Ion traps. Trapping of charged particles in electromagnetic. Laser cooling, sympathetic cooling, optical clocks

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1 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

2 The Penning trap AAMOP

3 The Penning trap AAMOP

4 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

5 Time-of-flight signal from a Penning trap AAMOP

6 Image charge induced current In general the resistor R is replaced by a frequency resonant RLC-circuit with a high Q AAMOP

7 Core of a Penning trap AAMOP

8 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

9 Mass measurements determine the binding energy of a system AAMOP

10 Every field requires different accuracy AAMOP

11 Development of accuracy in mass spectroscopy AAMOP

12 The g factor of a bound particle Energy splitting between levels Corrections due to QED AAMOP

13 Contributions to the g factor AAMOP

14 Larmor and cyclotron frequency Larmor frequency: spin flip frequency AAMOP

15 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 ( C ) ) = (3) (3) theoretical value value g J ( J ( C ) ) = (10)(44) measurement Error Error budget: budget: δg/g δg/g = exp. exp. systematics and and statistics δg/g δg/g = knowledge of of electron electron mass mass (Van (Van Dyck Dyck 1995) 1995) AAMOP

16 Double Penning traps for g factor AAMOP

17 Spin flips of single electrons AAMOP

18 Spin flip probability and analysis AAMOP

19 g e = (82) g C = (1)(1)(4) g 0 = (15)(44) From g C and g O factor the currently most precise value of the electron s mass was derived: m e = (4) u (to be compared to the four-times less precise CODATA value) m e = (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 = for an ion with mass A = 200 corresponds to a measurement of its electronic binding energy to δe= 20 ev. AAMOP

20 Recent results with 28 Si 13+ AAMOP

21 The g factor of a free proton Magnetic moment involved is three orders of magnitude smaller: Frequency shift hard to measure AAMOP

22 High gradient analysis trap A large magnetic field anisotropy magnifies the energy splitting Phase-sensitive detection of cyclotron motion enhances accuracy AAMOP

23 Spin flip probability Compare g-factors of proton and antiproton: Test of matter-antimatter symmetry S. Ulmer et al., Phys. Rev. Lett. 106, (2011) AAMOP

24 VP SE Experiment: 460.2±4.6 ev Theory : ±0.5 ev 2000 nuclear size The HITRAP project 2005 higher-order nuclear charge number, Z AAMOP s Lamb Shift, ΔE / Z 4 [mev]

25 Cooling scheme for HCI in HITRAP AAMOP

26 Cooling scheme for HCI in HITRAP AAMOP

27 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

28 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

29 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

30 Linear Paul trap AAMOP

31 Linear Paul trap AAMOP

32 The rotating potential in the Paul trap AAMOP

33 Motion in the pseudopotential AAMOP

34 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

35 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

36 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