Wednesday, February 15, 2017

BOSE EINSTEIN CONDENSATE

This amazing state of matter was mentioned years ago in my Very Hot, Very Cold article (2011). At first a curiosity, now scientists are starting to see that these condensates may not only pry open the inaccessible quantum world for us but they might offer us a wide variety of new breakthrough technologies as well. Meanwhile the techniques used to create and maintain matter in this ultra-cold condensed quantum state have steadily improved. Researchers at the University of Alberta (my old "home") just created the coldest Bose Einstein Condensate (BEC) ever, at just 40 billionths of a degree above absolute zero! What happens to atoms when their motion literally begins to freeze? This great little 1-minute video offers a glimpse into what a BEC is:



WHAT IS A BOSE EINSTEIN CONDENSATE (BEC)?

Some Background First

Just like a solid, liquid, gas or plasma, a BEC is a state of matter. We come across three states of matter - solids, liquids and gases - every day. Life on Earth relies on the fact that one substance in particular, water, exists in these three states within a relatively narrow temperature range. What determines the state of matter is the average kinetic energy of the atoms that make it up. Generally speaking, atoms are most tightly packed within solids, less so in liquids and farther apart still in gases, but when collections of atoms are subjected to pressure this trend can reverse. As you might know, increasing the pressure of a gas, liquid or solid will also increase its temperature. Solids, depending on the kinds of atoms making them up, are not very compressible but they will eventually compress under sufficient pressure into a dense liquid state when the internal energy increases enough to break apart the inter-molecular bonds that make the solid stiff. The resulting very dense liquid will compress into a very dense gas and the gas, a much more compressible state, will compress further into an extremely dense example of a fourth state called plasma. Not all plasmas are hot and dense like this, but the Sun's hydrogen/helium plasma is a good example. Plasmas can also be diffuse cold ionized gases such the those that populate interstellar nebulae. Excited atoms in plasmas emit electromagnetic radiation. You can witness the light emitted by plasmas when you see sunlight or a lit neon sign. In the case of sunlight, pressure and heat are both at work. In the case of the neon sign, atoms in the plasma are excited by an electrical current. Atoms in a plasma state have so much energy they can no longer hold onto their outermost electrons. They are in an excited state, creating a separation of electrical charge.

Under even more extreme pressure and heat, additional exotic physical states are possible, such as electron degenerate matter inside white dwarf star remnants (our Sun is destined to become one eventually). Atoms in this exotic state are crushed by pressure. Nuclei have lost all of their electrons and a high-energy dense sea of negative charge surrounds them. As pressure is increased further, neutron degenerate matter forms. In this case atoms are crushed into an ultra-dense neutron sea, the strange stuff of neutron stars, pulsars and magnetars. Electrons are so energetic that they combine with free protons to create additional neutrons. Increasing pressure further theoretically produces the densest state of matter possible - quark matter. In this state, neutrons are crushed into their normally confined component particles - quarks. Above this pressure, matter is completely crushed in the infinite gravity well of a black hole - a state, in which matter at the atomic scale can no longer be described using our current theory of quantum mechanics.

Just as there is a maximum threshold of energy above which atomic matter as we know it can't exist, there is a minimum threshold of energy below which atoms no longer behave in the ways we expect. Atoms become excited when their energy increases. In an analogous way, atoms become "de-excited" when their energy decreases. As atoms approach absolute zero, they become sluggish and ultimately condense into an additional physical state called a Bose Einstein Condensate (BEC). Consider a balloon filled with steam, the gaseous state of water. Cool it down to room temperature and it will contain a small puddle of water inside it. Put it in a freezer and that water will solidify into ice. It's easy to visualize the atoms in steam moving around fast and bumping into each other, or atoms sliding around one another in liquid water, but there is no visible motion within a block of ice. Yet, undetectable to our eyes, there is. As the water freezes into ice, the atoms get close enough and slow down enough to form attractive chemical bonds with each other. In the case of water ice, they create a three-dimensional lattice. The type of bond arrangement depends on the kinds of atoms involved. No matter what the solid material is, the bonds hold the atoms more or less in place but they don't stop the atoms from jiggling about, like a runner jogging in place. This jiggling or oscillating motion, averaged over the material, is what we perceive as its heat or temperature. Lets say we cool our balloon down much further inside a special box that removes energy. The oscillations, on average, will slow down. Eventually, the ice will theoretically get so cold that the atoms no longer oscillate at all. At this point it has reached absolute zero, a temperature measured as - 273.15°C or - 459°F or 0K. I say theoretically because it is not possible in practice to remove all the energy from a system (we are treating our balloon as a physical system). Scientists are finding ways to get very close to absolute zero, and as they do, matter begins to act very strangely. In theory, the ice in our balloon could transform from a solid into a BEC, and when it does it will exhibit some very interesting properties.

Now To the BEC Itself

Exotic states such as degenerate matter, which is thought to exist inside stellar remnants, represent the highest energy extreme of atomic matter, while BEC's represent matter's lowest energy extreme. Degenerate matter cannot be directly studied in the lab. Its creation would require an enormous input of energy that would be impossible to achieve and maintain. The gravitational pressure of an entire star is required. Unlike degenerate matter, which cannot be lab-created, no BEC should exist naturally at all. This state of matter is made in-lab only. Even the coldest atomic gas clouds in deep space are a million times too warm, at about 3K, to harbour any BEC matter. A temperature above even just a few microkelvins will disrupt the quantum mechanical quiescence of a BEC and transform it back into its original gas state. But why would such a cold state be a gas and not a solid? More on this to come.

Each particle in matter is described mathematically as a quantum wave function. Click on this HyperPhysics link to get an idea of what these kinds of equations looks like. Any matter particle exhibits wave/particle duality. It can act like a particle and like a wave. In a BEC, particles act completely like waves. These matter waves, as they are called, stretch out as the atoms slow down. They start to overlap one another, and eventually they completely overlap into one large matter wave. At this point the gas is condensed into a BEC state.

Though predicted decades earlier by Albert Einstein and Satyendra Nath Bose, the first BEC wasn't created until Eric Cornell and Carl Wieman succeeded in doing so in 1995. Hydrogen atoms were the logical first choice but providing the right conditions for BEC formation proved too difficult. Helium atoms were turned to next but they presented too many challenges as well. Instead, rubidium was the first successful BEC. Two techniques, lasers and evaporative cooling, which will be described in detail later on, were used to cool a diffuse cloud of rubidium atoms into a BEC state. The two men received the 2001 Nobel Prize in physics for their success in creating this new state of matter.

I mentioned that the universe is far too warm for natural BEC formation. It is possible, however, that all of the matter in the universe could very slowly transform into a BEC state as the universe continues to expand, and therefore, cool. Right now the universe is still "warmed" by radiation from the Big Bang. What were once the highest energy gamma rays possible are now stretched across the expanding universe into low energy microwaves, and they will continue to stretch into extremely long and imperceptibly weak radio waves. At this point, interstellar atomic gas clouds in the universe might be so cold that those atoms will begin to condense into BEC's.

We live within a very narrow range of temperatures, from about -50°C (for a few minutes) to about +50°C (for a few hours) with about 20°C being most comfortable. In this range, hydrogen is always a gas; iron is always a solid and so on, but every element can exist as a solid, liquid, gas and plasma, with each state having its own unique physical and chemical properties. As atoms are energized further, they lose their chemical and physical identities altogether when the nuclei themselves are torn apart. Although practical research is still at a young stage, BEC's also lose some of their original classical chemical and physical properties. In this case, a group of atoms takes on the properties of one single atom, and their normally hidden quantum nature reveals itself.

So, what does this look like? We can visualize what's going on by looking at how the atoms fall into a single lowest-possible energy state. The graphs below plot the energy distribution of a gas of rubidium atoms. At room temperature, the energy levels of the atoms (measured as their velocities) would be spread across a wide range. They would be evenly distributed across a grid like the ones shown below and it would be entirely red. Energy density increases from red, yellow, green, blue to white, the highest density. The three graphs below illustrate, left to right, an already very cold gas cooling into a BEC state. The change in energy distribution below is calculated using Bose Einstein statistics, which we will investigate further later on. The middle graph shows the energy distribution just before the appearance of a BEC and the graph on the right is of a nearly pure concentrate (notice the reduction in yellow around the peak). At this point, nearly all the atoms have condensed into identical lowest accessible (ground) quantum energy states, contributing to the peak density at the centre. Some researchers call this state a super atom, not to be confused with "superatom" which not a BEC but a cluster of distinct atoms.

Image created by NIST/JILA/CU-Boulder
A VARIETY OF BEC's HAVE BEEN MADE

The BEC state has been observed in very cold gases, in very cold liquids such as helium, and even within solid materials, in a special form. In addition to rubidium, lithium and other elements have been used, as well as a variety of molecules. Non-matter particles that have unique properties (these are boson particles such as quasiparticlescan also condense into BEC's. These particles do not form atoms. They can be thought of as localized excitations in an energy field. They include polaritons. A type of quasiparticle, polaritions are half matter/half light particles that will condense into a BEC state inside a solid semiconductor under the right conditions. Quasiparticle BEC's, like this example, can form at a much higher temperature than other BEC's do, at about 19 degrees above absolute zero. This makes them an interesting research focus because their unique BEC properties might have practical applications at temperatures that aren't too hard to achieve. Polaritons can also be created in gas BEC's, and as we will see later on, they play a key role in how light interacts with atoms in the BEC state. In 2010, researchers reported in Nature that they were even able to confine and condense photons (particles of light) into a BEC. Trapped in a "white box," blackbody radiation photons begin to act like a two-dimensional gas of massive bosons in a BEC state (photons are massless force-carrier bosons). As we will see, atoms also act like massive bosons in a BEC (in a three dimensional gas). It is fascinating that massless force-carrying bosons (photons) and matter particles (atoms) can be nudged into an identical quantum state. It is yet another hint at how closely light and matter interact with one another.

BEC's ARE RULE-BREAKERS

Normally, atomic matter doesn't act like boson particles of force. The particles follow very different rules. Atoms won't overlap in one spot. That's why even matter crushed down to a neutron star still takes up space. But photons, for example, can and do (think of constructive and destructive interference of light). Only when atomic matter is very cold will it fall into a single ground energy state (into a single matter wave), and when it does, it breaks a fundamental rule of matter called the Pauli Exclusion Principle (PEP). Matter particles are called fermions. Two or more identical fermions (electrons, protons, neutrons or composite particles such as atoms) cannot share the same quantum state at the same time. This energy distribution rule of atoms is laid out by Fermi-Dirac statistics from which the PEP is derived. It means that at most just one particle can occupy one quantum state in a system. Notice that this is NOT what you see happening in the graphs above. The atoms as matter waves are falling into the same energy state at the same place at the same time. The PEP is being broken.

This rule holds until the atoms approach BEC critical temperature. At this point, the atoms are quiet enough to fall into a single lowest possible energy state, breaking the PEP and now obeying Bose-Einstein statistics instead of Fermi-Dirac statistics. Bose-Einstein statistics describe the energy distribution of bosons (particles of force such as photons, and W and Z bosons of the weak force). Under these statistical rules, particles are described mathematically as symmetric wave functions (rather than fermionic asymmetric wave functions) and that means they can overlap. In a BEC, matter particles act like bosons.

They become one big single wave function. It is still atomic matter, but it is overlapped in one location. A BEC trapped in a magnetic bowl looks like a tiny spherical cloud with a dark dot in its centre. A gas cloud of atoms surrounds the actual BEC (the dark dot, which corresponds to the white peak in the graphs above). BEC's created from normally bosonic particles like photons and polaritons don't break the PEP because they don't fall under Fermi-Dirac statistics.

As an interesting aside, the Pauli Exclusion Principle (PEP) plays an essential role in atomic matter at the highest energy scales too. In these cases, rather than the principle being broken, it takes on a hero-like role that proves just how strong quantum forces within matter are. It explains degeneracy pressure. Ordinary atoms take up space because electron degeneracy pressure keeps electrons with the same quantum spin apart. Electrons also repel one another through electrostatic (same-charge) repulsion. That's a different force that's also at play here. Because of charge repulsion, electrons in atoms tend to spread out and partially occupy several orbitals, like passengers on a jet tend to do when it's half full. When outward nuclear fusion pressure no longer counteracts inward gravitational pressure, atoms are squeezed together and the electrons are forced to fill up the lower energy quantum states. (There's a bunch of cargo in the back of the jet so everyone has to fill up the first few rows). Electrons are forced to get close despite electrostatic repulsion, a classically described force. They refuse, however, to overlap into identical quantum states (two people can't sit in the same spot).

This much more powerful quantum, rather than classical, resistance is called quantum degeneracy pressure. Atomic matter in this state, with electrons forced into all the lowest but not identical orbitals, is found in the extremely dense electron degenerate matter of white dwarfs. In a more massive and even denser stellar remnant such as a neutron star, where gravitational pressure is much higher, the electrons, forced against the electrostatically repulsive (positively charged) nucleus are so energized they approach the speed of light. At this point it is more energetically favourable for them to undergo electron capture through inverse beta decay than to remain traveling near light speed because, at this velocity, their relative masses are approaching infinity, a prediction made by special relativity. Electrons combine with protons in the nucleus and transform them into neutrons (therefore the name "neutron" star). Unlike the white dwarf, just one kind of pressure prevents the neutron star from collapsing. This is the quantum degeneracy pressure of neutrons. These particles don't repel one another electrostatically because they are electrically neutral. In fact, they bind strongly to one another through the strong force, which operates at very short (intra-atomic) distances. As outlined by the PEP, neutrons, like electrons and protons, are matter particles whose wave functions cannot overlap. If the stellar remnant is more massive than a neutron star, matter collapses altogether into a black hole (of which a quantum mechanical description is not yet available). Are the neutron wave functions forced to overlap inside a black hole? Is it a BEC? There is currently no way to know. Isn't it fascinating? Even under the pressure of a massive collapsing star matter waves refuse to overlap one another. Yet, when energy approaches zero, matter waves expand and smear across one another of their own accord.

HOW A BEC IS MADE

The first rubidium BEC was made by trapping a tiny ball of a few rubidium atoms using lasers and magnetic fields. This process is tricky. If the atoms get too close to each other they will form Rb2 molecules. A gas at an ultra-cold temperature will condense into a liquid and then into a solid if the atoms are allowed to interact with each other. To cool the gas, infrared lasers bombard the atoms from every direction. One would think this should have the opposite effect of cooling. The intense photon energy should excite the atoms and add momentum to them, heating them up.

One trick to laser cooling is to understand temperature as the average random kinetic energy of a group of atoms. By making the atomic motions less random, lasers narrow the energy distribution of the group of atoms (and create the single sharp peak in the series of graphs above.). When a photon strikes an outer electron in an atom, it can be absorbed, exciting the atom, and then be re-emitted or it can be reflected. An electron will only absorb a photon that matches its orbital energy (called transition energy). This is where the word quantum derives its meaning; energy can only transition in discrete packets. In this case, a laser with a frequency just below that of the transition energy is used. A stationary atom in the cloud won't even "see" the photons. It won't absorb them because they aren't the right energy. An atom moving away from the laser also won't absorb a photon. It will "see" it as red-shifted, having even lower energy in other words. An atom moving toward the laser, however, will "see" the photon as blue-shifted, and therefore at just the right energy to absorb. The atom is excited and then re-emits the photon, in a random direction. Now statistics comes into play: the photon hits the atom coming toward it. The photon slows it. That's a pure loss of momentum. But the atom then re-emits a photon (with the same energy) in a random direction. This time the direction is random so the change in momentum is not a pure gain. When absorption and emission are repeated many times over a group of atoms, the average random kinetic energy of the group decreases (pure losses and not-pure gains) and that means the temperature decreases. In other words, the lasers eventually align all the velocity vectors of the atoms, and when that happens they are close to transforming into a BEC. Just like the laser light (which is made of aligned in-phase photons) used to make a BEC, the BEC itself is made of aligned particles. They act like waves in phase with one another rather than as discrete particles of matter.

Atoms are also tiny magnets because their spinning electrons create magnetic fields. By applying a carefully aligned magnetic field to the group of atoms, they can be held in one place once they are cooled. The lasers can be turned off at that point. The lasers aren't perfect; some atoms will still have higher kinetic energy than others. They are still "hot." These atoms simply jump out of the magnetic trap, and are eliminated, leaving only the coldest atoms, the ones that can't jump out, inside. This is evaporative cooling. Heisenberg's uncertainty principle ensures that even in a quiet state such as this, there are tiny random movements in the system that eventually destroy the perfectly aligned quantum state. The original group of about 2000 rubidium atoms, that formed a BEC in 1995, lasted for about 20 seconds before it lost its coherence and dissipated back into ordinary gas.

This 6-minute video describes how a Bose Einstein Condensate is made:



As mentioned earlier, the technology has steadily improved since 1995, creating new kinds of BEC's that last longer, as well as solid-state quasiparticle BECs that can exist at higher temperatures.

WHY RUBIDIUM?

Any element's physical and chemical properties change as they transform from one physical state to another. For example, rubidium, the first element made into a BEC, is a very soft silvery white metal at room temperature. Rubidium gets its name from the dark purplish red colour of its flame. With a melting point of just 39.3°C, it is partly melted in the vacuum sample tube shown below.

Dnn87;Wikipedia
A very reactive alkali metal, rubidium can explosively react with just the moisture in the air. As oxidation starts, it warms the solid into a liquid state, which is even more reactive. If this vacuum sample tube were broken, the rubidium would quickly explode. Rubidium readily vapourizes under ordinary pressure. Even an ordinary heating element (at around 700°C) will boil rubidium into a fairly colourless gas, which is one reason why it made the prefect first candidate for a BEC. How do we keep the rubidium gas in a gas state when we expect it to condense and then to freeze into a solid, and an exceptionally hard one at close to absolute zero? The answer is to start with a very hot (hundreds of degrees Celsius), therefore very diffuse gas. As it is cooled, conditions are carefully monitored to keep its density very low - about a million times less dense than air at Earth's surface. This prevents the atoms from condensing as they normally would.

The most important reason why rubidium works as a BEC is that these atoms are bosonic atoms. They are not actually bosons as we've previously learned, but under the right conditions they can display a bosonic nature. The general rule for bosonic atoms is simple (but the actual calculations are usually very complex). If an atom contains an even number of subatomic particles, it's a "boson." All neutral atoms have an equal number of electrons and protons so it's the neutron number that matters. Rubidium-87 is an isotope of rubidium with 50 neutrons, an even number, so it is a boson. From a quantum mechanical point of view it means that all the subatomic particles in rubidium can be spin-matched or polarized. This doesn't mean that all bosonic atoms make good BEC's (again, it's complicated). It also doesn't mean that a fermionic atom can't make a BEC. Helium-3, for example, is a fermionic atom - it has an uneven number of neutrons (one). It will, however, under extreme cooling, form a pair with another helium-3 atom (a Cooper pair like those in superconductors), which in effect creates a bosonic composite particle, which will condense into a BEC. Because it is fermionic, helium-3 must be much colder than helium-4, a bosonic atom, to condense.

In addition to being plentiful, fairly easy to vapourize, and bosonic, rubidium-87 atoms have one lone electron outside a completely filled electron shell and this lone (interactive) electron makes it ideal for magnetic trapping.

HOW DOES A BEC BEHAVE?

BEC's act a lot like superfluids. Superfluid helium, for example, is created when liquid helium is cooled to almost absolute zero. Helium happens to be the only element that will remain liquid under normal pressure right down to absolute zero. Interactions between helium atoms are so weak that its ground state energy stays too high to allow it to condense into a solid, unless additional pressure forces the atoms closer together. Helium will, however, transition into a superfluid state. In this state, these atoms, like those in a gaseous BEC, no longer vibrate much at all with heat energy. Instead, they enter a calm state where many atoms begin to vibrate in unison like a single particle. This sounds like a BEC but there are key differences. Still, the two states are strongly linked and it is easy to see why many of the strange behaviours of superfluids also apply to BEC's.

Comparison to a Superfluid

A condensed gaseous atomic BEC is not a liquid. Nor does it follow the laws of ordinary gas behaviour. But is it an example of a superfluid? The little bead of rubidium BEC in the magnetic trap is a very rare case of a macroscopic fully coherent quantum object. Loss of phase coherence is the hallmark of the transition from quantum BEC into classical gas. The group of rubidium atoms will grow out of phase with each other in a matter of seconds and return to a classical object, an ordinary gas. Superfluids such as ultra-cold helium exhibit many of the same strange behaviours we explore here with BEC's and they are of quantum origin as well, but these behaviours are hidden in the dense liquid - you can't directly track the gradual loss of interference and other behaviours, as you can with a gaseous BEC. Furthermore, with a BEC, you can fine-tune experimental parameters such as the kinetic energy of the atoms, or its density (more about this in a bit), things you cannot readily do with a superfluid.

Even though the interactions between helium atoms are weak compared to other elements in a liquid state, helium atoms in a superfliud state interact quite strongly with each other compared to those in a diffuse gas BEC. These atom-atom interactions complicate the behaviour of a superfluid, complications generally not encountered in BEC's.

Both superfluids and BEC's rely on bosonic atoms. Cold liquid helium-4 transitions into a superfluid at about 2.17K. Below 1K (well below superfluid transition temperature), it exhibits zero viscosity even though only about 7% of the atoms are at ground state. Compare this to a BEC, where all the atoms are at ground state. Helium-3 will not transition into a superfluid until temperatures dip to 2.5 mK (milli-Kelvins). At this point, helium-3 atoms pair up into bosonic Cooper pairs. A BEC must be much colder than a superfluid. A gas will not transition into a BEC until the temperature dips to just a few uK (micro-Kelvins). There is some disagreement among researchers whether a BEC is type of superfluid but most researchers agree that a superfluid is an example of partial Bose Einstein condensation.

Macroscopic Quantum Behaviour

You might be wondering at this point how you can observe a physical wave when what you seem to have is a coherent singular quantum wave, or mathematically put, a wave function. At this point quantum mechanics students get riled because they know a quantum wave function is a purely mathematical construct made up of a real part and an imaginary (not physically possible) part. You can't see one: it doesn't exist in the real world. However, there is a way around this conundrum. The probability density of the wave, which is the absolute value of the wave function squared, always gives you a real and positive value, a value, which amounts to the real standing wave that you can observe. In other words the probability density is the mathematical description of the physical phenomenon. Can we ever "see" the quantum wave function in action? Yes, we can. We can generate and observe a BEC interference pattern. Rather than mixing together like two gases would, two BEC's in different phases will interfere when they combine, setting up positive and negative lines of quantum interference, a quantum effect, which can be observed. In the negative lines there is only vacuum. Here, the matter waves of atoms interfere resulting in a space with no atoms. Although the total number of atoms in the mixture is conserved, the atoms simply disappear along lines of negative interference, a purely quantum effect that you can observe.

Quantum Vortices

Perhaps the most intriguing behaviour of BEC's is the quantum vortex, a behaviour that is already well studied in superfluids such as superfluid helium. The classical analogue is stirring a cup of coffee. A little liquid tornado forms with a depression or hole in its centre. Internal friction eventually slows down the rotational motion and this classical vortex dissipates. Both superfluids and BEC's are frictionless. They exhibit zero viscosity and this means the fluid flows without any loss of kinetic energy. If you could stir a superfluid it would just flow around the spoon with no resistance. You can't stir a BEC with a spoon because all current BEC's are too small. The "dot" mentioned earlier tends to be a spherical or pancake shape that is around a millimetre across. But you can whirl it around by rotating the magnetic trap that contains it and, when you do, you create multiple tiny string-like whirlpools in it. Unlike any classical system, all the rotational motion of the BEC is sustained only by these quantized vortices because all the atoms in a BEC are in one quantum wave function. Because these vortices are quantum, their angular momenta must be quantized. The angular momentum can only be expressed in whole integer packets. When a wave rotates (any wave, even a quantum wave), it forms a closed curve. In this case, those closed curves are confined to de Broglie wavelengths. Like any standing wave, the wavelengths must be whole (an integer value). In a classical fluid like coffee the velocity of rotation increases smoothly from the spoon in the centre toward the walls of the cup. In a quantum fluid (superfluid or BEC), the velocity can only increase in packets like 0, 1, 2, . . .  It takes less energy for the system to form lines rather than sheets, so you get a series of string-like vortices. In the BEC, the vortices tend to be multiple and they have very tiny holes, the width of which can vary depending on the atoms used. These holes, called filaments in a quantum system, don't decay by diffusion as they would in a classical system.

Put mathematically, a BEC quantum vortex is a direct result of the macroscopic wave function of the system. A BEC rotates by puncturing the condensate with filaments along which the quantum wave function vanishes to zero. These filaments are singularities in the wave function. A number in the wave equation, called the winding number, must be a whole integer (0,1,2, . . .). Mathematically this ensures that the wave function doesn't change value after each rotation. In physical terms this means that the velocity of the circulation has to be quantized. A quantum vortex can only spin at a discrete set of speeds and it can never die down smoothly like a classical vortex does. However, the motion around each vortex, called superflow velocity, acts classically like it does in the cup of coffee, and it can be described using ideal fluid dynamics.

The study of quantum turbulence (in which vortices are an example) began in the 1950's using superfluid helium. The availability of cold gas BEC's now offers a great advantage in this study because the turbulence can now be directly visualized in a BEC, rather than being hidden inside a dense liquid, which, depending on the temperature, can contain a complicating mixture of superfluid and classical viscous fluid. Even with this advantage, a lot of questions remain. It is not yet possible to predict where and how many vortices form and what their shapes will be. This problem isn't limited to the quantum vortex. Turbulence itself is a very complicated phenomenon. It is strongly nonlinear and this means you can't input data into an equation and get a predictably straightforward answer. This is why weather forecasts are notoriously unpredictable.

The study of quantum vortices might make the study of turbulence easier. A classical vortex tends to be messy: it's unstable, it appears and disappears randomly and its circulation is not conserved. Quantum turbulence is a simpler system. It is composed of a tangle of vortices that all have the same conserved circulation in the BEC. Even so, quantum turbulence is complicated; it is still a system with many (albeit fewer) degrees of freedom.

In a perfectly condensed BEC, well below its critical temperature, you might expect vortices to be indefinitely stable because there is no friction to diffuse them, but they do decay over time. Quantum vortices spontaneously and randomly reconnect, much like water spouts over an ocean do. This behaviour is analogous to eddies that form in a turbulent classical fluid. A quantum vortex can lose energy, dissipate over time in other words, by emitting sound. Sound appears to come from two processes. First, during the process of reconnection (depending on the angle of reconnection), vortex line length is destroyed. When this happens a rarefaction pulse is emitted, a sound in other words. A second source of sound emission may come from a cascade of Kelvin waves, which are excitations in the BEC that result from vortex reconnections. These particular waves, which usually have very long wavelengths in nature, may be short enough to cause sound radiation in this case. By these mechanisms of energy dissipation (loses through sound energy), all quantum vortices eventually decay.

The Bosenova

Under the right conditions, a BEC made of rubidium-85 will explode in a manner that resembles a tiny supernova, a bosenova (also less cutely called a BEC loss). Rubidium-85 is one of two naturally occurring isotopes of rubidium, the other being rubidium-87, the isotope which created the first BEC. Like rubidium-87, rubidium-85 is a bosonic atom, this time with 48 neutrons. One of the key differences between the two isotopes is that rubidium-87 has a positive s-wave scattering length. This means that the atoms naturally repel each other at low temperatures so it is easy to evaporatively cool the gas. Rubidium-85, in contrast, has a negative scattering length. This means that a condensate made of this isotope will tend to collapse in on itself, especially in a zero magnetic field. Because the atoms attract each other, it's also more difficult to cool it into a stable (non-interacting) BEC. It has to be just 3 billionths of a degree K above zero. Even with these challenges, rubidium-85 offers a unique bonus. In 2001, physicist Carl Wieman (half of the team that created the first BEC in 1995) adjusted the fine-tuning of a BEC droplet of rubidium-85 by changing the magnetic field in which the atoms are trapped. Doing this amounted to adjusting the self-interactions of the wave function (remember a BEC is a superimposed macroscopic wave function). In effect, he could dial between repulsion and attraction.

Dialed to repulsion, all the parts of the wave function push each other apart. The BEC droplet swells accordingly. Dialed to attraction, they pull together, and this is when unexpected dramatics begin. It starts to shrink gradually as expected, but then it shrinks suddenly, triggering an outward explosion that is tiny by everyday standards but with significant energy (about 100 nano Kelvins, nK) considering only a few thousand very low energy atoms are involved. After a few microseconds a much smaller remnant of BEC is left behind, surrounded by an expanding gas cloud of rubidium-85 atoms. This sudden collapse followed by an explosion that leaves behind a remnant and a gas cloud reminds one of a supernova, although the actual mechanisms involved are very different.

About half the original atoms vanish during the explosion. Researchers first thought that they might have either formed Rb2 molecules in the explosion or that some atoms flew out of detector range before they were measured. Or (sharp breath in), they really disappeared. Perhaps an even deeper mystery presented here is how very cold BEC atoms with minimal energy available to them could explode in the first place. The thermal energy released is greater than the free energy of the original BEC. And, just to season the broth, why does some of the BEC survive?

In 2003, Masahito Ueda and Hiroki Saito explained theoretically how a BEC collapses and explodes, thus resolving some of the mystery. The idea is that even though the BEC state is a single matter wave, it still consists of a diffuse gas of atoms and they will interact when they are nudged closer together. When the magnetic field is tuned to just barely favour attractive atomic interactions, the number of inelastic (interactive) collisions between atoms remains negligible at first. But as the atomic density gradually increases, the density of the concentrate increases toward it centre. After a short period of time, the collision rate suddenly jumps and becomes significant, but just within a tiny localized central portion of the BEC (about a millionth of the volume). This triggers instability in the BEC. Not one but several intermittent explosions/implosions occur in rapid-fire, and each time several tens of atoms are lost from the condensate. These researchers determined that atoms are removed due to three-body loss. Three-body loss, or three-body decay, occurs when three rubidium atoms get very close to each other, as they do in a shrinking condensate. Two of the atoms form a molecule (Rb2) in an excited state while the third atom carries away the energy released by the formation of the chemical bond. Each of these energies is much higher than the depth (energy confinement) of the magnetic trap, so three atoms (and their energies) fly off out of the system.

Although atoms are not lost irretrievably, the implosion viewed in terms of a closed system acts like a tiny atom drain, a tiny black hole. After the atoms are lost, outward kinetic pressure from the atoms minus the combined mass of the lost three atoms just surpasses the attractive force. This slight surplus in kinetic energy is enough to trigger a subsequent burst or explosion. Afterward, attractive energy then dominates and the BEC shrinks again. The cycle repeats until the number of atoms remaining is too small for attraction to overcome outward kinetic pressure. Because the collision-heavy region is confined to such a small portion of the BEC, some it survives the ensuing explosion.

BEC's Can Slow Down and Stop Light

The bosenova is a very interesting phenomenon but it seems to have few practical applications. The interaction between light and a BEC, on the other hand, is not only fascinating, it hints at new possibilities for storing and communicating information in the future.

The speed of light in a vacuum is an exact value, approximately 300,000,000 m/s (denoted c). In practice, however, a pulse of light contains many particles of light, or photons. Their average velocity is c. A pulse of light slows down (it refracts) when it travels from one medium such as air into another medium of different density such as water. If it strikes the new medium at an angle, the pulse of light appears to bend as its speed differs on different points along its wave front. The individual photons in that pulse do not slow down, however. They remain at vacuum light speed. What slows down is the pulse, because multiple interactions between the photons and the atoms in the medium take tiny amounts of time. As density increases, so does the number of photon-electron interactions, because there are more atoms for the photons to interact with. Photons may reflect off atoms and resume travel or they may be absorbed by an atom's outermost electron and then be re-emitted. These interactions mean it takes longer for the group of photons as a whole to get from point A to point B through the medium. The light pulse slows.

How about the photons themselves? Can anything slow a photon down? It turns out that a BEC can. In fact, it can even stop a photon (in effect) for a few seconds, then reconstitute it (with all the quantum information it contains still intact) and allow it to resume its course.

In 1999, Lene Hau and her associates slowed a light pulse down to just 17 m/s (that's 20 million times slower than light traveling in a vacuum, c) in a BEC. A BEC, as we know now, is a condensate of atoms. The atoms are still a diffuse gas. As matter waves, however, they spread or smear out as their atomic vibrations slow down. Compared to an ordinary gas at room temperature, the matter waves (the de Broglie wavelengths) are about 10,000 times shorter than the average distance between the atoms. These waves are longer than the distances between the atoms, so the matter waves overlap. It might be tempting to imagine a BEC as a clump of super-dense matter where the atoms themselves have all collapsed into one spot, but it is not. Only the matter waves superimpose.

Refraction, even at its extreme, slows light only by a small fraction (about a third). For example, gallium phosphide has one of the highest known refractive indexes of any material, and even through this, light slows only to about 86,000,000 m/s. A diffuse gas generally has a refractive index of just one, which means it does not slow light at all. To achieve slowing on the extreme scale here, something other than refraction must be involved. There are currently three theories used to explain how extreme slowing occurs. They are briefly described on the Wikipedia entry here. I will focus on the polariton (more precisely called microcavity exciton-polariton) approach. It's the theory that best explains stopped light (which we will talk about next). A polariton is a not a physical particle in the same sense that a particle of matter is a physical particle. It is a quantum-only entity that is a hybrid light/matter quasiparticle. It is an emergent phenomenon called a collective electromagnetic excitation. It can take on particle characteristics, which, as a result, can have physical (measurable) effects on a system. These particular particles act like a gas, they can be trapped, and they can move just like real particles do.

Normally you can't shine light through a BEC gas condensate. As the gas cools, it changes from transparent to opaque. However, Lene Hau and her associates were able to electromagnetically induce transparency in a BEC within a very narrow spectral range. In this case, a cloud of sodium atoms is treated the same way as the rubidium BEC explored earlier. It is cooled by lasers and by evaporative cooling into a BEC state that is confined within a magnetic trap. The BEC is then made transparent by exposing it to a specific arrangement of laser beams. The lasers also allow photons traveling through the BEC to combine with atoms to create polariton quasiparticles. More technically put, the laser treatment induces strong light-matter coupling into a structure that combines quantum wells (think of an atom stuck in one spot as a standing wave) and photon cavities (imagine a photon trapped between two very close tiny mirrors). This coupling is equivalent to a boson particle that is composed of a quantum well exciton and an optical cavity photon. Polaritons get mass from the atoms, so they travel slower than c. Remember that a BEC is, in effect, one big super-atom. It has the mass of all the atoms condensed into a single quantum state. It's mass is therefore the sum of the masses of all the atoms, so polaritons formed with incoming photons are likewise very massive and this means they must travel much slower than light speed. It is a quantum effect that significantly slows the photons traveling through the BEC because they enter a different particle state. This slowing effect is an entirely different mechanism from refraction, described earlier.

This 3-minute video describes how a BEC is used to slow down light.



In 2001, Ron Walsworth and his associates went one big step further. They stopped the propagation of light through a BEC altogether (and then restarted it). This time, using rubidium atoms once again, they gradually turned down the lasers once they had made the BEC transparent. The behaviour of the polaritons in the BEC shifted accordingly from photon toward atom. Eventually the polariton nature turned entirely into atom nature, and at this point the photons were effectively stopped in their tracks inside the BEC. Light stored in the polaritons as quantum information was now hidden in their atom-nature. Perhaps a better way of looking at it is to consider all the quantum information encoded in the light now trapped within the BEC gas, not in the atoms themselves but as quantum excitations within the gas. An exciton-polariton is a localized quantum excitation. Light in this way can be stored for up to seconds inside a BEC (and perhaps longer as the technique improves).

When the lasers were turned back up, the photon component of the polaritons increased and the light resumed its travel.

The ability to stop and restart photons could be very useful in a number of technologies. Imagine that instead of solid-state electronic qubits delivering information in a computer, photons could be used instead. They carry information faster, they don't heat up sensitive components and as we just saw their information storage can now be precisely controlled. One problem with using photons in communications has been how to stop them and decode their information. After flying down an optical cable they have to be stopped at your computer somehow. Nowadays, the information is transferred into an electronic system. The only way to stop a photon is to interact with it. A photon is absorbed by an ordinary atom. As it is absorbed it loses its quantum information, for example its polarization state, and an entirely new photon of equivalent energy is re-emitted in a random direction. In a laser-irradiated BEC, the laser is tuned in a way to prevent photons from being absorbed by the electrons in the gas atoms. The atoms instead form a cluster around each photon, creating a polariton quasiparticle. A BEC can stop and capture each photon, store its information intact (again, polarization could be used instead of 0's and 1's) for a specific period of tine and then send it on its way as a signal.

MANY POTENTIAL USES FOR BEC's

There is a potential goldmine of possibilities for BEC's both as research tools and in practical applications. This research is still in its early stages; it is less than two decades old, but as BEC-making technology improves and the list of BEC's with various properties grows, there is no doubt that some of their exciting quantum features will be exploited in new technologies. Because BEC's greatly magnify phenomena confined to the formerly inaccessible quantum world, BEC's might be manipulated as tools to directly observe and verify currently theoretical quantum behaviours such as the mass acquisition of a normally massless particle called a quasi-Nambu-Goldstone boson, which is thought to be the result of tiny quantum fluctuations. Until now, almost all investigations into the quantum world must be carried out in incredibly large and expensive particle accelerators. As well as expense, this limits the kinds of questions that can be asked. BEC's could be used as customizable quantum laboratories. They might also provide a direct window into the mysterious phenomenon of quantum entanglement. BEC's don't normally contain entangled atoms but researchers have very recently discovered it might be possible to fine-tune the magnetic field around the condensate in such a way to entangle all the atoms in it.

BEC's are already being exploited to learn more about solid-state physics. You can create an optical lattice in a BEC by using several lasers to make an interference pattern that looks (and acts) much like the crystal lattice patterns of atoms found in many solid materials. The big advantage here is that the same optical lattice can be repeatedly tuned and manipulated in different ways to see what happens. When using a solid, you have to regrow your sample every single time (and I assume you've got to be very consistent). The fine-tune-ability of a BEC also means it could be potentially used as a variety of high-precision measuring instruments. There is no obscuring noise to tune out in a purely quantum system. In quick succession science and technology have evolved through the golden age, the industrial age and the information age, Now, it seems that BEC's will help us usher in a quantum age.

1 comment:

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