EPTI think we struck gold with last week's topic, and I just have to thank you all for such stimulating conversations! I learned so much in attempts to answer your questions and by reading other’s answers and I hope you guys learned something too. I might fall back to that post for inspiration for future blog topics, as a lot of really deep questions were asked that are just begging for more attention.
I already had a draft prepared for this week, however, so I’m going to stick with it. It’s a pretty cute and common technique now, but you might not know much about it if you haven’t played around in an atomic physics lab before.
Lesson 6: Laser Cooling
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Scientists have been extremely interested in performing experiments at ultra-low temperatures. If you can isolate and almost freeze an atom in its tracks, it becomes much easier for you to probe the atom and investigate its structure. You can also observe a lot of crazy quantum effects, like Bose-Einstein condensation, superfluidity, etc. We’ll probably talk about those things in the future.
There are several variations on the theme of laser/atomic cooling these days, but we’re going to start with the simplest and most common method: Doppler cooling.
Say you have a little cloud of atoms; a gas of some particular element. We know by now that atoms can absorb/emit photons of certain discrete energies, right? We shine a laser (say the beam is traveling to the left, for example) of a frequency that is slightly red-shifted from an allowed atomic energy transitions. Any atom that is just sitting still will see a photon with a wavelength that is too long, so it can’t absorb the light. This is where the word Doppler comes in.
The atoms in our cloud aren’t stationary; they have some nonzero velocity. These atoms see frequencies that are Doppler shifted up or down by an amount:
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An atom that is moving to the left, with the beam, will see an even further red shifted beam and it won’t absorb the photons. An atom moving to the right (at the correct velocity), however, will see a photon with just the right energy for absorption. Note that there is a bit of "bandwidth" for the absorption probability; it isn't huge, but the velocities don't have to be so exactly perfect that the probability of absorption is almost zero.
+ Show Spoiler +
![[image loading]](http://i.imgur.com/9un3YEq.png)
A. A stationary atom "sees" light with a wavelength that is too long for it to absorb.
B. An atom moving in the same direction as the beam sees a wavelength that is too long, and also will not absorb a photon.
C. An atom moving toward the beam sees a shorter wavelength that is resonant with the atomic transition, and absorbs a photon.
(disclaimer because some people take over-simplifications too much to heart; the colors are of course exaggerated, the frequency shifts are not so huge that the wavelength changes by hundreds of nm, its just for illustrative purposes)
The atom absorbs the photon and its associated momentum (which was in the opposite direction to the atom’s direction) and the atom slows down a little. The atom is now in an excited state though, because of this extra energy, and it’ll emit a photon in return. If the photon beam is weak enough, emission is usually spontaneous (there aren’t enough photons around to stimulate emission in many of the atoms). Spontaneous emission, if you recall, is when the atom emits the photon in a random direction. When this happens to the atom in our cloud, it’ll receive a momentum kick.
+ Show Spoiler +![[image loading]](http://i.imgur.com/0d96nYH.png)
The net result of this interaction is that the atom originally moving right with a high velocity has been slowed down and redirected, if only by a little bit. In a real cloud of atoms with real lasers, these interactions will happen frequently and the atoms will slow down to very low speeds rapidly.
Of course, as the atoms slow down, they no longer “see” the appropriate frequency of light and cannot continuously absorb photons, so the frequency of the laser must be adjusted.
An alternative to frequency sweeping is something called “Zeeman slowing” (related to the Zeeman effect) that uses magnetic fields. Simply put, the application of a magnetic field to an atom causes changes in its resonance frequency- the frequency of photon it’ll readily absorb.
We want to slow our atoms in all directions though, not just slow the ones moving to the right. To accomplish this we simply add a laser traveling in the opposite direction. Extending this idea, 3 perpendicular sets of oppositely directed beams would allow us to slow atoms in all directions, creating a cloud of low-velocity, and therefore low kinetic energy, atoms. The relationship between kinetic energy and temperature is where the term “cooling” came from, and so we often report how slow we can get the atoms in units of temperature. This sort of cooling set up alone gets us down to the hundreds of mili-Kelvin range.
When you use counter-propagating circularly polarized beams in this configuration, you can create what the call “optical molasses”. Without going into too many details, the appropriately polarized laser beams create a polarization gradient (a change in the polarization with location) and the atoms lose energy as they climb “up” the gradient. This sort of acts like a viscous drag force, hence the name “molasses”.
Laser cooling is often coupled with magnetic trapping, creating a “magneto-optical trap”, or a MOT. A magnetic field is set up to so that when an atom approaches the edges of the “trap” it is redirected back toward the center.
+ Show Spoiler +![[image loading]](http://i.imgur.com/BencO2u.png)
+ Show Spoiler +![[image loading]](http://i.imgur.com/a1KgbEl.jpg)
An actual MOT with Ytterbium atoms.
Image from: http://www.quantum-munich.de/research/ytterbium-quantum-gases-in-optical-lattices/
Doppler cooling is limited, as eventually the atoms become so slow that absorbing/re-emitting photons actually increases their energy as often as it decreases their energy. The lower bound on the temperature we can achieve using this simple idea is appropriately called the Doppler limit.
The use of polarization gradients to overcome this limit is very common, as is evaporative cooling.
It’s not uncommon to see all of these things combined; start by slowing the atoms considerably using Doppler cooling, load them into a MOT and further cool them by applying particular magnetic fields or polarization gradients. These sort of setups have achieved temperatures on the order of micro-Kelvin.
We should also note that not all atoms can be laser cooled by Doppler cooling; they have to have an energy level structure that works with the lasers (=photon energies) we have available.
This was an extremely short entry compared to my others, so for entertainment and because it’s relevant, pictures! Once upon a time I built a laser for an atomic physics lab, and now it’s being used for laser cooling experiments. It was a terribly tedious project, but finally getting it to lase correctly was the best feeling ever. They aren't high quality or that interesting of photos, but this was the first laser system I ever made and I just adore it.
+ Show Spoiler +
![[image loading]](http://i.imgur.com/WAYy2rZ.png)
This is the majority of the main laser setup, except a few things were changed after this photo was taken... nothing important though, just re-arranging and the addition of a lens. If you're familiar with lasers, this is actually a slave in a master/slave system. It's coupled via the fiber you see on the left to the master in another lab a few rooms over, which is where the rest of my set up is. If you want more details on master/slave lasers, just ask.
+ Show Spoiler +
![[image loading]](http://i.imgur.com/IQyN7Bi.png)
This includes the diagnostic equipment used to get everything running right.
+ Show Spoiler +
![[image loading]](http://i.imgur.com/2Stz7Jt.png)
Anddd with the lights dimmed, so you can see that yes, it is actually producing light. Of the correct wavelength, even!
There are several variations on the theme of laser/atomic cooling these days, but we’re going to start with the simplest and most common method: Doppler cooling.
Say you have a little cloud of atoms; a gas of some particular element. We know by now that atoms can absorb/emit photons of certain discrete energies, right? We shine a laser (say the beam is traveling to the left, for example) of a frequency that is slightly red-shifted from an allowed atomic energy transitions. Any atom that is just sitting still will see a photon with a wavelength that is too long, so it can’t absorb the light. This is where the word Doppler comes in.
The atoms in our cloud aren’t stationary; they have some nonzero velocity. These atoms see frequencies that are Doppler shifted up or down by an amount:
+ Show Spoiler +
∆f=(V/c) f_laser
V=velocity of atom, c= speed of light, f_laser is the laser frequency
V=velocity of atom, c= speed of light, f_laser is the laser frequency
An atom that is moving to the left, with the beam, will see an even further red shifted beam and it won’t absorb the photons. An atom moving to the right (at the correct velocity), however, will see a photon with just the right energy for absorption. Note that there is a bit of "bandwidth" for the absorption probability; it isn't huge, but the velocities don't have to be so exactly perfect that the probability of absorption is almost zero.
+ Show Spoiler +
A. A stationary atom "sees" light with a wavelength that is too long for it to absorb.
B. An atom moving in the same direction as the beam sees a wavelength that is too long, and also will not absorb a photon.
C. An atom moving toward the beam sees a shorter wavelength that is resonant with the atomic transition, and absorbs a photon.
(disclaimer because some people take over-simplifications too much to heart; the colors are of course exaggerated, the frequency shifts are not so huge that the wavelength changes by hundreds of nm, its just for illustrative purposes)
The atom absorbs the photon and its associated momentum (which was in the opposite direction to the atom’s direction) and the atom slows down a little. The atom is now in an excited state though, because of this extra energy, and it’ll emit a photon in return. If the photon beam is weak enough, emission is usually spontaneous (there aren’t enough photons around to stimulate emission in many of the atoms). Spontaneous emission, if you recall, is when the atom emits the photon in a random direction. When this happens to the atom in our cloud, it’ll receive a momentum kick.
+ Show Spoiler +
The net result of this interaction is that the atom originally moving right with a high velocity has been slowed down and redirected, if only by a little bit. In a real cloud of atoms with real lasers, these interactions will happen frequently and the atoms will slow down to very low speeds rapidly.
Of course, as the atoms slow down, they no longer “see” the appropriate frequency of light and cannot continuously absorb photons, so the frequency of the laser must be adjusted.
An alternative to frequency sweeping is something called “Zeeman slowing” (related to the Zeeman effect) that uses magnetic fields. Simply put, the application of a magnetic field to an atom causes changes in its resonance frequency- the frequency of photon it’ll readily absorb.
We want to slow our atoms in all directions though, not just slow the ones moving to the right. To accomplish this we simply add a laser traveling in the opposite direction. Extending this idea, 3 perpendicular sets of oppositely directed beams would allow us to slow atoms in all directions, creating a cloud of low-velocity, and therefore low kinetic energy, atoms. The relationship between kinetic energy and temperature is where the term “cooling” came from, and so we often report how slow we can get the atoms in units of temperature. This sort of cooling set up alone gets us down to the hundreds of mili-Kelvin range.
When you use counter-propagating circularly polarized beams in this configuration, you can create what the call “optical molasses”. Without going into too many details, the appropriately polarized laser beams create a polarization gradient (a change in the polarization with location) and the atoms lose energy as they climb “up” the gradient. This sort of acts like a viscous drag force, hence the name “molasses”.
Laser cooling is often coupled with magnetic trapping, creating a “magneto-optical trap”, or a MOT. A magnetic field is set up to so that when an atom approaches the edges of the “trap” it is redirected back toward the center.
+ Show Spoiler +
+ Show Spoiler +
An actual MOT with Ytterbium atoms.
Image from: http://www.quantum-munich.de/research/ytterbium-quantum-gases-in-optical-lattices/
Doppler cooling is limited, as eventually the atoms become so slow that absorbing/re-emitting photons actually increases their energy as often as it decreases their energy. The lower bound on the temperature we can achieve using this simple idea is appropriately called the Doppler limit.
The use of polarization gradients to overcome this limit is very common, as is evaporative cooling.
It’s not uncommon to see all of these things combined; start by slowing the atoms considerably using Doppler cooling, load them into a MOT and further cool them by applying particular magnetic fields or polarization gradients. These sort of setups have achieved temperatures on the order of micro-Kelvin.
We should also note that not all atoms can be laser cooled by Doppler cooling; they have to have an energy level structure that works with the lasers (=photon energies) we have available.
This was an extremely short entry compared to my others, so for entertainment and because it’s relevant, pictures! Once upon a time I built a laser for an atomic physics lab, and now it’s being used for laser cooling experiments. It was a terribly tedious project, but finally getting it to lase correctly was the best feeling ever. They aren't high quality or that interesting of photos, but this was the first laser system I ever made and I just adore it.
+ Show Spoiler +
This is the majority of the main laser setup, except a few things were changed after this photo was taken... nothing important though, just re-arranging and the addition of a lens. If you're familiar with lasers, this is actually a slave in a master/slave system. It's coupled via the fiber you see on the left to the master in another lab a few rooms over, which is where the rest of my set up is. If you want more details on master/slave lasers, just ask.
+ Show Spoiler +
This includes the diagnostic equipment used to get everything running right.
+ Show Spoiler +
Anddd with the lights dimmed, so you can see that yes, it is actually producing light. Of the correct wavelength, even!
Thanks for reading! As always, I really, really appreciate your questions and feedback, good or bad!
Your responses always make these blogs so much fun to post. <3
