Welcome back for our second guided hike in the quantum mechanical forests! Last week we saw how particles move like waves and hit like particles and how a single particle takes several paths. Surprisingly, it is a well-researched area of quantum mechanics – it is on the paved nature trail around the visitor center.
This week I want to get off the paved trail and go deeper into the forest to talk about how particles fuse and merge. This is a subject that is usually reserved for physics majors; it is rarely discussed in popular articles. But the gain is to understand how exact lidar works and to see one of the great inventions it makes from the laboratory, the optical comb. So let’s make our (quantum) hiking boots a little dirty – it’s worth it.
Two particles
Let’s start with a question: if particles move like waves, what happens if I overlap the particles of two particles? Or to put it another way: do particle waves just alternate with themselves, or do they mix together?
Miguel Morales
We can test it in the lab by changing the setup we used last week. Instead of dividing the light from one laser into two paths, we can use two separate lasers to create the light that enters the last half-silver mirror.
We have to be careful with the lasers we use, and the quality of your laser pointer is no longer up to the task. If you measure the light of a normal laser accurately, the color of the light and the phase of the wave (when the wave peaks occur) wander around. This color change is not noticeable to our eyes – the laser still looks red – but it seems that the exact color of red varies. This is a problem that money and modern technology can fix – if we pay enough cash, we can buy lasers with a precision mode locked. Thanks to this, we can have two lasers that both emit photons of the same color with wavy crests.
When we combine the light of two high quality lasers, we see exactly the same stripe pattern as we have seen before. The waves of particles produced by two different lasers are interacting!
So, what happens if we go to the single photon boundary again? We can turn off the intensity of the two lasers so low that we see that the photons appear on the screen one by one, like small paintballs. If the rate is low enough, there will be only one photon between the lasers and the screen at a time. When we perform this experiment, we will see that the photons arrive at the screen one by one; but if we look at the accumulated pointillism painting, we will see the same streaks as we saw last week. Again, we see interference from single particles.
It seems that all the experiments we have done before give exactly the same answer. Nature does not care if one particle interacts with itself or if two particles interact with each other – a wave is a wave, and particle waves work just like any other wave.
But now that we have two precision lasers, we have a number of new experiments we can try.
Two colors
Let’s first mix in photons of different colors. Let’s take the color of one of the lasers and make it slightly more blue (shorter wavelength). When we look at the screen, we see stripes again, but now the stripes are slowly running sideways. Both the appearance of stripes and their movement are interesting.
First, the fact that we see stripes indicates that particles of different energies are still interacting.
The second observation is that the striped pattern is now time dependent; the stripes run sideways. As we increase the color difference between the lasers, the speed of streaks increases. The musicians in the audience will already recognize the beating pattern we see, but before we get the explanation, let’s improve our experimental setup.
If we are satisfied with narrow laser beams, we can use a prism to combine the light currents. A prism is usually used to divide a single ray of light and send each color in a different direction, but we can use it backwards and with careful alignment use the prism to turn the light of two lasers into a single ray. to combine.
Miguel Morales
If we look at the intensity of the combined laser beam, we see the intensity of the light ‘beating’. Although the light from each laser was steady, the resulting beam fluctuated from bright to dim when combined lightly with slightly different colors. Musicians will recognize this by tuning their instruments. When the sound of a tuning fork is combined with the sound of a slightly tuning string, one can hear the ‘beats’ while the sound alternates between loud and soft. The speed of the beats is the difference in the frequencies, and the string is set by adjusting the clock speed to zero (zero difference in frequency). Here we see the same with light – the beating frequency is the color difference between the lasers.
While it makes sense when you think of instrument strings, it’s quite surprising when you think of photons. We started with two steady streams of light, but now the light is put together in times when it is bright and times when it is dim. As the difference between the colors of the lasers increases (they are tuned down), the faster the pulsing becomes.
Paintballs mean
So, what happens if we turn off the lasers very low again? Once again we see that the photons hit our detector one by one like small paintballs. But if we look closely at the time when the photons arrive, we see that they are not random – they arrive on time with the beats. No matter how low we turn the lasers – the photons can be so rare that they only show every 100 beats – but they will always arrive on time with the beats.
This pattern is even more interesting when we compare the arrival time of the photons in this experiment with the stripes we saw with our laser pointer last week. One way to understand what happens in the two-slot experiment is to represent the wave nature of quantum mechanics where the photons can land from side to side: the paintballs can hit in the bright regions and not in the dark areas. We see a similar pattern in the paintball’s arrival in the two-color ray, but now the paintballs are directed back and forth in time and can hit them just in time with the beats. The beats can eventually be considered stripes.