ATOMIC CLOCKS: BASIC PRINCIPLES AND APPLICATIONS

Transcription

1 ATOMIC CLOCKS: BASIC PRINCIPLES AND APPLICATIONS Lecture 1 Introduction to the lecture and to atomic clocks Cs thermal beam standards Gaetano Mileti, Laboratoire Temps Fréquence (LTF), Université de Neuchâtel Conférence CUSO Conférence Universitaire Universitaire de Suisse de Occidentale Suisse Occidentale Programme doctoral doctoral en de physique, Physique Printemps Printemps PLAN OF LECTURE 1 Introduction to the series of lectures Introduction to the topic and bibliography Program of lectures Organisation aspects Lecture 1: Introduction to atomic clocks Basic principles, categories and applications Magnetic resonance and generalised Bloch equations Tunable lasers and basics of atom-light interaction Thermal Cs standards 1

2 A) INTRODUCTION TO THE TOPIC AND BIBLIOGRAPHY Picture: View from Observatoire Cantonal de Neuchâtel, founded in HISTORICAL OUTLOOK The metamorphosis of time measurement Precision / Stability in seconds per day 1 ps Marine chronometers Space atomic clocks Atomic clocks (195) Hydrogen Maser, Caesium beam, Rubidium clock 1 ps 1 ns 1 ns Quartz oscillators (193) 1 s Earth rotation 1 ms Marine chronometers (175), Harrison Huygens Pendulum (165) pendulum 1 s 1 s Tower clocks (13) verge-and-foliot mechanism 1 s 4

3 OBSERVATOIRE CANTONAL DE NEUCHÂTEL (1858 7) 5 ESSENTIAL BIBLIOGRAPHY FOR THESE LECTURES Jacques Vanier, Claude Audoin, The Quantum Physics of Atomic Frequency Standards, Bristol: Adam Hilger, Claude Audoin, Bernard Guinot, Stephen Lyle, The Measurement of Time: Time, Frequency and the Atomic Clock, Cambridge, (Original in french: Masson, 1998). Fritz Riehle, Frequency standards Basics and applications, Wiley-VCH, 5. Special issue of Metrologia: Special issue: fifty years of atomic time-keeping: 1955 to 5, Volume 4, Number 3, June 5. Time & Frequency conferences proceedings (including tutorials) (free) EFTF-14 in Neuchâtel (June ) (on subscription) (on subscription) European Time and Frequency Seminar (EFTS) July 14 in Besançon (F) NIST Time & Frequency Seminar June 14 in Boulder (CO, USA) Previous editions of the CUSO lectures on atomic clocks (1 & 1) 6 3

4 B) PROGRAM OF CUSO LECTURES 14 (3 RD EDITION) Thursday February, lecture # 1 G. Mileti, Laboratoire Temps Fréquence (LTF), Université de Neuchâtel Introduction to the lectures and to atomic clocks, Cs thermal beam standards Thursday February 7, lecture # L. G. Bernier, Laboratoire de Photonique, Temps et Fréquence, Institut fédéral de métrologie (METAS) Atomic time scale, Allan deviation, time transfer, Hydrogen Masers & its applications Thursday March 6, lecture # 3 S. Schilt and R. Matthey, Laboratoire Temps Fréquence (LTF), Université de Neuchâtel Fundamentals in laser spectroscopy and laser frequency stabilisations. Examples of applications Thursday March 13, lecture # 4 G. Mileti and C. Affolderbach, Laboratoire Temps Fréquence (LTF), Université de Neuchâtel Vapour cell standards, chip scale atomic clocks, applications in telecommunications and navigation Thursday March, lecture # 5 J. Guéna, LNE SYRTE (Laboratoire National de Métrologie et d'essais, SYRTE), Observatoire de Paris Atomic fountains, primary frequency standards Thursday March 7, lecture # 6 T. Südmeyer, LTF UniNe and T. Kippenberg, Laboratoire de Photonique et Mesures Quantiques, EPFL Introduction to optical combs and applications. Examples of recent developments. Thursday April 3, lecture # 7 C. Salomon, Laboratoire Kastler Brossel, Département de Physique Ecole Normale Supérieure, Paris Laser cooling and trapping of atoms. Bose Einstein Condensation. The ACES experiment on the ISS Thursday April 1, lecture # 8 S. Bize, LNE SYRTE (Laboratoire National de Métrologie et d'essais, SYRTE), Observatoire de Paris Optical frequency standards and applications 7 C) REGISTRATION, REIMBURSEMENTS & EXAM Please register if you have not done it yet: Please fill the participation list (every Thursday) You may ask for reimbursement of travel costs: %C%AD%E%8%9doctoraux/administration/formulaires/ If you wish to take an exam and receive credits for your doctoral school: - Please check with your PhD advisor and doctoral school responsible - The exam is in the following form: - You agree with me (and your PhD advisor) on a topic related to the lectures - The topic may be also connected with your PhD thesis topic (if related to T&F) - You give a seminar followed by Questions & Answers Contacts: Gaetano.mileti@unine.ch, Salman.abdullah@unine.ch Esther.hofmann@epfl.ch; Alessandro.bravar@unige.ch 8 4

5 CONTENTS OF LECTURE 1 1. Basic principles, categories and applications. Magnetic resonance and generalized Bloch equations 3. Tunable lasers and basics of atom-light interaction 4. Thermal Cs beam standards 9 CONTENTS OF LECTURE 1 1. Basic principles, categories and applications. Magnetic resonance and generalized Bloch equations 3. Tunable lasers and basics of atom-light interaction 4. Thermal Cs beam standards 1 5

6 ATOMIC CLOCK: FREQUENCY-STABILIZED OSCILLATOR Interrogation Reference for the user (5 MHz) Feed-back Quartz oscillator Atoms Definition in SI system The second is the duration of periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of cesium 133 (1967) F=4 F=3 6 S ½ E E1 Frequency Hz h This would be the frequency of an atomic clock in which the atomic transition is not perturbed and the stabilisation perfect This topic will be developed in lecture # & 6 11 WHY WE NEED TO STABILIZE THE QUARTZ? Slide from: John Vig, tutorial on «Quartz crystal resonators and oscillators» 1 6

7 BASIC PHYSICA PRINCIPLE: MAGNETIC RESONANCE Magnetic resonance allows spin flip. Magnetic resonance is a frequency selective phenomenon Signal Probing frequency Linewidth Q 1 : resonance «duration» I y Q.( S. 1 N ) J. Vanier, L. Bernier, IEEE Trans. on Instr. and Meas., Vol. IM 3, No 4, Dec In an atomic clock you exploit this phenomenon to frequency stabilise a quartz oscillator In each type of clock it is realised on different species, in various configurations and with different detection techniques 13 STABILITY AND ACCURACY Frequency : Systematic bias Statistical fluctuations Stable but not accurate Not stable and not accurate Not stable but (relatively) accurate Stable and accurate Stable but not accurate Not stable and not accurate Not stable but (relatively) accurate Stable and accurate Inspired by: John Vig, tutorial on «Quartz crystal resonators and oscillators» How to measure / evaluate the stability and accuracy? By comparing to a more stable and/or accurate oscillator Statistical and non-statistical analysis 14 7

8 CATEGORIES OF ATOMIC CLOCKS Primary (Cs) Secondary Passive Active (H-Maser) Commercial (Rb, Cs, H) Ground or Space applications Laboratory In development Microwave Optical Neutral atoms Ions Molecules Nuclear - 15 EXAMPLES OF COMMERCIAL ATOMIC CLOCKS Rb cell clock (Spectratime) Cs beam (OSA) Passive H maser (OSA) Rb cell clock (Kernco) Active Hydrogen maser (T4S) Cs beam (Symmetricom) 16 8

9 EXAMPLES OF COMMERCIAL-SPACE-LAB ATOMIC CLOCKS Rb cell clock (Spectratime) Passive H maser (SpT) CSAC (NIST) Rb cell laser pumped clock (LTF) Miniature cell (LTF) CSAC (Symmetricom) 17 EXAMPLES OF PRIMARY AND OPTICAL CLOCKS F1 fountain (NIST) FOCS 1 fountain (METAS) Ytterbium ion clock (NPL) Cs1 & Cs beams and CSF1 & CSF fountains (PTB) 18 9

10 GENERAL SCHEME OF ATOMIC CLOCKS Servo loop Oscillator Atomic reference Interrogation 19 BLOC DIAGRAM OF AN ATOMIC CLOCK Magnetic resonance Hz Typically 5 or 1 MHz 1

11 IMPORTANT PARAMETERS Detection noise Discriminator slope D Frequency noise The most important parameters for the clock performances are: The resonance quality factor Q The signal to noise ratio S/N 1 LIMITATIONS RELATED TO THE «LOCAL OSCILLATOR» LO (quartz) - Direct AM noise and FM AM noise - Aliasing effects (Phase noise) Dick effect Transmitted light Microwave frequency y 1/ C S nf PM noise n1 n m See Deng et al., PRA 59 (1) 773 (1999) Finally (in the case of cell standards): total Inoise PM noise ls ( ) ( ) ( ) ( ) y y y y See Mileti et al., IEEE J. of Q. Electr. 34 () 33 (1998) This is a general limitation occurring in any type of atomic clock, including optical standards (see lecture Optical Clocks ) 11

12 EXAMPLE 1: RUBIDIUM VAPOUR CELL STANDARD Double resonance P Discharge lamp vapour cell Transmitted light khz light Microwave frequency S wave microwave resonator & source x Quartz LO 1s 1 s This topic will be developed in lecture #4 3 EXAMPLE : HYDROGEN MASER 1s 1s () 1/ 1 kg This topic will be developed in lecture # 4 1

13 EXAMPLE 3: CS BEAM STANDARD 1s but accurate and very stable in the long term 5 EXAMPLE 4: OPTICAL FREQUENCY STANDARDS 1 1 Q : Hz This topic will be developed in lectures #3, 6 &

14 MICROWAVE AND OPTICAL CLOCKS This topic will be developed in lectures # 6 & 8 7 EXAMPLE OF RECENT ACHIEVEMENTS 8 14

15 OVERVIEW OF APPLICATIONS AND NEEDS Agriculture (seasons) ~ 1 s Calendar (solstices, equinoxes) Daily activities (professional, social, etc.) Determination of the longitude (sea navigation) Common electronic and telecommunication devices Advanced telecommunication devices Future smart power grids Satellite navigation Scientific research and primary metrology ~ 1 s ~ 1 s ~ 1 s ~.1 s ~. 1 s ~. 1 s ~. 1 s <. 1 s Need of atomic clocks (in the device or to calibrate the device) 9 OVERVIEW OF APPLICATIONS OF ATOMIC CLOCKS Radioastronomy, Geodesy (VLBI, Radioastron, etc.) Scientific Research, Instrumentation (Microgravity, ACES, HYPER, etc.) Navigation & Positioning (Galileo, GPS, GLONASS, etc.) Telecommunications (Networks synchronisation, etc.) Power distribution networks (Smart power grids.) Metrology, Time scales (Primary and secondary standards, H-Masers) 3 15

16 GNSS (GLOBAL NAVIGATION SATELLITE SYSTEM) Example of European system GALILEO (GPS / GLONASS / COMPASS / Etc.) In space: Rubidium, passive Hydrogen Maser (1 generation) On earth: (quartz), Rubidium, Cesium beams, active H Masers (1 generation) GIOVE-A (launched 8 Dec 5) GIOVE-B (launched 6 April 8) 11 and 1: launch of first operational satellites (IOV In Orbit Validation) 31 EUROPEAN SATELLITE NAVIGATION SYSTEM (GALILEO) 3 16

17 WHY RB CLOCK AND PASSIVE H MASER ON GALILEO? For 3 cm accuracy Allan dev Cs beam, magnetic Cs-beam, laser H-maser, active H-maser, passive Rb cell, lamp Rb or Cs cell, laser CS cold Maximal Time error: 1 nanosecond for 1s < t < s y (' s) Time interval (s) Allan deviation will be defined in lecture # 33 VLBI (VERY LONG BASE INTERFEROMETRY) H-Masers ~1-1 s) are used to increase the resolution Angular resolution: ~ / Diameter 1 radio-telescope: ~ 1 mrad (1-3 rad) radio-telescopes: ~ 1 nrad (1-9 rad) Earth rotation: 1 mrad 6 km 14 s B sin c B This topic will be developed in lecture # 34 17

18 FUNDAMENTAL PHYSICS IN SPACE Atomic Clock Ensemble in Space Micro-gravity Relativity 1 1 Q This topic will be developed in lecture #7 35 CONTENTS OF LECTURE 1 1. Basic principles, categories and applications. Magnetic resonance and generalized Bloch equations 3. Tunable lasers and basics of atom-light interaction 4. Thermal Cs beam standards 36 18

19 CLASSICAL MAGNETIC RESONANCE (NMR) Magnetic moment d dt m m( t) m( t) B( t) (or ensemble of magnetic moments) interacting with a magnetic field B B Static magnetic field B o : Larmor precession B m B o B 1( t) Static magnetic field and resonant rotating magnetic field : magnetic resonance (frequency selective process) B pulse o s B 1( t) pulse 37 LARMOR PRECESSION Description of the system: Ensemble of paramagnetic particles exposed to a static magnetic field. Magnetic moment: Gyromagnetic ratio: Torque on : Evolution: Result: The magnetic moment rotates around the magnetic field with the angular velocity 38 19

20 MAGNETIC RESONANCE What happens if we add a small rotating magnetic field? perturbation Evolution of the total magnetisation: When the small perturbation produces a dramatic change of the magnetisation resonance! 39 MAGNETIC RESONANCE (IN ROTATING FRAME) Evolution in the lab frame: Evolution in the rotating frame: fictitious magnetic field 4

21 MAGNETIC RESONANCE: PULSE Pi-pulse in the lab frame Pi-pulse in the rotating frame 41 CLASSICAL BLOCH EQUATIONS (WITH RELAXATIONS) d dt d dt m ( t) ( m( t) B( t)) x m ( t) ( m( t) B( t)) y x y mx( t) T my ( t) T Stationary solutions d dt ( mz ( t) m m ( t) ( m( t) B( t)) ) z z T 1 T : longitudin al relaxation time 1 T : transverse relaxation time (collisions and magnetic inhomogeneities) FWHM 1 T T 1 T 1 / 4 1

22 CLASSICAL BLOCH EQUATIONS (WITH RELAXATIONS) Magnetic moments relax toward an equilibrium magnetisation due to collisions and B inhomogeneities. Longitudinal and tranverse relaxation rates are different The resulting equations are called Bloch equations: 43 STATIONARY (STEADY STATE) SOLUTIONS Relaxation + Power broadening 44

23 BLOCH EQUATIONS: INTERACTIVE DEMONSTRATION Available on the internet : Wolfram demonstrations project 45 GENERALISATION: THE BLOCH VECTOR (SEMI-CLASSIC) Atom (or ensemble of atoms) E E 1 Interacting field (RF, microwave, optical) i t e E E 1 Bloch vector (fictitious spin) The state of an atom ( levels) may be represented with a vector ( Bloch vector, or Fictitious spin ) and its behavior when interacting with a resonant field as a magnetic moment in a magnetic field. Microwave transitions, optical transitions, / pulses, etc. u v w atomic dipole in atomic dipole in quadrature difference of s phase populations R. Feynman, F. Vernon, R. Hellwarth, Geometrical representation of the Schrödinger equation for solving Maser problems, J. App. Phys, Vol. 8, p. 49, (1957). 46 3

24 EXAMPLES OF BLOCH VECTORS (AND ATOMIC STATES) Atoms in fundamental state (no resonance field) E E 1 s u v w 1 B o s Atoms after excitation (and field switched off) E E 1 s u v w 1 B o s Atoms after excitation (and field switched off) quantum superposition of states E E 1 s u v w cos( t) sin( t) B o s 47 GENERALISATION: ATOM INTERACTING WITH EM FIELD Spin 1/ + magnetic field (classical or quantum) Atom + laser (dipolar approximation) Atom + microwave B S H S B ds S B dt S B 1 B eff. B RF ˆ d :atomic Hˆ d ˆ E db fo b dt 85 nm ( MHz) fo B fo opt opt d 1 E 1 1 Laser electric moment ˆ : atomic H ˆ ˆ B db fm b dt RF 1RF 9. GHz magnetic moment fm B 1 B 1 fm RF 48 4

25 GENERALIZED BLOCH EQUATIONS S S S x y z u v w in phasecomponent of thedipole moment Re( 1) inquadrature component of thedipole moment Im( 1) population difference ( 11) Stationary solutions u w st 1 T1 1 1 T T u v w 1 u T u v 1 v T 1 v 1 1 T 1 w w w 1 1 T vst w T1 1 1 T T wst w T1 T T1 1 T T 49 THE BLOCH SPHERE pi/ pulse Coherent superposition of states and pi/ pulse 5 5

26 WHAT HAPPENS IN AN ATOMIC CLOCK Generalised magnetic resonance allows spin flips Or series of pulses such as The Ramsey scheme (/) It is a frequency selective phenomenon In an atomic clock you exploit this phenomenon to frequency stabilise a quartz oscillator Signal Linewidth In each type of clock it is realised on different species, in various configurations and with different detection techniques Probing frequency 51 ALKALI ATOMS IN A «MICROWAVE» CLOCK Hydrogen-like atoms: 1 unpaired electron Hyperfine structure: interaction of Simplified structure: e with nucleous P 3/ P 1/ Ground state: (Thermal equilibrium) s u v w lumière (1 14 Hz) S 1/ micro-onde ( Hz) 5 6

27 THE CASE OF CESIUM AND RUBIDIUM F J I 87 Rb m F = 87 Rb F= m F = 1 m F = m F = -1 m F= - 5S 1/ GHz F=1 m F = 1 m F = m F = Cs m F = 4 m F = 3 m F = 85 Rb 133 Cs F=4 m F = 1 m F = m F = -1 m F= - m F = -3 m F = F=3 Rb m F = 3 m F = m F = 1 m F = m F = -1 6S 1/ GHz 5S 1/ m F= - m F = GHz m F = F=3 m F = 3 m F = m F = 1 m F = F= m F = 1 m F = m F = -1 m F= - m F = -1 m F= - m F = GENERAL SCHEME (OR SEQUENCE) IN ATOMIC CLOCKS - Have the atoms available and as isolated as possible from the outside undesired interactions / perturbations; - Put (or select) as many atoms as possible atoms in one (of the two) levels; - Perform the magnetic resonance (in one or more steps); s 1 - Detect the result of the magnetic resonance (level transition) ; - Apply the necessary correction to the quartz oscillator Open loop (synthesizer) or closed loop mode 54 7

28 CONTENTS OF LECTURE 1 1. Basic principles, categories and applications. Magnetic resonance and generalized Bloch equations 3. Tunable lasers and basics of atom-light interaction 4. Thermal Cs beam standards 55 MOTIVATION Some types of traditional atomic clocks exploit the atoms-light interaction (lamp-pumped Rubidium clocks) Most of the new atomic clocks exploit stabilized lasers because they allow: A more efficient atomic state preparation / selection: Examples: optical pumping in Rb, Cs, Maser An improved detection of atomic states (S/N): Examples: optical pumping in Rb, Cs, Maser The possibility to slow (cool) or trap atoms Examples: cold atoms frequency standards To explore new physical phenomena Examples: Coherent Population Trapping The very existence of optical frequency standards Note however that their use in some cases (commercial product, space applications, etc.) require additional developments (reliability, cost, etc.) 56 8

29 HYPERFINE OPTICAL PUMPING IN RUBIDIUM CLOCKS Rb 85 - F= 3 Rb 85 - F= Absorption spectrum of natural rubidium D line (78 nm) with 3 mb of nitrogen Rb 87 - F= Rb 87 - F= 1 Lamp Rb 87 filter Rb 85 cell Rb Optical frequency detuning [ GHz] Thermal equilibrium Partial optical pumping Complete optical pumping P P P S S S This topic will be developed in lecture #4 57 PLASMA DISCHARGE RUBIDIUM LAMP excitation of a 87 Rb lamp with an RF oscillator (~1 MHz) Rb 85 - F= 3 Rb 85 - F= Absorption spectrum of natural rubidium D line (78 nm) with 3 mb of nitrogen Rb 87 - F= Rb 87 - F= Optical frequency detuning [ GHz] Isotopic filtering with a 85 Rb cell This topic will be developed in lecture #4 + Rb 85 - F= 3 Rb 85 - F= Absorption spectrum of natural rubidium D line (78 nm) with 3 mb of nitrogen Rb 87 - F= Rb 87 - F= Optical frequency detuning [ GHz] 58 9

30 LASER-PUMPED RUBIDIUM (VAPOUR-CELL) CLOCKS Microwave cavity detector Lampe Rb 87 filtre Rb 85 Resonance cell 6.8 GHz This topic will be developed in lecture #4 Potential advantages of using a laser: Rb 85 Optical filter Laser (1 line, < 1 MHz wide) Rb 87 Discharge lamp (several lines, > 1 GHz wide) 3 GHz Improve the stability Reduce the cost Reduce SWAP Possibility to introduce a redundancy Possibility to use other schemes Possibility to use of other atoms than Rubidium (example: Cs) 59 LASER-PUMPED BEAM STANDARDS Optical pumping 6 3

31 TUNABLE AND FREQUENCY-CONTROLLED LASER DIODES Examples of employed Laser diodes Solitary Fabry-Perot (FP) Extended cavity lasers (ECDL) Distributed Bragg Reflectors (DBR) Distributed Feedback (DFB) FP with DBR optical fiber Vertical Cavity Surface Emitting (VCSEL) MEMS based ECDL and VCSELs Discrete mode lasers Etc. 78, 795, 85, 894nm the atom may be changed Single mode, mode-hop free tuning Typical specs: 5-1 mw, LW < 5 MHz Low intensity and frequency noise 1.5um FP (RWL) ECDL DFB DBR VCSEL This topic will be developed in lecture #3 61 LINEAR OPTICAL ABSORPTION (WITH A LASER) Note: With a slow optical frequency (or wavelength) scan, this spectrum is visible only if there are collisions that destroy optical pumping. P S 3 5 Photocurrent [ma] F = F = 1 D lines of Rb Laser diode frequency [GHz] 6 31

32 ATOMS-LIGHT INTERACTION: LINE SHAPES i I ( ) i Rb [ W / cm ] 1 ( ) d [ cm ] [ s ] h [ J] Rb Absorption rate: number of photons absorbed per second by the atom (in level i) ( ) g( ),691 g ( ) [ cm ] g( ) o g( ) o o o ( ) ( ) natural width 5.9 MHz (Lorentzian) for an atom at rest ln 4ln( ) k T B g( ) e ln Mc Doppler (inhomogeneous) broadening: (Gaussian) 57 MHz, for 6 C 63 BUFFER GAS BROADENING (OF ABSORPTION LINES) Buffer gas (Lorentzian) Homogeneous broadening Convolution of a gaussian with a Lorentzian Voigt profile g ( ) Lineshape function g() [1-1.s] Rubidium 87 - D T = 6 C = 57 MHz No broadening = 1 MHz = MHz = 4 MHz = 6 MHz = 1 GHz Optical frequency detuning [ GHz] ( ) ln ln ( i ) ln ln ( ) ln Ree erfc ( i ) 64 3

33 EXPERIMENTAL EXAMPLES (USING AN ECDL) CO 1-3 CO -3 Rb 87 Rb 85 Photocurrent Laser locking range for the clock 3 Laser reference cell (natural Rb) CO 3-34 CO Mode hop Laser locking range for the prel. exp. on laser stabilisation Resonance cell transmission (modified TNT RAFS) MHz Piezo voltage 65 LASER FREQUENCY STABILIZATION 1-9 Spec Rb clock. Allan deviation of the laser frequency y () Doppler sub-doppler signal d'erreur U err (V) fréquence laser (MHz) With a cm-scale cell Sampling time (s) The laser stabilization method and the clock physical principle/parameters should be adapted in order to match the desired clock performances. It is a key issue for the medium and long term stability. This topic will be developed in lecture #

34 EXTENDED CAVITY LASERS beam collimation Diode & collimator Piezo Tiltable support: grating & optical isolator grating angle a sin Cavitylength L m Laser output 67 LASER RADIATIVE FORCES E( r, t) ê E cos[ Lt ( r)] F ê dab ust E( r) ê dab vst E( r) ( r) dipolar reactive force or dissipative or radiation pressure force ~ light-shift ~ absorption Optical trapping (lattice, tweezers, etc.) Optical molasses Motivations: reduce the Doppler effect, increase interaction time, etc. 1 This topic will be developed in lecture #

35 CONTENTS OF LECTURE 1 1. Basic principles, categories and applications. Magnetic resonance and generalized Bloch equations 3. Tunable lasers and basics of atom-light interaction 4. Thermal Cs beam standards CS CLOCK TRANSITION 6 P Coulomb 6 P 3/ 6 P 1/ D1 = 895 nm 51 MHz 1 MHz 151 MHz 1168 MHz 919 MHz F =5 F =4 F =3 F = F =4 F =3 6 S 1/ F = 4 Structure fine D = 85 nm = Hz F = 3 Structure hyperfine Hydrogen like atom Fine structure: LS coupling Hyperfine structure: IS coupling The fundamental term 6 S 1/ splits in two hyperfine levels (total ang. momentum F= I J = 7/ 1/ = 3 or 4), separated by E 1 = h 9. GHz and with a F+1 fold degeneratacy Clock transition 7 35

36 133 CS CLOCK (MAGNETIC DIPOLE) TRANSITION Cesium ground state : Magnetic dipole interaction: Clock transition Evolution of the system: We lift the degeneracy with a magnetic field. Two-level atom : Resonant behavior: 71 ATOMIC BEAM FREQUENCY STANDARDS Ramsey fringe Rabi pedestal Linewidth

37 MAGNETIC SELECTION 73 ATOMIC BEAM FREQUENCY STANDARDS Stern-Gerlach (State selection) and Ramsey interrogation s 1 1 sin( t) cos( t)

38 RAMSEY SCHEME For a monokinetic beam 75 ONE RF INTERACTION: RABI RESONANCE One interaction between RF field and atoms, of duration Atoms starting in the ground state The resulting state is given by solving Bloch equations. It depends on the RF field frequency detuning : RF? t= t= t= t= t= t= with 76 38

39 ONE RF INTERACTION: RABI RESONANCE RF Rabi resonance : with Wings, valid for >> 1 : 77 TWO RF INTERACTIONS: RAMSEY INTERROGATION Generation of Ramsey fringes : two Rabi interactions with separated by a free evolution time T T RF RF? Evolution of the Bolch vector : 1 st Rabi pulse nd Rabi pulse Free precession T= T= = 78 39

40 TWO RF INTERACTIONS: RAMSEY INTERROGATION 79 TWO RF INTERACTIONS: RAMSEY INTERROGATION 8 4

41 RAMSEY SCHEME WITH MONOKINETIC CS BEAM 81 RAMSEY SCHEME: NON-MONOKINETIC CS BEAM 8 41

42 COLD ATOMIC BEAM CLOCKS (FOUNTAINS) Linewidth 1 Thermal beam: v = 1 m/s, = 5 ms = 1 Hz Cold fountain: v = 4 m/s, =.5 s = 1 Hz.4.3 Lock-in signal Microwave frequency detuning :5:6 Next step: microgravity This topic will be developed in lecture #7 83 PRIMARY FREQUENCY STANDARDS Frequency : Systematic bias Statistical fluctuations See lecture of J. Guénat for an updated version of the accuracy budget of fountains This topic will be developed in lecture #5 84 4

43 ATOMIC TIME (TAI) AND ASTRONOMICAL TIME (UTC) Leap second This topic will be developed in lecture # 85 SUMMARY Compact high performance and miniature atomic clocks find many applications in every day life (positioning, telecoms, etc.) Atomic clocks (and stabilized lasers) are key instruments for fundamental physics experiments on ground and in space Thanks to the latest discoveries in atomic physics and photonics (or photon engineering) the precision of atomic clocks is being improved down to 1-17 and beyond More precisely, it is the manipulation of atoms photons and the availability of tunable laser sources and optical combs which is allowing such dramatic improvements ( In) stability 1 : : cooling going optical 86 43

44 THANK YOU FOR YOUR ATTENTION! Prof. Gaetano Mileti Laboratoire Temps Fréquence (LTF) Faculté des Sciences, Université de Neuchâtel Avenue de Bellevaux 51 CH- Neuchâtel, Switzerland