Ultracold atoms and molecules
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1 Advanced Experimental Techniques Ultracold atoms and molecules Steven Knoop VU, June 014 1
2 Ultracold atoms laser cooling evaporative cooling BEC Bose-Einstein condensation atom trap: magnetic trap or optical dipole trap Temperature: nk mk Atom number: up to 10 8 Density: up to cm -3 (air cm -3 )
3 LevT lab, Innsbruck 3
4 Lecture 1: Overview of lectures Laser cooling of neutral atoms Trapping of neutral atoms Lecture : Evaporative cooling Bose-Einstein condensation (BEC) Lecture 3: (Ultra)cold molecules Laser cooling of molecules + labtour 4
5 5
6 Lecture 1 Laser cooling of neutral atoms Trapping of neutral atoms 6
7 Atomic level structure Group I, alkali-metal atoms ground state: (closed shells)+ns first excited state: (closed shells)+np n P 3/ S=1/ L=1 J=1/, 3/ I F= I-3/,..., I+3/ F=I-1/, I+1/ n P 1/ fine-splitting hyperfine-splitting D1 D n S 1/ S=1/ L=0 J=1/ I F=I-1/, I+1/ n S+1 L J 7
8 87 Rb Zeeman Paschen-Bach D Zeeman effect: E g F m F m B B m B h 1.4 MHz/G fine-structure hyperfine-structure 8
9 Light-atom interaction Frequency, wavelength, linewidth and lifetime e E g 1 c polarization m Saturation intensity Optical cross section I sat hc di dz ni Beer s law 9
10 Laser cooling and trapping Nobelprize 1997 e e g Doppler effect g Zeeman effect B Chu Cohen-Tannoudji Phillips atomic beam source Zeeman slower Phillips et al, PRL 198 magneto-optical trap (MOT) Raab et al, PRL
11 Radiation pressure atomic beam source 11
12 Radiation pressure atomic beam source (scattering rate) momentum) (photon scatt F 3 sat 3 hc I scatt scatt k kr F max max M k M F a sat sat scatt I I I I R 1
13 Zeeman slower atomic beam source e v0 v az B mbb( z) Zeeman slower 0 k z 1/ v 1 z B B 0 L 0 bias g Zeeman effect m B v z B 0 L 0 v a v 1 0 hv0 m B 0 max z L B B bias /
14 Zeeman slower He* lab, Amsterdam 14
15 Optical molasses e g Doppler effect F molasses k F scatt Fscatt scatt kv F kv kv -v 0 4k I I sat scatt 1 0 F friction force-> molasses 0 0 red-detuned 15
16 Doppler cooling limit randow walk F F abs F abs spont F spont 1 k B T 4 k B T D F Example: Na 10 MHz 40 mk T D Doppler temperature 16
17 Magneto-optical trap 17
18 Magneto-optical trap F MOT F scatt ω kv ω βz F kv ω βz Fscatt kv 0 F scatt 0 z scatt v z k friction force-> molasses 0 mb db dz restoring force -> trap 18
19 Loading schemes background gas vapor cell (Monroe et al PRL 1990) very simple high background pressure (limited lifetime and atom number) slow beam Zeeman slower D-MOT another MOT Zeeman slower MOT 19
20 Fluoresence imaging NaLi lab, Heidelberg R scatt N I sat 1 I Isat 4 I 3D-MOT loading from D-MOT dn dt L N 0
21 Absorption imaging di dz ni Beer s law 3 1 I0 n( x, y) log I( x, Atom Cloud y) n( x, Camera I( x, y) I0 exp n( x, y) y) n( x, y, z) dz I(x,y) I 0 n(x,y) light with atoms light without atoms 1
22 Temperature n(x,y) Absorption imaging for variable expansion time kbt ( t) 0 t m time-of-flight
23 MOT s MOT NaLi lab, Heidelberg first: sodium, Na (1987) latest: holmium, Ho (014) 3
24 Laser cooling of alkali-metal elements example: rubidium ( 87 Rb) cycling transistion F= -> F =3 need repumper F=1 -> F = 4
25 Locking the laser on atomic transition Rb vapour cell / /4 Wedge photodetector Saturated absorption spectroscopy 87 Rb 85 Rb 5
26 Lasers laser cooling Near-resonant laser light, wavelength atom specific Dye laser (visible, tunable) Ti:Sapphire (NIR, tunable) Diode laser (visible-nir) Far off-resonant laser light (IR, NIR, FIR) Nd:YAG (1064nm) Ytterbium fiber laser (1064nm) Erbium Fiber Lasers (1550nm) CO laser (10.6mm) optical dipole trap 6
27 Light frequency and power control: AOM Acousto-Optical Modulator RF Bragg diffraction v f v i nv RF tunable frequency tunable output power fast switch on/off (<ms) 7
28 Trapping of neutral atoms Limitation of laser cooling temperature (sub)-doppler (sub)-recoil density light-assisted collisions reabsorption NaLi lab, Heidelberg Magnetic trap and/or optical dipole trap loaded from MOT (+cmot+optical molasses+optical pumping) evaporative cooling 8
29 Vacuum requirements Collisions with hot background atoms and molecules lead to trap loss loss 1 i ni v i N( t) N0 t exp cross section velocity density v n 8k B T πm P k T B ~ cm, very crude guess (R 1 +R ) v=1.8*10 3 m/s P 10 9 n 510 We need Ultra-High Vacuum (UHV) conditions! 7 cm -3 mbar for 10 s 1 mbar = 100 Pa = 0.75 Torr 9
30 Magnetic trapping U mag ( r) μ B( r) U mag gfm B M F B db dx x db y dy 1 db dz z B x y 4z Quadrupole magnetic trap 30
31 Quadrupole magnetic trap QMT (asymmetry due to gravity) Only low-field seeking states are trappable! 31
32 spin-polarizing Optical pumping F = + F= F=1 m F dark state 3
33 QMT limitation: Majorana loss nonadiabatic spin flips to untrapped states at the magnetic field zero at the center of the QMT loss: heating: N( t) N 0 e T( t) Mt T 0 M M t Solutions: harmonic potential with magnetic field offset -> Ioffe-Pritchard type magnetic trap plugged QMT (with blue detuned laserbeam) hybrid QMT + optical dipole trap m m k B T M 8 m 9 m kb 33
34 Optical dipole trap U dip ( r) d E( r) Re( ) c 0 I( r) scatt ( r) Im( ) c 0 I( r) Chu et al, PRL
35 Optical dipole trap: -level system 0 D<0 red-detuned D>0 blue-detuned 35
36 Optical dipole trap: Rb 0, 0,1 D-line 780nm; D1-line 795nm 5W 50mm Typical wavelengths ODT Rb: 1064 nm, 1550 nm 36
37 Optical dipole trap: exp. realization r z waist Rayleigh length w 0 f w i U 0 P w 0 Rb 1557nm 5W 50mm Crossed dipole trap 37
38 Optical dipole trap Advantages All Zeeman states (lowest spin-state) Mixture of Zeeman states (spinor BEC) Add homogeneous magnetic field (Feshbach resonances) Disadvantages Shallow (<1 mk) Small (<1 mm) MOT -> Magnetic trap -> Optical dipole trap 38
39 Plugged QMT Optical-plug beam prevent atoms from the center of the QMT Blue-detuned (shorter wavelength than optical transition) 39
40 Hybrid QMT+optical dipole trap Add single optical dipole beam to QMT, misaligned from QMT center 40
41 Levitated optical dipole trap U grav =mgz 0.W 0.5W 1W Rb 1557nm 50mm add quadrupole and bias field to compensate gravity magnetic field gradient needed: mg db m dz Example 87 Rb (F=1, m F =1): m=m B / db dz m Rb g m B 30.5 G/cm 41
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