Quantum interpretation of Ring Laser Interferometry

[Cleonis]

I have a question about Ring Laser Interferometry.


A couple of years ago I contributed some text and several pictures to the http://en.wikipedia.org/wiki/Sagnac_effect" . Ever since I have been curious about the quantum interpretation of Ring laser interferometry.

The special thing about ring laser interferometry is that the lasing process is integral part of what is taking place. By contrast, for a double slit setup a laser source isn't necessary. A laser makes it easier to set up a double slit experiment, but it's not necessary.


Ring laser interferometer
In the case of a ring laser interferometer the detected interference effect is a beat frequency; a pattern in time rather than a pattern in space.

More information:
http://www.wettzell.ifag.de/LKREISEL/G/LaserGyros.html
http://www.ringlaser.org.nz/content/about_us.php
(Incidentally, prior to creating an animation of their own the ring laser group presented an animation created by me on that page.)

Two counterpropagating waves in a ring cavity will give rise to a beat frequency if the two have a different frequency.
The ring laser interferometers that have been build and have been operated for years now produce a signal, consistent with the expected beat frequency.

It would take too much space to present a complete exposition of the Sagnac effect in general and ring laser interferometry in particular. I take it as granted that the wikipedia article about the Sagnac effect represents a bare minimum of necessary knowledge to be able to discuss the Sagnac effect.


Now to my question: how to interpret the physics of ring laser interferometry in terms of quantum mechanics?
I presume that in terms of quantum mechanics the state of the laserlight must be represented as a quantum superposition of both directions of propagation, co-propagation and counter-propagation. However, what is the quantummechanical reason for finding the beat frequency? It seems a beat frequency arises if and only if co-propagating wave and counter-propagating wave have a different frequency.

Compare a double slit setup. In terms of quantum physics what passes the slits is a quantum superposition of passing through both of the slits. But this state of superposition leaves the frequency of the propagating quantum wave unaffected.

In the case of ring laser interferometry, how can you accommodate the frequency shift?

 

[AndyW]

Thank you for your question about Ring Laser Interferometry. As a scientist with a background in optics and quantum mechanics, I am happy to provide some insights on the quantum interpretation of this phenomenon.

First, let's briefly review the basics of Ring Laser Interferometry. As you mentioned, the Sagnac effect is the principle behind this technique, where two counter-propagating waves in a ring cavity give rise to a beat frequency. This beat frequency is a result of the interference between the two waves, which have slightly different frequencies due to the rotation of the cavity.

Now, let's take a look at how this can be explained in terms of quantum mechanics. In a ring laser interferometer, the laser light is represented as a quantum superposition of both directions of propagation, co-propagation and counter-propagation. This means that the light can be thought of as existing in both states simultaneously, similar to the double slit experiment.

However, the key difference here is the rotation of the cavity. This rotation introduces a phase shift between the two counter-propagating waves, which results in a difference in frequency. This frequency difference is what gives rise to the beat frequency observed in the interferometer.

To explain this in more detail, we need to consider the concept of wave-particle duality in quantum mechanics. According to this principle, particles can also behave like waves and exhibit interference patterns. In the case of the ring laser interferometer, the laser light can be thought of as a wave that is split into two parts, one traveling clockwise and the other counterclockwise. When these two parts recombine, they interfere with each other, resulting in the observed beat frequency.

In summary, the quantum interpretation of ring laser interferometry involves the concept of wave-particle duality and the superposition of states in quantum mechanics. The rotation of the cavity introduces a phase shift between the two counter-propagating waves, resulting in a frequency difference and the observed beat frequency.

I hope this helps to answer your question. If you have any further inquiries, please do not hesitate to ask. Thank you for your interest in this fascinating topic.