PHARAO frequency accuracy: preliminary evaluation on the FM 

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Atom cooling (Doppler and sub-Doppler cooling) and the launch

Doppler cooling (32, 33, 34, 35, 36) is based on the Doppler effect. Three pairs of laser beams are positioned in opposite directions and tuned a little below the transition frequency of 6S1/2(F = 4) → 6P3/2(F = 5). Due to the Doppler effect, atoms moving inside the laser beams in the counter propagating direction absorb more photons and their momentum is decreased.
However, the atoms can also be excited in the 6S1/2(F = 4) → 6P3/2(F = 4) (every ≈ 1000 transitions) and can decay in the 6P3/2(F = 4) → 6S1/2(F = 3) transition. In that case the atoms are no longer submitted to the laser cooling process. That is why another laser beam tuned to the 6S1/2(F = 3) → 6P3/2(F = 4) transition pumps them to the 6S1/2(F = 4) level. Using the optical Bloch equations (37), the scattering rate for atoms is: 2 1 + I/Is + 4(Δ/ )2  sc = I/Is (2.5).
where is the natural linewidth, Δ = (ω − ω0 − k × v) is the frequency detuning, I is the photon intensity and Is is the saturation photon intensity (1.1 − 1.6mW/cm2 depending on the beam polarization).
After time τ , inversely proportional to the natural linewidth (3.3 × 107s−1) of the excited state, the state 6P3/2(F = 5) decays and emits a photon. This emission has an isotropic angular distribution so the overall result after many recoil events is the reduction of average atom velocity, and therefore its kinetic energy and temperature.
The laser beam intensity needs to be large in order to be able to decelerate a wide range of initial velocities. The maximum recoil impulse amounts to hk¯l × /2 per unit of time, where ¯hkl is the momentum of a photon. The force a cesium atom experiences is dpdt = ¯hkl 2 . From that the acceleration can be calculated: v rec = hk¯l = 3.52mm/s. (2.6).

Perspective and other clocks

Other atoms besides cesium are also studied to use as a secondary standard. For example, a 87Rb clock (42) is physically similar to a cesium clock and has an electronic structure favourable for laser cooling. Due to a lower cross section of 87Rb atoms, the frequency shift due to cold collision is reduced by a factor of 15. Based on the work on the double cesium-rubidium FO2 clock at LNE-SYRTE in Paris over several years, the secondary representation of the definition of the second is given by the hyperfine transition of frequency f (87Rb) = 6 834 682 619. 904 312 with a relative standard uncertainty of 1.3 × 10−15 (43). Another alternative for a frequency standard are optical clocks. Optical frequency standards are based on an optical electronic transition with narrow bandwidth that stabilizes the frequency of the laser. The atoms are trapped using the Penning trap or optical trap and laser cooled. Optical clocks can be constructed using atoms (for example Ca, Rb, Sr, Yb, Mg or H), ions (Hg+, Sr+, Yb+, In+, Al+) or molecules (I2, CH4, C2H2). Some of the advantages of optical clocks are higher accuracy and stability due to the higher frequency of the resonance.
In 2001, femtosecond laser techniques (44) broke the gap between frequency com-parisons in the optical and microwave domains. The development of laser locking on a high finesse cavity (to provide very low noise optical oscillators), atom cooling and trapping processes have lead to a significant optical clock technology advancement. In July 2013, two optical lattice strontium clocks were able to stay in synchrony at 1.5 × 10−16 (45) at 1s. In August of the same year NIST ytterbium optical clocks achieved a frequency stability of 2 × 10−18 (46) at 1s, a new record in atomic clock stability.
Transfer of atomic clocks to space will open new possibilities in clock development and usage. The scientific and technological performances will be improved because of the microgravity environment, the possibility of additional fundamental physics test, possibility of high performance intercontinental clock comparison, etc. Next chapter introduces the ACES mission which is dedicated to high space clock performances and fundamental physics.

ACES payload and requirements

The ACES payload (shown on Figure 3.8) has a volume of about 1m3, a total mass of 230 kg and a power consumption of 450 W (11). It includes the hydrogen maser SHM, the cold cesium clock PHARAO, a GPS/GALILEO receiver, a two way time transfer in the S and Ku band MWL and a two way time transfer in the optical band (500nm) ELT. The FCDP measures the phase/frequency difference between PHARAO and SHM and distributes the reference signal to the transfer links. XPLC is the payload computer.

Signal merging and data handling

Telecommand, telemetry and data handling for all ACES instruments and short and long-term servo loop is ensured by the eXternal PayLoad Computer (XPLC), developed by ASTRIUM under ESA responsibility.
ACES will operate a phase locked loop which will stabilize the medium term stability of the PHARAO local oscillator on the clock signal generated by SHM which has a better medium term stability (Figure 3.11). Data corrections are sent every 250 ms. Short, medium and long term stability are defined on time intervals of 0.0001s to 1s, 1s to 1000s and 1000s to ∞, respectively. In order to compare the 100 MHz signals of SHM and PHARAO the Frequency Comparison and Distribution Package (FCDP) is used. It was developed by ASTRIUM and TimeTech under ESA responsibility. FCDP is the central node of the ACES signal management also responsible for signal distribution to the time and transfer link.
Instability of the hydrogen maser for τ > 3000s will be measured and corrected by a second servo loop. XPLC receives the PHARAO measurements and sends the correction to SHM at a rate of several hundreds seconds. Resulting fluctuations of the ACES timescale based on the SHM signal are expected to be around 10 ps per day.

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Time and frequency transfer: MWL and ELT

The implemented microwave link MWL (57), developed by ASTRIUM, Kayser-Threde and TimeTech, is one of the key elements of ACES surpassing the performances of the currently used transfer links (TWSTFT and GPS) by one to two orders of magnitude. It is a two-way system with two different frequencies that allows both space to ground and ground to ground clock comparisons. It has 4 channels allowing 4 simultaneous ground users. MWL has a high carrier upload and download frequencies (13.5 and 14.7 GHz, respectively). Another frequency in the downlink S-band (2.2 GHz) is used to correct the ionosphere time delay by measuring Total Electron Content (TEC). A code phase measurement removes the phase ambiguity between separated ground space clock comparisons.
To evaluate instrumental errors, ground MWL stations will have electronics similar to the on-board MWL.
Medium term stability after ≈ 300s is driven by the noise performance of the DLL (Delay-Locked Loop) boards, while the long term stability is provided by continuous calibration by a built-in test-loop translator.
ACES will also accommodate a GALILEO/GLONASS/GPS receiver as part of the payload directly connected to the ACES signal. It will provide orbit determination and payload positioning information. Comparison of ground clocks is possible using the common view and the non-common view technique. Common view technique is used when both clocks are ge-ographically close enough to be in view of ACES. Two channels of the MWL are used simultaneously. By comparing two clocks, common-mode noise from the space clock is rejected and a direct comparison between ground clocks provided. The instability is only due to the noise of the time and frequency link. Due to low orbit height of the ISS, this technique can be utilized for comparing clocks over distances within a continent and for periods of short duration (∼ 300-400 s) for 3-5 comparisons per day on average. Example of the ISS number of passes over Paris is given on Figure 3.13.

Table of contents :

1 Introduction 
2 Atomic clocks 
2.1 Principle and performances
2.1.1 Clock accuracy
2.1.2 Clock stability
2.1.3 Clock development
2.1.3.1 Selection of cesium and alternatives
2.2 Atomic fountain – primary frequency standard
2.2.1 Cesium atomic fountain operation
2.2.1.1 Atom cooling (Doppler and sub-Doppler cooling) and the launch
2.2.1.2 Ramsey interrogation
2.3 Perspective and other clocks
3 ACES mission 
3.1 International Space Station
3.1.1 Orbit and environments
3.1.2 Instrument positions
3.1.3 Vehicle support
3.2 ACES payload and requirements
3.2.1 SHM
3.2.2 PHARAO
3.2.2.1 Operation
3.2.3 Signal merging and data handling
3.2.4 Operation modes
3.2.5 Time and frequency transfer: MWL and ELT
3.3 Scientific objectives
3.3.1 Fundamental physics
3.3.1.1 Gravitational red-shift
3.3.1.2 Drift of fine structure constant
3.3.1.3 Anisotropy of light
3.3.2 Geodesic application
3.3.3 International Atomic Time contribution
4 PHARAO 
4.1 PHARAO architecture
4.2 PHARAO development
4.3 Microwave source
4.3.1 Microwave synthesis chain
4.4 Laser source
4.4.1 Optical bench layout
4.4.1.1 ECDL
4.4.1.2 ECDL output
4.5 Electronic control system
4.6 Cesium tube and operation
4.6.1 Atom capture
4.6.2 Atom cooling
4.6.3 Preparation and selection
4.6.4 Interrogation
4.6.5 Detection
4.6.6 Magnetic shields
4.6.7 Experimental ground operation
4.6.7.1 Experimental setup
4.6.7.2 Initial starting, optimization an results of the clock
5 PHARAO frequency stability 
5.1 Sources of noise in PHARAO
5.1.1 Quantum projection
5.1.2 Detection system noise
5.1.3 Detection laser noise
5.1.4 Local oscillator noise – Dick effect
5.1.5 Micro-vibration effect
5.2 Experimental results and discussion
6 PHARAO frequency accuracy: preliminary evaluation on the FM 
6.1 Second order Zeeman effect
6.1.1 Flight model shields characterization with a magnetic probe
6.1.1.1 Shield architecture
6.1.1.2 Shield characterization experimental setup
6.1.1.3 The external B3 shield
6.1.1.4 Individual B2 and B1 shields
6.1.1.5 Shield combinations B1+B2, B2+B3 and B1+B2+B3 .
6.1.1.6 Magnetic field homogeneity
6.1.1.7 Space qualification of the shield
6.1.2 Magnetic results of the flight model by using cold atoms
6.1.2.1 Axial and transverse field attenuation
6.1.2.2 Magnetic field evaluation
6.1.2.3 Conclusion to FM shield experiments
6.1.3 Active compensation
6.1.3.1 Introduction
6.1.3.2 Experiment
6.1.3.3 Model description
6.1.3.4 Postulate I
6.1.3.5 Postulate II
6.1.3.6 Postulate III
6.1.3.7 Active compensation system
6.1.3.8 Experimental setup
6.1.3.9 Axial external field pattern and results
6.1.3.10 Orbital external field testing
6.1.3.11 Axial results
6.1.3.12 Degradation of results for the total field and the tracking procedure
6.1.3.13 Shield attenuation as a function of external field amplitude and demagnetization
6.1.4 Conclusion to Zeeman shift
6.2 Black body radiation
6.2.1 Introduction
6.2.2 PHARAO thermal architecture, development and temperature uncertainty
6.2.2.1 STM experimental results and modelization
6.2.2.2 FM modelization
6.2.2.3 FM experimental results
6.2.2.4 Measurement uncertainties
6.2.3 Conclusion to black body
6.3 Cold collision
6.3.1 Introduction
6.3.2 Collision frequency simulation
6.4 Doppler effect (DCP)
6.5 Conclusion to systematic effects
7 Conclusion 
8 Appendix 1 
8.1 Ramsey interrogation
8.1.1 Classical representation
8.1.2 Quantum physical interpretation of interference
8.1.3 Semiclassical representation
8.1.3.1 Single oscillatory field – Rabi magnetic resonance method225
8.1.3.2 Double oscillatory field – Ramsey magnetic resonance method
8.1.4 Fictitious spin representation
9 Appendix 2 
9.1 Sub-Doppler
10 Appendix 3 
Bibliography 

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