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: http://www.physics.brown.edu/physics/demopages/Demo/modern/demo/7a5520.htm

-         A short video from Brown University of photon-by-photon interference: http://www.physics.brown.edu/physics/demopages/Demo/modern/demo/7a5520.htm

http://phys.educ.ksu.edu/vqm/html/singleslit.html

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/.

p

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

x1

p = h/

p

p = p x1/L = h x1/L

= w/2 * x1 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 45o?

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 ???

?

Will the photon go through the second filter? Yes, No or ???

?

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 45o, the pattern returns. Why?

After a photon passes through a 45o 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.