Every single type of atom has a fingerprint. This fingerprint tells us how valence electrons – or the electrons on the outermost part of the atom – can move in an atom when they are excited. You can excite electrons using light. In the quantum world, energies can be quantized. This means that a bound electron can only exist at energies specific to the type of atom it lives in.

If you were to look at these fingerprints, you would notice that atoms located under hydrogen on the periodic table (see red boxes on periodic table) are all pretty simple. These are neutral Alkalai atoms and they all have exactly one valence electron. As you start to work your way across the periodic table, these fingerprints become very complicated because more electrons can be excited in those atoms.

Check out below to see some examples of fingerprints, or spectra, of some common elements!

Periodic Table of Elements

Fingerprint, or spectrum, of various common elements. Image Credit: NASA JPL, “Using light to study planets,” Classroom activity.

Now that you know some more about atoms and the way electrons can move inside an atom, we can talk about laser cooling!

Light-Matter Interaction

Light is pure energy and all light comes about from charged particles moving – specifically accelerating! When an atom is submerged in light – or a bath of photons – electrons in the atom can become excited by absorbing the energy of a photon. The electron then jumps to a higher energy state. However, electrons are like kids on a sugar high – they only have a finite amount of time that they stay THAT excited. After that, they jump back into a lower energy state, perhaps even to the same energy where they started. But to do this, an electron must re-emit energy. It does this in the form of a photon of a very specific energy. This is where those fingerprints shown above come from!

Laser cooling and the Doppler effect

In laser cooling, we use the internal structure of atoms to excite electrons to higher energies. Only now, we use the Doppler effect to excite the atoms! You see, the electrons in atoms are very particular about the type of light that they like to absorb. So, instead of shining just the right type of light onto the atoms, we shine light that has a slightly lower energy, or red-detuned.

The Doppler effect tells us that if a wave-producing object is moving towards us, the waves will be compressed, whereas an object moving away from us will have stretched waves. Compressed waves have a higher frequency and stretched waves have lower frequency. The Doppler effect we typically think of has to do with sound waves from a car horn or siren, but it also works for light – this is how astronomers know if a star is moving away or towards us!

When we tune our laser light to be slightly less energetic than what we would need to excite atoms sitting still, we make the assumption that our atoms are moving. Then, if an atom is moving towards a beam of light, the light will compress and become just the right energy to be absorbed. Otherwise, an atom moving away from the light will see the light stretched and will not be excited. In this way, we tune our light so that atoms only absorb photons from one direction!

Well, now the light has been absorbed from one direction and the electron is excited. Just like a ball at the top of a hill, the electron wants to be at lower energy, so it spontaneously re-emits a photon in a random direction, and thus changing the speed and direction of the atom’s motion. This process of absorbing and re-emitting happens over and over again, rapidly, until the atoms reach a limit of how slow – or cold – they can be. This limit is proportional to the intensity of the light on the atoms over the amount we have tuned away from where the atoms are excited when sitting still, or the detuning.

Now, our atoms are pretty cold – approximately 150 micro-Kelvin. That is, we are 0.000150 degrees above absolute zero, the limit of temperature. To put this into perspective, the distance between Pullman, WA and Boston, MA is approximately 2800 miles. If absolute zero is Pullman and room temperature is Boston, the temperature of our atoms at this point would be 2 1/4 meters away from the center of Pullman. Atoms at this temperature can be used for various types of sensors, but for our purposes they still aren’t cold enough!

Trapping atoms with magnets and lasers

Now that our atoms are really cold, we want to capture them in either a trap made of magnets or laser light!

Magnetic Trapping

A magnetic trap creates a potential well for our cooled atoms to sit in, like a bowl, where the potential is proportional to the strength of the magnetic field. However, a uniform magnetic field cannot trap the atoms. Instead, we need a magnetic field with a gradient, which simply means that the strength of the magnetic field varies over space. This can be easily created by taking two coils with opposite flowing current, depicted below.

The two copper colored windings represent two sets of wound wire, known as a coil. The direction of the current, I, in one coil is opposite to the other. The green arrows represent the direction of the magnetic field around the coils. This orientation is called anti-Helmholtz and creates a magnetic field with a gradient in the center, which is where the atoms like to collect.

A magnetic trap, similar to a bowl. The hot, high energy atoms (red) move high in the bowl, while the cold, low energy atoms (blue) like to live near the bottom of the trap.

Optical Trapping

Before, when we were initially cooling the atoms, the 6 intersecting laser beams created a trap for the atoms. The confinement there was pretty weak. For the next stages in cooling, we want the atoms to help us out and do some of the cooling by bouncing off one another, or scattering. This requires that the atoms sit in a tighter trap. Using a high intensity focused laser beam that has a larger wavelength, i.e. red detuned light, than the light used for laser cooling, we can strongly trap the atoms with light!

Concept of an optical trap, where the light source is focused down and the atoms sit at the center of the trap, where the potential is deepest. This is the same technique used for optical tweezers!

The force applied on the atoms by the laser is proportional to the spatially (radially) dependent intensity over the detuning of the light from the resonant transition (the light used to cool the atoms initially).

Evaporative Cooling

Now that our atoms are relatively chilly and strongly trapped, we can proceed with the second, and sometimes final, stage of cooling our atoms!

Concept of evaporative cooling process. Left: The thermal distribution of atoms prior to evaporative cooling at temperature T1. Middle: Distribution after applying an evaporative cooling method, still at temperature T1. Right: Thermal distribution after rethermalization, at temperature T2, where T2<T1.

…In a magnetic trap

If the atoms are tightly confined in a magnetic trap, we can apply radio frequencies (RF) or microwave (MW) frequencies to kick hot atoms out of the trap, allowing the remaining cold atoms to rethermalize to a colder temperature.

In addition to the atomic fingerprints mentioned previously, the internal states of an atom will separate further with the application of a magnetic field. This is called the Zeeman effect!

(a) Rubidium-87

(b) Potassium-39

Explanation of above figures: Zeeman splitting of the 5s level ground state for increasing magnetic fields in (a) Rubidium-87 and (b) Potassium-39 atoms. The lower lines are the F = 1 hyperfine manifold (m_F = -1, 0, +1) and the upper lines are the F = 2 hyperfine manifold (m_F = -2, -1, 0, +1, +2). Lines with a downward slope are non-magnetically trappable. The vertical dashed line indicated the magnetic field at which the (F, m_F) = (1, -1) state is no longer magnetically trappable.

If the field is constant across the system, the atoms will see the same magnetic field all have the same state separation, or Zeeman splitting. However, if the atoms are sitting in a magnetic trap, the state separation changes as a function of position! So hot atoms, moving with higher energy, are on average farther from the center of the trap and therefore at higher magnetic fields!

Zeeman splitting in a magnetic trap with magnetic gradient of 180 G/cm. We can apply RF frequencies to excite atoms from the m_F = -1 state to the m_F = 0 and then m_F = +1 states.

At this point, we can eliminate these hot atoms at high fields by applying RF or MW frequencies to the system. This causes hot atoms in the magnetically trappable m_F = -1 state to transition to the slightly non-trappable m_F = 0 state. The atoms then start to roll out of the trap, and are then resonantly excited to the m_F = +1 state, which is highly non-trappable and the atoms are ejected out of the system.

The remaining atoms in the trap can then scatter off of one another, coming to a new thermal equilibrium. This process is known as rethermalization and must be done slowly. If done too quickly, the atoms cannot go through this process and you do not efficiently cool your atoms! In our apparatus at WSU, this process takes 4 seconds.

Now, if you have a special type of magnetic trap where there is no region of the trap where the magnetic field goes to zero, such as an Ioffe-Pritchard type trap or a Time-averaged Orbiting Potential (TOP) trap, you can perform this evaporative cooling technique until all of your atoms Bose condense into a single energy state. The TOP trap was first used by the Cornell JILA group and successfully cooled atoms to Bose condensation for the first time in 1995. To hear more about this discovery, I recommend taking the time to watch or read Eric Cornell’s Nobel lecture.

If you trap has a magnetic zero, your atoms will become unhappy when they are cooled past a specific point in your trap and undergo dynamics where they cannot maintain the direction of their spin in the trap. These are called Majorana losses and cause rapid loss of atoms. One way to overcome these losses is to “optically plug” the center of the magnetic trap. By using a wavelength of light that is repulsive to the atoms, i.e. less than the resonant frequency, the atoms are not able to pass through regions of the field that are near or at zero magnetic field. This is the technique used by the MIT team to Bose condensed their sodium atoms in 1995 (see page 129 of Ketterle’s Noble lecture for a diagram of the experimental setup).

If not using a special magnetic trap, or an optical plug, you must load your atoms into a strong optical trap to eliminate any issues having to do with losses due to magnetic fields. This is a technique used in my old lab at WSU.