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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