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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 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 Temperature Landmark To appreciate something is a good motivation to learn something! core of sun surface of sun L N 2 106 103 L He room temperature 1 3He sub-Doppler superfluidity cooling 10-3 MOT 10-6 2003 MIT Na BEC 10-9 0 (K) typical TC of BEC 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 h – – – – 2mkBT ~1μm for Na @ 100nk Quantum statistics Uncertainty principle, zero-point energy System must be in an ordered state Quantum phase transition Trends in Ultracold Research Cold Molecule From atomic to condensed-matter Many-body Physics physics From Physics to Chemistry Cold Atom From fundamental to application Quantum Computation Atom Chips… Cold Plasma & Rydberg Gas From ground to highly-excited states From isotropic to anisotropic interaction Dipolar Gas 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” The Light Force: Concept E i p ki E ' s ' p ks absorption emission An exchange of momentum & energy between photon and atom ! Photon posses energy and momentum ! dp F dt Force on atom Net moentum exchange from the photon to atom Energy and Momentum Exchange between Atom and Photon • Photon posses momentum and energy. • Atom absorbs a photon and re-emit another photon. p p' p (ki k s ) 2 2 2 2 ( ki k s ) ( p' p ) K K ' K ( ki k s ) v 2m 2m p' (ki ks ) p always positive, recoil heating If Criteria of laser cooling ( ki k s ) v 0 the momentum decrease, and if ki avg ( ki k s ) v avg 2 ( ki k s ) the kinetic energy decrease, 2m avg 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! ks The Light force : quantum mechanics • Ehrenfest theorem, the quantum-mechanical analogue of Newton’s second law, • Interaction potential: for an atom interacting with the laser field, Vˆ d E d p d2 F V (r , t ) m 2 r dt dt 2 p ˆ H V (r , t ), 2m where V(r,t) is the interaction potential. 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 , Validity of semi-classical treatment • Momentum width p is large compared with photon momentum k. k p 1 • an upper bound on v 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)) v 1 , or kv 1 an lower bound on v • Two conditions are compatible only if • If the above conditions is not fullified, full quantummechanical treatment is needed. e.g. Sr narrow-line cooling, =27.5kHz ~ ωr=2k/2m=24.7kHz 2 k 2 2m 1 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 U V d E F U d E E eˆE0 (r ) cos(t (r )) it it d Tr ( d ) 12d 21 21d12 d12 ( 12e 21e ) 2d12 (u cos t v sin t ) Where d12=d21 are assumed to be real and we have introduced the Bloch vectors u,v, and w. 1 ( 12 21 ) 2 1 v ( 12 21 ) 2i 1 w ( 22 11 ) 2 u 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. Optical Bloch equation d 1 d [H , ] dt i dt dij dii ( ) spon ii , ( ) spon ij dt dt 2 Incoherent part due to spontaneous emission or others relaxation processes d11 i 22 ( 21 12 ) dt 2 d 22 i 22 ( 12 21 ) dt 2 d 12 i ( i ) 12 ( 22 11 ) dt 2 2 11 22 1, where (r ) dE0 (r ); 12 12 exp( it ); 0 S 0 I / I sat ; I sat steady state solution s0 2 i 22 ; 21 2 1 s0 (2 ) 2( 2 i )(1 s0 ) 2 1 (2 ) hc 33 Isat ~ 1-10 mW/cm2 for alkali atom Two types of forces Without loss of generality, choose At r =0, (r 0) 0 (E ) j e j (cos tE0 sin tE0 ) d j 2(d12 ) j (u cos t v sin t ) Take average over one optical cycle F ( d j E j ) avg (eˆ d12 )(uE0 vE0 ) j dE0 (r ) dE0 (r ) F Fdip Frp ( )( 12 21 ) ( )i ( 12 21 ) 2 2 dipole force or gradient force a reactive force Origin of optical trapping radiation pressure or spontaneous emission force a dissipative force Origin of optical cooling Light force for a Gaussian beam Frp k Fdip F z Spontaneous emission force d11 i From 22 ( 21 12 ) dt 2 i ( 12 21 ) 22 for steady-state 2 Decay rate, (r ) k r ; k ; E0 0!! For a plane wave Frp k 22 k Rsp Rsp ( ) 22 ,where Rsp is the flourescence rate. S0 2 1 S 0 (2 ) 2 Max deceleration a k 50000 g , for Na D2 line ! 2m Dipole Force in a standing wave • A standing wave has an amplitude gradient, but not a phase gradient. So only the dipole force exists. E (r , t ) eˆx E0 cos kz cos t ( 2 ) Fdip 4 2 2 4 2 2 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. Fdip U 2 2 U ln[ 1 2 ] 2 2 4 Velocity dependent force Atom with velocity v experiences a Doppler shift kv. s0 Frp k 2 1 s0 (2( k v ) ) 2 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. k v 2 1 s0 Doppler Cooling F F F s0 k F 2 1 s0 [2 ( kv) ]2 8k 2s0 v kv 4 F v , if ( ) 1 2 2 (1 s0 (2 ) ) For δ<0, the force slows down the velocity. [/k] δ/ 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. p x2 2k 2 E heat m v2 s0 2 1 s0 ( 2 ) 2 p x2 2m E cool F v v 2 k BT 2 2 1 s0 ( 2 ) 2 k BT 4 2 For low intensity s0<<1 k BT 2 ( ) 2 2 Minimum temperature k BTD , when, 2 2 TD ~ 100-200 K 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 • 1. 2. 3. 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 ! (5s5p)1P1 32MHz F=5 6 2P3/2 5.2MHz 2 3P2 1.6MHz 4 (5s5p)3P1 4.7kHz 3 2 1083nm 2 3S1 metastable cooling 852.35nm repumping 460.73nm Broad-line cooling 689.26nm Narrow-line cooling ~20eV by discharge 4 6 2S1/2 133Cs, 3 alkali metal, I=7/2 (5s2)1S0 88Sr, alkali earth, I=0 1 0S1 4He, nobel gas, I=0 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 MOPA Tampered amplifiier ECDL in Littman-Metcalf configuration 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 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 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. 18 16 Axial magnetic gradient (G/cm) 14 12 10 Coil radius=6 cm 8 Current=5 A 6 Turn number=120 4 2 0 0 5 10 15 coil distance(cm) 20 25 30 Imaging n ( x, y , z ) CCD camera Itransmitted(x,y) I0(x,y) z From experiment From theory I t I 0 ( x, y )e OD( x , y ) OD ( x, y ) n( x, y, z ) absl ( x, y ) I I dark OD ( x, y ) ln( 0 ) I t I dark OD( x, y)dxdy n( x, y, z)l ( x, y)dxdy Considering the dark count of CCD abs abs N 3* 2 1 abs 2 1 I I s (2 ) 2 3* = 0~3, depends on laser polarization and population distribution around Zeeman sublevels How to determine the temperature? 2 (t ) 02 v 2t 2 v 2 k BT m t=200 s t=500 s t=1000 s MOT laser 1.88 t=2100 s x 10-3 data fit 1.86 1.84 Magnetic field t Sigma X (m) 1.82 1.8 1.78 1.76 Image beam 1.74 1.72 1.7 1.68 200 400 600 800 1000 delay (us) 1200 1400 1600 1800