bose-einstein condensation

Apr 22, 2023 presentation by Dr. K.Y. Rajpure 1

When Atoms Become Waves


BosonsBosonsFermionFermionss

Satyendra Nath Bose

No two identical fermions can be in the same

quantum state at same time.

Possible to put a large group of atoms in a single quantum

state

Integral multiple spin

Half integral spin

Particles

Enrico Fermi

Obey

Pauli exclusion principle

Phenomenon


Albert Einstein - adapted the work to apply it to other Bosonic particles and atoms. At a finite T, almost all of ples in a Bosonic system would congregate in the GND state. Quantum wave fns of each particle start to overlap,

Atoms get locked into phase with each other,

And loose their individual identity.

"Bose-Einstein condensation"

Bose - statistics for photons (the particles which make up light).

BEC historical background


o Absolute temperature T of a sample is proportionalto the quantity <v²>

o T <v2> / kB

o T is a measure of the velocity fluctuations inthe sample.

Then, the absolute temperature must by definition belarger than zero, and in addition, that if T = 0, then allparticles in the sample must be at rest.

Absolute temperature


5000 K. surface of the sun300 to 400 K. boiling and freezing points of water70 K. the freezing point of N2, high Tc superconductivity3 K. superconductivity and superfluidity.

Now possible to cool atomic systems to one millionth of a degree Kelvin, and even lower.

At these extreme temperatures, the world is an utterly strange place where our everyday's common sense is useless, quantum physics rules with its counterintuitive laws, and atoms behave as waves.

Absolute temp graph


A French prince and waves of matter

de Broglie’s wavelength:

= h / p as p associated .

To understand why it is so useful to think of ultracold atoms aswaves, let us relate their de Broglie wavelength totemperatures.

T <v2>

As p = mv p v p2 v2.

T <p2> T <p>

As = h / p 1/p

The (thermal) de Broglie wavelength of a sample is inverselyproportional to the square root of its temperature,

Colder sample, larger the de Broglie wavelength !!!

T

1


R.T. very small, Ao.

Impossible to observe with visible

light.

To image an atom X- ray. Much

energy destroy atoms

This is why at RT, the wave nature

of atoms is normally irrelevant,

and it is most useful to think of

them as particles.

If T to few K of less, very

large, comparable to, the

wavelength of visible light.

Visible light can impinge on atoms

without destroying them.

de Broglie’s wavelength/ 3


Above "conventional" methods, Magnetic trap 20 nK 2000 Rb atoms, This is the lowest temperature ever achieved.

Laser cooling

1. Atom-Light I nteraction

Spontaneous emissionh = E2 - E1

Momentum conservation, theatom experiences a kick inmomentum by the amountm = h/ in the directionopposite to the direction ofphoton emission.

Intensity of the light beam .

Cooling Atoms


Atom at rest irradiate 2lasers[right & left]

Frequency (Green) is chosen No absorption of a photon

nothing happens.

Now Atom moving [v] Frequencyappears higher; The light seems"more blue" Doppler effect

Frequency shift to v. Absorption Velocity kick: Velocity of the atom

is reduced. Same argument Effects of spontaneous emission.

2. Doppler cooling


3. Below the Doppler limit

Few mK, the so-called Dopplerlimit.

Detailed understanding reqd. By clever choice of electronic

orbits and laser arrangements,possible to force the atoms tomove in much the same way asmarbles on a corrugated roof.

Trick 2 "roofs" atoms jump one other located nearmaxima of the surface

As a result, the atoms areforced to always move "uphill",very much like Sisyphus of theGreek legend. Lose most oftheir energy

Few K for alkali atoms suchas Sodium.

Sisyphus cooling


Quite familiar from everydaylife.cup of coffeeHigh-velocity particles easilyescape from a trap<v2> lower, hence T.Gradually trap depth, T keep .Atomic densityExceedingly low temperatures,T ~ nK

4. Evaporative cooling


How are the atoms trapped?

300 m/s 20 m/s

Oven350 oC

LASER VacuumChamber[MOT]

[

Atoms tended to flow out of the pit at its centre. There they lost

their magnetic orientation because the magnetic field was zero.

By rotating the magnetic field of the atom trap, the hole could be

shut, and in June 1995 the researchers achieved BEC of a few

thousand rubidium atoms with mass number 87.

Method to achieve BEC


Higher Velocity atoms

Medium Velocity atoms Lower Velocity atoms

LASER Magnetic field

How to cool atoms ?

Atoms are cooled by laser beams from all

directions

They are confined by the laser beam and magnetic field

After optical laser cooling, the light is turned OFF and the atom cloud is confined in the magnetic field.

Method to achieve BEC/ 2


LASER and Magnetic Field Arrangements

MOT imagined picture


BEC result/ 1


The three pictures, obtained by the group of W. Ketterle at MIT, show the velocity distribution in the atomic sample, Zero velocity is at the center of the pictures.

Right picture, which corresponds to the lowest temperature, the broad distribution has all but disappeared, all atoms finding themselves in the condensate.

Lower temperatures (middle picture) Curve shape : qualitative change. Two distinct contributions, a broad one quite similar to that of the preceding case, and superimposed to it a sharply peaked one, also centered at v = 0. This contribution : fraction of atoms that form a condensate at the bottom of the trap.

The left picture : relatively high temperature, above the transition from "normal" gas to condensate. Broad velocity distribution with smooth distribution decreasing from the maximum at v = 0.

BEC result/ 4


Ketterle’s first interference

pattern.

The interference pattern between two expanding condensates resembles

that formed by throwing two stones into still

water.

Experimental proof of de Brogile’s hypothesis:

Interference


Atom lasers


Condensate Atoms studied to date


A BEC first achieved at 10:54 a.m. June 5, 1995, in a laboratory at JILA, a joint institute of CU-Boulder and NIST. The apparatus that made it is now at the Smithsonian Institution.

Bose-Einstein condensate of about 2,000 rubidium atoms that lasted for 15 seconds to 20 seconds. New machines can now make condensates of much greater numbers of atoms that last for up to 3 minutes.

Made visible by a video camera, the condensate looks like the pit in a cherry except that it measures only about 20 microns in diameter or about one-fifth the thickness of a sheet of paper.

Some more about BEC…..


Too new and we know too little about it for me to give you an answer. There are also some engineering problems that will have to be solved before BEC can be used for very much.

Jin and DeMarco cooled atoms that are fermions, the other class of quantum particles found in nature. This was important to physicists because the basic building blocks of matter -- electrons, protons and neutrons -- are all fermions.

Made possible by nudging super-cold atoms into a beam, the breakthrough could lead to a new technique for making extremely small computer chips, according to NIST Nobel Laureate William Phillips, who led the team. Eventually, such a device might be able to construct nano-devices one atom at a time.

Today, scientists around the world are manipulating condensates made from a variety of gases to probe their scientific properties. The condensate can be used to form an atomic laser and could one day lead to a better atomic clock.

What is Bose-Einstein condensation good for ?

Applications:


The Royal Swedish Academy

of Sciences has awarded the

Nobel Prize in Physics for Nobel Prize in Physics for

20012001 jointly to Eric A. CornellEric A. Cornell,

Wolfgang KetterleWolfgang Ketterle and

Carl E. WiemanCarl E. Wieman

“for the achievement of Bose-

Einstein condensation in

dilute gases of alkali atoms,

and for early fundamental

studies of the properties of

the condensates”.

Nobel prize 2001


Prof. Pierre Meystre - AvH FellowProfessor of Optical Sciences and PhysicsThe University of Arizona

Dr. C.D. Lokhande - AvH Fellow

My dear participants

bose-einstein condensation

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