One of the quietest revolutions Our century today was the entry of quantum mechanics into our everyday technology. In the past, quantum effects were limited to physics laboratories and delicate experiments. However, modern technology increasingly relies on quantum mechanics, and the importance of quantum effects will only increase in the coming decades. As such, the physicist Miguel F. Morales has taken on the Herculean task of explaining quantum mechanics to the rest of us laypeople in this seven-part series (not mathematics, as we promise). Below is the second story in the series, but you can always find the starting story here.
Welcome back to our second guided walk into the quantum mechanical forests! Last week we saw how particles move like waves and how particles meet and how a single particle takes multiple paths. While surprising, this is a well-researched area of quantum mechanics – it's on the paved nature trail around the visitor center.
This week I want to get off the paved path and go a little deeper into the forest to talk about how particles merge and combine as you move. This is a topic usually reserved for physics majors. It is rarely discussed in popular articles. But the payoff is in understanding how precision lidar works and seeing one of the great inventions that make it out of the lab, the optical comb. So let's get our (quantum) hiking shoes a little dirty – it will be worth it.
Let's start with a question: if particles move like waves, what happens if I overlap the paths of two particles? In other words: do particle waves only interact with themselves or do they mix?
Enlarge /. On the left you can see the interferometer from last week, in which a single particle is split by the first mirror and takes two very different paths. On the right you can see our new setup where we start with particles from two different lasers and combine them.
We can test this in the lab by changing the setup we used last week. Instead of splitting the light from one laser into two paths, we can use two separate lasers to create the light that goes into the final semi-silvered 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 carefully measure the light from a regular laser, the color of the light and the phase of the wave (when the wave peaks appear) will wander around. This color migration is not noticeable to our eyes – the laser still looks red – but it turns out that the exact shade of red varies. This is a problem that money and modern technology can fix. If we spend enough money, we can buy precise mode-locked lasers. Thanks to this, we can have two lasers that both emit photons of the same color with time-aligned wave crests.
When we combine the light from two high quality lasers, we see exactly the same stripe pattern that we saw before. The waves of particles created by two different lasers interact!
So what happens when we go back to the single photon limit? We can set the intensity of the two lasers so low that the photons appear individually on the screen like small paintballs. If the rate is sufficiently low, there is only one photon between the lasers and the screen at a time. If we do this experiment, we will see the photons arrive on the screen one at a time. But if we look at the accumulated pointillism painting, we will see the same streaks we saw last week. We see single particle faults again.
It turns out that all of the experiments we've done before give the exact same answer. Nature does not care whether a particle interacts with itself or whether two particles interact with each other – a wave is a wave, and particle waves act like any other wave.
But now that we have two precision lasers, we have a number of new experiments to try.
First, let's try to perturb photons of different colors. Let's take the color of one of the lasers and make it a little bluer (shorter wavelength). When we look at the screen we see stripes again, but now the stripes are slowly moving sideways. Both the look of the stripes and their movement are interesting.
First, the fact that we see streaks shows that particles of different energies are still interacting.
The second observation is that the stripe pattern is now time dependent; The stripes go to the side. The greater the color difference between the lasers, the faster the stripes will be. The musicians in the audience will already recognize the beat pattern we are seeing, but before we get to the explanation, let's improve our experimental set-up.
If we are content with using narrow laser beams, we can combine the luminous fluxes with a prism. A prism is typically used to split a single beam of light and send each color in a different direction. However, we can use it backwards and with careful alignment use the prism to combine the light from two lasers into a single beam.
Enlarge /. The light from two lasers of different colors combined with a prism. After the prism, the light “strikes” in its intensity.
If we look at the intensity of the combined laser beam, we see the intensity of the lightning strike. While the light from each laser was constant, when their rays are combined with slightly different colors, the resulting beam resonates from bright to dim. Musicians recognize this by the fact that they tune their instruments. When the sound of a tuning fork is combined with the sound of a slightly detuned string, you can hear the “beats” when the sound oscillates between loud and soft. The speed of the beats is the difference in frequencies, and the string is tuned by setting the beat speed to zero (zero frequency difference). Here we see the same thing with light – the beat frequency is the color difference between the lasers.
While this makes sense when thinking about instrument strings, it is rather surprising when thinking about photons. We started with two steady streams of light, but now the light is focused in times when it is bright and in times when it is weak. The greater the difference between the colors of the lasers (they are out of tune), the faster the pulsing becomes.
Paintballs on time
So what happens when we turn the lasers all the way down again? Again we see how the photons hit our detector one after the other like small paintballs. However, if we look closely at when the photons arrive, we can see that it's not random – they arrive on time for the beats. It doesn't matter how deep we turn the lasers – the photons can be so rare that they only show one every 100 beats – but they always arrive on time for 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 is happening in the two-slit experiment is to envision the wave nature of quantum mechanics, which determines where the photons can land back and forth: the paintballs can hit in the light areas, not the dark areas . We see a similar pattern when the paintball arrives in the two-tone beam, but now the paintballs are directed forward and backward in time and can only hit with the beats in time. The beats can be viewed as streaks in time.