1. Laser Cooling and Trapping of Atom
Ying-Cheng Chen, 陳應誠
Institute of Atomic and Molecular Science, Academic Sinica,
中研院原分所

2. Outline Basic idea & concept
Overview of laser cooling and cold atom study
The light force
Doppler cooling for a two-level atom
Sub-Doppler Cooling
Others cooling scheme
Practical issues about a Magneto-Optical Trap (MOT)
Atomic species
Lasers
Vacuum
Magnetic field
Imaging

3. Temperature Landmark
To appreciate something is a good motivation to learn something!
106
103 1
10-3
10-6
10-9
(K)
core of sun
surface of sun
room
temperature
L N2
L He
3He superfluidity
2003 MIT
Na BEC
typical TC
of BEC
MOT
sub-Doppler
cooling
Laser cooling and trapping of atom is a breakthrough to the exploration of the
ultracold world. A 12 orders of magnitude of exploration toward absolute zero temperature from room temperature !!!

4. What is special in the ultracold world?
A bizarre zoo where Quantum Mechanics governs
Wave nature of matter, interference, tunneling, resonance
Quantum statistics
Uncertainty principle, zero-point energy
System must be in an ordered state
Quantum phase transition
~1μm for 100nk

5. Trends in Ultracold Research
Cold Molecule
From atomic to
condensed-matter
physics
Many-body Physics
From Physics
to Chemistry
Cold Plasma &
Rydberg Gas
Cold Atom
From ground to
highly-excited states
From fundamental
to application
From isotropic to
anisotropic interaction
Dipolar Gas
Quantum Computation
Atom Chips…

6. Useful References Books, Review articles
H. J. Metcalf & P. van der Straten, “Laser cooling and trapping”
C. J. Pethick & H. Smith ,“Bose-Einstein condensation in dilute gases”
P. Meystre, “Atom optics”
C. Cohen-Tannoudji, J. Dupont-Roc & G. Grynberg “Atom-Photon interaction”
Review articles
V. I. Balykin, V. G. Minogin, and V. S. Letokhov, “Electromagnetic trapping of cold atoms” , Rep. Prog. Phys. 63 No 9 (September 2000)
V S Letokhov, M A Ol'shanii and Yu B Ovchinnikov Quantum Semiclass. Opt. 7 No 1 (February 1995) 5-40 “Laser cooling of atoms: a review”

7. The Light Force: Concept
absorption
emission
An exchange of momentum &
energy between photon and atom !
Photon posses energy
and momentum !
Net moentum exchange
from the photon to atom
Force on atom

8. Energy and Momentum Exchange between Atom and Photon
Photon posses momentum and energy.
Atom absorbs a photon and re-emit another photon.
always positive, recoil heating
Criteria of laser cooling
If the momentum decrease, and if
the kinetic energy decrease,
where avg stands for averaging over photon scattering events.
A laser cooling scheme is thus an arrangement of an atom-photo
interaction scheme that satisfy the above criteria!

9. The Light force : quantum mechanics
Ehrenfest theorem, the quantum-mechanical analogue of Newton’s second law,
where V(r,t) is the interaction potential.
Interaction potential: for an atom interacting with the laser field, , where d is atomic dipole moment operator.
Semi-classical treatment of atomic dynamics:
Atomic motion is described by the averaged velocity
EM field is treat as a classical field
Atomic internal state can be described by a density matrix which is determined by the optical Bloch equation

10. Validity of semi-classical treatment
Momentum width p is large compared with photon momentum k.
Atom travel over a distance smaller than the optical wavelength during internal relaxation time. (Internal variables are fast components and variation of atomic motion is slow components in density matrix of atom ρ(r,v,t))
Two conditions are compatible only if
If the above conditions is not fullified, full quantum-mechanical treatment is needed. e.g. Sr narrow-line cooling, =27.5kHz ~ ωr=2k/2m=24.7kHz
an upper bound on v
an lower bound on v or
J. Dalibard & C. Cohen-Tannoudhi, J. Phys. B. 18,1661,1985
T.H. Loftus et.al. PRL 93, ,2004

11. The light force for a two-level atom
Where d12=d21 are assumed to be real and we have introduced the Bloch vectors u,v, and w.
Remark: dipole moment contain
in phase and in quadrature
components with incident field.
ρij (or σij)can be determined by the optical Bloch equation of atomic density matrix.

12. Optical Bloch equation
Incoherent part due to spontaneous
emission or others relaxation processes
steady state solution
Isat ~ 1-10 mW/cm2 for alkali atom

13. Two types of forces Without loss of generality, choose At r =0,
Take average over one optical cycle
dipole force or
gradient force
a reactive force
radiation pressure or
spontaneous emission force
a dissipative force
Origin of optical trapping
Origin of optical cooling

14. Light force for a Gaussian beam
Frp
Fdip F k z

15. Spontaneous emission force
From
for steady-state
Decay rate,
For a plane wave
,where Rsp is the flourescence rate.
Max deceleration for Na D2 line !

16. Dipole Force in a standing wave
A standing wave has an amplitude gradient, but not a phase gradient. So only the dipole force exists.
Where s0 is the saturation parameter for each of the two beams that form the standing wave.
For δ<0 (red detuning), the force attracts atom toward high intensity regions.
For δ>0 (blue detuning), the force repels atom away from high intensity regions.

17. Velocity dependent force
Atom with velocity v experiences a Doppler shift kv.
The velocity range of the force is significant for atoms with velocity such that their Doppler
detunings keeps them within one linewidth considering the power broadening factor.

18. Doppler Cooling For δ<0, the force slows down the velocity. δ/
[/k]

19. Doppler Cooling limit
Doppler cooling : cooling mechanism; Recoil heating : heating mechanism
Temperature limit is determined by the relation that cooling rate is equal to heating rate.
Recoil heating can be treat as a random walk with momentum step size k.
Minimum temperature
TD ~ K for alkali atom
For low intensity s0<<1

20. Magneto-optical trap (MOT)
Cooling, velocity-dependent force: Doppler effect
Trapping, position-dependent force: Zeeman effect
1-D case
3-D case

21. SubDoppler cooling
Many cooling schemes allow one to cool atoms below the Doppler limit, or even down to the recoil limit.
Polarization gradient cooling (Sisyphus cooling)
Raman cooling
Velocity-selective-coherent-population-trapping(VSCPT)
cooling …
But we won’t discuss in this course.

22. Part II: Practical Issues about a magneto-optical trap

23. Laser cooling : demonstrated species

24. Atomic species Different atomic species has its unique feature !
(5s5p)1P1
32MHz
2 3P2
1.6MHz
6 2P3/2
5.2MHz
F=5 4 3
(5s5p)3P1
4.7kHz
1083nm 2
cooling
2 3S1
metastable
460.73nm
Broad-line
cooling
689.26nm
Narrow-line
cooling
852.35nm
repumping
~20eV
by discharge 4 3
6 2S1/2
(5s2)1S0
1 0S1
133Cs, alkali metal, I=7/2
88Sr, alkali earth, I=0
4He, nobel gas, I=0

25. Lasers
Diode lasers are extensive use in laser cooling community due to inexpensive cost and frequency tunability.
Diode lasers in external cavity configuration are used to reduce the laser linewidth.
Master oscillator power amplifier (MOPA) configuration is used to increase the available laser power.
ECDL in Littrow configuration
master
Diode laser
ECDL in Littman-Metcalf configuration
Tampered
amplifiier
MOPA

26. Laser frequency stabilization
Frequency-modulated saturation spectroscopy is the standard setup to generate the error signal for frequency stabilization.
Feedback circuits are usually built to lock the laser frequency.
laser
Background subtracted saturation spectrometer
spectrometer
Error signal
Feedback
circuit

27. Vacuum
Two different kinds of vacuum setup are mainly used, one is glass vapor cell, the other is stainless chamber.
Ion pump and titanium sublimation pump are standard setup to achieve ultrahigh vacuum.
Vapor-cell MOT
Chamber MOT

28. Magnetic field Anti-Helmholtz coils for the MOT
Magnetic field reach maximum if the distance between two coils equal to the radius of the coil
Arial field gradient is twice the radial field gradient.
Helmholtz coils for earth-compensation
Magnetic field is most uniform ~ x4 when the distance between two coils equal to the radius of the coil
Earth compensation is critical to get good polarization gradient cooling.
The magnitude of magnetic field scales ~  for different atomic species.

29. Imaging Itransmitted(x,y) I0(x,y) z CCD camera From experiment
From theory
Considering the dark count of CCD
3* = 0~3, depends on laser polarization and
population distribution around Zeeman sublevels

30. How to determine the temperature?
t=200 ms
t=500 ms
t=1000 ms
t=2100 ms
MOT laser
200
400
600
800
1000
1200
1400
1600
1800
1.68
1.7
1.72
1.74
1.76
1.78
1.8
1.82
1.84
1.86
1.88
x 10 -3
delay (us)
Sigma X (m)
data
fit
Magnetic field t
Image beam