# A Description of the Uncertainty Principle You've (Probably) Not Seen Before: Squeezed Light Parth G

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Parth G
Published at : 29 Sep 2021
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There is a way to mess with Heisenberg’s Uncertainty Principle by squeezing light… but probably NOT in a way you’ve seen before!

The Uncertainty Principle is a relationship between two linked quantities, known as "conjugate variables", that tells us we are not allowed to know both with perfect precision at the same time. The more we know about one quantity, the less we know about the other. One example of this is the position and momentum of a particle in the same direction. In this video, we briefly look at how to understand this - though I have also made a video in the past explaining the Uncertainty Principle itself in more detail: https://www.youtube.com/watch?v=iZ96TuP_veY

Light waves are classically thought of as excitations (wobbles) of the electromagnetic field. And they have an amplitude (size of jiggle) and phase (a measure of how far through the full cycle a wave is at a point in space and time). Why is phase measured as an angle? https://encyclopedia2.thefreedictionary.com/Phase-angle+measurement

In quantum mechanics, these two quantities are related by the Uncertainty Principle. We cannot precisely know both the amplitude and the phase of light at a given time. The uncertainties in both quantities must have a minimum value when multiplied together. We see a really visual way to represent a wave with uncertainty in amplitude and phase, in this video.

So why does this uncertainty exist? And what does squeezed light have to do with it? Well, let’s imagine we want to create light waves from the exact same source, over and over again in the exact same way each time. When we measure the amplitudes and phases of these waves, we will get different results each time. This is despite the fact that we did everything exactly the same to create each wave.

In simpler terms, we have no way of predicting the exact phase and amplitude of the NEXT wave that our source will create. Hence, we deal with uncertainties when predicting our next wave. And this is a property of the whole universe according to quantum theory, not just a bad wave source.

The really interesting thing to note is that we can actually lower the uncertainty in one quantity (say, the phase) to below what is expected in an average "minimum uncertainty" state. But to compensate, the uncertainty in the other quantity must increase so the product between them is still at least the minimum allowed value. This is a "squeezed state" of light!

Squeezed light can be used in interferometer experiments, to lower the noise level of the experiment (though this does not affect the signal directly). Squeezed light was also used in the LIGO experiment used for detecting gravitational waves for the first time! Read more about the uses of squeezed light here: https://en.wikipedia.org/wiki/Squeezed_states_of_light

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Timestamps:
0:00 - Heisenberg’s Uncertainty Principle: The Basics
1:53 - The Uncertainty Principle for Light: Amplitude and Phase
3:29 - How to Represent Uncertainties in Amplitude and Phase of Electromagnetic Waves
4:04 - One Way to Understand Why Uncertainty Exists in Quantum Mechanics
5:14 - The Basic, Easy-to-Understand Minimum Uncertainty State
6:08 - Reducing the Uncertainty in One Variable (Squeezed State of Light!)
7:13 - Why Bother? Applications of Squeezed Light