Lecture Trapping of neutral atoms Evaporative cooling Foot 9.6, 10.1-10.3, 10.5 34
Why atom traps? 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 35
Magnetic trapping ) ( ) ( mag r μ r U 36 z M g F F F d d M g U F F mag div 0 z y x z y x d d 1 d d d d z y x z y x e e e ˆ ˆ ˆ 4z y x Quadrupole magnetic trap
Quadrupole magnetic trap QMT (asymmetry due to gravity) Only low-field seeking states are trappable! 37
spin-polarizing Optical pumping F = s + F= F=1 m F - -1 0 1 dark state 38
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 k T M 8 9 m k 39
40 Ioffe-Pritchard magnetic trap y x y x d d d d 0 ˆ ˆ e e y x y x 0 0 0 r r y x r 0 mag 1 ) ( r m U r U r m 0 M g F F r
Ioffe-Pritchard magnetic trap 41
Cloverleaf magnetic trap other type of magnetic traps: QUIC (quadrupole-ioffe-configuration) 4
Advantages Large (>mm) and deep (>mk) Efficient transfer from MOT Easy Magnetic trap Disadvantages Only low-field seeking states Not energetically lowest spin-state (two-body loss) Limited optical access Type of magnetic trap Quadrupole magnetic trap, simple (same coils as MOT), but Majorana heating (no EC), extension plugged QMT or hybrid trap Ioffe-Pritchard magnetic traps, more involved, but no limitation in temperature (EC), most popular cloverleaf (optical access) Atom chips 43
Atom chip (magnetic microtrap) Reichel et al, PRL 1999 44
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 1986 45
Optical dipole trap: -level system 0 D<0 red-detuned D>0 blue-detuned 46
Optical dipole trap: Rb 0, 0,1 D-line 780nm; D1-line 795nm 5W 50m Typical wavelengths ODT Rb: 1064 nm, 1550 nm 47
Optical dipole trap: exp. realization r z waist Rayleigh length P U0 0 Rb 1557nm 5W 50m Crossed dipole trap 48
Optical dipole trap Advantages All Zeeman states (lowest spin-state) Mixture of Zeeman states (spinor EC) Add homogeneous magnetic field (Feshbach resonances) Disadvantages Shallow (<1 mk) Small (<1 mm) MOT -> Magnetic trap -> Optical dipole trap 49
Plugged QMT Optical-plug beam prevent atoms from the center of the QMT lue-detuned (shorter wavelength than optical transition) 50
Hybrid QMT+optical diple trap Add single optical dipole beam to QMT, misaligned from QMT center 51
Levitated optical diple trap U grav =mgz 0.W 0.5W 1W Rb 1557nm 50m add quadrupole and bias field to compensate gravity magnetic field gradient needed: mg d dz Example 87 Rb (F=1, m F =1): = / d dz m Rb g 30.5 G/cm 5
Evaporative cooling 53
Plain evaporative cooling allow the gas to thermalize at a fixed trap depth T U 0 7 Maxwell-oltzmann distribution for T = 1 mk 7*T 54
Forced evaporative cooling dynamically lowering the trap depth 55
Temperature vs. atom loss Figure of merit: ln ln T' N' T N typically a factor 10 lower temperature costs a factor 10 in atom number: = 1 56
Phase-space density vs. atom loss More important figure of merit: ln ln D' N' D N 3 D n d phase-space density d h mk T De roglie wavelength n 0 N 4 kt 3 n 0 m N k T 3/ QMT harmonic trap 57
Speed of evaporation c n v sv 16k T m collision rate mean relative velocity s 8a if c increases: runaway evaporation elastic cross section (T->0 limit) a = scattering length Dubessy et al, PRA 01 58
Runaway evaporation t loss =30 s & =10 G/cm good collisions / bad collisions R>00 R<100 elastic two-body collisions collisions with background gas inelastic two-body collisions inelastic three-body collisions 59
Lifetimes of trapped ultracold gases n L n L n L n 1 3 3 Inelastic collisions in which release of energy >> trap depth L 1 : background collisions L : spin exchange & spin relaxation L 3 : three-body recombination 60
Evaporative cooling in ODT r U 0 z U P 0 Forced evaporative cooling by lowering the power of optical dipole beam...... also reduction of trap frequencies n 0 N m k T 3/ 61
Evaporative cooling in magnetic trap m F RF 1 F= 0-1 - F=1 U 0 h D RF MW -1 RF 0 1 or h ( D) RF h ( ) HFS ( D) MW h D U0 MW HFS microwave horn RF coil RF or MW knife 6
Evaporative cooling in magnetic trap MW knife on F=, m F = -> F=1,m F =1 63... no reduction of trap frequencies
Elastic cross section V(r) +: even l F+F: odd l X+X : all l r lim ( k) k0 l k l 1 lims ( E) k0 lim k0 4 sin k ( k) 0 ()4a a: scattering length tan 0( k) a lim k0 k 64
Scattering length E b = - ħ /(a ) orkowski et al, PRA 013 a 0 a 0 repulsive attractive a 65
osons vs. Fermions for T->0 +: even l F+F: odd l X+X : all l identical bosons: s-wave scattering (l=0) distinguishable particles: s-wave scattering (l=0) identical fermions: p-wave scattering (l=1) s 8a s 4a s T How to do evaporative cooling with fermions? Different spin states (Zeeman or hyperfine) Different isotopes (e.g. 6 Li with 7 Li) Different species (e.g. 6 Li with Na) 40 K sympathetic cooling DeMarco et al, PRL 1999 66
Sympathetic cooling Example : 6 Li+ 174 Yb (Ivanov et al, PRL 011) 67