Dear friends,
Recently I was told about a so-called Beth experiment. But I am not sure of its description that I found in some article on Internet, so, I am asking the question.
The configuration is described as follows:
A beam of circularly polarized light is sent upon a round quartz half-wave plate suspended with its plane horizontal. The plate, suspended by a quartz fiber, can rotate in the horizontal plane, i.e. around the vertical fiber. Very closely above this plate (4mm), there is a another quartz plate, but this one is fixed and is a quarter-wave plate. Its top side is coated with a reflecting metal layer. The half-wave plate is supposed to rotate under the influence of the circularly polarized beam. This tiny rotation can be observed with a telescope.
Does anybody know this experiment? Is the above description correct?
Also, what in fact is the purpose of the experiment? And how the experiment goes, what is actually measured, only the rotation of the plate?
check this one:
https://www.st-andrews.ac.uk/~photon/manipulation/images/pdfs/AJPTweezers.pdf
I hope it helps ...
Dear Sofia,
The description that you quote is correct. It is important to note that the quartz plate used in the original experiment is birefringent.
More recent related work (from the Leiden quantum optics group) can be found in
http://spie.org/Publications/Proceedings/Paper/10.1117/12.584515
or using microwaves:
https://hal.inria.fr/docs/00/77/64/94/PDF/AES_Final.pdf
The purpose of the experiment is to show that light contains spin angular momentum. If light indeed carries angular momentum it should be possible to transfer this to matter, which results in a torque. The transfer of angular momentum is done by the birefringent plate, because the polarization of the incoming and outgoing light is different. This difference corresponds to a change in the spin angular momentum of the photons. The change in angular momentum should generate a torque on the birefringent plate that could, in principle, be measured using a torsion balance.
In practice this is very difficult to measure because you need to measure a small rotation of the birefringent plate. This is hard because you will need a very high sensitivity of the setup even if you have access to large optical powers. There are several systematic errors you need to deal with before drawing conclusions from the experiment. To name a few: (i) the system will be extremely sensitive to vibrations that may cause the plate to move (ii) a large power optical beam may lead to heating effects that disturb the measurement (iii) linear momentum (radiation pressure) may also generate a measurable torque if the beam is not exactly centered on the plate. (iv) the exact nature of the wire might be important because of-the-shelf wires might be twisted or contain stress that breaks rotational symmetry.
It is good to keep in mind that Beth used a torsion balance in 1936 at a time when these devices were common laboratory equipment. Hence, his device was probably as good or better than a modern home-built torsion balance. For a review on the use of torsion balances see Gillies and Ritter, Rev. Sci. Instr vol 64, p283 (1993)
Johannes and Michiel,
many thanks for the references, and, Michiel, many thanks for the explanations. I will gladly read the material you kindly sent me. Just some questions, please:
Michiel, you say "This difference corresponds to a change in the spin angular momentum of the photons". Actually, since it's a half-wave plate, the spin should be flipped, e.g. from ħ to -ħ. Is that correct?
Also, I understand that there may be photons that pass through the plate. How is this possible? If the photon delivers to the plate angular momentum (in fact, not ħ but 2ħ, because of the flip) it also has to be absorbed. By causing the plate to rotate, the photon delivers also energy to the plate. Or, alternatively, the photon passes the plate and is red-shifted?
With many thanks,
Sofia
The Beth experiment is an optical analogue of the celebrated Einstein-de Haas experiment. Just as the latter showed for electrons, Beth showed that the angular momentum carried by EM-fields/photons can set macroscopical objects into mechanical rotation. Based on the fact that angular momentum is a conserved quantity, Beth set up an experiment such that the polarization (the spin part of the angular momentum, SAM) of the EM/photon beam changed from left-handed to right-handed (spin +1 to -1) due to its interaction with a half-wave plate. Since the angular momentum for the total system, i.e. the incident beam plus the half-wave plate plus the outgoing beam, has to be conserved and the photons change their (spin) angular momentum by 2ħ there must be an change of the (mechanical) spin angular momentum of the half-wave plate of -2ħ. Beth's experiment confirmed this. Similar findings from a more general experiment, performed at radio frequencies and involving the total angular momentum, i.e. the (vector) sum of the spin angular momentum (SAM) and the orbital angular momentum (OAM) of the EM/photon beam were reported last year:
Emile, O. et al. Electromagnetically Induced Torque on a Large Ring in the Microwave Range. Phys. Rev. Lett. 112, 053902 (2014).
Since. in Beth's experiment, the half-wave plate does not have a translational motion relative to the source or the detector, there is no Doppler shift involved.
Article Electromagnetically induced torque on a macroscopic object
Bo
There is no translational motion, but the plate gains rotational energy. Where does this come from if the photons do not change energy? Is there an energy change in the photons due to changing their angular momentum that does not correspond to a change in frequency?
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