Welcome back to our second guided tour of the Quantum Mechanical Jungle! We saw it last week How particles move like waves and hit like particles And how a single particle takes multiple paths. Although surprising, this is a well-explored area of quantum mechanics – it sits on the natural paved path around the visitor center.
This week, I’d like to take off the paved trail and dive a little deeper into the woods to talk about how particles fuse and come together in motion. This is a subject usually reserved for the Physics majors; It is rarely discussed in popular articles. But the payoff is understanding how micro-lidar works and getting to know one of the great inventions out of the lab, the optical comb. So let’s go get our (sleeve) hiking boots a little dirty – it’ll be worth it.
Let’s start with a question: If particles move like waves, what happens when the paths of two particles overlap? Or say another way, do the particle waves only interact with themselves, or do they mix together?
We can test this in the lab by tweaking the setting we used last week. Instead of dividing the light from a single laser into two paths, we can use two separate lasers to create the light coming into the final half-silver mirror.
We need to be careful about 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 crests occur) wander. This color fugue is blurred 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 new technology can solve – if we spend enough money, we can buy a precision closed position laser. Thanks to these, we can have two lasers that emit photons of the same color with time-balanced wave peaks.
When we combine the light from two high-quality lasers, we see exactly the same stripe pattern that we saw before. Particle waves produced by two different lasers interact!
So what happens if we go again to the single photon limit? We can lower the intensity of the two lasers down so that we see photons appearing one after the other on the screen, like little paintballs. If the rate is low enough, only one photon will be present between the laser and the screen at a time. When we run this experiment, we’ll see photons arrive on the screen one by one. But when we look at the scoreboard overhang, we’ll see the same lines we saw last week. Once again, we see a single interference of the particle.
It turns out that all of the experiments we had before give exactly the same answer. Nature does not care whether one of the particles is interacting with itself or if there are two particles interacting with each other – a wave is a wave, and the particle waves act just like any other wave.
But now that we have two types of precision lasers, we have a number of new experiments that we can try.
First, let’s try interfering with photons of different colors. Let’s take the color of one of the lasers and make it a little more blue (shorter wavelength). When we look at the screen, we see lines again, but now the lines slowly go sideways. Both the appearance and movement of the lines are interesting.
First, the fact that we see lines indicates that particles of different energy are still interacting.
The second observation is that the planned pattern now depends on time; Stripes walk to the side. Since we make the color difference between the lasers bigger, the speed of the lines increases. Musicians in the audience will already recognize the batting pattern we’re seeing, but before we get to the explanation let’s fine-tune our experimental setup.
If we are satisfied with the use of narrow lasers, we can use a prism to incorporate light streams. Usually a prism is used to split a single light beam and send each color in a different direction, but we can use it backwards and with fine alignment, use a prism to combine the light from two lasers into one beam.
If we look at the intensity of the built-in laser beam, we will see the intensity of the light “pulsating”. While the light emitted from each laser was constant, when their beams of slightly different colors merged, the resulting beam oscillated from bright to faint. Musicians will learn about this by tuning their instruments. When the sound of a tuning fork is combined with the sound of a slightly disharmonious string, one can hear “tones” as the sound oscillates between loud and soft. Pulse velocity is the difference in frequencies, and the chord is adjusted by setting the pulse velocity to zero (zero frequency difference). Here we see the same with light – pulse frequency is the color difference between lasers.
While this makes sense when thinking about the strings of a machine, it is surprising when thinking about photons. We started with two constant streams of light, but now the light aggregates at times when it’s bright and times when it’s dim. Since the difference between the colors of the lasers becomes larger (de-tuned), the faster the pulse becomes.
Paintballs just in time
So what happens if we again lower the laser really low? Once again we see photons hitting our detector one by one like little paintballs. But if we look carefully at the timing of the arrival of the photons, we find that they are not random – they arrive in time with the pulses. It doesn’t matter how far we lower the laser – photons can be so rare that they only appear once every 100 pulses – but they will always arrive in time with the chimes.
This pattern is more interesting if we compare the arrival time of the photons in this experiment with the lines we saw with our laser pointer last week. One way to understand what happens in the two-slit experiment is to visualize the wave-like nature of quantum mechanics that steers where photons can land side by side: Paintballs can hit in bright areas rather than in dark areas. We see a similar pattern in the arrival of paintballs in the two-tone package, but now the paintballs are directed forward and backward at the right time and can only hit in time with beats. The beats can be thought of as streaks in time.