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

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

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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

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87 87Sr

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

Katori et al. PRL 91, 173005 (2003) light shift wavelength (nm) 461 679 2560

813

1S0 3P0

1S0 3D1 3S1 1P1 3P0 698 nm Clock transition Γ = 1 mHz 461 nm Γ = 32 MHz 2,56 µm 679 nm

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Differential Differential light shift light shift cancellation cancellation ? ?

⇒ Feasibility is conditioned by the magnitude of higher order effects => Scale as E4 α U0

2

Higher order terms : Hyperpolarizability Neutral atoms in an optical lattice : At the magic wavelength, the first order term cancels U0=10 Er (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

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Hyperpolarizability Hyperpolarizability effects effects on

  • n the

the clock clock frequency frequency

Theoretical prediction of -2 µHz/Er

2,

@ the theoretical magic wavelength: 800 nm Second order light shift: magic wavelength close to two two-photon transitions 5s5p 3P0 -> 5s7p 1P1 fortunately forbidden: J=0 -> J=1

  • G. Grynberg, B. Cagnac, Rep. Prog. Phys. 40, 791 (1977)

5s5p 3P0 -> 5s4f 3F2

5s2 1S0

5s5p 1P1 5s5p 3P0 5s4f 3F2 698 nm Clock transition 5s7p 1P1

2 x 818,57 nm 2 x 813,36 nm

H Katori, M. Takamoto, V.G. Pal’chikov, and V.D. Ovsiannikov, Phys. Rev. Lett., 91, 173005 (2003)

λm = 813,428 nm

Need for an experimental evaluation of the effect

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Optical Optical lattice lattice

Need for high peak intensity > 100 kW/ cm 2 Max trapping depth 1400 ER ~ 4,5 MHz ~ 200 µK

R< 5 % @ 6 9 8 nm

λ/ 4

pol.

  • Laser Ti: sapph ~ 7-800 mW @ 813 nm
  • Linear build-up cavity
  • Finesse ~ 100
  • Waist 89µm
  • Peak intensity ~ 400 kW/ cm 2
  • Linear polarization (to within ~ 10-4)
  • probe transmission @ 698 nm

vac. w indow s

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Servo Servo-

  • loop

loop system system

3 servos to ensure optimal stability

  • 1. Hänsch-Couillaud
  • 2. Intracavity power control
  • 3. offset HC

Vref

100 1000 10000 1E-13 1E-11 1E-9 1E-7 1E-5

Fréquence (Hz) RIN (1/Hz)

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loading the dipole trap

3P 3S1 1 1P1 2 Blue MOT (2 mK)

Dipole trap beam (w0 = 90 µm, U0=200 µK) 688 nm + 689 nm : atomic drain (w0 = 50 µm)

λtrap

461 nm (32 MHz) Laser cooling

689 nm 688 nm

1S0

continuous loading 4-10 104 at/s

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loading the dipole trap

3P 1 1P1 3S1 2

707 nm 679 nm

1S0

707 nm + 679 nm : repumpers (w0 = 200 µm) Dipole trap beam

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Narrow line cooling in the dipole trap

3P 1 1P1 3S1 2 1S0

689 nm Γ = 7.6 kHz

689 nm : narrow line cooling Dipole trap beam

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Clock transition spectroscopy

3P 1 1P1 3S1 2 1S0

698 nm clock transition

698 nm laser referenced to an ultrastable cavity w0=200 µm Dipole trap beam

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Detection

3P 1 1P1 3S1 2 1S0

Dipole trap beam

Blue probe

Fluorescence detection

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Detection

3P 1 1P1 3S1 2

707 nm (7 MHz) 679 nm (1.75 MHz)

1S0

707 nm + 679 nm : repumpers (w0 = 200 µm) Dipole trap beam

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Detection

3P 1 1P1 3S1 2 1S0

Dipole trap beam

Blue probe

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Sideband spectrum

Longitudinal temperature given by sidebands ratio

1S0

Tz = 2 µK, 95 % of the atoms in |nz=0>

nz=0 3 2 1 Ground state Excited state

3P0

nz=0 3 2 1

Longitudinal sidebands frequency depends on the transverse excitation. Shape of sidebands gives the transverse temperature. Tr = 10 µK

  • 200
  • 100

100 200 0.0 0.1 0.2 0.3 0.4

Transition probability detuning [kHz]

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Atomic Atomic carrier carrier resonance resonance

698 nm probe : 15 ms, 3 µW ECL @ 698 nm USC Optical AOM

Laser frequency is locked to the atomic resonance via an AOM

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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

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  • Measurements done at different wavelengths and different depths

First First order

  • rder light shift

light shift

λm = 813,428 (1) nm

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Second Second order

  • rder light shift

light shift near near the the 3

3P

P0

0-

  • 1

1P

P1

1 transition

transition

No visible effect around the 3P0 – 1P1 transition contribution <1 µHz/Er

2 at λm ( 0,1 mHz @ 10 Er )

813.32 813.36 813.40 813.44 813.48

  • 0.05

0.00 0.05 0.10

Quadratic shift (mHz/E

2 R)

lattice wavelength (nm)

magic wavelength

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818,55 818,56 818,57 818,58

  • 5

5 10

  • 0,5

0,0 0,5 1,0

Quadratic shift [Hz @ U0=10 Er] Quadratic shift [mHz/E

2 r]

lattice laser wavelength [nm]

13/2 11/2 9/2 7/2 5/2

Contribution of this resonance @ λm < 2 µHz/ ER

2 ( 0,2 mHz @ 10 Er )

Second Second order

  • rder light shift

light shift near near the the 3

3P

P0

0-

  • 3

3F

F2

2 transition

transition

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0,0 0,5 1,0 1,5 2,0

  • 2000
  • 1000

1000 2000 3000 4000

Lightshift (Hz)

Potential depth (a.u.)

818.5670 nm 818.5679 nm

Quadratic shift clearly visible once the first order term has been removed

Second Second order

  • rder light shift

light shift near near the the 3

3P

P0

0-

  • 3

3F

F2

2 transition

transition

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Hyperpolarizability Hyperpolarizability effects effects at at λ λm

m

  • Hyperpolarizability shift of -4 (4) µHz/Er

2

(-0.4(4) mHz @ 10 Er), corresponding to a -1(1).10-18 relative frequency shift @ 10 Er

  • This effect will not limit the clock accuracy down to the 10-18 level
  • A. Brusch et al. PRL 96, 103003, 2006
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Frequency Frequency chain chain

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

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1st 1st order

  • rder Zeeman

Zeeman effect effect

3P0 F=9/2 δ=-0.08 Hz/mG/mF 1S0 F=9/2 δ=-0.18 Hz/mG/mF

Frequency shift due to residual field, asymetry in Zeeman population and depending on probe polarization

Assigned uncertainty 5 Hz future improvement by bias field+state preparation

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Residual Residual light shift light shift

1 Hz uncertainty @ 400 Er (1.4 MHz). Control of the light shift at a level of 7 10-7

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Pulling Pulling by transverse by transverse sidebands sidebands

  • probe 2 w0=400 µm => kr~10-3 k
  • residual probe-lattice angle
  • wavefront distortion

Line pulling < 1 Hz

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Cold collisions Cold collisions

a few 10 atoms per lattice site : N0 ~ 1011 at/cm3

No resolved shift: -1(1) Hz @ N0

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Accuracy Accuracy budget budget

Effect Correction (Hz) Uncertainty (Hz) Fractional Uncertainty (10-14) First order Zeeman Lattice AC Stark shift (400 Er) Lattice 2nd order Stark shift (400 Er) Line pulling (transverse sidebands) Cold collisions BBR shift 4.5 0.6 1 2.4 5 0.9 0.6 1 1 <1 1.2 0.2 0.1 0.2 0.2 <0.1

Total 8.5 Hz 5.3 Hz 1.2 10-14

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Frequency Frequency measurements measurements

ν1S0-3P0=429 228 004 229 879 (5) Hz

40 80 120 160

Ludlow et al. RPL 93 033003 (2006) Takamoto et al. Nature 435, 321 (2005)

  • J. Ye et al.
  • Proc. ICAP 2006

Le Targat et al. PRL 97 1308001 (2006) Takamoto et al. arXiv:physics/0608212

This work

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€: LNE, CNES,ESA, DGA