Angular momentum of the photon – experimental proposal J erzy Kosek, Poland

1. Angular momentum of the photon – experimental proposalJerzy Kosek, Poland • 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.

2. 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.

3. 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?

4. 2. Linear and angular momentum of the photon The magnitude of the total spin is given by the equation: For photon we have quantum spin number s=1. It gives: Projection of the photon spin on the direction of photon propagation is equal to ћ or -ћ for left or right circularly polarized light. a). Left–circularly polarized photon a). Right–circularly polarized photon Projection of the photon spin; s=+1 Direction of photon propagation Direction of photon propagation s=-1

5. 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

6. Absorbing plate rotation a) α =+45o λ/4 rotation α =-45o λ/4 b) 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. Source of the light 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.

7. Linear polarizer α =90o Plate λ/4 Absorbing plate no rotation c) no rotation α =0o λ/4 d) 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. Source of the light Source of the light

8. 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: Plate Linear polarizer α =90o Absorbing plate λ/4 c) 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. no rotation α =0o λ/4 d) 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.

9. 6. Description of the photon state in the Quantum Theory of Light In right-circularly polarized light every photon is in the state: having the same momentum –ћ. Total momentum transmitted from circularly polarized light to absorbing object is the sum of momentums of every photon. Absorbing plate Similarly we can describe left-circularly polarized photons. a) λ/4 α =+45o rotation λ/4 α =-45o b)

10. 7 8 vacuum pump 6 5 2 2 1 4 laser 3 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.

11. 7 8 vacuum pump 6 5 2 2 1 4 laser 3 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 diameter ≈3 cm with output to vacuum pump 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

12. 7 8 vacuum pump 6 5 2 2 1 4 laser 3 9. Realization of experiment Prepare experimental setup without plate λ/4. Light have to be uniformly distributed on absorbing plate 6. Insert plate λ/4. Polarizer 4 adjust in position α=00 later α=900. No rotation of absorbing plate will be observed. 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 direction of propagation.