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

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

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Temperature Landmark

To appreciate something is a good motivation to learn something!

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 !!!

What is special in the ultracold world?

• A bizarre zoo where Quantum Mechanics governs
• Wave nature of matter, interference, tunneling, resonance

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• Quantum statistics
• Uncertainty principle, zero-point energy
• System must be in an ordered state
• Quantum phase transition

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~1μm for Na @ 100nk

Cold Atom

Cold Molecule

Cold Plasma &

Rydberg Gas

Dipolar Gas

Many-body Physics

Quantum Computation

Atom Chips…

From Physics

to Chemistry

From ground to

highly-excited states

From isotropic to

anisotropic interaction

From fundamental

to application

From atomic to

condensed-matter

physics

Trends in Ultracold Research

Useful References

• Books,
• 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) 1429-1510.
• 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”�

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The Light Force: Concept

Photon posses energy

and momentum !

An exchange of momentum &

energy between photon and atom !

Force on atom

Net moentum exchange

from the photon to atom

absorption

emission

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

If the momentum decrease, and if

the kinetic energy decrease,

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where avg stands for averaging over photon scattering events.

Criteria of laser cooling

A laser cooling scheme is thus an arrangement of an atom-photo

interaction scheme that satisfy the above criteria!

The Light force : quantum mechanics

• Ehrenfest theorem, the quantum-mechanical analogue of Newton’s second law,

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where V(r,t) is the interaction potential.

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• Interaction potential: for an atom interacting with the laser field, , where d is atomic dipole moment operator.

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• 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

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Validity of semi-classical treatment

• Momentum width Δp is large compared with photon momentum k.

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• 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))

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• Two conditions are compatible only if

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• If the above conditions is not fullified, full quantum-mechanical treatment is needed. e.g. Sr narrow-line cooling, Γ=2π×7.5kHz ~ ω_r=²k/2m=2π×4.7kHz

or

an upper bound on v

an lower bound on v

J. Dalibard & C. Cohen-Tannoudhi, J. Phys. B. 18,1661,1985

T.H. Loftus et.al. PRL 93, 073001,2004

The light force for a two-level atom

ρ_ij (or σ_ij)can be determined by the optical Bloch equation of atomic density matrix.

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.

Optical Bloch equation

Incoherent part due to spontaneous

emission or others relaxation processes

steady state solution

I_sat ~ 1-10 mW/cm² for alkali atom

Two types of forces

radiation pressure or

spontaneous emission force

a dissipative force

dipole force or

gradient force

a reactive force

Without loss of generality, choose

At r =0,

Take average over one optical cycle

Origin of optical trapping

Origin of optical cooling

Light force for a Gaussian beam

z

k

F_rp

F_dip

F

Spontaneous emission force

Decay rate,

,where R_sp is the flourescence rate.

Max deceleration for Na D₂ line !

From

for steady-state

For a plane wave

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.

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.

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Doppler Cooling

For δ<0, the force slows down the velocity.

[Γ/k]

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.

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For low intensity s₀<<1

Minimum temperature

T_D ~ 100-200 μK for alkali atom

Magneto-optical trap (MOT)

• Cooling, velocity-dependent force: Doppler effect
• Trapping, position-dependent force: Zeeman effect

1-D case

3-D case

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.

Part II: Practical Issues about a magneto-optical trap

Laser cooling : demonstrated species

Atomic species

• Different atomic species has its unique feature !

852.35nm

6 ²P_3/2

5.2MHz

6 ²S_1/2

F=5

4

3

2

4

3

cooling

repumping

¹³³Cs, alkali metal, I=7/2

(5s²)¹S₀

(5s5p)³P₁

4.7kHz

(5s5p)¹P₁

32MHz

460.73nm

Broad-line

cooling

689.26nm

Narrow-line

cooling

⁸⁸Sr, alkali earth, I=0

1 ⁰S₁

2 ³S₁

metastable

~20eV

by discharge

⁴He, nobel gas, I=0

2 ³P₂

1.6MHz

1083nm

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

ECDL in Littman-Metcalf configuration

master

Tampered

amplifiier

MOPA

Diode laser

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.

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Background subtracted saturation spectrometer

laser

spectrometer

Error signal

Feedback

circuit

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.

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Vapor-cell MOT

Chamber MOT

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 ~ Γ for different atomic species.

Imaging

I₀(x,y)

I_transmitted(x,y)

z

From experiment

Considering the dark count of CCD

CCD camera

From theory

3* = 0~3, depends on laser polarization and

population distribution around Zeeman sublevels

How to determine the temperature?

MOT laser

Magnetic field

Image beam

t

t=200 μs

t=500 μs

t=1000 μs

t=2100 μs