Tunneling in optical lattice clocks

Transcription

1 Tunneling in optical lattice clocks - RTG 1729 Workshop Goslar - K. Zipfel, A. Kulosa, S. Rühmann, D. Fim W. Ertmer and E. Rasel

2 Outline Motivation Spectroscopy of atoms Free vs. trapped atoms Horizontal lattice & tunneling Magnesium Current setup & limits Vertical lattice & tunneling suppression Klaus Zipfel 2

3 PPolarisability/(10-39 Cm 2 /V) Motivation Optical atomic clocks with neutral atoms Spectroscopy of trapped atoms Trap should not change clock states Magic Wavelength No 1 st order differential light shift Tightly confined atoms Singlet 1 S 0 Triplet P Lamb-Dicke-Regime 1 st order Doppler- & recoil-shift vanish Realization of tight trap: Lattice Periodic potential Tunneling Magic Wavelength 1 S 0 3 P 0 Wavelength / nm Klaus Zipfel 3

4 Excitation Spectroscopy of atoms Free atoms Dispersion relation of a free atom % Frequency Limiting effects Recoil shift: Accuracy Doppler broadening: Stability Klaus Zipfel 4

5 Energy Excitation Spectroscopy of atoms Trapped atoms Dispersion Harmonic relation Oscillator of a free atom Spectroscopy Signal 1,8 1,0 0,6 0,5 0,3 Frequenz Position Lamb-Dicke-Parameter: Klaus Zipfel 5

6 Atoms in a lattice Hamiltonian: Lattice: Electrons Coupling External Lattice Potential Klaus Zipfel 6

7 E [E r ] Atoms in a lattice Hamiltonian: Lattice: Electrons Coupling External Bloch-Theorem: Trap-Eigenstates Band-Index Dispersion relation of an atom in a lattice Quasi-Momentum [1] P. Lemonde and P. Wolf Minimizing the Required Trap Depth in Optical Lattice Clocks Klaus Zipfel 7

8 Atoms in a lattice Pure state: All atoms with same quasi-momentum Dispersion relation of an atom in a lattice Width of lattice bands Line shift: Scales down with trapdepth [1] P. Lemonde and P. Wolf Minimizing the Required Trap Depth in Optical Lattice Clocks (DOI: /FREQ ) For 87 Sr: U 0 = 100 E r mhz Klaus Zipfel 8

9 Atoms in a lattice Mixture of different q: Broadening (residual Doppler) Excitation probability [1] P. Lemonde and P. Wolf Minimizing the Required Trap Depth in Optical Lattice Clocks (DOI: /FREQ ) Klaus Zipfel 9

10 Atoms in a lattice Conclusion: Tunneling limits accuracy (shift) and stability (broadening) Deep trap ( E r ) required to reduce tunneling + Line-shift & broadening becomes less - Technical problems (e.g. laserpower) - Higher-order shifts (2-photon resonances 2 nd order AC-Stark) - Tensorial lightshift (Hyperfine) Klaus Zipfel 10

11 Magnesium Lattice Clock Horizontal lattice at predicted magic wavelength of 469 nm Vacuum windows Go vertical! Trap parameters: Input power: 150 mw Not enough to trap atoms Enhancement: Waist: 65 µm 40 khz Trapdepth: 12 µk (10 E r ) Trapfrequency: 150 khz Lamb-Dicke-Parameter: 0.51 Width of lowest band: ~ 3 khz 50 µk (40 E r ) 300 khz 0.36 < 17 Hz 3 khz Klaus Zipfel 11

12 Vertical lattice Tunneling is a resonant process Idea: Lift degeneracy of neighbouring lattice site Accelerated lattice (via gravity): Potential for a vertical lattice Gravitation shifts energy levels of neighbouring wells by Suppression of tunneling if greater than witdth of band (in horizontal case) For magnesium: Klaus Zipfel 12

13 Vertical lattice Properties of a vertical lattice: Solution of the Hamiltonian: Wannier-Stark states Wannier-Stark ladder Sideband transition probability rapidly decreases with well depth Transition frequencies well know Landau-Zener tunneling scales down exponentially with trap depth 87 Sr: U 0 = 5 E r τ Tunnel =10 10 s Klaus Zipfel 13

14 Vertical lattice Pure Wannier-Stark state : Unshifted/unbroadened carrier with sidebands Sidebands separated by gravitational shift Sideband transition probability rapidly decreases with trap depth Transition probability for different trap depths [1] P. Lemonde and P. Wolf Minimizing the Required Trap Depth in Optical Lattice Clocks (DOI: /FREQ ) Klaus Zipfel 14

15 Vertical lattice Mixture of Wannier-Stark states More complex situation Residual wavefunction overlap of neighbouring wells Modification of carrier transition probability ~ Linepulling ~ E.g. for 87 Sr: 10 Er and Shift of 2x10-17 Shift oscillates with Wannier-Stark amplitude distribution Carrier shift over interaction time Chose interaction time so shift cancels Lattice site Klaus Zipfel 15

16 Conclusion Tightly bound atoms 1 st order Doppler- and recoil-free spectroscopy Lattice Periodicity Tunneling Line shifts and/or broadening High power required to compensate tunneling Technical difficulties Higher order & tensorial light-shifts Accelerated lattice (e.g. via gravity) High tunneling suppression Moderate power requirement More complex dynamics, but well understood Klaus Zipfel 16

17 Thanks to our groupleaders Prof. Dr. Wolfgang Ertmer Prof. Dr. Ernst M. Rasel Klaus Zipfel 17

18 The Magnesium team Thank you for your attention Klaus Zipfel 18