Marc ReppAG Weidemüller

Quantum dynamics of atomic and molecular systemsRuprecht-Karls-University Heidelberg

Physics Institute

Emmi seminar PI Heidelberg, 16.11.2009

Evaporative Cooling

What is evaporative cooling?

In the Office: In the Lab:

Remove hottestatoms

Thermalization

Trappedatoms

Evaporation in the Lab

K. Dieckmann, Thesis, University of Amsterdam (2001)

Outline

Thermalization of an ultracold gas

Model of evaporation

Efficiency of evaporative coolingSpeed of evaporative coolingInfluence of loss processes

Conclusion

Outline

Thermalization of an ultracold gas

Model of evaporation

Efficiency of evaporative coolingSpeed of evaporative coolingInfluence of loss processes

Conclusion

Thermalization of an ultracold gas

Elastic collisions in a dilute and cold gas

k3

k2

k4k1

Dilute gasonly binary collisions

Elastic collision of two particelsExchange of energy and momentum

S-wave cross-section and collision rate

Thermal Equlibrium: Ocupation number (for Bosons)

Zero – energy limitUnitärity limit

Thermalization of an ultracold gas

D.W. Snoke and J.P. Wolfe, Phys. Rev. B . 39, 4030 (1989)

Numerical simulation of the thermalizationStarting with an uneqilibrium

e.g. f(k)= f0 d (k-k0)

Probability for bosons with wavevectors (k1 , k2) to scatter to (k3, k4):

Scattering rate into/ out of state with momentum k:

Equlibrium: Only 4 collision events necessary (harmonic quadrupole trap: 2.7 collisions)

Davis et all., PRL 74, 5202 (1995)

Thermalization of an ultracold gasMeasurement of thermalization

Density of a thermalizedsample

in a anisotropic harmonictrap (σx≠σy):

Elongation of the cloudealong one axisleads to oszillationalong this axis

Elastic collisions distributethe energy to all degreas of freedom

Thermalization when the aspectratio reached his original value

Blue: Potential with an aspect ratio of 2:1Red: Density distributions along two axis

Mesurement principle

Radial direction Axial direction

Thermalization of an ultracold gas

Davis et all., PRL 74,5202 (1995)

Á

Thermalization of sodium atoms in a quadrupol trap with an aspect ratio of 2:1

t= 1s for n = 5x1010 atoms/cm³

t = 13s for n = 4x109 atoms/cm³

Determinating the elastic cross section:

n = 5x1010 atoms/cm³

n = 4x109 atoms/cm³

Thermalization near a resonance

C. Chin et all., arXiv 0812.1496v2

Feshbach -Resonances Zero-Energy resonance in 133Csin F=3 mF=+3

Magnetic Field [G]

M. Lee et all., Phys. Rev. A 76,12720 (2007)

Scat

terin

gle

ngth

Thermalization near a resonance

Thermalization at a=0

V. Vuletic et all., PRL 82,1406 (1999)

-> no thermalization at a=0

Thermalization rate for Cs near 17G

Magnetic Field [G]

Thermalization near a resonance

Thermalization in the unitarity limit

Collision rate now depends on the relative velocity: Monte-Carlo simulations: 10.7 collisions instead of 2.7 needed for thermalization

M. Arndt et all., PRL 79, 625 (1997)

Messurement of the thermalization Temperatur dependent

cross-section

T=53 µK

T=24.5 µK

T=6.7 µK

Magnetic Field [G]

Outline

Thermalization of an ultracold gas

Model of evaporation

Efficiency of evaporative coolingSpeed of evaporative coolingInfluence of loss processes

Conclusion

Evaporation in the Lab

K. Dieckmann, Thesis, University of Amsterdam (2001)

Model of evaporative cooling

Truncation parameter

Truncated Boltzman distribution

Evaporation rate:Removing all particels with an energie E>e

For large η:fraction of atoms with E>e

Rate of evaporation:

Ratio of elastic collisions and time constant for evaporation:O. Luiten et all., Phys. Rev. A 53, 381 (1996)

Remove atoms with potential energy

The system looses the energy

Total Energy of the system:

Model of the evaporation

Decrease of the temperature

Temperature change:

K. Dieckmann. Thesis, University of Amsterdam (2001)

O. Luiten et all., Phys. Rev. A 53, 381 (1996)

Density and phasespace-density behavior:

Model of the evaporation

Phasespace density D (for BEC: Dª1 )

Increase of the phasespace-density

K. Dieckmann. Thesis, University of Amsterdam (2001)

O. Luiten et all., Phys. Rev. A 53, 381 (1996)

Outline

Thermalization of an ultracold gas

Model of evaporation

Efficiency of evaporative coolingSpeed of evaporative coolingInfluence of loss processes

Conclusion

Loss ProcessesCollisions in an ultracold sample

“Good collisions”: Elastic collisionsThermalization

“Bad collisions”: Inelastic collisionsLoos of atoms

• Inelastic one-body collisions– Collisions with background gas

• Inelastic two-body collisions– Dipolar and spin relaxation

• Inelastic three-body collisions– Three-body recombination

Na

H

Loos Mechanism for n=nBEC

W. Ketterle and N. J. van Druten, Advances in Atomic, Molecular, and Optical Physics 37, 181 (1996)

Speed of evaporation

Change of the elastic collision rate:Limit for Runaway evaporationIn a harmonic trap

W. Ketterle and N. J. van Druten, Advances in Atomic, Molecular, and Optical Physics 37, 181 (1996)

Elasitic collision rate increasesfor („Runaway Evaporation“)

Efficiency of evaporative cooling

Increase of phase space density(per 100 elastic collisions)

Efficiency of one step:

Efficiency of the whole process:

W. Ketterle and N. J. van Druten, Advances in Atomic, Molecular, and Optical Physics 37, 181 (1996)

Maximizing phase-space density Calculated Phasespace densityincrease

Efficiency of evaporative cooling:Calculated efficiency parameter

tll/ tloss = ∞= 500= 200= 100

= 50

linear potentiales

parabolic potentialestll/ tloss=5000

=1000

=200

Efficiency of evaporative cooling

C. Hung et all. ,Phys. Rev. A 78, 011601 (2007)

Evaporation of Cs atoms in an opticaltrap at different truncation parameters

Evaporation in an optical dipole trapProblem:Lowering the trap depth also decreasesthe collision rate

Solution:Evaporation via a magnetic gradiant

Red:

Black:

Conclusion

Thermalization of an ultracold gas

Model of evaporation

Efficiency of evaporative coolingSpeed of evaporative coolingInfluence of loss processes

Literature• W. Ketterle, N. J. van Druten,

Evaporative cooling of atoms,Advances in Atomic, Molecular, and Optical Physics 37, 181 (1996)

• Luiten, O. J., Reynolds, M. W., Walraven, J. T. M.,Kinetic theory of the evaporative cooling of a trapped gas,Phys. Rev. A 53, 381 (1996)

• D. W. Snoke, J. P. Wolfe,Population dynamics of a Bose gas near saturation,Phys. Rev. B 39, 4030 (1989)

• K. B. Davis, M.-O. Mewes, M. A. Joffe, M. R. Andrews, W. Ketterle,Evaporative Cooling of Sodium Atoms,Phys. Rev. Lett. 74, 5202 (1995)

• Chen-Lung Hung, Xibo Zhang, Nathan Gemelke, Cheng Chin,Accelerating evaporative cooling of atoms into Bose-Einstein condensation in optical traps,Phys. Rev. A 78, 011601 (2008)

• M. Arndt, M. Ben Dahan, D. Guery-Odelin, M. W. Reynolds, J. Dalibard,Observation of a Zero-Energy Resonance in Cs-Cs Collisions,Phys. Rev. Lett. 79, 625 (1997)

• Vladan Vuletic, Andrew J. Kerman, Cheng Chin, Steven Chu ,Observation of Low-Field Feshbach Resonances in Collisions of Cesium Atoms,Phys. Rev. Lett. 82, 1406 (1999)

• Kai Dieckmann

Bose-Einstein Condensation with High Atom Number in a Deep Magnetic TrapUniversity of Amsterdam, 2 March 2001 ;Thesis advisor: Prof. Dr. J.T.M. Walraven

from www.staff.science.uva.nl/~walraven/walraven/Theses.htm