BOSE EINSTEIN CONDENSATION

Asish.B.GeorgeThe King’s school,

Kollam, Kerala, Indiaasishbgeorge516@gmail.com

Bose Einstein condensation, the realization of the principles of quantum physics into visibility at macroscopic scales, is one of the most exotic phenomena physics has seen. BEC is in itself the manifestation of the weird and abstract nature of quantum mechanics, its life and working, right under the naked eye.

History

The 20th century was only taking the first steps and the idea of quantum was still a not-so-digestible concept among the physicists. All the foundational principles of classical physics, dominated by the laws of newton, were just going to be rewritten. The blur and weirdness of quantum physics were already dimming the well lit, ‘absolute’ ideas and formulations of the past centuries. Planck’s idea of quantization sparked off the century, while Einstein, Bohr and the other eminent physicists had been chewing on the concept with experiments after experiments. It was at this lap of time, that Satyendranath Bose, an Indian physicist derived the Planck law for black-body radiation by treating the photons as a gas of identical particles. The paper was sent to Einstein for review. Einstein generalized Bose's theory to an ideal gas of identical atoms or molecules for which the number of particles is conserved and, in the same year, predicted that at sufficiently low temperatures the particles would become

locked together in the lowest quantum state of the system. This occurrence to a class of particles known as bosons was the first theoretical prediction of what we now know as the Bose-Einstein condensate. Einstein’s justification for his theory was that if particles were waves, as was supposed by de Broglie’s new idea, then they should be subject to the same statistics as photons. This was the first use and reference in the literature to de Broglie waves—quantum mechanics would be developed about a year after this paper!

Introduction

Matter is made of matter waves. The concise conceptual summary of the famous Wave -particle duality, an integral foundational stone of quantum mechanics is that “We detect particles, but they propagate as waves” where, the debroglie wavelength = h/(mass * velocity)

The simple reason why we do not perceive the wave nature of matter lies more or less in our answer to the question: how do we perceive something as a wave? Consider sound; the property of sound diffraction at edges of an obstacle shows us it is a wave,but when you similarly place the case of light, the property is not as vividly observed i.e. the bending /diffraction of light is lesser. This is because light is having a million times smaller wavelength than sound. And when it comes to matter waves the wavelength is even smaller. And so, if you could note the relation between wavelength and the wave property, in these comparisons

it becomes vivid that matter wavelengths are so small, for the wave nature to be observed.

But, there lies an important relation between this matter wavelength and temperature which was actually a simple theoretical derivation in the whole thinking of Bose and Einstein. The equation could be literally simplified to show an important relationship: debroglie wavelength = constant* (temperature)^(-1/2). This relationship simply meant that, the cooler the matter was cooled, the more bigger the debroglie wavelength became.

BEC - coming to the picture

At room temperature the matter wavelength is smaller than an atom. Matter is all the time wave packets or quantum mechanical waves, but at very short wavelengths (athigh temperatures), those wave packets are much localized and we are able to follow the motion of those wave packets as if they were particles or miniature billiard balls!

But when the cooling brings matter to micro or nano-scales of temperature, the debroglie wavelength becomes quite big, big enough to be comparable to the interatomic distances in the gas. The weird thing that happens at these ultra low temperatures is the fact that the debroglie wavelengths become so long that it equals the spacing between the atoms under consideration. At this point, the new form of matter, the BEC, is born. As the smearing or spread of the matter waves increases, eventually there is more than one atom in each cube of dimension ^.dB. The wave functions of adjacent atoms then "overlap", causing the atoms to lose their identity, and the behavior

of the gas is now governed by quantum statistics. Bose-Einstein statistics dramatically increase the chances of finding more than one atom in the same state, and we can think of the matter waves in a Bose gas as "oscillating in concert". All the particles oscillate in phase, in unison, identically and the individuality of the atoms is lost as the matter forms one giant matter wave, which is the BEC. The result is Bose—Einstein condensation, a macroscopic occupation of the ground state of the gas.

Having a macroscopic fraction of the particles is in the same quantum mechanical state, or the indistinguishability of identical particles has interesting consequences such as those related to super fluidity or superconductivity. The difference between normal, usual matter and the BEC can be seen analogous to the light from a bulb and a laser beam respectively.

Criterion for BEC

All matter cannot form BEC. Even from the idea Einstein borrowed from Bose, it is clear that only those atoms that behave similarly to photons could show this property. More clearly only those particle species called bosons, which can at the same time occupy the same quantum mechanical state, to which the Pauli’s exclusion principle does not apply, and whose behavior is as predicted by the Bose-Einstein statistics can form BEC.

The second specification is the temperatures needed. The temperatures should be sufficiently lower, such that it results in matter waves with wavelengths comparable

to the interatomic distances, which can overlap and become one giant matter wave.

The other point worth notice, was actually one of the first baseless criticisms to the newly found idea of BEC. It was the case of density. For example, in water the BEC cannot be realized, due to the formation of molecule, or cluster formation and solidification due to the relatively strong interactions between the particles. But otherwise BEC should form at 1 K in water. The only other way this mountain of difficulty could be crossed was to take ultra cooled dilute gases, with very low densities. BEC could form in these. But the price that needed to be payed to finally witness this BEC having a lifetime of seconds to minutes, was a temperature that would be the lowest ever attained!

This one requirement had almost been that one obstacle which was strong enough to keep physicists for years in great trouble, until time and technology brought novel cooling methods that could in fact bring about temperatures a million times colder than the coldest places on the universe. BEC was no longer the pot of gold at the end of the rainbow; it was an attainable objective!

The cooling experimental setup employs a combination of laser cooling and forced evaporative cooling to produce cold and dense atomic clouds in a vacuum system. A double magneto-optical trap system captures and cools up the atoms using laser light. Although responsible for achieving temperatures as low as 0.03 mK, the light sets a lower limit for the temperature. To overcome this limitation, the gas is transferred into a magnetic trap, where it is

further cooled by radio-frequency evaporation. This method selectively removes the hottest atoms from the trap, so that the ones left behind are colder and denser on average, pretty much like how the usual evaporation happens to a cup of hot coffee. After seconds of evaporative cooling, the critical temperature is reached and a Bose-Einstein condensate forms in the center of the trap.

Conclusion and future directions

For the 21st century, we have switched from a quantum reductionist approach to single atoms and have begun a quantum constructivist approach. The objective is to start building up systems of atoms that are assembled completely at the quantum level. BEC is of tremendous interest to condensed matter physicists because you can study collective behavior: exciting collective excitations of the condensate, making sound waves, or stirring the atoms to create vortices and vortex lattices. You can visualize them, you can observe them form in real time.

A quantum computer is a system of atoms where every single one of the bits can be separately controlled and interrogated on the quantum level. Atomic physicists can see single atoms with lasers. We can put them in a trap, couple them together, and interrogate them. This is a promising route to realize quantum computers. We may be able to contribute to nano-fabrication using this quantum control of atoms. Instead of trying to get smaller and smaller instruments to controllably deposit or remove materials, we may be able to fabricate structures on the nanometer length scale by controlling the

quantum state of atoms and putting them into a quantum system exactly where we want them.

References

Wikipedia

Britannica online encyclopedia

Colorado physics 2000