Ion traps Trapping of charged particles in electromagnetic fields Dynamics of trapped ions Applications to nuclear physics and QED The Paul trap Laser cooling, sympathetic cooling, optical clocks Coulomb crystals and molecular ions AAMOP 2011-2012 2012-01-18 1
The Penning trap AAMOP 2011-2012 2012-01-18 2
The Penning trap AAMOP 2011-2012 2012-01-18 3
The Penning trap Charged particles stored with a superposition of a magnetic field and a static electric field. B field forces the particle into a cyclotron motion Confinement in the B-field direction by electrodes creating a electrostatic potential minimum Ion motion in three degrees of freedom: three uncoupled harmonic oscillations (reduced cyclotron, axial, and magnetron oscillation Cyclotron oscillation: 24 MHz Axial oscillation: 360 khz Magnetron oscillation: 2.5 khz AAMOP 2011-2012 2012-01-18 4
Time-of-flight signal from a Penning trap AAMOP 2011-2012 2012-01-18 5
Image charge induced current In general the resistor R is replaced by a frequency resonant RLC-circuit with a high Q AAMOP 2011-2012 2012-01-18 6
Core of a Penning trap AAMOP 2011-2012 2012-01-18 7
Bound-state QED and fundamental constants: g-factor measurements in a series of elements up to U 91+ low-z electron mass m e medium-z fine-structure constant a high-z test of bound-state QED AAMOP 2011-2012 2012-01-18 8
Mass measurements determine the binding energy of a system AAMOP 2011-2012 2012-01-18 9
Every field requires different accuracy AAMOP 2011-2012 2012-01-18 10
Development of accuracy in mass spectroscopy AAMOP 2011-2012 2012-01-18 11
The g factor of a bound particle Energy splitting between levels Corrections due to QED AAMOP 2011-2012 2012-01-18 12
Contributions to the g factor AAMOP 2011-2012 2012-01-18 13
Larmor and cyclotron frequency Larmor frequency: spin flip frequency AAMOP 2011-2012 2012-01-18 14
g-factor of the bound electron in HCI Larmor precession frequency of the bound electron ω L = g 2 J e m e B B Cyclotron frequency of the trapped ion ω c = Q M ion B g m M L e J 2 c ion = ω ω Q e measurement external input parameter g J ( J ( 12 12 C 5+ 5+ ) ) = 2.001 2.001 041 041 590 590 18 18 (3) (3) theoretical value value g J ( J ( 12 12 C 5+ 5+ ) ) = 2.001 2.001 041 041 596 596 4 (10)(44) measurement Error Error budget: budget: δg/g δg/g = 5 10 5 10-10 -10 exp. exp. systematics and and statistics δg/g δg/g = 2 10 2 10-9 -9 knowledge of of electron electron mass mass (Van (Van Dyck Dyck 1995) 1995) AAMOP 2011-2012 2012-01-18 15
Double Penning traps for g factor AAMOP 2011-2012 2012-01-18 16
Spin flips of single electrons AAMOP 2011-2012 2012-01-18 17
Spin flip probability and analysis AAMOP 2011-2012 2012-01-18 18
g e = 2.0023193043737 (82) g C = 2.001041596 (1)(1)(4) g 0 = 2.0000470254 (15)(44) From g C and g O factor the currently most precise value of the electron s mass was derived: m e =0.0005495799096(4) u (to be compared to the four-times less precise CODATA value) m e =0.0005495799110(12) u Investigating ions with high nuclear charge Z would allow for an alternative determination of the fine-structure constant since the g factor of the ground state of a hydrogen-like ion to lowest orders is given by Nuclear ground-state properties such as radius, nuclear polarization, or (in case of nuclei with spin) nuclear magnetic moments can be determined for stable and long-lived nuclei. An accuracy of δm/m = 10-10 for an ion with mass A = 200 corresponds to a measurement of its electronic binding energy to δe= 20 ev. AAMOP 2011-2012 2012-01-18 19
Recent results with 28 Si 13+ AAMOP 2011-2012 2012-01-18 20
The g factor of a free proton Magnetic moment involved is three orders of magnitude smaller: Frequency shift hard to measure AAMOP 2011-2012 2012-01-18 21
High gradient analysis trap A large magnetic field anisotropy magnifies the energy splitting Phase-sensitive detection of cyclotron motion enhances accuracy AAMOP 2011-2012 2012-01-18 22
Spin flip probability Compare g-factors of proton and antiproton: Test of matter-antimatter symmetry S. Ulmer et al., Phys. Rev. Lett. 106, 253001 (2011) AAMOP 2011-2012 2012-01-18 23
VP SE 1991 1996 Experiment: 460.2±4.6 ev Theory : 464.26±0.5 ev 2000 nuclear size 10-1 10-2 10-3 10-4 The HITRAP project 2005 higher-order 10 20 40 60 80 100 nuclear charge number, Z AAMOP 2011-2012 2012-01-18 24 1s Lamb Shift, ΔE / Z 4 [mev]
Cooling scheme for HCI in HITRAP AAMOP 2011-2012 2012-01-18 25
Cooling scheme for HCI in HITRAP AAMOP 2011-2012 2012-01-18 26
Laser cooling Light force is due to multiple photon scattering Interaction with a directed laser beam transfers a momentum hk for each absorbed photon Spontaneous emission is isotropic: zero net momentum transfer Spontanteous force is limited by saturation AAMOP 2011-2012 2012-01-18 27
Magneto-optical trap (MOT) v F + F - 2 counterpropagating beams, tuned below resonance (δ<0). Doppler shift δ v =kv brings 1 beam closer to resonance: Capture in velocity space. Lithium: v c =4m/s; 13.3mK 1D-toy model of a (J=0 J =1)- MOT Zeeman-shift δ by B-field gradient adds position dependent detuning: Restoring force Cooling and trapping in position space Net force: F + + ( δ ( v, z ) ) + F ( δ ( v, z ) ) F η v κ z Cooling limit: photon momentum hk futher cooling towards BEC: evaporation AAMOP 2011-2012 2012-01-18 28
Linear Paul trap 2r e 2r 0 RF is applied to all electrodes confinement in radial direction DC is applied to end cap electrodes confinement in z-direction AAMOP 2011-2012 2012-01-18 29
Linear Paul trap AAMOP 2011-2012 2012-01-18 30
Linear Paul trap AAMOP 2011-2012 2012-01-18 31
The rotating potential in the Paul trap AAMOP 2011-2012 2012-01-18 32
Motion in the pseudopotential AAMOP 2011-2012 2012-01-18 33
Slowing down atoms with light Light force due to photon scattering Interaction with a laser beam transfers a momentum hk for each absorbed photon Spontaneous emission is isotropic zero net momentum transfer Spontanteous force is limited by saturation (maximum rate due to lifetime) laser beam momentum transfer n hk isotropic emission of n photons AAMOP 2011-2012 2012-01-18 34
Optical molasses red detuning velocity of atom Atoms moving toward the laser experience a force roughly proportional to their velocity: friction Several laser beams generate a dense, viscous atom cloud AAMOP 2011-2012 2012-01-18 35
Magneto-optical trap (MOT) v F + F - 2 counterpropagating beams, tuned below resonance (δ<0). Doppler shift δ v =kv brings 1 beam closer to resonance: Capture in velocity space. Lithium: v c =4m/s; 13.3mK Zeeman-shift δ by B-field gradient adds position dependent detuning: Restoring force Cooling and trapping in position space Net force: F + + ( δ ( v, z ) ) + F ( δ ( v, z ) ) F η v κ z Cooling limit: photon momentum hk futher cooling towards BEC: evaporation AAMOP 2011-2012 2012-01-18 36