Microwave clocks and fountains

Transcription

1 Microwave clocks and fountains Filippo Levi - INRIM "METROLOGY AND PHYSICAL CONSTANTS" Varenna 24 July 2012

2 Lecture outline Microwave clocks Physical principle Various type of clocks Cell clocks Cs beam H maser Cs Fountain Primary Frequency Accuracy evaluation

3 Two main categories Primary Frequency Standard If we need to know at our best the value of a frequency with respect to its definition. In this case the absolute phase of the microwave is not important. Time keeping devices If we want to keep time or synchronize oscillators. In this case the absolute phase of the microwave is the fundamental parameter.

4 What is a microwave clock INRIM Cryogenic fountain Fare clic per modificare stili del testo dello s Secondo livello er modificare stili del testo dello schema Terzo livello o livello Quarto livello Quinto livello lo o livello uinto livello NIST Chip scale atomic clock

5 Atomic Clocks: Basic Principle Local oscillator Clock output Correction Atomic sample Frequency stability depends on S/N (Sqrt of detected atoms nat) atomic quality factor Qat σ y (τ ) 1 1 2π Q S τ N Transition probability Interrogation Detuning

6 Most of the physics of a microwave clock can be model with: two-level atom magnetic dipole interaction The actual working mechanism of a real microwave clock needs also excited states (for optical pumping, laser cooling etc), but as long as we deal with the clock transition the above model is quite satisfactory.

7 Basic interaction The hyperfine energy separation of a general ground state can be written as c1 (t ) ψ E1 1 ω 0 = E1 E2 E2 2 c2 (t ) ψ 2 C1 + C2 = 1 2 We should now study what happens if a nearly resonant electromagnetic field is applied ( H i = g s µ B B e iω t + e i ω t )

8 Solving the Schrëdinger equation for this interaction we obtain: [ gµ B d c1 = ic2 s B 1 e i ( ω + ω 0 ) t + e i ( ω ω 0 ) t dt 4 [ ] Rapid oscillating terms d g s µ B B1 i ( ω + ω 0 ) t c2 = ic1 e + ei ( ω ω 0 ) t dt 4 ] Rabi Frequency: ω1 Probability of occupation of states Defining: Ω0= ω ω0 [ Ω = (ω ω 0 ) + ω 1 2 ] 2 1/ 2 P1 = c1 P2 = c Ω ω = 1 sin 2 t 2 Ω 2 Ω0 2 Ω 2 Ω = cos t+ t sin 2 2 Ω

9 Rabi Oscillations 0 Transition probability 1,0 ω= ω0 π 2π 3π 4π c2 2 0,8 c1 2 I.I. Rabi Nobel Prize ,6 0,4 0,2 0,0 ω- ω0= ω ω1 t In general terms, a µw pulse drives the atom in a states superposition whose phase is set by that of the µw field.

10 Linewidth Setting x= Ω ω 12 t / 2 where Ω 0 = ω ω 0 we obtain P1 = c1 2 2 Ω ω = 1 sin 2 t 2 Ω P1 = ( ω 1t ) 2 sen x 2 4 x 0, ,0 In small field approximation x (ω ω 0 ) t / 2 The linewidth is a function of the interaction time t Transition Probability 0,8 0,6 0,4 0, Detuning

11 From Rabi to Ramsey interaction To get a narrower line it is necessary to increase the interaction time. Extended field and high uniformity doesn t fit. A new technique was developed by Ramsey in 1949: Separate oscillatory fields Two short in phase interactions separated by a long free flight time TR Linewidth 1/TR N. F. Ramsey Nobel prize in 1989

12 Ramsey fringes The idea of Ramsey is to interrogate an atom through an interference process between atomic and electromagnetic phases. τ 1 T R τ 2 An interference take places! Atomic phase EM phase

13 Ramsey technique 1. During the free flight the atomic phase evolves with its own frequency. 2. If the microwave oscillates at the same frequency of the atom, the second interaction zone generates a constructive interference. 3. If the microwave oscillates at different frequency any combination is possible, depending on the TR duration.

14 Ramsey fringes observed in IT-CSF2 1,0 Transition Probability 0,8 0,6 0,4 0,2 0, Center frequency 90

15 Ramsey fringes with thermal beams or cold atoms Th R Thermal beam Cold atoms fountain

16 State selection To excite a microwave atomic transition (energy splitting is too small to allow natural decay) it is necessary to perturb the thermal equilibrium. Two major techniques have been developed: 1. Magnetic state selection 2. Optical pumping

17 Magnetic state selection: Stern & Gerlach experiment An electron with spin 1/2 has an intrinsic magnetic dipole moment. Passing through a magnet it is deflected Ms = gs e S 2me Alkali atoms like H, Na, K, Rb, Cs - having the lower energy shells complete - behave as spin 1/2 particles. O. Stern: Nobel Prize 1943

18 Classical Cs beam frequency standard Stern-Gerlach deflection principle.

19 Optical Pumping The second method used to realize a population inversion is known as optical pumping (developed by Kastler). This method uses light to excite atoms to higher energy states, wait for natural decay, and continue the cycle to unbalance the ground state population. A. Kastler Nobel Prize

20 An excited atom can decay spontaneously to the ground state. The decay branching ratios to the gs sub-levels are different, allowing various optical manipulation.

21 Discharge lamp pumping

22 Laser pumping A laser is a tunable monochromatic radiation. The perfect mean to realize optical pumping. 87Rb F=0 F=1 F=2 F=2 F=1 D1 λ=794 nm F=35P3/2 5P1/2 D2 λ=780 nm F=2 5S1/ GHz F=1

23 Rb cell frequency standard Magnetic shield C-Field 87Rb lamp 85Rb + buffer Laser gas Light Absorption cell Rb-87 + buffer gas Photo cell Filter Cell Cavity Frequency input 6.834,685 GHz rf lamp exciter Power supplies for lamp, filter and absorption cell thermostats Servo system C-field power supply Detector output

24 Doppler Effect Rejection Atoms are generally moving fast. Doppler shift (and broadening) are very annoying effects in high accuracy spectroscopy. Means to avoid the Doppler effect should be implemented: Saturation spectroscopy Laser cooling Buffer gas Standing wave interrogation

25 Doppler shift v k f 0 f = 1 c f = v cos θ f0 c Even for cold atoms (1µK -> v 1cm/s) f v = f0 c 3 10 Need of Doppler Cancellation: Transverse interrogation Saturation spectroscopy Standing wave Buffer gas localization Very large shift!

26 Laser beams Saturation spectroscopy θ m Ato v cos θ f0 c v cos θ f2 = + f0 c f1 = ity c o l ve If θ =π/2 the two shift are coincident. Pump laser saturates the transition inducing a transparency (Lamb dip) in the medium at resonance. Level crossing appears in the Doppler free spectrum (pump and probe excite two different transitions).

27 If the atom has an average zero velocity no Doppler shift is observed This is the case of the buffer Gas, where Rb atoms experience multiple collisions and many velocity changes during the interaction, resulting in a Doppler cancellation. If the Electomagnetic wave is a standing wave no Doppler shift is observed This is the case of interaction inside a resonator, where a standing wave is extablished. In this case the absorbed photonkcarries no and no Doppler shift is observed.

28 Relativistic Doppler effect f0 = v2 1 2 f c Atomic beams: 2 10 f f Cold atom spectroscopy 2 f f This effect is always present and we must account for it in accuracy evaluation of frequency standards.

29 Active and Passive µw clocks A clock is said to be active when we observe the photons emitted by the atoms and we use their frequency to servo our oscillator (phase locked loop). A clock is said to be passive when we interrogate an atomic sample with a EM filed and we observe the atomic resonance and we use the resonance signal to servo our oscillator (frequency locked loop).

30 Review of the most important microwave clocks Maser H

31 H maser Very high stability Very expensive Heavy and power consuming Laboratory device

32 Hyperfine structure of H atom Zeeman structure of H

33 Working scheme Atomicflux 1012/s

34 H Maser start-up emission An oscillating behavior can be observed before a staedy state emission is reached. The exponential time constant depends on the Maser gain (flux and cavity Q)

35 H-maser stability

36 Rubidium cell

37 Rubidium cell clock The most common clock Cheap Very rough Very small Low power consumption Well performing Can be installed almost anywhere

38 Double resonance scheme

39 Magnetic shield C-Field 87Rb lamp 85Rb + buffer gas Filter Cell rf lamp exciter Power supplies for lamp, filter and absorption cell thermostats Light Rb-87 + buffer gas Absorption cell Photo cell Cavity Frequency input 6.834,685 GHz C-field power supply Detector output

40 Commercial Rb clocks modificare stili del testo dello schema ello o vello

41 Caesium Beam frequency standard

42 Commercial device Fare clic per modificare stili del testo dello schema Secondo livello Terzo livello Quarto livello Quinto livello

43 Zeeman effect in Cs Fare clic per modificare stili del testo dello schema Secondo livello Terzo livello Quarto livello Quinto livello

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45 Cs beam Medium stability (7x10-12 τ-1/2). Low frequency drift. Best accuracy performances in commercial clocks. Poor absolute accuracy (compared to its long term stability).

46 Stability performances of various standards -9 Log (σy(τ)) -10 ar u Q -11 tz -12 um i d i ub R Cesium beam H Maser Log (τ), σ day 1 month

47 Accuracy Evaluation of a Cs Fountain Primary Frequency Standard

48 The Second Definition In 1967, the 13th General Conference on Weights and Measures, redefined the International System (SI) unit of time, the second, in terms of atomic time rather than the motion of the Earth. Specifically, a second was defined as: the duration of 9,192,631,770 cycles of microwave light absorbed or emitted by the hyperfine transition of 133Cs atoms, at rest in their ground state undisturbed by external fields (at 0K).

49 In 1955 Essen and Parry realized the first Cesium beam Atomic Clock at the National Physical Laboratory, UK. It kept time to a second in 300 years (10-10 accuracy). Nowadays laser cooled Cs fountains realize the second with an uncertainty of few parts in Six order of magnitude better than the first Cs clock developed by Essen and Parry!

50 lic per modificare stili del testo dello schema ondo livello o livello Quarto livello Quinto livello Fare clic per modificare stili del testo Secondo livello Terzo livello 1E-9 1E-10 1E-11 de m o d em o de m o d e m o Relative accuracy Essen and Parry Clock (1956) 1E-12 1E-13 1E-14 1E-15 1E-16 1E-17 de m o d em o de m o d e m o d em o de m o d em o de m o d e m o d em o de m o d em o de m o d e m o d em o de m o d e m o d em o de m o d e m o d em o Cs clocks d em o Optical clocks de m o de m o d em o Quarto livello Quinto livello d em o Optical comb era 1E-18 Laser cooling era Year INRIM criogenic Fountain (2010)

51 Operating cycle of a fountain Fare clic per modificare stili del testo dello schema Secondo livello Terzo livello Quarto livello Quinto livello (animation by NIST) Without going into details of laser cooling, it is sufficient to know that it is possible to cool atoms to very low temperature (1 µk) and to efficiently manipulate their state.

52 TAI calibration TAI is realized mainly with an ensemble of commercial clocks, good stability but poor accuracy. PFS are used to measure, to the highest possible accuracy level, the frequency of a clock that participate to TAI scale. Accuracy of the PFS is transferred to the clocks. Transfer of frequency data to BIPM done via TWSTFT or GPS CP. Time must be realized at a given gravitational potential (mean sea level).

53 ACCURACY EVALUATION OF IT CSF1 IEN CsF1 frequency is corrected for: Zemman effect Atomic density Black body radiation Gravitational red shift Microwave effects

54 ZEEMAN EFFECT CALCULATION Φ=0, µ=±1 ν = 350 x107x B ( Hz/T ) 1.0 Transition Probability 0.8 Low frequency pulse when atoms reach apogee Frequency (Hz)

55 C-FIELD MAP 1,03 1,01-7 C Field (10 T ) 1,02 1,00 0,99 0,98 0,97 0,96 0,0 0,1 0,2 0,3 Height above cavity (m) 0,4 0,5

56 RAMSEY FRINGES: MAGNETIC 1-1 TRANSITION ν = x107x B ( Hz/T ) 3,-1> -> 4,-1> 0.9 Transition Probability Frequency detuning (Hz) -600

57 COMPARING C-FIELD MAPPING METHODS calculated by low frequency map Ramsey 1-1 central fringe method Central fringe frequency (Hz) ,0 0,1 0,2 0,3 0,4 0,5 Height above cavity (m) We predict the central fringe frequency with an uncertainty < 200 mhz The resulting relative uncertainty on the clock transition is 3x10-17

58 DIFFERENTIAL MEASUREMENTS MEASUREMENT A TA MEASUREMENT B TB (νa-νlo) - (νb-νlo) = νa- νb We can vary most of the parameters at will (e.g. density, state selection frequency, microwave power, shutter timing etc.) No matter of the noise process and color, differential measurements yeld white noise

59 P.J. Leo et al. Collisional Frequency Shifts in 133Cs Fountain Clocks PRL

60 Density shift evaluation Density shift is evaluated with differential techniques in IT Cs F1 and also in many other fountains. y0 yld ν yhd ν NLD NHD coll y HD y LD = ρ LD ρ HD ρ LD meas ν coll Only if RV = 1 the linearity holds! = y HD y LD N LD N HD N LD = RV RN 1 ν RN RV meas

61 Atom density bias and uncertainty y0 = 2 σ 2 y0 RN σ = R N -1 RN 1 y LD y HD + R N -1 R N yld 1 σ + R N -1 2 yhd Type A y LD y HD σ + 2 ( RN 1) 2 RN + σ 2 Type B It is evident that: the contribution to the uncertainty of the LD measurement is the dominant one the ratio R should be kept as high as possible, its fluctuation are almost irrelevant in the final uncertainty The best uncertainty is obtained with asymmetric time distribution in favor of low density

62 -15 y(iencsf1)- y(ienhm2) (x10 ) Density bias and uncertainty Measured data Linear fit Quadratic fit < < σ 6 4 σ Detected Signal (a.u.) σ 2 y0 ( ) + ( 2 10 ) 16 2 ( ( 0.1 ( y0 y LD ) ) ) 2

63 Gravitational Red Shift According to its definition the second can be realized, as a proper time, in any gravitational field. In order to contribute to TAI, that is a Coordinate Terrestrial Time scale, the local realization must be referred to the Geoid gravity equipotential surface, defined as the mean sea level. INRIM has a geodetic antenna contributing to the IGS network, giving the geodetic height at mm level. The orthometric height is obtained, by the use of the Italian quasi-geoid model at 5 cm level.

64 Gravitational Red Shift Gravitational Red shift is given by W(r) has two components: gravity and centripetal We define a normal gravity and a perturbation, the ellipsoid approximate the normal gravity, the perturbation is the undulation (Geoid).

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67 undulation is obtained by satellite missions (GOCE and GRACE)

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69 Blackbody Radiation shift Cesium atoms are observed in a given temperature environment. A blackbody is a theoretical definition, only approximated in nature. Each body has its own temperature and emits pseudoblackbody radiation. This radiation produces a Stark effect on the atom resulting in a frequency shift.

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71 νbb = x 10-4 x (343/300)4 Hz = x 10-4 Hz (Relative 2.93 x 10-14)

72 Microwave related problems Operating the fountain at increasing microwave power (multi-π/2 pulses) is a common technique to investigate the presence of microwave anomalies. This method indeed is not able to distinguish between a certain number of microwave related effects. Leakage, spurious, Distributed Cavity Phase, Δm=1 transitions, are enhanced sometime in undistinguishable ways.

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74 Microwave tests 1. Frequency sensitivity to the Ramsey excitation power: i) varying the pulse at multiple of the optimum power (2n+1)π/2, or ii) above or below the optimum power (π/4, ¾ π) 2. Frequency sensitivity to the State selection excitation power. 3. Measurement of the amplitude of the most intense spur in the microwave spectrum. 4. Phase and amplitude balance between the two feeding arms of the Ramsey cavity. None of the experiments give a measurable shift at level. σ µw

75 ITCsF1 Accuracy budget Physical effect Zeeman Blackbody Gravitation Atomic density Microwave effects Total Bias (E-15) Uncertainty

76 ITCsF2 Accuracy budget Physical effect Zeeman Blackbody Gravitation Atomic density Microwave effects Total Bias (E-15) Uncertainty

77 Frequency ratios and fundamental constants Hyperfine structure Cs H Rb Hg+.. m α gp e mp I2 Ca H Hg+ α 2 gi gi gp me mp m gp e mp m gi e mp Cs Mg Ca α 2 gi CH4 OsO4 Vibrational me mp me M Fine Structure Electronic 2 d me gp / yr dt m p Godone et al. PRL 71, (1993)

78 Laboratory test of α variations Relativistic corrections : the energy of the hyperfine frequency of an alkaly depend on α and Z The ratio of the hyperfine energies of different atomic species explicitely depends on α Hg+ vs H : Prestage et al., PRL 74, 3511 (1995) d υ2 α α ln = [ Ld Frel ( α, Z 2 ) Ld Frel ( α, Z1 ) ] = K 21 dt υ 1 α α

79 Hg+, Yb+, Al+ Cs comparisons Fare clic per modificare stili del testo dello schema Secondo livello Terzo livello Quarto livello Quinto livello

80 Conclusions We have described some of the operation principles of microwave clocks. Made evident the difference between clocks and PFS. Discussed how Fountain accuracy is evaluated. Presented how microwave clocks are used to test fundamental physical theories