Experimental Aspects of BEC

The following is an introductory level discussion about experimental aspects of Bose-Einstein condensation, intended for a general audience.  This is an updated version of a feature article which appeared in the New Zealand Science Monthly magazine (entitled How to bait an atom trap, July 1998 issue).
 

1.  Introduction

In 1997 the laser and atomic research group in the Physics Department at the University of Otago began a quest to produce a recently discovered and elusive new state of matter called a Bose-Einstein condensate (BEC). The primary motivation behind this work is to be able to perform elegant experiments on a macroscopic scale which clarify some of the mysterious aspects of quantum physics. Predicted more than 70 years ago by Einstein and Bose, and observed for the first time in July 1995 at JILA in Boulder (Colorado), BEC is difficult to observe because it involves reaching very cold temperatures. Although the process of making a Bose condensate is complex, the methods involved are based on relatively simple concepts.
 

The concept of "temperature" is familiar to everybody, and for example most people would describe Antarctica as a cold place, but for physicists looking for a Bose condensate, Antarctica is a billion times too hot! To understand this we need to understand temperature, and particularly the idea of "absolute zero": an unattainable goal which the temperature can approach ever more closely, but never reach. Without being precise to the point of being incomprehensible, the temperature of an object is related to the energy of its atoms: the faster the atoms are moving about, the higher the temperature. In a gas this motion is the random motion of the atoms "flying around" and colliding with each other (typically billions of times a second), while in a liquid or solid the atoms are in relatively stable positions but move randomly a small amount around these. As a material is cooled, the amount of motion gets smaller and smaller, and things become more ordered: water turns to crystalline ice, air turns to a liquid, and atoms in a gas are slowed to standstill (or more precisely, as close to standstill as quantum mechanics will allow). On the familiar celsius scale of temperature, absolute zero occurs at around 273 °C. However, very low temperatures are more conveniently measured on the kelvin scale, which assigns 0 K (zero degrees kelvin) to "absolute zero", so that temperatures are measured upward from this.
 

Figure 1. Temperature in the kelvin scale can approach absolute zero, but never actually reach absolute zero.

 
 

As temperature is reduced, at +273 K (0°C) water freezes to form ice, at +77 K (~196 °C) the nitrogen in air condenses to a liquid, and at +4 K (~269 °C) helium condenses to a liquid. However, the technologies described below have enabled physicists to cool tiny amounts of gas much closer to absolute zero.  At temperatures around 100 nano-kelvin (100 billionth of a degree above absolute zero) we observe Bose-Einstein condensation.
 

2.  Cooling Atoms with Lasers

In 1997 the Nobel Prize in Physics was awarded to three physicists for "the development of methods to cool and trap atoms with laser light". Their work, which began in 1975, broke two barriers originally thought to limit the temperature to which atoms could be cooled, and provided a laboratory technique essential to the discovery of Bose-Einstein condensation. Laser cooling is a technique which has been used in the laser and atomic research laboratory in Physics Department at the University of Otago since 1993.
 

Today it is possible to use inexpensive diode lasers, similar to those found in compact disk players, to slow (cool) atoms in a vapour to micro-kelvin temperatures and confine (trap) these atoms in a tiny "cloud" at a point in space. The primary force used to slow atoms in laser cooling and trapping is the momentum transferred to an atom when photons scatter from it. This force is analogous to that applied to a bowling ball when it is bombarded by a stream of ping-pong balls. The momentum kick that the atom receives from each scattered photon is small: the velocity of an atom in a gas at room temperature is a few hundred metres per second and the typical change in velocity from scattering one photon is only about 1 cm per second. However, by tuning the laser to a particular frequency (called an "atomic resonance"), it is possible to scatter more than 10 million photons per second, and produce accelerations on the order of 10,000 times that of gravity. On resonance, this acceleration will speed the atom up if the kicks are in the same direction as the atom is already moving (i.e. the atom is moving in the same direction as the light beam), or slow the atom down if it is moving in the opposite direction.
 

The trick to cooling atoms with laser beams is to make the rate that photons are scattered (the force) dependent on the velocity of the atom. This can be achieved using the Doppler effect. (A familiar example of this is the sudden drop in pitch of a car engine as it passes you by while you wait to cross a road, but the Doppler effect works for light as well as sound.) There is an apparent change in the frequency of light "seen" by an atom due to relative motion. Atoms moving towards a laser see a higher frequency than those moving in the opposite direction. By tuning the laser below the atomic resonance frequency, an atom moving towards the laser beam sees a higher frequency, scatters more photons and is slowed (cooled). Conversely an atom moving in the same direction as the laser beam sees a frequency Doppler shifted away from resonance, scatters (ideally) no photons, and so is not sped up (not heated) by the laser beam. By arranging six laser beams in three orthogonal pairs of counter-propagating beams, (figure 2) we can arrange that, whichever direction an atom moves, it always encounters a beam in the opposite direction which slows it down. This six laser beam configuration used to cool a sample of atoms from a vapour was given the descriptive name "optical molasses", since the light bath always opposes the motion of the atoms as if they were submerged in molasses (or Golden Syrup if in New Zealand!).
 

Figure 2. Six laser beams and a pair of magnetic field coils forming a magneto-optical trap can cool more than a billion atoms to micro-kelvin temperatures.

 
 

Although optical molasses will cool more than a billion atoms to micro-kelvin temperatures, the atoms are still not confined to be in one place. There is no position dependent force, and since the atoms are not slowed to complete standstill, they diffuse out of the laser beams and fall away under gravity. Position dependence is introduced by using (s+/s-) polarised laser beams and applying a weak magnetic field which is zero at the intersection of the six laser beams and increases in all directions away from this point. The position of the magnetic field zero within the six laser beams is the centre of the trap. The polarisations of the laser beams are arranged so that an atom has zero force on it at the trap centre, but when displaced from the trap centre it will scatter photons in such a way as to push it back to this point. As well as holding the atoms at a point in space, the trapping force compresses them into a dense cold cloud. This atom trap is referred to as the "magneto-optical trap" (MOT), since the cooling and trapping force is optical, and the weak magnetic field defines the point in space about which the atoms are trapped.
 

Surprisingly, the cooling and trapping processes in a MOT work far better than expected. The temperature is approximately ten times colder than a theory based on the Doppler effect predicts: a rare violation of Murphy’s Law. Instead of temperatures around milli-kelvin, measurements reveal temperatures as low as a few tens of micro-kelvin. This "sub-Doppler cooling" is the result of complex spatial changes in the polarisation of the overlapping laser beams, resulting in changes to the energy level structure of atoms. Atoms are fated to always climb a sequence of potential hills created by the light and thereby slow down, but never get the chance to speed up by rolling down a potential hill. This process was dubbed "Sisyphus cooling" after the character in Greek mythology fated to endlessly roll a rock up a hill. Once at the top of the hill, the rock would always roll to the bottom so that Sisyphus would have to start over.
 

Applications of laser cooling include: improved atomic clocks, better frequency standards for fibre optic communication enabling multiple wavelength channels and coherent detection, and the manipulation of atoms with light for precision lithography and nano-technology. In the laboratory, laser cooling has had a profound effect on atomic spectroscopy, but Otago's primary use for laser cooling is that it provides a source of cold atoms that can be further cooled to the lower temperatures needed to observe Bose-Einstein condensation.
 

3.  Evaporative Cooling of Atoms Confined in a Magnetic Trap

Having beaten the Doppler limit, the challenge is then to beat the so called "recoil limit": the temperature of a gas in which the atomic velocities are around the level which comes from the kick given to an atom as a result of scattering a single photon. This is equivalent to cooling from the micro-kelvin to the nano-kelvin regime. Elegant optical techniques with esoteric sounding names like "velocity selective coherent population trapping" were devised which can do better than this limit, but these don’t work well for the dense atomic clouds needed to observe BEC. To get around the recoil limit set by the light, the simplest solution developed to date is to laser cool to micro-kelvin, then turn the light off, trap the atoms with a magnetic field, and continue cooling with a non-optical method.
 

Atoms have weak magnetic properties which allow us to confine them in a strong magnetic field: the same type of field as used in a MOT, but much stronger. The attractive magnetic force is familiar to anyone who has ever played with magnets, but for atoms the forces are weak. Even for the strongest magnetic trap, the "cup" in which atoms are held is very shallow, so that only laser cooled atoms move slowly enough that they cannot escape over the sides. Also, the atoms must be prepared in the correct atomic state to be confined; in other states the atoms are not confined. This feature of magnetic traps allows us to continue cooling below the recoil limit.
 

The new cooling method is called "evaporative cooling" and works in a similar way to the cooling of hot coffee by blowing the steam from the surface. (Another example is the way wet skin feels cold in a breeze.) By removing the hottest atoms from the coffee (the steam), a lot of energy is removed and the temperature (average energy) of the remaining water molecules drops. Continuing to cool involves continuing to blow the steam (hottest atoms) away. The atomic equivalent of this is to confine laser cooled atoms in a magnetic trap, and evaporate away the hottest atoms "bubbling" at the top of the trap by carefully lowering the sides (figure 3). The hottest atoms have the highest velocity, so they climb the highest up the sides of the magnetic trap. The method of lowering the sides of the magnetic trap is to tune a radio frequency field (about one tenth the frequency of a typical FM radio station) to transfer only the hot atoms into an atomic state which is not confined by the magnetic field so that they fall away. Continuing to cool involves continuing to lower the sides of the magnetic trap. The result is a dense atomic sample at nano-kelvin temperatures. This is dramatically colder than occurs naturally anywhere in the present Universe, and cold enough to observe Bose-Einstein condensation.
 

Figure 3. Evaporative cooling. (a) Atoms held in a magnetic trap. (b) Cooling works by slowly lowering the sides to release the hot atoms at the top.

 
 

4.  Bose-Einstein Condensation and the Atom-laser

The interest at Otago in cooling gases to unimaginably cold temperatures is because we need to create these conditions in order to observe Bose-Einstein condensation. When bosonic atoms trapped in a magnetic field are slowed to near standstill (by evaporative cooling), their fundamental quantum mechanical nature causes them to spread out as pure matter waves merging together and locking into a single coherent quantum state. In effect, the atoms lose their separate identities and become one "super-atom". Although small, typically 0.1 mm across, a Bose condensate can be seen with weakly magnifying lenses and a video camera, so in this sense it is a macroscopic object. The excitement created in the physics community by BEC is because a Bose condensate is to matter what a laser beam is to light: a coherent state in which the usually microscopic laws of quantum mechanics govern the behaviour of a macroscopic system. A Bose condensate allows us to see the quantum nature of matter without having to look at sub-atomic particles. The term "coherent" encapsulates quantum statistical properties, which in the case of laser light are harnessed to make holograms, the navigational gyroscopes found in aircraft, and for high speed fibre optic communications. The Otago BEC Group produced Bose-Einstein condensates in August 1998, making them one of only a handful groups around the world to do so.
 

Figure 4. Cooling to progressively colder temperatures resulting in the formation of a Bose condensate (far right)

 
 

A Bose condensate is a source of coherent matter, has remarkable superfluid-like properties, and can be used to make an atom-laser. The laser- like properties of a Bose condensate were confirmed at MIT when matter wave interference fringes were observed. The atom-laser is the atomic analogy to the optical laser, producing a coherent beam of matter waves rather than a coherent beam of light. An atom-laser consists of a source of coherent matter (a Bose condensate) and a method for extracting a coherent beam of atoms. The extraction process is called "output coupling", and must be done in a way which does not destroy the statistical properties of the coherent source. Simple types of atom-lasers have been demonstrated by a number of research groups, including ours. At Otago we modified the methods used to remove hot atoms during evaporative cooling to make two different sorts of output couplers, both resulting in pulses of coherent atoms.
 

Figure 5.  A pulsed atom-laser output beam.

 
 

In operation the atom-laser is so different from a conventional laser that the comparison may seem ridiculous, and applications are likely to be rather specialised. For example, unlike photons, atoms will not travel very far in air, so that the atom laser must be used in a vacuum. However, the atom-laser is likely to be the instrument of choice for those who wish to explore both fundamental aspects and the potential applications of coherent matter, and the development of the atom laser is considered comparable in scientific importance to the development of the optical laser.