bombs) test. 1RZDSKRWRQLVVHQWLQWRWKHPHDVXUHPHQWVHWXS
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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).
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Figure 9:Experimental setup of the Michelson Interferometer
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Figure 10:Expanded experimental setup of the Michelson Interferometer
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Figure 11:Adjustment of the laser to define the optical axis
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Figure 13:Adjustment of the reference mirror
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Figure 14:Adjustment of the translation mirror
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