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1 Towards a Space Optical Clock with 88 Sr Titelmasterformat durch Klicken bearbeiten Influence of Collisions on a Lattice Clock U. Sterr Ch. Lisdat J. Vellore Winfred T. Middelmann S. Falke F. Riehle ESA Workshop,

2 ESA Project Space Optical Clocks Design & develop components for compact optical lattice clocks for space applications: PTB: 88 Sr optical lattice clock design parameters - collisions - interrogation schemes transportable clock laser - low noise cavities - compact laser systems 2

3 Sr la attic ce clo ocks f =30 mm f = 300 mm U/h (MHz ) 1 dichroic mirror clock laser 698 nm λ/2 PBS 3 w 0 = 34 µm; P = 300 mw; U 0 = k B 40 µk

4 Sr la attic ce clo ocks up to 1000 atoms per site f =30 mm f = 300 mm U/h (MHz ) 1 dichroic mirror clock laser 698 nm λ/2 PBS 4 Katori et al. PRL 91, (2003)

5 Fermion: 87 Sr Boson: 88 Sr Sr la attic ce clo ocks state mixing by hyperfine interaction smaller systematics p-wave collisions (should be suppressed, but shifts have been observed) state mixing by B-field higher abundance simpler laser cooling s-wave collisions U/h (MHz ) 5 Campbell et al. Science 324, 360 (2009)

6 87 Sr: Hyperfine structure F = 9/2 7 Sr la attic ce clock ks 87 (arb. units s) populatio on in 3 P first order sensitive to magnetic fields 1 khz/mt m F, 461 nm MOT: 800 ms 689 nm MOT: 90 ms 689 nm MOT: 50 ms Spin-polarization: 1 ms atoms B = 1.2 mt unpolarized m F = 9/2 m F = -9/2 U/h (MHz ) detuning (khz) 6

7 87 Sr m F = 9/2 - m F = 9/2 clock transition 7 Sr la attic ce clock ks 87 excita ation proba ability natural lifetime ~130 s, excitation with low power - small light shifts P ~ 2 µw w 0 U/h = 40 (MHz µm ) pulse length (ms) 7

8 87 Sr m F = 9/2 - m F = 9/2 clock transition F F Sr la attic ce clock ks 87 on (arb. un nits) P 0 populati 3 P U/h (MHz ) detuning (Hz) 8

9 Boson: 88 Sr Fermion: 87 Sr Sr la attic ce clo ocks state mixing by B-field higher abundance simpler laser cooling s-wave collisions state mixing by hyperfine interaction smaller systematics p-wave collisions U/h (MHz ) (shifts have been observed) 9 Campbell et al. Science 324, 360 (2009)

10 Mixture of atoms in 1 S 3 0 and P 0 88 Sr of S 0 only, lifetime ~ 8 s 1 Los sses P 0 atom nu umber / 1 3 P P 0 only 1 S and 3 P 0 0 Losses via collisions 3 P P 0 and 1 S P trapping time (s) 10

11 Modelling the losses 88 Sr of S 0 only Los sses P 0 atom nu umber / 1 3 P P 0 only 1 S and 3 P trapping time (s) 11 Traverso et al. Phys. Rev. A 79, (R) (2009)

12 Br road denin ng 1 number / 10 3 S0 atom 0 3 atom number / 1 1 S0 a low density excitation pulse length (ms) Fourier limited FWHM (Hz) 0 3 atom number / 1 1 S0 a linewidth atom number / 10 3 high density broadening reduced contrast clock laser detuning (khz) clock l k laser detuning (khz)) 12 B = 3 mt; P clock = 2.5 mw; t clock = 5 ms

13 Modelling the dynamics Br road denin ng laser linewidth elastic, dephasing collisions inelastic losses 13

14 Modelling the dynamics N = N = Br road denin ng fit with no dephasing fit with dephasing N = N = N = N =

15 Modelling the dynamics 0.6 Br road denin ng excitation probability Hz clock laser detuning (Hz) Narrow lines are nevertheless possible 15 N = 10 4 ; B = 0.75 mt; P clock = 0.5 mw; t clock = 35 ms

16 Interleaved stabilization Coll lision nal shift shift = 1/2(f A (t) + f A (t+t)) f B (t') T A B r l r l f A f B f time 16 Degenhardt et al. PRA 72, (2005)

17 1E-14 Interleaved stabilization Colli ollision ional shift calculated single st tab. rel. Allan devia ation 1E-15 1E-16 single laser contribution σ y (τ) ~ τ -1/2 linewidth 25 Hz linewidth 40 Hz linewidth id 175 Hz 1E time (s) atoms; 200 ms cycle time; 3 P 0 detection only

18 Interleaved stabilization 25 Coll lision nal shift Hz) shift ( correction to 4% 5 0 ft (Hz) shi excitation probability (%) x x x x10 4 atom number difference 18

19 Lattice design for a 88 Sr 1D-lattice clock Des sign Latt tice typical lattice depth: k B 10 µk, 300 mw lattice laser power: waist w 0 = 75 µm for relative accuracy and 4%-correction of collisional shift: 1 Hz shift acceptable, 10 4 atoms (broadening: 1 Hz) with better shift correction, 10 Hz linewidth: 10 5 atoms, QPN (1 s, 200 ms cycle) Lisdat et al. Phys. Rev. Lett. 103, (2009) 19

20 Additional difficulties with 88 Sr: 8 Sr latti ice clock Sr requires magnetic field to induce transition dipole matrix element: quadratic Zeeman effect B high intensities required to drive the transition: laser light shift L Rabi frequency Ω = 0.3 B L A. V. Taichenachev h et al., Phys. Rev. Lett. 96, (2006) 20

21 Ramsey Excitation 0.6 ms pulses, 15 ms dark time Ram msey Fringes excitation probability 21 detuning (Hz)

22 Co onclu usio ons Suppression of excitation related shifts: A. Taichenachev, V. Yudin (Novosibirsk), NIST, PTB: make shifts appear only during pulses, combine Ramsey spectroscopy with NMR techniques to suppress these shifts vary independently: detuning, phase, duration of pulses Reduction of shift by at least a factor of 20 is possible, compared to Rabi single pulse excitation of same resolution. A. V. Taichenachev, V. I. Yudin, C. W. Oates, Z. W. Barber, N. D. Lemke, A. D. Ludlow, U. Sterr, Ch. Lisdat and F. Riehle arxiv: v2 3716v2 [physics.optics] (2009) and follow up 22