On the path to Bose-Einstein condensate (BEC)

Basic concepts for achieving temperatures below 1 μK

Author: Peter FerjančičMentors: Denis Arčon and Peter Jeglič

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Introduction

• Bose-Einstein condensate – Atomic gasses cooled to VERY low temperatures (<μK)

• Predicted in 1925 by Bose and Einstein• produced by Eric Cornell and Carl Wieman in

1995 – Nobel prize in 2001• Tc ≈ 3.3 (ħ2n2/3 )/ (m kb)• For alkali atoms at n=1014/cm3

Tc ≈ 0.1 μK

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What is Bose-Einstein condensate

• 107 condensed gas atoms• large fraction of the bosons occupy the lowest

quantum state – atoms become indistinguishable

• Basically we have one single “super atom”• Potential uses:– Simulation of solid state physics systems– Precision measurement– Quantum computing

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Used techniques

• Slowing an atomic beam• Optical molasses technique• The magneto-optical trap• Dipole / Magnetic trapping• Evaporative cooling

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Slowing an atomic beam

• Photon momentum: p=ħk• Absorbed photon – fixed direction• Emitted photon – random direction• For λ=589 nm and Na atom, recoil velocity

Δv=3 cm/s

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Slowing an atomic beam

• Need to compensate for Doppler effect– Frequency shift ~1.7 GHz (Natural width ~10 MHz)– Zeeman cooling– Chirp cooling

• Laser cooling –Nobel 1997

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Optical molasses techique

• 3 pairs of counter-propagating laser beams• When moving towards beam, absorption

increases → slowing force• Force proportional to velocity• Doppler cooling limit: ~3 cm/s

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Magneto-optical trap (MOT)

• Atoms diffuse from molasses in seconds for 1 cm wide beam – we should stop them!

• Magnetic quadrupole – B=0 in the center, increases as we move away

• If photons move from centerzeeman eff. causes resonance

• atoms are pushed back by laserbeams → F(x)

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MOT – how to cancel reppeling?

• Circularly polarized lasers: ΔM = +1 for right handed or ΔM = -1 for left handed

• Add polarized laser beams -> F(x)• Change only in rate of photon

absorption• These are OPTICAL forces!!!

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First stage cooling experiment

• First MOT then molasses• Prediction: ~240 μK• Result: an order of magnitude LOWER

temperature

• But why?

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Sisyphus cooling

• A sort of optical pumping mechanism

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Dipole light force

• Refracted light excerts force on object (photon momentum: p=ħk)

• Particles are attracted to areas of high light intensity

• = Optical tweezers• Wavelength is far

from resonance!

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Evaporative cooling

• Atoms with high enough energy escape the potential – taking above average energy with them

• Lowering borders speeds up the process

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The experiment

• Laser slowing of an atomic beam 900 K-> ~5 K• Magneto-optical trap ~300 mK• Optical molasses ~240 μK• Sisyphus cooling ~ 10-100 μK• Evaporative cooling in dipole trap <100 nK• Bose-Einstein condensate!!! • (note: temperatures are informative and

highly dependant on the experiment)

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De jure

• 1 slowing beam

• 3 pairs of counter propagating beams

• 1 pair of coils• 2 dipole force

lasers

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De facto

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Conclusion & future

• What are other potential uses for BEC?– Bikes vs. Light races (c=25 km/h)– Light-> matter -> light transitions- 2007– Single spin addressing– Excellent tool for quantum mechanics

• 2010 – first photon BEC• Cold atoms today under 500 pK

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RY.htm• http://en.wikipedia.org/wiki/Bose-Einstein_condensate• http://theory.physics.helsinki.fi/~quantumgas/Lecture4.pdf• http://www.nobelprize.org/nobel_prizes/physics/laureates/1997/illpres/

doppler.html• http://physicsworld.com/cws/article/news/41246• http://arstechnica.com/science/news/2011/01/pqe-2011-small-atoms-big

-ideas-in-gravity-detection.ars• http://www.deas.harvard.edu/haulab/slow_light_project/remote_revival/

remote_revival.htm• http://prl.aps.org/files/RevModPhys.70.721.pdf• http://www.phys.ens.fr/~dalibard/publi2/EuroPhysNews_98.pdf• http://www.asu.edu/courses/phs208/patternsbb/PiN/rdg/polarize/polari

ze.shtml