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Angular momentum of the photon -

VIEWS: 129 PAGES: 12

									  Angular momentum of the
photon – experimental proposal
     Jerzy Kosek, Poland

 1.   Introduction
 2.   Linear and angular momentum of the photon.
 3.   Measurement of the photon spin – Beth, 1936.
 4.   Angular momentum of the circularly polarized photon.
 5.   Angular momentum of the linearly polarized photon.
 6.   Description of the photon state in Quantum Theory of Light.
 7.   Setup of the experiment.
 8.   List of accessories.
 9.   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                      a). Right–circularly
polarized photon                         polarized photon


   Projection of the      Direction of                          s=-1 Direction of
   photon spin; s=+1      photon                                     photon
                          propagation                                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.
                                                 Absorbing plate
     a)           α =+45o         λ/4
                                                 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.

              Linear polarizer   Plate        Absorbing plate
 c)           α =90o             λ/4          no rotation


 Source of
 the light



 d)           α =0o              λ/4           no rotation

 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                  Linear      Plate       Absorbing
 fact that measurement of spin         c)      polarizer   λ/4         plate
 carried on linearly polarized light
                                               α =90o
 gives on average half photons
 having a left circular polarization
                                                                     no
 state |L> and half a right |R> one.   d)      α   =0o     λ/4       rotation
 The total momentum of that
 ensemble of photons is equal to
 zero.

 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.

                                  Absorbing
  a)       α =+45o     λ/4
                                  plate


                                              Similarly we can describe left-
                                  rotation    circularly polarized photons.
  b)       α =-45o     λ/4
           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)           7
                                                                  8
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                                vacuum
                                                              6
to torsion of the thread. Vacuum in tube is                           pump
created to minimalize rotation resistance of
                                                          5
the plate due to environment. 1             2         2
                                                          4

                                 laser
                                                          3
                      8. List of accessories
1.Laser – high power or mercury-vapor lamp with interference filter – 1
piece
2. Lenses, focal length:                                                      7
                                                                                  8
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
                                                                                      vacuum
7. Thread – 2 m                                                               6
                                                                                      pump
8. Plastic tube - 1 piece
length l = 2m                                                             5
diameter ≈3 cm                                  1             2       2
                                                                          4
with output to vacuum pump
transparent                                    laser
9. Vacuum pump – 1 piece                                                  3
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
          9. Realization of experiment
1. Prepare experimental setup without plate λ/4.
   Light have to be uniformly distributed on                     7
   absorbing plate 6.                                                8

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         6       vacuum
   two possible directions of the photon “rotation” –                    pump

   clockwise and counter clockwise in respect to its         5
                                      1           2      2
   direction of propagation.                                 4
                                     laser
                                                             3

								
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