Cold Atom Clocks on Earth and in Space Fundamental Tests and Applications C. Salomon Laboratoire Kastler Brossel, Ecole Normale Supérieure, Paris http://www.lkb.ens.fr/recherche/atfroids/welcome Varenna school on atom optics and space physics, July 2007
Summary 1) What is an atomic clock? Frequency stability Accuracy 2) Atomic fountains Performances Limits 3) Fundamental tests with space clocks the ACES mission: Redshift measurement Search for drift of fundamental constants Applications in Geodesy and GNSS 4) Perspectives
1997 Nobel prize in physics S. Chu, C. Cohen Tannoudji, W. Phillips Laser manipulation of atoms 2001 Nobel prize in physics E. Cornell, W. Ketterle, C. Wieman Bose-Einstein Condensation In atomic gases 2005 Nobel prize in physics J. Hall, T. Haensch,, R. Glauber Laser precision spectroscopy and optical frequency comb
Time measurement Find a periodic phenomenon: 1) Nature: observation: Earth rotation, moon rotation, orbit of pulsars,.. 2) Human realization: egyptian sandstone, Galileo pendulum. simple phenomenon described by a small number of parameters The faster the pendulum, The better is time resolution T = 2 π l/ g
Time measurement (2) Electromagnetic field: Quartz oscillator, vibration of crystal coupled to an electrical circuit Atomic Clock: Intrinsic stability of energy levels (Quantum Mechanics) Control of atomic motion Laser cooling: low velocities : 1 cm/s Long measurement time: Narrow atomic resonance Better clocks, better sensors
Precision of Time 1s 1ms 1μs 1ns 1ps 100 ps/day 10 ps/day
Atomic Clock An oscillator of frequency ν produces an electromagnetic wave which excites a transition a - b The transition probability a b as a function of ν has the shape of a resonance curve centred in ν A = (E b -E a ) / h and of width Δν A servo system forces ν to stay equal to the atomic frequency ν A An atomic clock is an oscillator whose frequency is locked to that of an atomic transition The smaller Δν, the better is the precision of the lock system E b E a ν Α hυ A Δν Atomic transition Oscillator
Atomic clock Definition of the second : The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground electronic state of cesium 133 Intrinsic stability of atomic energy levels Laser cooling to 1 µk Corresponding to rms velocity of 7mm/s 1) Fountain geometry 2) Microgravity environment 1. Stability 2. Accuracy F=4 6 S 1/2 F=3 υ = 0 9 192 631 770 Hz
Phase/ Frequency Stability Idea of a "perfect" frequency in practice AM+PM Pure AM Pure PM s(t) s(t) s(t) Time Time Time
Frequency fluctuations Instantaneous frequency Frequency stability: "magnitude" of relative frequency fluctuations Frequency Stability is caracterized with the Allan variance, typical frequency fluctuations averaged over converges for most of the types of noise met experimentally
Frequency stability Allan standard deviation : log σ ( τ, N ) / τ 1 2?? τ + τ 0 White frequency noise τ 1 τ 2 Flicker frequency noise log averaging time τ 2 σ 1 N = y y k+ 1 2 1 ( τ, ) k= N 1 ( N ) k = 1 ( ) k 2
White frequency noise 3 0-3 3 0-3 3 0-3 3 0-3
Flicker frequency noise 2 0-2 2 0-2 2 0-2 2 0-2
atomic fountain Ramsey method: 2 successive interactions 1 Pa b = (1 + cos( ω ωat ) T ) 2
Ramsey fringes in atomic fountain S/N= 5000 per point
The fundamental noise in the fountain : The quantum projection noise W.Itano et al. (1993) State of the system : ψ >=α g >+β e> The measurement projects the system in g> or e> With probabilities p = α 2 and 1 α 2 When p=1/2, an atom has equal chances to be found in g> or e> For N uncorrelated atoms : p=1/2 to within 1/2N 1/2 The expected fountain frequency stability is : σ τ ( ) : Allan standard deviation ( ) = 1 / ( δυ / υ )( 1 N )( T / ) 1/ 2 1/ 2 / c σ τ π τ cs 6 Example : N = 10, δυ = 1 Hz, Tc = 1. 1s, υcs = 92. GHz 14 1/ 2 σ ( τ) = 3 10 τ Santarelli et al., PRL 99
Participants F. Chapelet, M. Abgrall, S. Zhang, Y. Maksimovic, F. Allard, C. Vian, C. Jentsch, C. Mandache, S. Bize, P. Lemonde, P. Laurent, G. Santarelli, P. Rosenbusch, P. Wolf, D. Rovera, A. Clairon Laboratoire National d essais Systèmes de Références Temps-Espace, SYRTE Observatoire de Paris M. Tobar, J. Hartnett, A. Luiten, University of Western Australia
Atomic Fountains 15 fountains in operation at SYRTE, PTB, NIST, USNO, Penn St, INRIM, NPL, ON, JPL. 6 with accuracy at 1 10-15. More than 10 under construction. LNE-SYRTE, FR PTB, D NIST, USA
Stability/Accuracy ν clock (t)= ν cesium (1+ ε+y(t)) Where ν cesium is the transition frequency of a cesium atom at rest in absence of perturbation ε : frequency shift, ε= ε 1 +ε 2 +ε 3 +. y(t): frequency fluctuations with zero mean value. Accuracy: ε To what extent does the clock realize the definition of the second? Cesium and rubidium fountains: ε ~ 4 10-16 Frequency stability Measurement duration τ: y(τ) averaged frequency instability For τ = 1s, y(τ) = 1.4 10-14 fundamental quantum limit For τ= 50 000 s, y(τ) ~ 1.4 x 10-16
Comparison between two Cesium Fountains FO1 and FO2 (Paris) cs14 τ 1/2 τ τ S. Bize et al. C. Rendus Acad. Sciences 2004 τ Measured Stability: 1.4 10-16 at 50 000 s Best measured stability for fountains! Factor 5-10/Hydrogen Maser Agreement between the Cesium frequencies: 4 10-16
Applications of atomic clocks Navigation, Positioning GPS, GLONASS, deep space probes Datation of millisecond pulsars VLBI Synchronisation of distant clocks TAI Geodesy Fundamental physics tests Ex : general relativity Einstein effect, gravitational red-shift : 10-4 10-6 Shapiro delay : 10-5 10-7 Search for a drift of fundamental constants such as the fine 1 17 structure constant α : α d α / dt at 10 / year
Fundamental Physics Tests
A transportable cold atom clock Transport to Bordeaux: 1997 MPQ:1999, 2003 PTB: 2002 Innsbruck: 2007
PHARAO in in parabolic flights in in Zero-G G Airbus Mai 1997
Connecting microwaves to optical frequencies Measurement of 1S-2S transition of Hydrogen at MPQ in Hänsch lab using the mobile cold atom fountain atomic hydrogen cryostat Faraday cage 2S detector ν 1S-2S = 2 466 061 413 187 103 (46) Hz Accuracy : 1.8 10-14 x 2 I chopper 243 nm 4/7 x f dye x4/7 70 fs Ti:sapphire mode locked laser vacuum chamber x1/2 f dye 1/2 x f dye λ 9.2 GHz dye laser 486 nm time resolved photon counting microwave interaction cold atom source detection M. Niering et al, P.R.L. 85, (2000) M. Fischer et al., PRL, 92 (2004) Multiplication by 250 000 of the cesium frequency to the UV range, 243 nm New limits on time change of fundamental constants, α and strong interaction constant
Frequency Comb J. Reichert et al. PRL 84, 3232 (2000), S. Diddams et al. PRL 84,5102 (2000)
Search for variations of fundamental constants and Einstein Equivalence Principle In any free falling local reference frame, the result of a non gravitational measurement should not depend upon when it is performed and where it is performed. EEP ensures the universality of the definition of the second It implies the stability of fundamental constants: α=e 2 /4πε 0 hc, m e, m p, In particular: the ratio of the transition frequencies in different atoms and molecules should not vary with space and time The EEP can be tested by high resolution frequency measurements regardless of any theoretical assumption EEP revisited by modern theories: g μν g μν,ϕ, Fundamental constants depend upon local value of ϕ : α(ϕ), m(ϕ), Violations of EEP are expected at some level!! For instance: T. Damour, G. Veneziano, PRL 2002
Do fundamental physical constants vary with time? G, α elm, α strong, m e / m p Principle : Compare two or several clocks of different nature as a function of time ex: Microwave clock/microwave clock rubidium and cesium Microwave/Optical clock Optical Clock/Optical clock
87 87 Rb - 133 Cs Comparison over 6 years 10 Relative frequency (10-15 ) 5 0-5 -10-15 -20 υ Rb = 6 834 682 610. 904 335 ( 12) Hz Within Prestage et al. theoretical framework : 1997 1998 1999 2000 2001 2002 2003 2004 Year d υ Rb 16 ln = ( 0.5 ± 5.3) 10 / year dt υcs α 16 = ( 1.0 ± 12) 10 / year α H. Marion et al., PRL (2003), Bize 2004
Test of Local Position Invariance Stability of fundamental constants Current limits: 1-3 10-16 /year See V. Flambaum lectures Bize et al. PRL 90, 150802 (2003) Fischer et al. 0312086, PRL 2004 Peik et al., PRL 0402132 (2004) Ashby et al., PRL 07 Fortier et al. PRL07
Further Reading Atom Interferometry ed. Paul Berman, Academic Press, 1997 Atoms quanta and relativity, special Issue of J Phys B: Atomic, Molecular and Optical physics, IoP (2005) ed., T. Haensch, H. Schmidt-Boecking and H. Walther C. Bordé, metrologia, 39, 435 (2002) C. Cohen-Tannoudji, lectures at Collège de France 1992-1993 Applied physics B special issue on cold atom sensors (2006) Next lecture: space clocks and fundamental physics