## From ars technica: “A curious observer’s guide to quantum mechanics pt. 2- The particle melting pot”

From ars technica

1/17/2021
Miguel F. Morales

In which lasers do things that make absolutely no sense but give us great clocks.

Aurich Lawson / Getty Image.

Welcome back for our second guided walk into the quantum mechanical woods! Last week, we saw how particles move like waves and hit like particles and how a single particle takes multiple paths. While surprising, this is a well-explored area of quantum mechanics—it is on the paved nature path around the visitor’s center.

This week I’d like to get off the paved trail and go a bit deeper into the woods in order to talk about how particles meld and combine while in motion. This is a topic that is usually reserved for physics majors; it’s rarely discussed in popular articles. But the payoff is understanding how precision lidar works and getting to see one of the great inventions making it out of the lab, the optical comb. So let’s go get our (quantum) hiking boots a little dirty—it’ll be worth it.

Two particles

Let’s start with a question: if particles move like waves, what happens when I overlap the paths of two particles? Or said another way, do particle waves only interact with themselves, or do they mix together?

On the left is the interferometer from last week, where a single particle is split by the first mirror and takes two very different paths. On the right is our new setup where we start with particles from two different lasers and combine them.
Credit: Miguel Morales.

We can test this in the lab by modifying 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 coming into the final half-silvered 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 normal laser, the color of the light and the phase of the wave (when the wave peaks occur) wander around. This color wander is not discernible to our eyes—the laser still looks red—but it turns out that the exact shade of red varies. This is a problem money and modern technology can fix—if we shell out enough cash we can buy precision mode-locked lasers. Thanks to these, we can have two lasers both emitting 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 stripey pattern that we saw before. The waves of particles produced by two different lasers are interacting!

So what happens if we again go to the single photon limit? We can turn the intensity of the two lasers down so low that we see the photons appear one at a time on the screen, like little paintballs. If the rate is sufficiently low, only one photon will exist between the lasers and the screen at a time. When we perform this experiment we will see the photons arrive at the screen one at a time; but when we look at the accumulated pointillism painting, we will see the same stripes we saw last week. Once again, we’re seeing single particle interference.

It turns out that all the experiments we performed before give exactly the same answer. Nature does not care if one particle is interacting with itself or if two particles are interacting with each other—a wave is a wave, and particle waves act 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

First, let’s try interfering 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 again see stripes, but now the stripes walk slowly sideways. Both the appearance of stripes and their motion are interesting.

First, the fact that we see stripes indicates that particles of different energy still interact.

The second observation is that the striped pattern is now time dependent; the stripes walk to the side. As we make the difference in color between the lasers larger, the speed of stripes increases. The musicians in the audience will already recognize the beating pattern we are seeing, but, before we get to the explanation, let’s improve our experimental setup.

If we are content to use narrow laser beams, we can use a prism to combine the light streams. A prism is usually used to split a single light beam and send each color in a different direction, but we can use it backwards and with careful alignment use the prism to combine the light from two lasers into a single beam.

The light from two lasers with different color combined with a prism. After the prism the light ‘beats’ in intensity.
Credit: Miguel Morales.

If we look at the intensity of the combined laser beam, we will see the intensity of the light ‘beat.’ While the light from each laser was steady, when their beams with slightly different colors are combined, the resulting beam oscillates from bright to dim. Musicians will recognize this from tuning their instruments. When the sound from a tuning fork is combined with the sound of a slightly out-of-tune string, one can hear the ‘beats’ as the sound oscillates between loud and soft. The speed of the beats is the difference in the frequencies, and the string is tuned by adjusting the beat speed to zero (zero difference in frequency). Here we are seeing 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 of photons. We started with two steady streams of light, but now the light is bunched into times when it is bright and times when it is faint. As the difference between the colors of the lasers is made larger (they’re de-tuned), the faster the pulsing becomes.

Paintballs in time

So what happens if we again turn down the lasers really low? Again we see the photons hit our detector one at a time like little paintballs. But if we look carefully at the timing of when the photons arrive, we see that it is not random—they arrive in time with the beats. It does not matter how low we turn the lasers—the photons can be so rare that they only show up one every 100 beats—but they will always arrive in time with the beats.

This pattern is even more interesting if we compare the arrival time of the photons in this experiment with the stripes we saw with our laser pointer last week. One way of understanding what is happening in the two-slit experiment is to picture the wave nature of quantum mechanics directing where the photons can land side to side: the paintballs can hit in the bright regions and not in the dark regions. We see a similar pattern in the paintball arrival in the two-color beam, but now the paintballs are being directed forward and back in time and can only hit in time with the beats. The beats can be thought of as stripes in time.

A little over the top

Well, if two lasers were fun, what would happen if we used a lot of fancy lasers? With a prism we can in principle add the light of any number of different colored lasers, and the theory of what we should see is pretty clear. As we add more lasers, each locked in time and with evenly spaced steps in color, the duration of the light pulses in the combined beam gets smaller and smaller. All of the photons still have to show up, so when there is a pulse of laser light, it is very bright. But the dark times between the pulses get wider and wider as we add more lasers. It starts to look like a strobe light—bright white flashes separated by long periods of darkness.

The light from many fancy lasers combined with a prism would produce very strong beating: the resulting beam would look like the white flashes from a strobe light. Unfortunately assembling this many fancy lasers is very hard to do in practice.
Credit: Miguel Morales.

If the strobed light from our hypothetical many-laser setup were passed through a second prism, as expected we’d see the continuous light beams of the original lasers. Credit: Miguel Morales.

While this kind of laser cascade is entirely possible in theory, in practice they are a pain in the butt to set up. Lasers of this precision are expensive and fickle beasts. They are like Italian sports cars—incredible when they are running, but they spend as much time in the shop as lazing. Chaining them together and keeping them all working in sync requires incredible patience—a set of ten locked lasers is a major technical achievement.

But there is a kind of laser that emits very short pulses of light (creatively called a pulsed laser). By repeatedly firing our laser like a precision strobe light, we can create a stream of light pulses that looks just like the light stream after the prism in our hypothetical many-hundred-laser setup. So let’s reverse our prism and send the strobed laser pulses through it.
The light from a white pulsed laser looks just like the strobed light in our hypothetical many-laser setup, and if we send the pulsed light through a prism we see the same result—many steady laser beams evenly spaced in color. This is called an optical comb.

The light from a white pulsed laser looks just like the strobed light in our hypothetical many-laser setup, and if we send the pulsed light through a prism we see the same result—many steady laser beams evenly spaced in color. This is called an optical comb. Credit: Miguel Morales.

When we look at the light from the strobed laser after the prism, it looks like a set of steady lasers equally spaced in frequency. In certain ways, this makes sense—if steady lasers can beat in time to make strobed light, the reverse should be true, too. In other ways, it makes no sense at all.

If I look at the light from one of the colors after the prism and time when the photons arrive, they arrive steadily in time. This means most of the photons arrive at times between the original laser pulses. The light in the individual ‘lasers’ after the prism is perfectly steady and is just as bright between the strobe pulses as during them. This is a purely quantum effect.

This strobed laser is called an Optical Frequency Comb, because the colors look like the teeth of a hair comb as seen in the upper line below.

A folded spectrum from the High Accuracy Radial velocity Planet Searcher (HARPS) at the La Silla Observatory in Chile. The bottom line is the spectrum of a star with characteristic absorption lines (dimmer/narrower regions), while the top line is the spectrum of an optical frequency comb from a pulsed laser to provide absolute color reference. The individual beams of the optical comb can be clearly seen and are used to measure tiny doppler shifts in the star’s spectrum due to orbiting planets.
Credit: ESO.

The optical frequency comb is one of the great inventions of our century, and it is hard to overstate the importance it is having on measurements; its development was awarded the 2005 Nobel Prize in Physics. To work properly, an optical frequency comb requires timing the pulses with an atomic clock and exquisite control of the shape of each pulse, but you can now just buy one of them. They aren’t cheap, at least not yet, but several companies will sell you one complete with a warranty and a service plan.

Back at the Visitor’s Center

I’m very excited that we got to see temporal interference this week and how we can interfere with different particles. This is the kind of fun quantum effect that we rarely get to share with non-professional physicists.

We’re building on the idea of particles moving as waves by showing that particles from different sources can blend together. Temporal beats can be viewed as a time analog of the stripes we saw coming from the slits in aluminum foil from the first article. And just like those stripes, temporal beats persist even when the number of particles from the two sources is less than one particle at a time. The mixing of colors to form beats is reversible, and an optical frequency comb uses strobes of light to create steady laser sources at many precise colors.

There are two neat applications I’d like to highlight: coherent lidar and optical clocks.

Lidar is the optical or infrared light analog of radar. Like any really useful technology, there are multiple versions and implementations. Many lidars work by bouncing pulses of light off distant objects. By measuring how long it takes for the light to return, they can determine how far away the objects are. But coherent lidars work on a different principle and are particularly well suited for precise speed measurements such as imaging the air flow near wind turbines.

In coherent lidar, a single color laser is bounced off an object, and the doppler-induced color shift of the reflected light indicates that object’s relative speed. The trick is that the color shift is small, and it would be very difficult to actually measure the color with the necessary accuracy—the prisms needed would be prohibitively expensive. Instead, these devices combine the reflected light with a copy of the outgoing light.

Because the color of the reflected light was doppler shifted, we observe temporal beats when it is combined with the original laser beam. Measuring the speed of the beats measures the doppler shift of the reflected beam, and thus the speed of the object that the beam is bouncing off. Coherent lidars use the temporal beats of different colored light beams to measure speed.

The best optical clocks

Which brings us to optical clocks, one of the new wonders of the world. All clocks work by counting what we can call “swings.” In a grandfather clock, a pendulum slowly swings back and forth, once a second, and the clock works by counting the swings. In a mechanical watch, it is the twisting of a small wheel on a spring (typically three swings/second); in a quartz watch, it is the vibrations of a quartz crystal, typically 32,768 vibrations a second.

While many factors such as temperature affect the accuracy of a clock, one of the key contributors is simply how many swings it makes per second. It is easier to make an accurate quartz clock than a grandfather clock because it is oscillating more than 30,000 times more quickly.

Atomic clocks oscillate a few billion times a second. In an atomic clock, what is being counted are the oscillations of microwave light absorbed by an atom (cesium and rubidium are favorite targets). Fundamentally, we are still just counting swings like in a grandfather clock. But because we get billions of oscillations per second, an atomic clock can be vastly more accurate.

But there are optical atomic transitions that are even faster—hundreds of trillions of oscillations per second. How do you count that fast? Even the fastest computers have no hope of counting a hundred trillion oscillations a second.

Because we timed out the white pulses accurately with an atomic clock, the color of each beam after the prism is accurately known. If we select one of the colors and combine it with the light of a reference atom using another prism, the resulting beam will beat at the difference in frequency. Effectively we are using the beam of the optical comb to allow us to count the very fast oscillations of the reference atom. If the beat speed changes, we know our atomic clock has drifted a little in time and we can correct it. Credit: Miguel Morales.

A beautiful photo of a Ytterbium lattice optical clock. Credit: NIST.

The answer is to count beats instead. Because the pulses of light in an optical frequency comb were timed out with an (old-fashioned) atomic clock, the colors of the ‘lasers’ after the prism are at known stable frequencies. So we can take a Ytterbium atom, for instance, and select the light from a particularly stable oscillation of electrons deep inside the atom. The light from this transition can then be combined with the light from the nearest ‘laser’ of the optical comb. And just like with the two lasers of different color, we can measure the beat frequency.

We cannot count a 100 trillion oscillations a second. But if we know the light from a laser in the comb has a frequency of a 100 trillion oscillations a second and we see 12 beats a second when we combine it with the light from the Ytterbium atom, then we know the Ytterbium light is oscillating 100 trillion + 12 times a second. We can use the combination of measured beats and a known reference to count very fast.

Because the Ytterbium atom oscillations are even more stable than our atomic clock, we know if the beat frequency changes, it is due to drifts in our atomic clock. We can then work backward to correct the ‘huge’ errors in our atomic clock.

The precision of current optical clocks is astounding. You may have heard that time goes more slowly when gravity is strong due to general relativity. Optical clocks are so sensitive they can measure the different flows of time 2cm apart in height. If I lay a book on the table, the bottom of the book is slightly closer to the center of the Earth than the top, so experiences slightly stronger gravity. This difference is measurable with an optical clock. Optical clocks are so sensitive we can no longer average the time of multiple clocks together—the ground you or a clock are sitting on typically rises and falls by ~5cm a day due to land tides. The seismic motion of the ground currently limits our ability to measure time.

Precise optical clocks are but one application of the optical comb. Optical combs are transforming precision measurement in many areas, from finding planets around distant stars (precision doppler measurements), to potentially measuring the expansion of space itself (time dependence of redshift). Optical frequency combs are one of the next big things working their way out of the laboratory and rely both on the mixing of particles and the measurement of beats between particles of different color.

Our next expedition

Congratulations on surviving another expedition into the quantum mechanical woods, this time to see effects rarely explored outside of advanced physics classes. In next week’s expedition, I’d like to head into a different part of the woods. The first two articles looked at how particles move and mix. There’s a natural question that arises when we see that a particle can take two paths: how big is a particle? This will be our question for the next two articles. Along the way we’ll learn why you buy ‘bandwidth’ when you want a lot of data and how all particles can be divided into ‘introverts’ and ‘extroverts.’ So keep your boots dry, and we’ll see you again next week.