laser_cooling_notes

8/7/2019 laser_cooling_notes

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PHY 411 / 412 / 436

QUANTUM OPTICS

Prof. Mark Fox

A sub-module of the

ASPECTS OF MODERN PHYSICS module

Spring Semester

10 lectures


2/27

Module Synopsis

Course text:Fox, M.

Quantum Optics, an IntroductionOxford University Press, 2006

I. Laser Cooling & Bose-Einstein Condensation(Lectures 1-5)

II. Photon statistics (Lectures 6-9)

III. Quantum Information Processing

(Cryptography) (Lecture 10)


3/27

Part I: Laser cooling & BEC

Reading: Fox, Quantum Optics, Chapter 11

Other useful books

Foot, Atomic Physics, Oxford, 2005, Chapters 9-10Demtrder, Atoms, Molecules and Photons, 12.1Haken & Wolf, Physics of Atoms & Quanta, 22.6, 23.11

Topics to be covered Techniques for laser cooling of atoms

Theoretical limits on the temperature Bose-Einstein Condensation of atoms


4/27

Useful resources

Web resources for laser cooling & BEC:

http://nobelprize.org/nobel_prizes/physics/laureates/1997/

http://nobelprize.org/nobel_prizes/physics/laureates/2001/

http://www.lkb.ens.fr/recherche/atfroids/tutorial/index2.htm *http://www.colorado.edu/physics/2000/bec/

http://bec01.phy.georgiasouthern.edu/bec.html/

* in French !


5/27

Atomic temperatures

oven, temp T

2

B

2

B

1 33 D

2 2

1 1

1 D2 2x

mv k T

mv k T

=

=

Principle of equipartition of energy:kBTper degree of freedom

atomic beam

B3mp

k Tv

m=

vmp = most probable velocity


6/27

Doppler cooling mechanism

0Lab

sorption

frequency

0

absorption

frequency

0a

bsorption

frequency

2

v

v

v

(a)

L

L

(b)

(c)

absorption only for case (b) laser must be tuned below

the transition frequency must be tuned as

atoms cool

velocity = vx

atom laser beam

L = 0 +

=0

xv

c


7/27

Absorption-emission cycles

t= 0

t=

1. Laser photon impinges on atom

2. Atom promoted to excited stateat t = 0

3. Atom re-emits at mean time in a random direction

Average momentum kick of (h/) in time d

d

x x

x

p p hF

t

= =


8/27

Limits on Doppler cooling

stop

min stop

2

min

B min

min

B

initial

per cycle /

22

~

2

x x

x

x

x

p muN

p h

mut Nh

m u

d h

k T h v

Tk

=

=

Number of absorption

- emission cycles tostop atom,time to do so, anddistance travelled

Doppler limit temperature

= 1 / 2 (natural linewidth) Factor of 2 from stimulated

emission


9/27

Sisyphus Cooling

Sisyphus

Laser cooling experiments using counter-propagatingbeams worked better than expected !

Tfinal < TDoppler

Caused by the Sisyphus cooling effect


10/27

Mechanism of Sisyphus cooling

Energy

MJ = 1/2

MJ = +1/2

abso

rptione

mission

x

excited state: J= 3/2

Position

ground state: J= 1/2

http://www.lkb.ens.fr/recherche/atfroids/tutorial/index2.htm

7. LE REFROIDISSEMENT DATOMES PAR LASER

counter-propagating

beams createinterference pattern Atomic levels shifted

by the AC-Starkeffect


11/27

Recoil limit temperature

p= h/

2 2

B recoil 2

2

recoil 2

B

1 ( )

2 2 2

p hk T

m mh

Tmk

= =

=

Photon recoil ultimately

limits Twhile atom isundergoing absorption-emission cycles


12/27

Magneto-optic traps

x

y

z

i

i

Magnetic quadrupole:

B (x2 + y2 4z2)1/2

Atomic energy shift:E= gJBBMJ

attractive for MJ

> 0

repulsive for MJ< 0

Optical Molasses6 counter propagating beams

+ magneto-optic trap


13/27

Experimental cooling kit

sodium

oven

tapered solenoid

cooling beam

probe

pulse

molasses

regioncamera

escapin

gatoms

precooling region

Lasers tuned to sodium D2 line (3s2S1/2 3p 2P3/2, 589 nm)

Use tapered solenoid to tune atoms as they cool

Further details in Dr Phillips Nobel Prize lecture:

see http://www.physics.nist.gov/News/Nobel/1997nobel.html

600 C

~2.5 K 40 K


14/27

Temperature achieved

0 10 20 30 400

200

400

600

Laser detuning (MHz)

Temperature

(K)

Doppler limit

Sodium D2 line at 589 nm: = 16 ns

Tmin (Doppler) = 240 K

Tmin (recoil) = 2.4 K


15/27

Ion traps

Cooling

laser

magnetic field

+

+

+

+

trapped ions

Ions easily trapped byelectric & magnetic fields

Two common designs:Penning & Paul traps

Use laser to cool ions to

Doppler limit temperature

Can trap and control singleions: used for quantum

information processing

Penning trap: Bfield traps in (x,y)plane & Efield traps in zdirection


16/27

Bose-Einstein Condensation

Main reference

Fox, Quantum Optics, Chapter 11

Other useful reading

Mandl, F., Statistical Physics, 2nd Edition,Wiley (1988), Section 11.6

Web resources:http://www.colorado.edu/physics/2000/bec/http://nobelprize.org/nobel_prizes/physics/laureates/2001/

http://ucan.physics.utoronto.ca/


17/27

Basic concepts of BEC

1 10 100 1000 100000

1

2

3

4

Temperature (K)

CVpe

rmolecule/kB

3/2 kB

5/2 kB

7/2 kBvibrational

motion rotational

motion

translationalmotion

?

Classical result: CV = kB per degree of freedom

Classical motion freezes out when kBT Equant

Heat capacity

of gas ofdiatomicmolecules


18/27

Quantization of translational motion

Third law of thermodynamics: CV 0 as T 0

Translational motion must eventually be quantized

at sufficiently low T

Most gases liquefy and solidify before quantumeffects observed for the translational motion.(Helium is the exception.) Atoms/molecules in liquidor solid phase are not non-interacting.

Need to get to very low temperatures but with non-interacting atoms/molecules. ie need to cool a gasto very low T without it liquefying.


19/27

Bose-Einstein condensation

From a certain temperature on, the moleculescondense without attractive forces, that is, theyaccumulate at zero velocity. The theory is pretty, butis there some truth to it.A. Einstein, letter to P. Ehrenfest, 29 Nov, 1924

Examples

- superfluid liquid helium TC = 2.17 K- cold atom gas TC 10

6 K

- Cooper pairs in superconductors, neutron stars

- excitons


20/27

Transition temperature

deB

22

BdeB

1/ 3

deBB

2 / 32

CB

1 3~

2 2 2

~ ~3

~3

p hk T

m m

h V

Nmk T

h NT

mk V

=


21/27

Statistical mechanics of BEC

BEC = accumulation of particles in the ground state

Fermions (e.g. spin particles) subject to Pauli

exclusion principle. Can only put one particle in theground state.

Hence only bosons (i.e. integer spin particles) can

undergo BEC.

2 / 32

C B

3/ 2

C

0.0839

( ) 1

h NT

mk V

Tf T

T

=

=

Condensation

temperature

Fraction in

condensed phase


22/27

Atoms: boson or fermion ?

Ions no good for BEC because they repel, sothat high densities are not possible. Hence need

to use neutral atoms.

Electrons, protons, and neutrons are spin fermions

Satom = Selectrons + Snucleus

Nelectron = Nproton in neutral atom.

Hence boson for Nneutron even.

Examples: 4He, 23Na, 87Rb


23/27

Recipe for BEC

magnetic trap

potential

x

Use laser cooling to cool atoms to near Trecoil

Confine atom cloud by using a magneto-optic trap

Turn off laser and reduce potential of trap toinstigate evaporative cooling.

most energeticatoms escape and

temperature goes

down

reduce magnetic field


24/27

Observation of BEC

atomic

gas

resonantlaserlight

t= 0

t= te

free

expansion

D ~ vte

Measure velocity distribution by time of flight

expansion and shadow image technique

shadow of atomic gason screen / camera


25/27

Experimental Results

BEC first observed in 1995 for 87Rb and 23Na

Now observed in many other atomic gases7

Li,1

H,85

Rb,4

He,41

K,133

Cs,174

Yb,52

Cr, Details of experiments from

http://ucan.physics.utoronto.ca/

Significant differences between:

2 / 32

CB

3/ 2

C

0.0839

( ) 1

h NTmk V

T

f T T

=

=

1/ 3CB

3

C

0.94

( ) 1

T Nk

T

f T T

=

=

BEC in free space BEC in harmonic trap


26/27

BEC experimental data

0.2

mm

87Rb

5S1/2 5P3/2

transition at780nm

Cooling with

laser diodes N/V~

2.51018 m-3

TC ~ 170 nK

See Anderson et al, Science269, 198 (1995)

http:/jilawww.colorado.edu/bec

400nK

200nK

50nK


27/27

Atom lasers

1.8 mm

3.9mm

1 mm

Trap is attractive only for MJ= +1/2 states

Apply RF pulse to tip the spin: trap becomes

repulsive and ejects pulses of atoms Interference between two atom pulses provescoherence

See Ketterle, Rev. Mod. Phys. 74, 1131 (2002)

23Na 200 Hz rep rate

10

5

10

6

atoms / pulse

http://cua.mit.edu/ketterle_group/Projects_1997/atomlaser_97/atomlaser_comm.html

Durfee and Ketterle, Optics Express, 2, 299 (1998)

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