What We Don't Know

The fifth state of matter: Bose-Einstein condensates

• Lana Howell • Season 1 • Episode 13

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Very early in our school career, we learn about the states of matter. This table is hard wood - it's solid. This water flows, we can drink it - it’s a liquid. And the air around us, even though we cannot see it, is a gas. But these three states of matter are not the only three. In fact, wikipedia describes around 20 different states of matter. 

One of these is the Bose-Einstein condensate (BEC). In this state, a number of separate atoms or subatomic particles are cooled to near absolute zero, and behave like a single quantum entity. Many become one in the eyes of physics and maths. Since these eyes tend to define our scientific reality, the existence and implications of BECs defy our expectations of how matter should behave. It is another mind-bending quantum phenomenon. Bose-Einstein condensates are interesting to consider from a theoretical perspective, but they also have practical purposes, such as in superconductors and atomic clocks, especially now that they have been created in labs.

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Bose-Einstein condensate

Hello everyone, welcome to the thirteenth episode of ‘What We Don’t Know’, a podcast that explores the boundaries of human knowledge, investigating the unanswered questions and theories that unravel them at the frontiers of science. During this podcast I hope to get you interested in new areas of science, maths and technology, teaching you about existing concepts and igniting a curiosity for the things we have yet to know.

Very early in our school career, we learn about the states of matter. This table is hard wood - it's solid. This water flows, we can drink it - it’s a liquid. And the air around us, even though we cannot see it, is a gas. You also learnt the ways that matter can change between states: melting, freezing, evaporation, condensation, and, later on, the elusive sublimation. But these three states of matter are not the only three. In fact, wikipedia describes around 20 different states of matter. 

One of these is the Bose-Einstein condensate (BEC). In this state, a number of separate atoms or subatomic particles are cooled to near absolute zero, and behave like a single quantum entity. Many become one in the eyes of physics and maths. Since these eyes tend to define our scientific reality, the existence and implications of BECs defy our expectations of how matter should behave. It is another mind-bending quantum phenomenon. Bose-Einstein condensates are interesting to consider from a theoretical perspective, but they also have practical purposes, such as in superconductors and atomic clocks, especially now that they have been created in labs.

This episode I will first provide background knowledge about states of matter and the relevant quantum mechanics (notably wave functions). I will then explain the theory behind Bose-Einstein condensates, with reference to Bose-Einstein statistics, the Pauli exclusion principle, and supercooling, before describing how BECs are made in reality. Then we shall explore many different possible practical applications of BECs. These include modelling and simplifying complex systems, creating superfluids and superconductors, and quantum information processing. 

Matter is defined as anything that takes up space and has mass. Usually, matter exists as atoms, which assemble into molecules, which vibrate inside a substance. Molecules are held together by intermolecular forces. If heat is applied to a substance, the molecules gain kinetic energy, so vibrate more vigorously. Heat also increases the potential energy of a substance, which is related to the distance between molecules. Total internal energy is the sum of kinetic energy and potential energy. 

Ultimately, increasing internal energy results in a change of state. This is why a block of ice in the hot sun melts into water, and a kettle of water boils into water vapour. Solid, to liquid, to gas. Classically, there are four states (also known as phases). Solids are generally hard. The molecules inside vibrate, but with little kinetic energy, so they remain roughly fixed in place. This gives solids a definite shape and volume. Liquid molecules have more energy and are loosely packed together, flowing over each other and allowing a liquid to adjust its shape. In a gas, molecules move rapidly and randomly with much kinetic energy and much space in between them. The gas will expand indefinitely if unconfined. If you keep heating a gas to an extremely high temperature, atoms and molecules can collide so forcefully that electrons are ripped out of the atoms’ orbital shells. The atoms, robbed of their normal electron number, become positively charged ions. This soup of positive ions and negatively charged electrons is called plasma, and it makes up most of the visible matter in the universe. Stars, nebulas, auroras, very hot flames, and fluorescent lighting are all examples of plasma.

Let’s take a closer look at an electron. It, like the other fundamental particles of the universe, behaves according to the laws of quantum mechanics. At this minute scale, matter is neither a wave or a particle, but both, an idea summed up in ‘wave-particle duality’. If a classical particle is a point-like object, and a classical wave is a disturbance transferring energy, experimental results suggest that any quantum entity cannot be fully understood unless described as both wave and particle. Moreover, this ‘matter-wave’ can only be described probabilistically, not deterministically. That is to say, we cannot exactly predict where it will be in the future using information from the present, we can only calculate the probability attached to different positions.

In 1926, Schrödinger combined the ideas of wave-particle duality and conservation of energy (i.e. the total energy in a closed system remains constant) to write the Schrödinger equation. Contained in a single particle’s Schrödinger equation is its kinetic energy, potential energy, and wave function. What is the wave function, you ask? The wave function is a mathematical description of the state of a quantum system (a system can be a single particle). From it, one can calculate the probabilities of finding a particle to be in a certain state after performing a measurement. More specifically, the square of the modulus, i.e. absolute, unsigned value, of the wave function, equals the probability distribution. If you use values of the wave function describing the particle’s position, the square modulus will tell you the probabilities of finding that particle at specific positions. If you use wave function values describing the superposition of spins, the square modulus will tell you the probability of measuring each spin. The wave function may change smoothly over time - these changes will be described by the particle’s time-dependent Schrödinger equation. But if a measurement is done, the wave function will change discontinuously, collapsing into a single experimental result. Remember how the Schrödinger equation involved the kinetic energy, potential energy, and wave function? This means that a quantum particle can have many different wave functions, depending on its energy level.

With that crash course in states of matter and wave functions completed, you should be ready to understand Bose-Einstein condensates!

Subatomic, fundamental particles that carry a force, such as photons which carry electromagnetism, and gluons which carry the strong force, are bosons. They have an integer spin of 1. In fact, any particle with zero or integer spin is a boson. Fermions are any particle with half an integer spin. They include quarks, electrons, neutrinos and many of the particles composed of those fundamental particles. 

In 1924, Satyendra Nath Bose developed mathematical tools describing the behaviour of photons when all occupying the same energy level. Soon afterwards, Einstein realised that this mathematics could also be applied to atoms under specific conditions. Hence, Bose-Einstein statistics was born. Bose-Einstein (B-E) statistics describe one of two possible ways that, quote, a collection of non-interacting, indistinguishable particles may occupy a set of available discrete energy states at thermodynamic equilibrium, end quote. That is to say, how do particles which seem the same, but do not interact with each other, have certain energies. Note that these energy levels are discrete, not continuous, so only exist at certain values. B-E statistics only apply to particles that do not obey the Pauli exclusion principle. 

Now, what’s that? The Pauli exclusion principle, formulated by Wolfgang Pauli in 1925 and extended in 1940, says that particles with half integer spin, i.e. fermions, cannot be in identical quantum states. This is why two electrons in the same orbital have opposite spins. It also forbids multiple fermions to exist in the same energy level. 

B-E statistics only applies to particles not following this Pauli exclusion principle, that is to say, bosons with integer spin. At low temperatures, bosons, as opposed to fermions, can occupy the same energy level as each other, so can become indistinguishable, at which point they obey B-E statistics. 

Note that fermions are not allowed to condense into the same energy state at low temperatures. In these conditions, they behave according to Fermi-Dirac statistics. 

It is not just low temperatures that trigger the application of B-E statistics. High densities can as well, which is why particles inside a white dwarf, the dead remnants of a star, may obey B-E statistics even at high temperatures.

Einstein used the mathematics of Bose-Einstein statistics to predict a new state of matter: Bose-Einstein condensates. He showed that at very low temperatures, within a few hundred billionths of a degree above absolute zero, bosonic atoms with even integer spins would share a quantum state at the lowest available energy. In this way, all the atoms could be described by the same wave function, and the separate atoms would act like a single quantum mechanical entity, even on a macroscopic scale. This condensate could exist probabilistically in many different places at once, for example. 

This is very bizarre. Usually, unfamiliar quantum effects only show themselves at the subatomic scale - as soon as you scale up, any quantum behaviour, like superposition of states or wave-particle duality, disappears amongst a sea of random interference. The behaviour of individual parts of matter in a macroscopic object averages to zero. This is why a real cat, unlike Schrödinger’s hypothetical feline friend, is never both dead and alive in different probabilities. It is why we see a tennis ball as a point-like particle, not a wave travelling across the tennis court. 

Therefore, Einstein’s prediction of a macroscopic object that we could see, with the naked eye, behaving like a wave and like a particle, all according to a single wave function - well, this prediction keenly demanded experimental proof. 

Unfortunately, the low temperatures required by BEC formation could not be realised in a lab until the 1990s. It was only with inventions in laser cooling and trapping, and improvements in magnetic confinement, that Carl Weiman and Eric Cornell created the first real Bose-Einstein condensate in June 1995. For this they received the 2001 Nobel Prize in physics.

After that first breakthrough came a rapid onslaught of innovations improving and refining the method of BEC creation. Nowadays, the traditional method is a two-step process. A cloud of gas is cooled in two stages while trapped by magnetic fields. 

First, the atom cloud is irradiated with laser light of an energy slightly below a chosen electronic transition. This laser light is blue-shifted to the transition frequency for the most energetic atoms trying to escape, so that they absorb a photon and are pushed back into the cloud. Photon absorption also promotes atoms to an excited state. When the excited atoms decay to the ground state, i.e. the lowest allowed energy state, they release a higher energy photon. The overall effect: the gas becomes cooler and denser. 

But now a problem appears! As the cloud becomes more dense, photons emitted by excited atoms are more likely to be absorbed by nearby atoms, so heat is merely shifted around the gas, rather than expelled. Furthermore, the atom absorbing the photon will recoil in the opposite direction, creating repulsive interatomic forces and stopping the density from increasing further.

So in step two, physicists resort to evaporative cooling. Here, higher-energy atoms are allowed to leave the magnetic trap, taking heat energy with them. The remaining atoms cool down.

This works to cool down the gas cloud enough for the atoms to all occupy the same energy level. As I’ve said, the same energy level means the same wave function, and quantum behaviour at a macroscopic scale of matter. On the other hand, evaporative cooling is time-consuming and results in the loss of many of the cloud’s atoms. Physicists want to remove the need for it. 

And some of them have. In 2013, Florian Schreck and colleagues at the Institute for Quantum Optics and Quantum Information in Innsbruck, Austria, created a small ‘dimple’ in the shallow magnetic trap, in which the trapping potential is higher. Atoms naturally collect here and have a higher density. Normally, higher density leads to higher pressure, which leads to higher temperature, but a second ‘transparency’ laser beam is focused on the dimple in order to increase the energy of the cooling transition there. This ultimately allows a Bose-Einstein condensate to form in the dimple. Such a convenient method, given a constant supply of atoms, enables continuous production of BECs. This could give it an advantage in the design of atom lasers. 

So far we have explored what Bose-Einstein condensates are and how they work. This peculiar state of matter exists at the boundaries of our knowledge, in the outlandish worlds where visible gas can act like a quantum particle, where temperatures and densities are so extreme that we must reframe our perspective on the natural world. But BECs are not just interesting from a theoretical standpoint. They can be, and have been, applied in the real world to technologies that make use of their unique properties. Finally, we can investigate these applications.

First is their ability to simplify many-body systems. Systems of many interacting particles can also be described by a Schrödinger equation, just like a system with a single particle, but the complexity increases exponentially with the number of particles. As the number increases, the equation quickly becomes too difficult to solve, resulting in the ‘quantum many-body problem’. Dr Carlos Benavides-Riveros and Jakob Wolff from the Institute of Physics at Martin Luther University are part of a group of physicists proposing a simpler method to study these many-body systems. They argue that particles in a Bose-Einstein condensate interact only in pairs, so the system can be described using simpler methods that already exist. Another team led by Sean Hodgman at the Australian National University demonstrated another way to approach the quantum many-body problem. By reconstructing the momenta of many atoms in a BEC before and after colliding with another BEC, they could calculate correlations between pairs and triplets of atoms, ultimately solving this system’s many-body problem.

Condensed matter physics is the branch of physics occupied with the macroscopic physical properties of matter, particularly the electromagnetic, structural, and thermodynamic properties of solids. It should come as no surprise that BECs are a useful tool here. For example, one can make an optical lattice from an interference pattern of multiple laser beams inside a BEC. This lattice has many interconnected sites where particles can be trapped. As the lasers are easily tunable, scientists can simulate a condensed matter system using this BEC-optical lattice, and change the parameters governing one sample, rather than needing to create a new condensed matter system for every new set of parameters. 

Condensed matter refers to solids and liquids existing as crystals, i.e. crystalline, or without a defined shape, i.e. amorphous. We already know that bosons in a gas cloud, when cooled to very low temperatures, can enter the state of a Bose-Einstein condensate. Condensed matter also enters weird and wonderful low-temperature states. There is superfluidity, where a liquid flows without friction and thus without loss of kinetic energy, as well as superconductivity, where an electrical current flows without resistance.

Both superfluids and superconductors contain atoms which behave as a single quantum entity, just like a BEC. However, atoms in a superfluid or superconductor can be pulled to higher momentum energy states, unlike BECs, and the phases of matter differ in the strength of interactions between atoms. Even so, BECs maintain interesting parallels to these other states which could open avenues of research and new developments in technology. 

Bose-Einstein condensates have also been used to break records of speed. In a vacuum, light travels at 3x10^8 m/s. That is 300,000 km/s, and actually sets the speed limit on the universe - nothing can travel faster than light. But light does not have to travel at this upper limit. In 1998, Lene Hau at Harvard University slowed light from its original 3 x 10^8 m/s to just seventeen m/s. She took the fastest possible bit of matter in the universe and slowed it to a speed befitting the slowest lane of a road. Two years later, she broke her own record, stopping light completely inside a Bose-Einstein condensate. 

More recently, she and her co-authors - Naomi Ginsberg and Sean Garner - managed to stop and then revive a pulse of light across two BEC clouds. Information about the optical light pulse is imprinted into a travelling matter-wave, which transfers information to the second BEC, where the original light pulse is recreated. Hau emphasised the importance of Bose-Einstein condensates in making this remarkable manipulation of optical information possible. For a few moments of time, optical information exists as a matter-wave between BECs, and it can be changed and controlled by researchers in ways that light waves have never allowed. This could revolutionise the fields of quantum information processing and quantum cryptography. 

In the time that I have, I could never do justice to the vast landscape of possibility that Bose-Einstein condensates inhabit. They could be used to solve the quantum many-body problem, a mathematical challenge that has vexed physicists for years. Their parallels to super cold condensed matter physics enable more effective simulations of condensed matter, as well as new ways to study superfluids and superconductors. And they can slow down, even stop light, potentially allowing new levels of control over optical information. There are many more fields to explore. These include use in quantum computers, modelling vortices to represent black holes, enhanced precision measurements, atomic clocks, and the synthesis of unusual chemical compounds in ultra-cold chemistry.

This episode took you on a journey through the domain of Bose-Einstein condensates, beginning with the fundamental theory behind states of matter and the wave functions that govern quantum behaviour. We saw how super low temperatures affect the statistical mechanics of bosons, and how Bose-Einstein statistics predicted a new state of matter, the BEC, for clouds of atoms cooled to near absolute zero. BECs show behaviour characteristic of quantum particles. But they show it on a macroscopic scale, like a single, huge atom. This strange behaviour makes them useful in the study of other physical phenomena, like superfluidity and superconductivity, and it may also be exploitable in new, fascinating technologies, particularly those involved with quantum information and computers.

Extreme physics plays with the boundaries of natural law in the universe. It finds loopholes in our expectations, unravels and recreates the physical theories that we hold so dear. Whether it be searching for the smallest stitches of matter, travelling at speeds so high they warp time, or, as with Bose-Einstein condensates, toying with the actions of atoms at the lowest possible temperatures, there is a wealth of scientific knowledge to uncover in extreme conditions. 

Bose-Einstein condensates offer a glimpse into the potential of new physical phenomena. The more we study, the more we learn, and the more we understand about the boundaries of the universe’s behaviour.

Thank you for listening. 


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Lana Howell

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