Introduction to BEC

Dallin Durfee (Ph.D. 1999) wrote this introduction into our research around 1997:

For those of you who aren’t familiar with our work, perhaps a few questions need to be answered…

What is the purpose of your atom trap?

We use our atom trap to trap and cool sodium atoms to extremely low temperatures. By cooling the atoms to just 0.000001
degrees centigrade above absolute zero (-273 degrees C), we can study quantum mechanical effects which are completely
obscured at higher temperatures. One special phenomenon that we study is called Bose-Einstein condensation.

What does your experiment look like?

It looks like a bunch of vacuum flanges bolted together and then covered with miles and miles of electrical cables and water tubing.
The vacuum chamber sits on top of an optics table, and several racks of electronics surround the table. Two computers control the
experiment. Next door to the atom trap is a climate-controlled room where our lasers and most of the optics for the experiment
can be found. Light from argon-ion R6G dye lasers are available from this room. Light from these lasers is split into several beams,
conditioned and shuttered, and sent through a tube which connects the laser room with the room that the experiment sits in.

What is quantum mechanics?

Quantum mechanics is a way to describe the laws of the universe by thinking of everything as waves. Quantum mechanics tells us
that you, your dog, and the computer that you are reading this on are all waves, just like waves on water or radio waves. If you drop
a rock into a pond and look at the wave that it creates, it is difficult to say where the wave begins or ends because it doesn’t have
sharp edges. In fact, as the wave spreads, it becomes increasingly difficult to say where the wave ends and the undisturbed part of
the pond begins. And if we drop two rocks into a pond side by side, when the waves created by both rocks begin to overlap interesting
patterns will appear. Some points in the pattern will be motionless as the waves pass through it. At those points whenever the peak
of one wave passes over it, the valley of the other wave passes at the same time. The two waves cancel each other out and leave an
undisturbed spot on the pond. At other points wave crests from both waves arrive at the same time. These spots fluctuate even more
than they would if we had dropped a single rock into the pond. Quantum mechanics tells us that all matter, including me, you and
your cat, exhibits these same wavelike properties.

The wave-like nature of matter is very apparent in the structure of atoms. In larger objects, like the ones we deal with in our every
day world, the wave-like nature is undetectable. In other words, it is easy to see that an electron orbiting an atom is a wave. But the
fact that your cat is a wave is obscured by its mass and thermal energy. The laws of physics that Isaac Newton and Galileo discovered
are really only approximations to the more fundamental laws of quantum mechanics.

In our experiment we take a gas of many atoms (about 5 to 10 million) and by lowering the temperature we make
the atoms wavelengths very long. This makes our atoms behave in ways that would have startled Sir Isaac.

For a more comprehensive introduction to quantum mechanics there are several good web pages you can read. One is maintained
by the University of Exeter. For a simpler and more entertaining introduction to modern physics (including quantum mechanics),
head to your local library and check out “Mr. Tompkins in Wonderland,” or “Mr. Tompkins in Paperback,” by George Gamow
(Cambridge University Press 1993 sbn 0 521 44771 2).

How are the atoms trapped?

The atoms start out in an oven which is held at 350 degrees centigrade. These hot atoms are allowed to escape through a hole
in the oven and shoot out in a beam traveling at about 800 meters per second (1800 miles per hour). We aim a laser beam in the
opposite direction of the atomic beam. The laser beam hits the atoms and slows them down to about 20 meters per second
(45 miles per hour) at the center of our vacuum chamber, where a magneto-optical trap (MOT) captures them. The MOT traps
the atoms with six laser beams coming in from all directions. These beams push the atoms into the center of the chamber.
After collecting a large number of atoms in the MOT, we turn off the lasers and turn on a large magnetic field which confines
the atoms magnetically. In the magnetic trap we cool the atoms down to very low temperatures and study them.

How are the atoms cooled?

The technique which we use to get extremely cold atoms is called rf-induced evaporation. It is very similar to the way
evaporation works in a cup of hot coffee. A cup of coffee is made up of many molecules flying around and bumping into each other.
The temperature of the coffee is just a measure of the average energy that these quickly moving molecules have. From time to time
two molecules will collide in such a way that one of the two ends up with most of the energy, sometimes even gaining enough energy
to fly out of the cup. Since these molecules are going relatively fast compared to the rest of the molecules, they take with them more
than their fair share of energy, and the molecules which are left behind have less energy on average than they did before the
fast molecules shot out. For every molecule that is kicked out, the temperature of the coffee decreases a tiny amount.

In our trap we actively induce evaporation using radio waves. Ground state sodium atoms can have several different spin orientations.
Atoms in one of the orientations are attracted to weak magnetic fields. These are the ones which are trapped in our experiment.
A different spin orientation is attracted to high magnetic fields. Since our magnetic trap has a magnetic field minimum at the center,
these “strong-field seeking” atoms are pushed out of the trap. To induce evaporation, we simply use radio waves to flip the spins of
the most energetic atoms in the trap. With their spins flipped, they fly out of the trap. Since we only eject the most energetic atoms,
they take away more than their fair share of energy. When the rest of the atoms re-thermalize (by bouncing off of each other
several times), the net energy per atom has dropped, and the atom cloud is cooler.

What is a Bose-Einstein condensate?

In the early part of this century, as quantum mechanics was just being discovered, it was found that all particles can be divided
into two classes. Fermions, named after Enrico Fermi, obey the “Pauli exclusion principle,” that no two identical fermions can
be in the same quantum state at the same time. This means that fermionic systems will have many energetic particles flying
around even as the temperature goes down to absolute zero, since only one particle can be in the lowest energy state.

The other type of particles are called Bosons, named after Satyendra Nath Bose. Bose, an Indian physicist, worked out the
statistics for photons (the particles which make up light). Albert Einstein then adapted the work by Bose to apply it to other Bosonic
particles and atoms. While doing this, Einstein found that not only is it possible for two Bosons to share a quantum state, but that
they actually prefer being in the same state. He predicted that at a finite temperature, almost all of the particles in a Bosonic system
would congregate in the ground state. When this happens, the quantum wave functions of each particle start to overlap, the atoms
get locked into phase with each other, and loose their individual identity. This phenomena was named “Bose-Einstein condensation.”
Using this effect it is possible to put a large group of atoms in a single quantum state and study the wave-like nature of matter.

For a time, Einstein’s prediction was considered to be a mathematical artifact or even a mistake. Then in the 1930’s, while Fritz London
was investigating superfluid liquid helium, he realized that the phase transition in liquid helium could be understood in terms of
Bose-Einstein condensation. The analysis of liquid helium was muddied, however, by the fact that helium atoms in a liquid interact
strongly with one another. For many years now scientists have been working towards the creation of a Bose condensate in a less
complicated system. It turned out that laser cooling combined with rf evaporation of alkali atoms was the key to make this possible.
In the summer of 1995, BEC was reported by scientists at
JILA, followed by similar reports from RICE and from our lab here at MIT.
Since that time, all three groups have been busy studying the properties of Bose-Einstein condensates.

Additional Notes on Atom Lasers

A brief commentary by Wolfgang Ketterle
Dept. of Physics and Research Laboratory of Electronics, MIT


Recent work at MIT has realized an atom laser. In this note, the concept and properties of an atom laser are discussed, and also the techniques which were necessary to demonstrate the atom laser.

What is an atom laser?

An atom laser is analogous to an optical laser, but it emits matter waves instead of electromagnetic waves. Its output is a coherent matter wave, a beam of atoms which can be focused to a pinpoint or can be collimated to travel large distances without spreading. The beam is coherent, which means, for instance, that atom laser beams can interfere with each other. Compared to an ordinary beam of atoms, the beam of an atom laser is extremely bright. One can describe laser-like atoms as atoms “marching in lockstep”. Although there is no rigorous definition for the atom laser (or, for that matter, an optical laser), all people agree that brightness and coherence are the essential features.

The parts of an atom laser

A laser requires a cavity (resonator), an active medium, and an output coupler. In the MIT atom laser, the “resonator” is a magnetic trap in which the atoms are confined by “magnetic mirrors”. The active medium is a thermal cloud of ultracold atoms, and the output coupler is an rf pulse which controls the “reflectivity” of the magnetic mirrors.

The gain process in an atom laser

The analogy to spontaneous emission in the optical laser is elastic scattering of atoms (collisions similar to those between billiard balls). In a laser, stimulated emission of photons causes the radiation field to build up in a single mode. In an atom laser, the presence of a Bose-Einstein condensate (atoms that occupy a “single mode” of the system, the lowest energy state) causes stimulated scattering by atoms into that mode. More precisely, the presence of a condensate with N atoms enhances the probability that an atom will be scattered into the condensate by N+1.

In a normal gas, atoms scatter among the many modes of the system. But when the critical temperature for Bose-Einstein condensation is reached, they scatter predominantly into the lowest energy state of the system, a single one of the myriad of possible quantum states. This abrupt process is closely analogous to the threshold for operating a laser, when the laser suddenly switches on as the supply of radiating atoms is increased.

In an atom laser, the “excitation” of the “active medium” is done by evaporative cooling – the evaporation process creates a cloud which is not in thermal equilibrium and relaxes towards colder temperatures. This results in growth of the condensate. After equilibration, the net “gain” of the atom laser is zero, i.e., the condensate fraction remains constant until further cooling is applied.

Unlike optical lasers, which sometimes radiate in several modes (i.e. at several nearby frequencies) the matter wave laser always operates in a single mode. The formation of the Bose condensate actually involves “mode competition”: the first excited state cannot be macroscopically populated because the ground state “eats up all the pie”.

The output of an atom laser

The output of an optical laser is a collimated beam of light. For an atom laser, it is a beam of atoms. Either laser can be continuous or pulsed – but so far, the atom laser has only been realized in the pulsed mode. Both light and atoms propagate according to a wave equation. Light is governed by Maxwell’s equations, and matter is described by the Schroedinger equation. The diffraction limit in optics corresponds to the Heisenberg uncertainty limit for atoms. In an ideal case, the atom laser emits a Heisenberg uncertainty limited beam.

Differences between an atom laser and an optical laser

  • Photons can be created, but not atoms. The number of atoms in an atom laser is not amplified. What is amplified is the number of atoms in the ground state, while the number of atoms in other states decreases.
  • Atoms interact with each other – that creates additional spreading of the output beam. Unlike light, a matter wave cannot travel far through air.
  • Atoms are massive particles. They are therefore accelerated by gravity. A matter wave beam will fall like a beam of ordinary atoms.
  • A Bose condensates occupies the lowest mode (ground state) of the system, whereas lasers usually operate on very high modes of the laser resonator.
  • A Bose condensed system is in thermal equilibrium and characterized by extremely low temperature. In contrast, the optical laser operates in a non-equilibrium situation which can be characterized by a negative temperature (which means “hotter” than infinite temperature!). There is never any population inversion in evaporative cooling or Bose condensation.

Historical roots

The atom laser is based on the quantum-mechanical wave nature of particles. Louis Victor de Broglie, during his Ph.D. thesis in 1923, predicted that all particles have wave properties and gave a famous formula stating that the wavelength of a particle varies inversely with its speed. (The wavelength equals Planck’s constant divided by the mass and the speed of the particle.) In 1917, Albert Einstein discovered theoretically the stimulated emission of light which is the basic mechanism generating laser light. In what was then unrelated work, in 1924, he and Satyendra Nath Bose predicted a novel form of matter which forms at very low temperatures which is now called a Bose-Einstein condensate.

Potential applications of an atom laser

Although an atom laser has now been demonstrated, major improvements are necessary before it can be used for applications, especially in terms of increased output “power” and reduced overall complexity. Laser-like atoms exist only in an ultrahigh vacuum environment, and so it is unlikely that the atom laser will ever improve supermarket scanners or CD players! However, there are many applications in fundamental research and industry where atomic beams are used, e.g., atomic clocks, atom optics, precision measurements of fundamental constants, tests of fundamental symmetries, atomic beam deposition for chip production (atom lithography), and, more generally, nanotechnology. The atom laser may have an impact on all of these applications. Today, if you have a demanding job for light, you use a laser. In the future, if there is a demanding job for an atomic beam, you may be able to use an atom laser.

The steps from a Bose condensate to an atom laser

An important intermediate step towards the atom laser was the realization of Bose-Einstein condensation (BEC), which was achieved in 1995 by a group at Boulder and Ketterle’s group at MIT. (In 1996, two more groups, a group at Rice and a second group at Boulder, observed BEC). The Bose condensate has frequently been compared to photons in a laser beam, but what was missing was a controlled way of extracting a beam of atoms and a method for determining whether the Bose condensed atoms are coherent as the photons in a laser beam. Both these steps have now been taken by the MIT team, thus realizing the atom laser.

Realization of an output coupler for a Bose condensate

(Phys. Rev. Lett., January 27, 1997) An output coupler is one of the essential elements of a laser. It allows the controlled extraction of atoms from the Bose condensate, i.e. the generation of a (quasi-) continuous beam or multiple pulses. Before the MIT group realized an output coupler, the entire condensate was either trapped or freely expanding.

The MIT group achieved the controlled extraction of atoms in the following way: Magnetically trapped atoms can be regarded as atoms bouncing back and forth between magnetic mirrors. The magnetic mirror is 100% reflective for atoms with their magnetic moment anti-parallel to the magnetic field, and fully transmissive for the opposite orientation. The MIT group tilted the magnetic moment of the atoms by a variable angle, thus adjusting the reflectivity of the magnetic mirror. This was done by using short pulses of an oscillating magnetic field.

When the MIT group realized the output coupler in July 1996, they had all the elements for an atom laser together. However, a crucial feature of a laser had yet to be demonstrated: the coherence of the condensed atoms. This was achieved in November 1996 through the observation of high-contrast interference between two Bose condensates.

Demonstration of coherence of a Bose condensate

(Science, January 31, 1997) It should be noted that laser light has two important features: Brightness and coherence. Brightness does not necessarily mean high absolute power, but the concentration of power into the direction of propagation and in a small frequency interval (monochromatic light). This is the reason why a laser pointer is brighter than the sun! The second important feature is coherence, i.e., all the photons in a laser form one macroscopic wave (they “oscillate synchronously”).

In the case of atoms, a Bose condensate is very cold and coherent. Coldness corresponds to brightness in the optical case, because a very low temperature restricts the quantum states which are accessible to the atoms to the lowest states of the system (Brightness in the optical case also means restricting the photons to a few modes of the laser resonator). It is the low energy of the condensate which was studied in previous experiments and used to identify the Bose condensate. However, although coldness and coherence are related, there has been some controversy about how coherent the atomic Bose condensate would be. It has been argued that the atoms first become very cold, but then it would take much longer (maybe forever) for the coherence to build up. Furthermore, collisions among the atoms and with background gas were predicted to destroy the coherence. The MIT results resolve these issues. They prove that a Bose condensate is coherent, and that a coherent beam of atoms can be extracted from it.

The proof of the coherence was obtained by observing a high contrast interference pattern when two Bose condensates overlapped. The MIT researchers could directly photograph this pattern which had a period of 15 micrometer, a gigantic length for matter waves. (Room temperature atoms have a matter wavelength of 0.04 nm, 400,000 times smaller). The interfering condensates were propagating with an energy of 0.5 nanokelvin – the coldest temperature ever reported. However, temperature has lost its meaning in this regime, it is only used as a measure for the residual (non-thermal) energy of the atoms.

When matter waves interfere destructively, it is as if one atom plus one atom give zero atoms! Of course, the matter is not destroyed, and the atoms appear elsewhere. Nevertheless, the interference of streams of atoms from separate sources is a dramatic phenomenon.

Other techniques used to realize the atom laser

A variety of schemes to realize an atom laser have been discussed during the last several years. The MIT group chose a particularly simple way. They cooled an atomic gas to extremely low temperatures until it spontaneously formed a Bose-Einstein condensate with “laser-like” properties, and then extracted these atoms into output pulses (see above).

The MIT work was based on powerful cooling techniques which were used to reduce the temperature of a sodium gas by a factor of a billion, from the temperature of an oven to around one microkelvin. These cooling techniques are laser cooling (the key techniques were invented at NIST (W. Phillips), Bell Labs/Stanford (S. Chu), MIT (D. Pritchard)) and evaporative cooling (developed at MIT (T. Greytak, D. Kleppner)). Many other groups in the atomic physics and condensed matter communities have contributed to these efforts (e.g., Amsterdam, Boulder, Cornell, Harvard, Paris). Between 1992 and 1995, Ketterle’s group pioneered ways to combine laser cooling and evaporative cooling. The combined cooling was key to the observation of Bose-Einstein condensation in Boulder in June and at MIT in September of 1995.

In laser cooling, the atoms are bombarded with laser light. The frequencies and polarizations of the laser beams are chosen in such a way that the photons emitted by the atoms are slightly more energetic than the absorbed photons. The energy difference is responsible for the cooling effect. After absorbing and emitting about 100,000 photons, the atoms reach a temperature of about 100 microkelvin. Subsequently, the atoms are cooled to BEC using evaporative cooling. In this technique, the hottest atoms are removed from the atomic sample, thus reducing the average energy (and therefore the temperature) of the remaining atoms. The same principle cools a cup of coffee and water in a bathtub.

The atoms have not only to be cooled, but also very well insulated from the room-temperature environment. This is accomplished by purely magnetic confinement inside an ultrahigh vacuum chamber.

The MIT team

Ketterle’s team includes potsdocs Christopher Townsend and Hans-Joachim Miesner, and graduate students Michael Andrews, Marc-Oliver Mewes, Dallin Durfee, and Dan Kurn. Over the years, 4 postdocs, 8 graduate students and 7 undergraduate students have contributed to the experiment. The experiment started as a collaboration with Prof. David E. Pritchard (until 1993). Funding was provided by ONR, NSF, JSEP, and the Packard foundation.