Tuesday, March 06, 2007

Application of BECs

In my previous post, I discussed what Bose-Einstein condensates are and how they are created. It is great to have a new state of matter, but it is not that breathtaking if there is no application. This post is going to deal with the application of Bose-Einstein condensates and is mostly based on Wolfgang Ketterle’s second McGill lecture, given on March 2nd. I incorporated some of my own understand and research into this, especially to simplify concepts. The two main benefits of BECs I will deal with is the creation of an atomic toolbox and increased headway into room temperature superconductors.

Atomic Physics Toolbox

There have always been differences between theoretical and applied physicists. Theorists love using perfect models to make prediction and calculations. Applied physicists have to use real materials with imperfections and need constant estimates. The imprecision of applied physics has slowed the field down a little, staying several steps behind theoretical physics. MIT hopes their BECs and cooling technology can serve as an atomic toolbox for many-body scientists to develop new materials.

The nanokelvin toolbox makes new physics possible. With the temperature approaching 0.5 nanokelvins and less, several rare physical phenomena can be observed. As explained in the previous post, the BEC phase transitions can be studied at this temperature. Also the atoms start to display quantum reflection and coherent chemistry. More importantly, at such low temperatures, the intermolecular forces overshadow kinetic energy and strong molecular interactions can be observed. These phenomena enhance knowledge of quantum mechanics and in many cases many-body physics as well.

MIT’s cold samples also simplify manipulation. When particles in a sample have lower kinetic energies they become easier to trap and move around. The magnetic field needed to confine the sample is significantly lower than its microkelvin equivalent. Individual atoms can be easily trapped via lasers. A laser as weak as a standard pointer starts to have enough power to trap and transport atoms. The ease of manipulation makes making optical traps, lattices and atom chips simpler. Less energy can be invested after cooling to achieve better results.

Many-body physicists can use the nanokelvin samples to solve systems with strong interactions and correlations. Normally, a gas has very weak interaction due to individual particles’ high kinetic energies. When super cooled the gas starts to display solid-like interaction and cohesion, but on a much easier to study scale. The ultra low density and ultra low pressure (reviling mediocre vacuum chambers in pressure) make the sample constituents far apart and organized in perfect structures. The dominant intermolecular forces make the system a good modeling tool for more complex many-body systems. The toolbox serves as a long awaited balance between theoretical and real systems.


First, it is vital to understand what makes superconductors important. Currently, semiconductors waste energy during transmission due to internal resistance to electron flow. To avoid this, the resistance on individual electrons inside a conductor has to be eliminated, so that the electrons can travel freely. The creation of effective superconductors has applications ranging from fusion, to medicine, to computer science.

Although, seemingly impossible, superconductivity has already been achieved. The current superconductors are hard to construct and operate at temperatures of 20 Kelvin or less. In 1986, “high temperature” superconductors were found, that operated at around 90 Kelvin. Most semiconductors’ resistance decreases with temperature, but even at 0 Kelvin, standard conductive matters like silver and copper still display a nonzero resistance. Superconductors work because some materials’ resistance abruptly drops to zero at a certain “critical temperature”. The reason that superconductors behave the way they do is explained by the Ginzburg-Landau theory and BCS theory. The first examines the macroscopic properties by mathematics and the second explains the quantum mechanics.

Under the BCS theory electrons pair up in Cooper pairs to facilitate resistance free travel. Normally electrons repel each other due to Coulomb’s law (opposites attract, alike repel). However, under low enough temperatures and proper magnetic conditions a positive charge develops between a pair of electrons, letting them overcome their natural repulsion and pair up.

Before pairing up a single electron is made up of one constituent and thus is a fermion. Fermions differ from Bosons (the ones that make BEC) in the number of constituents, or more fundamentally in their spin. Fermions have half-integer spin and Bosons have integer spin. Due to the Pauli Exclusion Principle (which explains why matter occupies space) the fermions are unable to gather at the low state like bosons. This exclusion leads to fermions having high kinetic energy even at 0 Kelvin and not being able to form Bose-Einstein Condensates. However, when two half-integers are added, an integer value is achieved and the possibilities expand.

A Cooper pair is considered a boson. The whole pair when created has an integer spin, allowing several pairs to accumulate on the lowest energy level. By accumulating several pairs at low energy state, a Bose-Einstein condensate can be formed. The only big difference between a standard boson and a Cooper pair remains in the spacing of the constituents. In a normal boson they are close together, but in a Cooper-pair they are farther apart and the orbit might even cross over other Cooper pairs. This “far apart” state of Cooper pairs as bosons is known as the BCS state.

Sadly, BCS’s unlike BECs do not display superfluid properties. Superfluids differ from normal liquids in that they experience no friction. Since a superfluid is a matter-wave (much like a BEC) it also displays various other strange properties. When rotated, a superfluid can only take on integer values for speed. This leads to a mosaic pattern of rotating mini-tornados created in the rotating sample (as opposed to the single tornado effect of a normal liquid). More importantly if superfluidity could be achieved for electrons then new superconductors will be possible.

Achieving superfluidity for electrons is precisely what Ketterle’s team at MIT is doing. Currently they can not work with electron samples, so they pair up Lithium ions (which are fermions) into boson pairs. Then, through various manipulations and cooling they achieve a transition, or hybrid state between a BEC and a BCS. In this state the sample displays superfluidity. The temperatures are still in the nanokelvin range, but temperatures can not be compared directly between different materials. Values have to be scaled by density to get the proper results. When the Lithium sample is scaled for density it turns out that it is actually 200 times warmer than a helium superfluid and 20 times warmer than the hottest superconductor. That means once such a technology can be applied to electrons and scaled for density, superconductors will be possible significantly above room temperature.


Should we expect Cooper pair super conductors to be part of our gadgets in ten years? I doubt it. However, the field is moving quickly and in the coming years’ electron BEC/BCS hybrid forms should appear and physics should begin with them. Also, the atomic physics toolbox should help physicists and engineers develop better materials for everything from clothes to space shuttles. There should defiantly be a lot of cool (and maybe even room-temperature) science over the coming decade.

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Sunday, March 04, 2007

Bose-Einstein Condensate

On March 1st and 2nd I attended two lectures by the physics Nobel laurite (2001) Wolfgang Ketterle on Bose-Einstein condensates and his current research. Most of this post comes from the notes I took at his lectures, textbooks, common sense and various online articles.

Most people know at least three states of matter: solids, liquids and gasses. From popular science and TV some even know a state of matter like plasma. To make plasma, normally a gas is superheated (among other things). Now, if instead we cooled the gas to extremely cold temperatures, we would get something else. That something else (for bosonic atoms) is known as a Bose-Einstein condensate.

Bose-Einstein Condensates

Before the quantum revolution in physics, atoms were thought of as particles and nothing more. Atoms were thought to follow the rules of classical mechanics and the field of physics was regarded as dead. However, scientists like Bohr, Einstein, Heisenberg and Schrödinger brought life back to physics by seeing the holes that classical mechanics left on the atomic level, and proposing the theory of quantum mechanics. Among the countless new principles that came from quantum mechanics, came the realization that atoms (and all other matter, for that matter) display wave like properties. Normally wave like properties are not observed in atoms, unless they are standing still, or close to it. To achieve that, the free energy of atoms has to be eliminated by cooling.

Cooling is precisely what Wolfgang Ketterle at MIT and his colleagues from other universities accomplished in 1995 when they formed the first BEC. Sodium gas was cooled until it reached the nanokelvin range and at that temperature the waves of individual sodium atoms overlapped so much that they formed one large matter-wave known as a Bose-Einstein Condensate. The men responsible for displaying the condensate Einstein and Bose predicted in 1924/25 received their Nobel Prizes in 2001 and currently continue their work on BECs, superfluids and fermonic condensates.

To easily picture a BEC it is best to think about lasers and light bulbs. A light bulb emits various wavelengths in various directions. A laser does its best to emit one continuous wave. Standard gasses are like a light bulb, they are randomly bouncing around in random directions. A BEC is like a laser, it is one continuous matter wave.

Temperature, Cooling and Measurement

We all have a basic understand of temperature from experiencing it first hand. Winter is cold, summer is hot. But what does temperature really mean? Under physical rules temperature is just another measure of energy; a measure of free energy in a system to be more precise. In a gaseous system, almost all of the free energy is expressed as kinetic energy, so when a gas is cooled it looses kinetic energy. At room temperature air molecules move at around 300m/s. At the temperatures achieved in the MIT-Harvard Center for Ultracold Atoms these same molecules would move at around 0.001m/s. In other words: it is so cold you might not even make it to the mall.

The record temperature achieved by MIT is 450 picokelvin (4.5*10^-10 Kelvin). Comparatively the temperature of outer space is around 3 Kelvin and room temperature is around 300 Kelvin (273.15 Kelvin = 0 Celsius). Basically, the temperature inside the experimental chamber is about a trillion times colder than your room.

Cooling atoms to such a low temperature poses many technical challenges. Ketterle’s team overcomes these challenges by laser and evaporative cooling the system. The sample is held inside an evacuated vacuum chamber by a magnetic field while lasers, microwaves and other magnetic fields are used to cool the system.

Laser cooling is the first step. Intuitively we perceive that shinning a light on something makes it hotter. That phenomenon is based on absorption of light. In laser cooling the light is bounced off the atoms in such a way that it has more energy leaving than it did entering. That seems impossible at first, but due to the Doppler Effect (also known as blue-shift) it is possible. The light is tuned to a frequency slightly below one that the atoms can absorb, and thus atoms can only absorb light when they are flying towards the light (when the light is blue-shifted to the right frequency by their movement). The atoms release the photon right after at the proper frequency, and thus energy is lost. The process looks very exciting. Sadly laser cooling can not take the atoms to the nanokelvin temperatures, so evaporative cooling has to be used.

For evaporative cooling, Ketterle states a very good metaphor: a coffee cup. Everyone knows what happens to a cup of coffee if it is left out on the table for a long time: it cools down. One of the reasons the coffee cools down, is because all the atoms are bouncing around inside of it, and atoms with high-kinetic energy are more likely to get enough energy to fly out of the cup. Thus, over time more and more atoms with higher than average kinetic energy are lost and the system cools.

If you are in a hurry, and you need to cool the coffee, then you blow on it. Blowing agitates the system more and helps speed the process of high-energy particles escaping. Evaporative cooling at MIT follows a similar principle. The sample is put in a “cup” and then the machine “blows” on it.

The atoms are suspended in a bowl shaped magnetic trap. The particles of various energies bounce around, and higher energy particles are more likely to reach the corners of the trap. At the corners, other magnetic fields or microwaves move the escaping particles away from the main system and thus the sample is quickly cooled to nanokelvin temperatures.

Once everything is cooled down, the scientists need to actually have a way to measure the temperature. Since it is impossible to just stick a thermometer into the system, another way needs to be used. Ketterle’s team simply uses gases’ property of expansion to measure an exact kinetic energy of the particles and thus the exact temperature. The magnetic field is turned off, and the sample starts to drop towards the ground and expand in all directions. The team takes a shadow picture of the sample as it drops and then records the temperature based on expansion of the system. This method is extremely precise and accurate, but sadly the sample is destroyed,

How to Know a BEC When You See One

The way a BEC is detected by the researchers is based on the density of the sample when it is dropped, and how it disassociates. When a standard gas sample is dropped it expands more or less evenly and has a density distribution that looks like a three dimensional bell curve. When the gas has transformed into a BEC it assumes the shape of the container (even though it does not expand to fill the whole container) and it is much denser. The whole process is recorded and analyzed with black and white shadow photography. If a BEC is present, then a sharp peek in density is observed.

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