Download Angular momentum of the photon

Angular momentum of the
photon – experimental proposal
Jerzy Kosek, Poland
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Introduction
Linear and angular momentum of the photon.
Measurement of the photon spin – Beth, 1936.
Angular momentum of the circularly polarized photon.
Angular momentum of the linearly polarized photon.
Description of the photon state in Quantum Theory of Light.
Setup of the experiment.
List of accessories.
Realization of experiment.
1. Introduction
The goal of this presentation is to
demonstrate the fact, that photon has
angular momentum (spin) - roughly
saying - spinning in two possible
directions: clockwise and counter
clockwise relative to the direction of its
propagation.
We hope that it allows students deeper
understand spin - basic property of every
elementary particle.
2.Linear and angular momentum of
the photon
In accordance with classical electrodynamics and also with
quantum mechanics light possesses linear momentum. It’s usually
demonstrated with use of a small whirligig with mirrors montage in
a vacuum bulb.
The quantum theory of light predicts that every photon in addition
to its linear momentum possesses also intrinsic angular
momentum (named spin) equal to 1.
•What does it mean?
•What do we learn from it?
•How can we measure it?
2. Linear and angular momentum
of the photon
The magnitude of the total spin is given by the equation:
S   s(s 1)
For photon we have quantum spin number s=1. It gives:
S  2

Projection of the photon spin S on the direction of photon propagation
is equal to ћ or -ћ for left or right circularly polarized light.
a). Left–circularly
polarized photon
Projection of the
photon spin; s=+1
a). Right–circularly
polarized photon
Direction of
photon
propagation
s=-1 Direction of
photon
propagation
3.Measurement of the photon spin
Experimental proof of that theoretical prediction was done
by R. Beth in 1936 in Princeton. As Beth announces in his
paper (R. A. Beth, Mechanical Detection and Measurement
of the Angular Momentum of Light, Physical Review, v. 50,
July 15, 1936) he had several discussion about the
experiment with Einstein. In this experiment Beth showed
that when linearly polarized light is converted to circularly
polarized one by doubly refracting slab, the slab
experiences a reaction torque.
It is difficult to demonstrate in high school laboratory this
experiment and no simple solutions were proposed so far.
Experimental setup of Beth’s experiment
4. Angular momentum of the
circularly polarized photon
According to the Quantum Theory of Light every photon of circularly
polarized light has the same angular momentum.
a)
α =+45o
λ/4
Absorbing plate
rotation
Source of
the light
b)
α =-45o
λ/4
rotation
Source of
the light
It’s expected that an object absorbing circularly polarized photons will
rotate clockwise or counter clockwise with respect to the type of
circular polarisation.
5. Angular momentum of the
linearly polarized photon
If light is linearly polarized then it doesn’t have angular momentum and
no rotation of an object will be observed.
c)
Linear polarizer
Plate
Absorbing plate
α =90o
λ/4
no rotation
α =0o
λ/4
no rotation
Source of
the light
d)
Source of
the light
6. Description of the photon state in
the Quantum Theory of Light
When light is linearly polarized then every photon can be considered as
a superposition of states of left and right circular polarization with equal
probabilities. For instance linearly polarized light at an angle at 450 to the
horizontal plane can be expressed as follows:
| 
1
(| L   | R )
2
The above equation expresses
fact that measurement of spin
carried on linearly polarized light
gives on average half photons
having a left circular polarization
state |L> and half a right |R> one.
The total momentum of that
ensemble of photons is equal to
zero.
c)
Linear
polarizer
Plate
λ/4
Absorbing
plate
α =90o
d)
α
=0o
λ/4
no
rotation
One of mysteries of the photon is fact that before measurement the photon in a
superposition state has an undefined angular momentum. The same applies to every
quantum particle.
6. Description of the photon state in
the Quantum Theory of Light
In right-circularly polarized light every photon is in the state:
| | R 
having the same momentum –ћ. Total momentum transmitted from
circularly polarized light to absorbing object is the sum of momentums
of every photon.
a)
α =+45o
λ/4
Absorbing
plate
rotation
b)
α =-45o
λ/4
Similarly we can describe leftcircularly polarized photons.
7. Setup of the experiment
Light emerging from laser (1) is transformed by
two lenses (2) into parallel beam of diameter
about 2 cm. Next, the light is reflected by mirror
(3), passes linear polariser (4), quarter plate (5)
and is incident on absorbing plate (6), hanging
on throat (7) in a plastic, tall and transparent
tube (8) with the output to the vacuum pump.
The tube is supported on a two heavy
retort stands. A long thread is used to
minimalize contrary force momentum due
to torsion of the thread. Vacuum in tube is
created to minimalize rotation resistance of
the plate due to environment. 1
2
7
8
6
2
5
4
laser
3
vacuum
pump
8. List of accessories
1.Laser – high power or mercury-vapor lamp with interference filter – 1
piece
2. Lenses, focal length:
f= 6 cm – 1 piece
f= 30 cm – 1 piece
f= 60 cm – 1 piece
3. Mirror 100% - 1piece
4. Linear polarizer – 1 piece
5. Plate λ/4 (λ – wavelength of light beam) – 1 piece
6. Absorbing plate (black) diameter < 3cm (less then tube diameter) –
possibly light
7. Thread – 2 m
8. Plastic tube - 1 piece
length l = 2m
2
2
diameter ≈3 cm
1
with output to vacuum pump
laser
transparent
9. Vacuum pump – 1 piece
10. Mountings – retort stands:
- height 2,5 m – 2 pieces (on picture shown only one retort stand),
- height 0,5 m – 4 pieces
11. Lens holders – 2 pieces
12. Handle (for polarizer and plate λ/4, for mirror 100%) - 2 pieces
7
8
6
5
4
3
vacuum
pump
9. Realization of experiment
1. Prepare experimental setup without plate λ/4.
Light have to be uniformly distributed on
absorbing plate 6.
2. Insert plate λ/4. Polarizer 4 adjust in position α=00
later α=900. No rotation of absorbing plate will be
observed.
3. Polarizer 4 adjust in position α=+450, later α=-450.
A small rotation of absorbing plate is expected to
be observed in two different directions. It will show
two possible directions of the photon “rotation” –
clockwise and counter clockwise in respect to its
2
2
1
direction of propagation.
7
8
6
5
4
laser
3
vacuum
pump