Sr optical lattice clock: hyperpolarizability effects and - PowerPoint PPT Presentation

LNE-S YRTE S ystèmes de Référence Temps-Espace Sr optical lattice clock: hyperpolarizability effects and preliminary accuracy evaluation A. Brusch, R. Le Targat, X. Baillard, M. Fouché, O. Tcherbakoff, G.D. Rovera and P.Lemonde LNE-S YRTE S ystèmes de Référence Temps-Espace

87 Sr 87 Sr Optical Optical lattice clock � Optical lattice clock with atoms confined in an optical lattice � Expected ultimate fractional accuracy: 10 -18 � Lattice @ “magic wavelength” => cancellation of first order differential light shift 3 S 1 Katori et al. PRL 91, 173005 (2003) 1 P 1 light shift 3 D 1 679 nm 813 461 679 2560 461 nm wavelength Γ = 32 MHz (nm) 2,56 µm 3 P 0 698 nm Clock transition 1 S 0 Γ = 1 mHz 3 P 0 1 S 0 LNE-S YRTE S ystèmes de Référence Temps-Espace

Differential light shift light shift cancellation cancellation ? ? Differential � U 0 =10 E r (36 kHz) is enough to cancel motional frequency shift P. Lemonde, P. Wolf, Phys. Rev. A, 72 033409 (2005) Accuracy of 10 -18 � Control at a level of 10 -8 x Light shift � Neutral atoms in an optical lattice : � At the magic wavelength, the first order term cancels = > Scale as E 4 α U 0 � Higher order terms : Hyperpolarizability 2 ⇒ Feasibility is conditioned by the magnitude of higher order effects LNE-S YRTE S ystèmes de Référence Temps-Espace

Hyperpolarizability effects effects on on the the clock clock frequency frequency Hyperpolarizability � Theoretical prediction of -2 µHz/E r 2 , λ m = 813,428 nm @ the theoretical magic wavelength: 800 nm 5s7p 1 P 1 H Katori, M. Takamoto, V.G. Pal’chikov, and V.D. 5s4f 3 F 2 Ovsiannikov, Phys. Rev. Lett., 91 , 173005 (2003) 2 x 813,36 nm � Second order light shift: magic wavelength 2 x 818,57 nm 5s5p 1 P 1 close to two two-photon transitions � 5s5p 3 P 0 -> 5s7p 1 P 1 fortunately forbidden: J=0 -> J=1 5s5p 3 P 0 G. Grynberg, B. Cagnac, Rep. Prog. Phys. 40, 791 (1977) � 5s5p 3 P 0 -> 5s4f 3 F 2 5s 2 1 S 0 698 nm Clock transition Need for an experimental evaluation of the effect LNE-S YRTE S ystèmes de Référence Temps-Espace

Optical lattice lattice Optical Need for high peak intensity > 100 kW/ cm 2 • Laser Ti: sapph ~ 7-800 mW @ 813 nm • Linear build-up cavity R< 5 % • Finesse ~ 100 @ 6 9 8 nm • Waist 89µm Peak intensity ~ 400 kW/ cm 2 • • Linear polarization (to within ~ 10 -4 ) λ / 4 pol. • probe transmission @ 698 nm vac. Max trapping depth w indow s 1400 E R ~ 4,5 MHz ~ 200 µK LNE-S YRTE S ystèmes de Référence Temps-Espace

Servo- -loop loop system system Servo 3 servos to ensure optimal stability 1. Hänsch-Couillaud 2. Intracavity power control 3. offset HC 1E-5 1E-7 RIN (1/Hz) V ref 1E-9 1E-11 1E-13 100 1000 10000 Fréquence (Hz) LNE-S YRTE S ystèmes de Référence Temps-Espace

loading the dipole trap Dipole trap 3 S 1 beam 1 P 1 (w 0 = 90 µm, U 0 =200 µK) 688 nm 461 nm Blue (32 MHz) MOT Laser cooling (2 mK) λ trap 2 1 0 1 S 0 3 P 689 nm 688 nm + 689 nm : continuous loading 4-10 10 4 at/s atomic drain (w 0 = 50 µm) LNE-S YRTE S ystèmes de Référence Temps-Espace

loading the dipole trap Dipole trap 3 S 1 beam 1 P 1 707 nm 679 nm 2 1 0 1 S 0 3 P 707 nm + 679 nm : repumpers (w 0 = 200 µm) LNE-S YRTE S ystèmes de Référence Temps-Espace

Narrow line cooling in the dipole trap Dipole trap 3 S 1 beam 1 P 1 2 1 0 1 S 0 3 P 689 nm Γ = 7.6 kHz 689 nm : narrow line cooling LNE-S YRTE S ystèmes de Référence Temps-Espace

Clock transition spectroscopy Dipole trap 3 S 1 beam 1 P 1 2 1 0 1 S 0 3 P 698 nm clock transition 698 nm laser referenced to an ultrastable cavity w 0 =200 µm LNE-S YRTE S ystèmes de Référence Temps-Espace

probe Blue Dipole trap beam Fluorescence detection Detection 2 1 0 3 S 1 3 P ystèmes de Référence Temps-Espace YRTE LNE-S S 1 P 1 1 S 0

Detection Dipole trap 3 S 1 beam 1 P 1 707 nm (7 MHz) 679 nm (1.75 MHz) 2 1 0 1 S 0 3 P 707 nm + 679 nm : repumpers (w 0 = 200 µm) LNE-S YRTE S ystèmes de Référence Temps-Espace

probe Blue Dipole trap beam Detection 2 1 0 3 S 1 3 P ystèmes de Référence Temps-Espace YRTE LNE-S S 1 P 1 1 S 0

Sideband spectrum 0.4 0.3 Transition probability 3 P 0 Excited 3 state 2 0.2 1 n z =0 0.1 1 S 0 0.0 3 Ground 2 -200 -100 0 100 200 state 1 detuning [kHz] n z =0 Longitudinal temperature given by sidebands ratio T z = 2 µK, 95 % of the atoms in |n z =0> Longitudinal sidebands frequency depends on the transverse excitation. Shape of sidebands gives the transverse temperature. T r = 10 µK LNE-S YRTE S ystèmes de Référence Temps-Espace

Atomic carrier carrier resonance resonance Atomic Optical USC AOM ECL @ 698 nm Laser frequency is locked to the atomic resonance 698 nm probe : via an AOM 15 ms, 3 µW LNE-S YRTE S ystèmes de Référence Temps-Espace

Measurement of the frequency shift due to the trap Measurement of the frequency shift due to the trap -Differential measurement atoms-cavity vs trapping depth repeated N times => -The cavity frequency fluctuations are filtered by a polynomial fit LNE-S YRTE S ystèmes de Référence Temps-Espace

First order order light shift light shift First λ m = 813,428 (1) nm • Measurements done at different wavelengths and different depths LNE-S YRTE S ystèmes de Référence Temps-Espace

3 P 1 P Second order order light shift light shift near near the the 3 P 0 - 1 P 1 transition Second 0 - 1 transition magic 0.10 wavelength R ) 2 Quadratic shift (mHz/E 0.05 0.00 -0.05 813.32 813.36 813.40 813.44 813.48 lattice wavelength (nm) No visible effect around the 3 P 0 – 1 P 1 transition 2 at λ m ( 0,1 mHz @ 10 E r ) contribution <1 µHz/E r LNE-S YRTE S ystèmes de Référence Temps-Espace

the 3 3 P - 3 3 F Second order order light shift light shift near near the P 0 F 2 transition Second 0 - 2 transition 10 1,0 13/2 5/2 9/2 7/2 11/2 Quadratic shift [Hz @ U 0 =10 E r ] r ] 2 Quadratic shift [mHz/E 5 0,5 0 0,0 -5 -0,5 818,55 818,56 818,57 818,58 lattice laser wavelength [nm] Contribution of this resonance @ λ m < 2 µHz/ E R 2 ( 0,2 mHz @ 10 E r ) LNE-S YRTE S ystèmes de Référence Temps-Espace

the 3 3 P - 3 3 F Second order order light shift light shift near near the P 0 F 2 transition Second 0 - 2 transition 4000 3000 818.5670 nm 2000 Lightshift (Hz) 1000 0 818.5679 nm -1000 -2000 0,0 0,5 1,0 1,5 2,0 Potential depth (a.u.) Quadratic shift clearly visible once the first order term has been removed LNE-S YRTE S ystèmes de Référence Temps-Espace

at λ λ m Hyperpolarizability effects effects at Hyperpolarizability m 2 • Hyperpolarizability shift of -4 (4) µHz/E r (-0.4(4) mHz @ 10 E r ), corresponding to a -1(1).10 -18 relative frequency shift @ 10 E r This effect will not limit the clock accuracy down to the 10 -18 level • A. Brusch et al. PRL 96 , 103003, 2006 LNE-S YRTE S ystèmes de Référence Temps-Espace

Frequency chain chain Frequency � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � FO2 frequency accuracy ~ 4 10 -16 stability ~ 1.6 10 -14 τ -1/2 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � D. Chambon et al. Rev. Sci. Inst. 76 , 094704, 2005 S. Bize et al. C. R. Physique 5 , 829, 2004. � � � � � � � � � � � � � � � Sr clock-Fountain comparison 6 10 -14 τ -1/2 Frequency resolution: ~1 Hz @ 600 s LNE-S YRTE S ystèmes de Référence Temps-Espace

1st order order Zeeman Zeeman effect effect 1st Frequency shift due to residual field, asymetry in Zeeman population and depending on probe polarization 3 P 0 F=9/2 δ =-0.08 Hz/mG/m F 1 S 0 F=9/2 δ =-0.18 Hz/mG/m F Assigned uncertainty 5 Hz future improvement by bias field+state preparation LNE-S YRTE S ystèmes de Référence Temps-Espace

Residual light shift light shift Residual 1 Hz uncertainty @ 400 E r (1.4 MHz). Control of the light shift at a level of 7 10 -7 LNE-S YRTE S ystèmes de Référence Temps-Espace

Pulling by transverse by transverse sidebands sidebands Pulling -probe 2 w 0 =400 µm => k r ~10 -3 k -residual probe-lattice angle -wavefront distortion Line pulling < 1 Hz LNE-S YRTE S ystèmes de Référence Temps-Espace

Cold collisions Cold collisions a few 10 atoms per lattice site : N 0 ~ 10 11 at/cm 3 No resolved shift: -1(1) Hz @ N 0 LNE-S YRTE S ystèmes de Référence Temps-Espace

Accuracy budget budget Accuracy Correction Uncertainty Fractional Effect (Hz) (Hz) Uncertainty (10 -14 ) First order Zeeman 0 5 1.2 4.5 0.9 0.2 Lattice AC Stark shift (400 Er) 0.6 0.6 0.1 Lattice 2nd order Stark shift (400 Er) 0 1 0.2 Line pulling (transverse sidebands) 1 1 0.2 Cold collisions 2.4 <1 <0.1 BBR shift 1.2 10 -14 Total 8.5 Hz 5.3 Hz LNE-S YRTE S ystèmes de Référence Temps-Espace