Hands-On Quantum Uncertainty This development of this workshop was supported by the Perimeter Institute of Theoretical Physics
Quantum uncertainty is present in the diffraction, polarization and interference of light.
Classical Diffraction of Light A laser pointer is shone through a narrow slit formed by two pencils. What will you see?
How do you explain this spreading of the light?
The width of the central maximum, is given by x = 2 L/w.
Quantum Diffraction of Light Draw the diffraction pattern above, and below that draw the pattern you would get if you used really, really, really, really faint light.
You spent a whole unit learning that light behaves as a wave – a spread out phenomena. How do we know that it consists of many, many, many individual and localized photons?
- A short video from Brown University of photon-by-photon interference:
- A short video from Brown University of photon-by-photon interference:
Diffraction is wave phenomena that is demonstrated by photons. This is an example of wave-particle duality.
The amount of diffraction is governed by Heisenberg’s Uncertainty Principle. The more certain you are of where a photon is, the less certain you will be of where it is going.
The uncertainty in position is determined by the width of the slit and x is roughly +/- w/2.
The photon has a momentum perpendicular to the slits of p = h/.
pp After the slit, it may be deflected up or down, producing an uncertainty in its momentum of p.
The uncertainty in momentum can be found using similar triangles. L x1x1 p = h/ pp p = p x 1 /L = h x 1 / L
= w/2 * x 1 h / L = w/2 * L/w * h/ L = h/2 The Heisenberg Uncertainty Principal restricts the product of these two uncertainties, x * p
Classical Polarization of Light
Put on the glasses, close one eye and then look at your neighbor's eyes. Try tilting your head. How do you explain this?
What if the filters are at 45 o ?
How do you explain this?
What if you put a third filter in between two crossed filters?
Quantum Polarization of Light ? Will the photon go through the second filter? Yes, No or ???
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? How do you explain this? Will the photon go through the second filter? Yes, No or ???
This is another example of Heisenberg’s Uncertainty Principle.
If it gets through a vertical polarizer, then we are certain that it is vertically polarized. It will go through a vertical filter but not a horizontal one.
However, we are uncertain about any other basis. We are reduced to probabilities. It has a 50% chance of going through a filter at 45 degrees.
Classical Interference You aim a laser beam at a double-slit. What will you see?
Up close. Far away.
Quantum Double-Slit Interference Does a photon go through one slit or both? What if the light is really, really low intensity?
An experiment was done in 2007 to test this with electrons. electron beam conducting plates detection screen top view charged pin
If an electron passes near enough to the conducting plate it will induce a measurable current. side view
Far from the plates - few electrons are detected, lots of interference Near the plates - lots of electron detection, little interference.
If you are certain of which way it went, there will be no interference.
What will you see if you put horizontal and vertical polarizers on either side of the slit?
What will happen if you add a third polarizer after the slits?
If the polarizer is at 45 o, the pattern returns. Why? After a photon passes through a 45 o filter, we are uncertain whether it was vertical or horizontal.
The polarizer is acting as a quantum eraser. It erases our knowledge of which way the photon went around the pin.
So, when an interference pattern is produced, which way does the photon go? We can’t be certain. An interference pattern is only produced if you are uncertain.