Quantum mechanics: The double slit experiment

This blog is part of a series I am doing to help demystify the concepts you need to understand for quantum computing. The double slit experiment helps us whittle away at a lot of the misconceptions about quantum mechanics so we can start to think about quantum computers and quantum algorithms in the right way and we can start to make sense of the maths. I assume at this point you have read my blog about the basic concepts of quantum mechanics and are ready to ask some more questions.

Setting up the experiment

The experiment is all about shooting particles at a screen that has two slits. We then have a second screen at the back where we measure where each particle hit. If we do this at a human scale with a tennis ball then we get two clusters behind each slit. The ball passes through one or the other. If we do the same experiment with waves and make the slits narrow — close to the wavelength of the wave — then we see an interference pattern. This is true of light and it is true of waves in a swimming pool.

Remember that interference is when waves reinforce or cancel each other out rather like when waves crash in and out of the beach or against a harbour wall.

The internet is filled with lovely pictures of interference patterns from real experiments and diagrams of what the waves look like spreading out from the screens in the double slit experiment so take a moment to do a Google image search and make sure you have the right picture in your head.

Now we know that light is quantized into photons with energy defined by Plank’s constant. Let’s make the slits really narrow and fire one photon at a time. When do this over and over and we measure the location of the photons hitting the second screen, we can see an interference pattern emerge. This means that the photon is behaving as a wave even though we know it is a single particle. The interference pattern emerges when the waves passing through each slit interfere. For a single photon to have an interference pattern it must be a wave that passes through both slits at once.

When we measure the point at which the photon strikes a screen on the other side of the slits it only has one location so in that sense it behaves as a particle, but while moving unobserved it has a superposition of waves taking both paths and those waves interfere. Both paths must exist at the same time, otherwise we wouldn’t see the interference.

At this point it is tempting to say that the photon is a particle that passes through both slits at once, but we know that isn’t the case because then we would end up with a cluster behind each slit, like with our tennis balls. If you try to detect which slit the photon passes through it will pass through one or the other and not exhibit the interference pattern, you will see the two clusters. Only if the particle passes through unobserved then the interference pattern is present. The behaviour of the photon depends on the interference of the waves and not on the idea of the photon passing through both slits at once.

This is why when we talk about qubits it is not helpful to talk about being in both |0⟩ and |1⟩ at the same time, but that we have a superposition of both states defined by a wave equation. Knowing that it is a wave and not some kind of multiverse of multiple states, means that we are able to manipulate the superposition of our qubits using wave interference. This is how we build up quantum gates that then can be used for quantum algorithms.