Building an extremely precise clock
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Clocks are not only good for meeting a friend at a specific time; they are also used to synchronize networks, like cell phone networks. Our GPS and navigation rely on them.
To build a clock, you need some kind of frequency reference. You can think of a pendulum in a grandfather clock. If you try to build two clocks that are exactly the same, you will fail, because you will never be able to manufacture two pendulums that are exactly the same, which have the same length and tick at the same rate. Luckily, quantum mechanics gives us frequency references that are absolutely identical everywhere. These are the optical transitions in atoms. If you have a certain transition in an atom, you need a laser beam of a certain frequency to drive this transition. If you build clocks based on the frequency of these laser beams driving these optical transitions, then a clock based on strontium atoms in Amsterdam, one in Beijing, or even one in another galaxy will all tick at exactly the same rate. |
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So what do you need to build an atomic clock? You need to be able to measure these transitions in these atoms very precisely. You can’t do this if the atoms are in a thermal gas, like the air in the room here, whizzing about at hundreds of meters per second, because you can’t observe the atoms long enough. So you need to cool these atoms essentially to a standstill before you observe them.
We do this in machines such as this one. Deep inside is a vacuum chamber in which we cool a gas of strontium atoms using laser cooling. You see mirrors here that direct the laser beams onto the atoms. The atoms come from an oven, then travel down here, and in the middle they are cooled to below 1 microkelvin.
At the end, we can use standard techniques, like optical frequency combs, to measure the frequency of the laser beam and feed that into electronics. Then we can do whatever we want with this frequency signal—for example, make the hands of a clock move. If you build an optical clock like this, the best ones in the world would go wrong by only about one second over the age of the universe.
We do this in machines such as this one. Deep inside is a vacuum chamber in which we cool a gas of strontium atoms using laser cooling. You see mirrors here that direct the laser beams onto the atoms. The atoms come from an oven, then travel down here, and in the middle they are cooled to below 1 microkelvin.
At the end, we can use standard techniques, like optical frequency combs, to measure the frequency of the laser beam and feed that into electronics. Then we can do whatever we want with this frequency signal—for example, make the hands of a clock move. If you build an optical clock like this, the best ones in the world would go wrong by only about one second over the age of the universe.
How to prepare ultracold atoms for an atomic clock
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An atomic clock uses the frequency of a narrow atomic transition as its frequency reference. To measure this frequency precisely, we need atoms that nearly stand still. Atoms in a gas at room temperature move at hundreds of meters per second — they would escape before we can precisely measure. To avoid that, we prepare a gas sample at a temperature just a millionth of a degree above absolute zero, at about −273 °C. Here the atoms move with just a few millimeters per second.
We prepare this gas sample inside a vacuum chamber, using lasers and magnetic fields. We zoom into an oven at one end of the vacuum chamber, where strontium atoms are stored as a chunk of metal. As we heat the oven, strontium atoms detach from the chunk and form a gas. The atoms bounce around the oven and, by chance, some escape through narrow tubes. These tubes ensure that most of the escaping atoms travel in the direction we want. |
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The atoms going out of the oven atoms have velocities of hundreds of meters per second. We slow them by directing a laser beam against them and ensuring that the atoms scatter photons from this laser beam. You can imagine each atom being hit by thousands of tiny ping-pong balls of light, each slowing the atom a tiny bit. Once the atoms reach the center of the vacuum chamber, the glass cell, they move with only a few ten meters per second.
To cool the atoms further and to trap them in the middle of the glass cell, we use six laser beams that slow the atoms and push them inwards, also guided by a special magnetic field. The atoms are thereby collected in the middle of the glass cell as a small gas cloud. Now we have an ultracold sample of strontium atoms. It allows us to precisely determine the frequency of an ultranarrow atomic transition by spectroscopy. This frequency is what makes our ultra–precise optical atomic clock tick.
To cool the atoms further and to trap them in the middle of the glass cell, we use six laser beams that slow the atoms and push them inwards, also guided by a special magnetic field. The atoms are thereby collected in the middle of the glass cell as a small gas cloud. Now we have an ultracold sample of strontium atoms. It allows us to precisely determine the frequency of an ultranarrow atomic transition by spectroscopy. This frequency is what makes our ultra–precise optical atomic clock tick.
Operating principle of an optical atomic clock
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An optical atomic clock ticks at the frequency of a narrow atomic transition. This frequency is provided to a user in the form of the frequency of a laser beam. The operating principle of the clock is to transfer the frequency stability of the atomic transition onto this laser. This is done by using this exact laser to probe the atomic transition and using the result of this probing to finely adjust the laser’s frequency and ensure it remains precisely tuned.
However, not just any laser will work — it must operate at the correct frequency for the transition and its frequency must be pre-stabilized before interacting with the atoms, as probing takes tens of seconds. |
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When we first turn the laser on, we can see that the frequency, the number of oscillations per second, jumps around a lot. The laser is still quite unstable - we cannot probe the atoms with it. To pre-stabilize the laser’s frequency, we adjust it to the resonance of an optical cavity, a bit like a singer might adjust her pitch to a note played on a guitar string. To determine how close the laser is to a cavity resonance, we send some of its light onto the cavity. On the way, the laser passes an electro-optical modulator, or short E-O-M, which modifies the laser’s spectrum a bit - it imprints sidebands. This makes it easier to obtain a signal that electronics can use to adjust the laser’s frequency to the cavity resonance.
Let’s turn our attention to the optical cavity. In its simplest form, it consists of two mirrors, with the mirror surfaces facing each other. When the laser hits the first mirror, a small fraction is transmitted into the cavity. Only if the laser frequency is on resonance with the cavity, a standing wave of light can form inside the cavity and light leaks through the other mirror. This happens for a few specific frequencies and we choose the one that is closest to the atomic transition.
A simple way to stabilize the laser’s frequency would be to adjust it untillight leaks out. We use a slightly more sophisticated method, capturing the light that is backreflected from the cavity on a photodetector. Electronics can use the signal from this detector to adjust the laser’s frequency to be on resonance with the cavity mode.
The cavity cannot provide a long-term stable reference as its length slowly changes - for example because of temperature fluctuations - which in turn shifts the cavity resonance frequency. To stabilize the laser’s frequency for long times, we need the atoms. They provide us with an unchanging reference frequency, given by nature.
With the pre-stabilized laser, we can now probe the atoms. We must determine if the laser’s frequency is on the atomic transition or slightly above or below, so that we can pull the laser’s frequency back to the atomic transition if it drifts away.
To probe the atoms, we shine the red laser that we just prepared briefly onto the atoms. To switch the laser on and off and to finely adjust its frequency we use an acousto-optical modulator, an A-O-M. If the laser is just at or close to the correct frequency, atoms will be excited. We measure how many atoms got excited by making them fluoresce in the light of a second, blue, laser beam. A photodiode collects the blue light emitted by the atoms.
Let’s look at three cases.
The first case shows when the laser is tuned nearly on resonance such that most of the atoms are excited into a higher energy state. When we now shine the blue laser onto the atoms, only those remaining in the ground state — the ones still blue in the video — are able to scatter the light.
The second case shows what happens when the laser is somewhat off resonance, in our case such that about half of the atoms are transferred into the excited state. This means that when we shine the blue laser on the atoms, we get a brighter signal, since more remain in the ground state — those that are blue.
The last case illustrates what happens when the laser is far off the resonance, so almost no atom is transferred into the excited state. Here most atoms are still in the ground state and can absorb and reemit the blue light, giving a high signal on the photodiode.
Overall, the fewer atoms remain in the ground state, the weaker the detected blue signal. Here we can again see the sequence: first a red laser pulse exciting part of the atoms, and then a second blue pulse to measure whether we were able to excite them with the first pulse.
A simple way to assure that the laser is referenced to the atomic transition is to keep it in the “In between” situation. If we then get less light on the photodiode, we know that the laser’s frequency has drifted towards resonance and we can pull it away again. Similarly, if we get more light, it must have drifted further away from resonance and we can push it back.
By preparing new samples of atoms and interrogating them over and over again in this manner, we can keep the laser close to the atomic transition.
With this, we have built a stable frequency reference, which is already extremely useful. To obtain a clock that can tell time, we just count the number of oscillation periods of this reference since a well defined moment in time. That’s it: we have built an optical atomic clock based on strontium atoms that would go wrong by only one second over the lifetime of the universe.
Let’s turn our attention to the optical cavity. In its simplest form, it consists of two mirrors, with the mirror surfaces facing each other. When the laser hits the first mirror, a small fraction is transmitted into the cavity. Only if the laser frequency is on resonance with the cavity, a standing wave of light can form inside the cavity and light leaks through the other mirror. This happens for a few specific frequencies and we choose the one that is closest to the atomic transition.
A simple way to stabilize the laser’s frequency would be to adjust it untillight leaks out. We use a slightly more sophisticated method, capturing the light that is backreflected from the cavity on a photodetector. Electronics can use the signal from this detector to adjust the laser’s frequency to be on resonance with the cavity mode.
The cavity cannot provide a long-term stable reference as its length slowly changes - for example because of temperature fluctuations - which in turn shifts the cavity resonance frequency. To stabilize the laser’s frequency for long times, we need the atoms. They provide us with an unchanging reference frequency, given by nature.
With the pre-stabilized laser, we can now probe the atoms. We must determine if the laser’s frequency is on the atomic transition or slightly above or below, so that we can pull the laser’s frequency back to the atomic transition if it drifts away.
To probe the atoms, we shine the red laser that we just prepared briefly onto the atoms. To switch the laser on and off and to finely adjust its frequency we use an acousto-optical modulator, an A-O-M. If the laser is just at or close to the correct frequency, atoms will be excited. We measure how many atoms got excited by making them fluoresce in the light of a second, blue, laser beam. A photodiode collects the blue light emitted by the atoms.
Let’s look at three cases.
The first case shows when the laser is tuned nearly on resonance such that most of the atoms are excited into a higher energy state. When we now shine the blue laser onto the atoms, only those remaining in the ground state — the ones still blue in the video — are able to scatter the light.
The second case shows what happens when the laser is somewhat off resonance, in our case such that about half of the atoms are transferred into the excited state. This means that when we shine the blue laser on the atoms, we get a brighter signal, since more remain in the ground state — those that are blue.
The last case illustrates what happens when the laser is far off the resonance, so almost no atom is transferred into the excited state. Here most atoms are still in the ground state and can absorb and reemit the blue light, giving a high signal on the photodiode.
Overall, the fewer atoms remain in the ground state, the weaker the detected blue signal. Here we can again see the sequence: first a red laser pulse exciting part of the atoms, and then a second blue pulse to measure whether we were able to excite them with the first pulse.
A simple way to assure that the laser is referenced to the atomic transition is to keep it in the “In between” situation. If we then get less light on the photodiode, we know that the laser’s frequency has drifted towards resonance and we can pull it away again. Similarly, if we get more light, it must have drifted further away from resonance and we can push it back.
By preparing new samples of atoms and interrogating them over and over again in this manner, we can keep the laser close to the atomic transition.
With this, we have built a stable frequency reference, which is already extremely useful. To obtain a clock that can tell time, we just count the number of oscillation periods of this reference since a well defined moment in time. That’s it: we have built an optical atomic clock based on strontium atoms that would go wrong by only one second over the lifetime of the universe.
Making an optical atomic clock useful through an optical frequency comb
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Once we have stabilized the laser onto the atomic clock transition, we have a very stable optical frequency reference. However, this reference ticks at 460 terraHertz, that is 460 trillion oscillations per second which is too fast for many applications. Often one needs a frequency reference for electronics, and to obtain that we need a way to convert the optical signal into a radio frequency signal.
The tool we use to achieve this is called a frequency comb. When looking at the laser beam and slowing down time, we see that it consists of a train of repeating short laser pulses. When we look at the frequency spectrum of this laser, we find a rainbow of discrete frequency components spaced by the repetition frequency of the laser pulses. The spectrum looks like a comb, hence the name. The teeth of this frequency comb can be used like a ruler for measuring optical frequencies. Zooming out again, we see a laser beam that appears white to the eye, as it contains colors across the whole rainbow. |
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The challenge of using a frequency comb is that it is unstable on its own - the repetition frequency drifts and thereby the comb teeth change frequency. To stabilize the repetition frequency, we reference one comb line to the stable laser provided by the atomic clock.
But how do we do that?
We look at the comb tooth closest to our laser frequency. The interference between the this tooth and the laser produces a beat note, which is apparent as intensity oscillations. This is similar to what one hears when one tunes one musical instrument to another, just before one matches their frequencies. In our case, the beat note is in the megahertz range, which we can easily measure with a photodetector. We then change the comb’s repetition frequency till this beat note has a well-defined value. This locks the comb’s repetition rate precisely. We can measure the repetition rate on a photodetector and thereby obtain a radiofrequency reference signal suitable for electronics.
Once the comb is stabilized to the atomic reference, it provides us with a rainbow of discrete and ultra precise laser frequencies. We can lock lasers at any other wavelength to the comb and thereby give them a frequency precision as good as the one of the atomic reference. This means we are no longer limited to the wavelength that nature gave us in the form of the atomic transition.
We can use this to distribute the optical atomic frequency reference across a continent. We just stabilize a telecom wavelength laser to the comb and send this laser through telecom fibre networks, alongside internet signals. In this way we can compare optical clocks at different locations, or synchronize networks.
As the flow of time depends on gravity, comparing clocks allows us to determine their geodetic height difference to one centimeter. If clocks are based on different atomic, molecular or nuclear species, we can explore if the fundamental constants of nature change over time, which would hint at beyond standard model physics. And we can use these techniques to synchronize telecom networks without easily to spam or spoof satellite navigation signals. With good synchronization, our telecom networks can even allow robust navigation at the 10cm level.
But how do we do that?
We look at the comb tooth closest to our laser frequency. The interference between the this tooth and the laser produces a beat note, which is apparent as intensity oscillations. This is similar to what one hears when one tunes one musical instrument to another, just before one matches their frequencies. In our case, the beat note is in the megahertz range, which we can easily measure with a photodetector. We then change the comb’s repetition frequency till this beat note has a well-defined value. This locks the comb’s repetition rate precisely. We can measure the repetition rate on a photodetector and thereby obtain a radiofrequency reference signal suitable for electronics.
Once the comb is stabilized to the atomic reference, it provides us with a rainbow of discrete and ultra precise laser frequencies. We can lock lasers at any other wavelength to the comb and thereby give them a frequency precision as good as the one of the atomic reference. This means we are no longer limited to the wavelength that nature gave us in the form of the atomic transition.
We can use this to distribute the optical atomic frequency reference across a continent. We just stabilize a telecom wavelength laser to the comb and send this laser through telecom fibre networks, alongside internet signals. In this way we can compare optical clocks at different locations, or synchronize networks.
As the flow of time depends on gravity, comparing clocks allows us to determine their geodetic height difference to one centimeter. If clocks are based on different atomic, molecular or nuclear species, we can explore if the fundamental constants of nature change over time, which would hint at beyond standard model physics. And we can use these techniques to synchronize telecom networks without easily to spam or spoof satellite navigation signals. With good synchronization, our telecom networks can even allow robust navigation at the 10cm level.
