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**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

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**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! 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 !!!

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**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

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**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…

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**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”

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**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

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**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!

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**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

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**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, =27.5kHz ~ ωr=2k/2m=24.7kHz 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

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**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.

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**Optical Bloch equation**

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

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**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

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**Light force for a Gaussian beam**

Frp Fdip F k z

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**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 !

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**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.

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**Velocity dependent force**

Atom with velocity v experiences a Doppler shift kv. 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. δ/**

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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

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**Magneto-optical trap (MOT)**

Cooling, velocity-dependent force: Doppler effect Trapping, position-dependent force: Zeeman effect 1-D case 3-D case

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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.

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**Part II: Practical Issues about a magneto-optical trap**

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**Laser cooling : demonstrated species**

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**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

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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

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**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

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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

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**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.

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**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

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**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

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