Shortt pendulum clock (1921) ... Next-generation atomic clocks will need operation in space ... Comparison with master clock (via microwave/optical link).
11th Marcel Grossmann Meeting, Berlin 23. - 29. 7. 2006
Satellite Optical Clocks: Fundamental Tests and Applications S. Schiller, A. Görlitz, J. Koelemeij, B. Roth, A. Nevsky, A. Wicht, Univ. Düsseldorf G.Tino, Univ. Firenze/LENS, P. Lemonde, BNM-SYRTE Paris U. Sterr, F. Riehle, E. Peik, PTB Braunschweig C. Salomon, ENS Paris, C. Lämmerzahl, H.J. Dittus, ZARM Bremen P. Touboul, ONERA Paris, A. Peters, Humboldt-Univ. Berlin E. Rasel, W. Ertmer, Univ. Hannover, P. Gill, H. Klein, NPL Teddington G. Mileti, Observatoire Neuchatel, R. Holzwarth, T. Hänsch, MPQ Munich
Introduction Precise time and frequency metrology are of fundamental importance in science and technology
First atomic clock: Cesium (NPL, 1955)
Shortt pendulum clock (1921) VLBI (1967)
Quartz clock ( ~1944)
Galileo (> 2006)
GPS (>1978)
DCF77 (1973)
Ultrastable clocks in Space Gravity Probe A: hydrogen maser (1976) - rocket flight to 10 000 km height - tested relativistic Doppler effect and gravitational redshift to 70 ppm
ACES: Atomic clock ensemble (2009) - PHARAO: cold atom microwave clock - instability 1.10-13 @ 1 s, 4.10-16 @ 50 000 s - accuracy ~ 1.10-16 - technology demonstrator - world-wide time dissemination and comparisons - test of special and general relativity
Optical Clocks 10-9 10-10
Optical Clocks
Relative Uncertainty
10-11 10-12 10-13
Microwave clocks , Ca
10-14 10-15
Yb+
Mikrowave clocks: ~ 9 GHz Optical clocks: ~ 400 000 GHz
10-16
Hg+ Al+
10-17
10-18
10-18 1950
1960
Review: P. Gill, Metrologia (2005)
1970
1980
Year
1990
2000
2010
Optical Clocks in Space Next-generation atomic clocks will need operation in space - Reduces influence of * uncertainty in gravitational potential: ∆U/U = 1.10-9 (corresponds to ∆h=1 cm) results in ∆ν/ν=1.10-18 * continental drift: plate velocity of 1 cm/year gives ∆ν/ν=1.10-18
Applications: - Time and frequency distribution on earth and in space („Master clock in space“) - Geophysics: Gravity field and elevation mapping Clock comparison measures the difference in gravitational potential U Map out U using movable clocks (trucks, airplanes, ships, satellites)
- Precision navigation in space - Space-VLBI - Fundamental physics: e.g. * high precision test of foundations of General Relativity (Mission proposal OPTIS) * Pioneer anomaly - Metrology (LISA (3.10-19), DARWIN,…) - Accurate link is essential (theory + technology)
Quantum matter–based sensors in space have strong European support: Letter of Support for the ELIPS-2 Programme – 30/11/2005, signed by 107 scientists from 58 institutions, incl. Nobel laureates T. Hänsch, W. Ketterle, C. Cohen-Tannoudji
Master clock
Gravity and its foundations
General Relativity
Gravitational redshift Lense-Thirring effect ....
Metric theory of gravity
Einstein Equivalence Principle Universality of Free Fall (Weak equivalence princip.)
Local Position Invariance (Universality of grav. Redshift constancy of constants)
Local Lorentz Invariance (Special Relativity)
Gravity and its foundations
General Relativity
Gravitational redshift Lense-Thirring effect ....
Metric theory of gravity
GP-B, LAGEOS, ACES, OPTIS, ...
Einstein Equivalence Principle Universality of Free Fall
Local Position Invariance
(Weak equivalence princip.)
(Universality of grav. Redshift constancy of constants)
MICROSCOPE
Local Lorentz Invariance (Special Relativity)
ACES, OPTIS
Complete test of metric gravity
Testing the Gravitational Redshift of Clocks
U Clock ensemble
Master Clock
ν1 ν2
ν0
∆ν i ¾ Satellite carries ensemble of dissimilar clocks, based on different particles and interactions ¾ Intercomparison of on-board clocks: - Gravitational redshift universality test:
ζ1=ζ2 ?
ν0
∆U = ζ i 2 + ... c 2.10-10
for eccentricty ε = 0.4 ¾ Comparison with master clock (via microwave/optical link) - Absolute gravitational redshift measurement - Test of higher-order relativistic corrections (Linet & Teyssandier, 2002, Blanchet et al
2001, Ashby 1998)
Principle of an cold atom optical clock Atoms single ion oder Ionen absorber Atome, Moleküle Laser Oszillator
Detector Detektor S
ν0
~ 400 000 GHz
Femtosecond frequency comb
ν0 ν
Feedback Regelungscontrol elektronik electronics Error signal Fehlersignal
Radio - frequency signal, 200 MHz
AbsorptionsAbsorption signal signal dS dν ν0
ν
Optical clocks Life time ~ 0.1 – 10 s
Transition frequency ~ 105 times higher
Use (almost) forbidden transitions between quantum states, with linewidth/interrogation time comparable to microwave clocks: ~ seconds
~ 1015 Hz
Ultimately, a gain of ~ 105 in stability should be possible:
instability ~ 10-18 on timescale of τ = 1 s
Accuracies ~ 1 part in 1018 are estimated to be possible
Atomic ions, neutrals
Quantum limit:
σ (τ ) 1 = ν 2πν
Techniques: - Atoms are ultracold, nearly at rest in trap (confined to within less than the wavelength of light) - Optical local oscillators required: ultrastable lasers - Transformation of optical frequency to the microwave domain is possible using optical frequency combs
1 N TRτ
Fundamental Constants and Clocks
Frequencies depend on fundamental constants
ν i = ν i (α ,α S , GF , me , mN , g N ,...)
Gravitational redshift experiments test whether some of these constants depend on the gravitational potential
⎛ −1 dν i β j = β j (U ) ? ⇒ ζ i = 1 + ∑ ⎜ν i dβ j j ⎝
⎞⎛ dβ j ⎞ ⎟⎜ 2 ⎟ ( )⎠ d U c ⎝ ⎠
Some constants can be related to more fundamental constants:
m p ∝ Λ QCD + corrections me ∝ φ ∆ ( mN m p ) mN m p
Strong interaction
= Higgs vacuum field Weak interaction = cα (∆α α ) + cφ (∆φ φ ) + cΛ (∆Λ QCD Λ QCD )
cα , cφ , cΛ
O (10−3 )
Optical clock types ¾ Scaling of transition energies (in units of Rydberg energy) Electronic energies (incl. relativistic effects) Vibrational energies in molecules
α −1
Cavity frequency
me mN
For a diatomic molecule XY:
νa νb
is a function of
mX me , mY mX
Can be calculated for simple molecules H2+ (Hilico et al. 2000) HD+ (Schiller and Korobov, 2005)
G (α )
Yb: Sr: Yb+:
0.31 0.06 (0.9, - 5.3)
Clock choice
A comparison of an atomic optical clock to a molecular optical clock is (within the Standard Model) sensitive to all non-gravitational interactions:
∆ (ν at ν vib )
ν at ν vib
= bα
bα , bφ , bΛ
∆α
α
+ bφ
∆φ
φ
+ bΛ
∆Λ QCD Λ QCD
O (1)
A second atomic or molecular clock with different sensitivity may be added to avoid possible cancellation effects
In gauge unification theories the dependencies of α and ΛQCD on U are correlated (Damour 1999, Langacker et al, Calmet & Fritzsch, 2002)
∆Λ QCD Λ QCD
40
∆α
α
Molecular Clocks are very sensitive probes!
Optical lattice clocks Metastable excited states in Ca, Sr, Yb, Hg (Life time ~ 10 s)
Sr / Yb
• Very narrow line widths: • in isotopes with nuclear spin I ≠ 0 ∆ν ~ mHz • in isotopes with I = 0, ∆ν ~ µHz for B ~ 1 mT
Katori (2003)
sp
cooling
cooling
461 / 399 nm
689 / 556 nm
• Large particle number (~ 105 - 107)
relative instability σ(τ)/ν ~ 10-16 τ -1/2
3P
J=2 J=1 J=0
clock 698 / 578 nm
• Small systematic effects (no electronic magnetic moment)
relative uncertainty < 10-16
sp
1P 1
s2 1S0
~ 107 Strontium neutral atoms
• Efficient laser cooling possible Optical lattice:
Cooling
• 3D interference pattern, ~ several W cw radiation • Atoms stored in interference maxima • For a lattice laser of “magic wavelength” (Sr: 814 nm, Yb: 759 nm) no major influence on clock transition
Cooling 698 nm
Clock
Optical Lattice Clock developments - Under development: Sr (Tokyo, JILA, PTB, SYRTE, Firenze), Yb (Kyoto, NIST, Seattle, Düsseldorf,…) Hg (Paris) - Optical frequency measurements have been performed on fermions and boson ensembles (1-D lattice only so far)
The Düsseldorf Yb lattice clock project A. Görlitz, A. Nevsky, A. Wicht, S. S.
Isotopes:
sp
sp
1P 1
cooling
cooling
399 nm
556 nm
3P
J=2 J=1 J=0
clock transition
578 nm
Blue MOT (399 nm) -
Polarization gradient cooling All 7 stable isotopes trapped 171Yb (I = 1/2): T = 80…250 uK 173Yb (I = 5/2): T = 10…150 uK Temperatures are density-limited
22 mm 174Yb
s2 1S0
Large numbers
Small numbers
Ultracold Yb atoms Second-stage cooling
sp
107 174Yb Atoms at 60 µK in MOT
sp
1P 1
cooling
3P
J=2 J=1 J=0
556 nm
clock transition 578 nm
Optical trapping -
Uses 532 nm laser 5% transfer efficiency from MOT to optical trap Initial temperature ~ 100 µK 100 s life time of atoms in trap Evaporation leads to 30 µK within a few seconds Forced evaporation leads to ~ 1 µK at 104 atoms
105 174Yb atoms at 40 µK in optical trap
100 µm
Both fermions and bosons reliably trapped optically
s2 1S0
Yb clock laser development
- 10 mW power - Further stabilization to ULE cavity - Compact, transportable setup
-
- Nd:YAG laser and diode laser stabilized to I2 with kHz-level instability
+
- Based on cw sum-frequency generation
Vibration isolation platform Transfer and enhancement cavity
Lock
1266 nm + 1064 nm
Diode laser 1266 nm
578 nm Lock +Nd:YAG laser 1064 nm/532 nm
Iodine cell Lock
AOM
pp-LiNbO3 Lock
+
-
532 nm ULE high-finesse cavity
+
-
~ 10 mW
Laser stabilization techniques
Technology development: -
Nd:YAG laser (1064 nm) ULE dual-cavity block Low-frequency FM lock Towards transportability Uses active vibration isolation
1,0 0,8 0,6
FWHM ∼ 1.2 Hz (FFT resolution 0.5 Hz)
0,4 0,2 0,0 0
50
Next steps: -
100
150
200
Frequency (Hz)
Development of a cavity for 578 nm Characterization of the clock Comparison to H-Maser/GPS via frequency comb Later: comparison to other optical clocks
Ultracold Molecules Schiller and Korobov (2005)
¾ For precision spectroscopy, ultracold, trapped molecules are necessary - reduces various line broadening mechanisms - allows best control over and characterization of systematic effects
Ultracold neutral diatomic molecules have been produced by photoassociation from ultracold atoms, e.g. Rb2 (Pillet et al, 1998)
Trapping in an optical lattice demonstrated (Rom et al. 2004)
Molecular ions have been cooled and trapped by sympathetic cooling (Aarhus/Düsseldorf)
Large variety of molecular ions possible, e.g. hydrogen molecular ions (Düsseldorf)
Cold Neutral dipolar molecules have been trapped in electric traps (Rhinhuizen/Berlin/München)
Molecular Clocks are complementary to Atomic Clocks - Similar performance as for optical atomic clocks is expected - Their development will profit from optical atomic clock advances
Ro-vibrational spectroscopy of HD+ Roth et al., PRL 94, 053001 (2005)
Blythe et al., PRL 95,183002 (2005) -
Dipole-allowed transitions v = 0 to v = 4 overtone transition is accessible to diode laser Long lifetime ~ 10 ms No detectable fluorescence use state-selective photodissociation and measure number of remaining HD+ ions λIR = 1430.3884 nm λIR = 1430.3889 nm
Beginning:
End:
Hyperfine spectrum Complicated hyperfine spectrum: coupling of 4 angular momenta
B. Roth et al., subm.
Theory with ~ 35 MHz broadening
(v, J) = (0, 2) Æ (4, 1)
Fermi contact interaction
. ~ ∼ See ⋅ Sdd
Spin-rotation interaction
∼~SSe e⋅ .LL
(v, J) = (0, 2) Æ (4, 3)
Fermi contact interaction
∼~ SSee ⋅. S pp
Residual linewidth due to: - unresolved hyperfine structure - finite temperature - laser linewidth
Theory: Ray & Certain 1976, Ryzlewicz et al. 1982, Carrington et al 1985, Bakalov et al. 2006
Optical clock mission: Science goals Lämmerzahl et al. Class. Quant. Grav. 18, 2499 (2001), Lämmerzahl et al., Gen. Rel. and Grav. 36, 2373 (2004) Schiller et al., Proc. ESLAB (2005)
General Relativity
Position Lorentz Invariance Invariance
Test
Isotropy of c Isotropy of Coulomb interaction Relativistic Doppler effect (time dilation) Universality of Gravitational redshift (me/mp) Universality of Gravitational redshift (α)
Current
4 ⋅10−10 1 ⋅10−15 2 ⋅10−7 1 ⋅10−3 2.5 ⋅10−5
Lense - Thirring effect Absolute gravitational redshift Perigee advance Newtonian potential Clocks: Time link:
[1] Antonini et al, Stanwix et al, Herrmann et al. (2005) [2] Saathoff et al, PRL (2003)
3 ⋅10−1 1.4 ⋅10−5 3 ⋅10−3 10−11
Improvement [1]
x 104
[1]
x 104
[2]
x 102
[3]
x 107
[4]
x 105
[5]
x 102
[6]
x 104
[7]
x 10
[8]
x 10
1.10-18 instability at τ = 7 h (half orbit period) 1.10-18 inaccuracy [3] Rovera & Acef, (2001) [4] Bauch & Weyers, PRD 65 081101 (2002) [5] Ciufolini, CQG 17, 2369 (2000)
[6] Vessot et al PRL, (1980) [7] Iorio et al., CQG 19, 4301 (2002) [8] Iorio et al., PLA 298, 315 (2002)
Space suitability Important optical clock components are already space-qualified - Single-frequency diode lasers (PHARAO) - Ultracold atom sources (PHARAO) - Opto-electronic components - Solid-state lasers and amplifiers (TESAT Spacecom) - Optical resonators (TESAT Spacecom) - Phase-locking (TESAT Spacecom)
PHARAO to be flown on ISS ~ 2009 LISA Pathfinder to be flown ~ 2009 Studies toward space qualification and space uses of frequency combs are under way (DLR, ESA)
Mass 22 kg, power 65 W
Ultracold atoms in free fall studies (Bose-Einstein Condensate) at ZARM Bremen (DLR) High-precision time transfer between satellites and earth to be tested in upcoming missions (ACES on ISS, T2L2 on JASON 2) Optical link experiments (LCT TerraSAR, LOLA,…) Necessary developments: ultrastable lasers (cavities + sources), atomic sources Transportable cold atom optical clocks could be implemented within ~ 3-4 yrs An engineering model within ~ 6 years
MAP project AO-2004-100 (ELIPS-2 Program)
Demonstrate lattice optical clocks with performance beyond the best cold atom microwave clocks -
Two atoms: Strontium and Ytterbium Local oscillator development Transportable subsystems
Develop concepts for space implementation Individuate critical issues Synthesize results and work out specifications Preparatory work towards industrial study proposal
Cosmic Vision 2015 – 2025 ESA’s new long term plan for space science 3.1 Explore the limits of contemporary physics Probe the limits of classical GR, symmetry violations (CPT Lorentz, isotropy), fundamental constants, Short Range Forces, Quantum Physics of Bose-Einstein Condensates (BEC), Cosmic rays to look for clues to Unified Theories . Use the stable and gravity-free environment of space to implement high precision experiments to search for tiny deviations from the standard model of fundamental interactions: Galileo’s equivalence principle, gravity at very small distances, gravity on Solar System scale, time variability of fundamental constants, quantum gravity (entanglement and decoherence experiments with BEC’s). Investigate dark matter from Ultra High Energy particles.
Tool: Fundamental Physics Explorer programme
Summary
Optical clocks with 10-18 instability in space and on earth open exciting possibilities: -
Time & frequency dissemination
-
Earth gravity field measurements
-
Navigation
-
Metrology
-
Fundamental physics (OPTIS, …)
The progress in the development of optical clocks is rapid, performance has already surpassed that of the best microwave clocks
Many groups world-wide are developing clock technology, several in Europe
Cold atom/ion clocks with instabilities/inaccuracy at 1.10-18 level are expected to be achieved in the laboratory within a few years
Several ongoing ESA studies on optical clocks and frequency combs for both ground and space use
Need for a development program toward space-suitable implementations – could initiate now for subcomponents
An optical clock fundamental physics mission has strong support in the scientific community
