Operating principle of the atomic clock
Atomic clock principle in microgravity
General principle
The optical bench provides the laser beams for cooling, manipulating and detecting the caesium atoms. Light is delivered to the core of the device, the interaction chamber, using optical fibres. In this ultra-vacuum chamber (residual pressure below 10-10 Torr) is located a microwave cavity with two zones fed with a 9.2 GHz signal which is tuned around the caesium hyperfine transition at frequency 
0. A highly homogeneously static magnetic field is applied to the atoms with solenoid coils to control the magnetic environment and the vacuum tube is surrounded by three layers of magnetic shields to reject external magnetic perturbations.
The Clock Operates in a Sequential Mode
Capture of the atoms, launch, final cooling, preparation, selection, interaction with the microwave field, detection, and frequency correction. The cycle duration depends on the capture time and the launching velocity. The sequence is driven by a main computer (UGB) monitored by the ground control centre.
Caesium Atom Handling Cycle
First, about 108 atoms are captured and cooled in optical molasses at the intersection of six laser beams. Using the same set of laser beams, they are launched through the tube with an adjustable velocity v. After launch, atoms are quickly cooled to 1 micro-Kelvin (final cooling phase). Atoms in the particular quantum state F=4, with magnetic sublevel m=0 are selectively transferred in F=3, m=0 with an auxiliary microwave cavity (preparation phase). Atoms remaining in F=4 with m different from 0 are pushed sideways by radiation pressure (selection phase) so that only F=3, m=0 atoms proceed further in the tube in free flight. They interact twice with the microwave magnetic field in the two Ramsey zones separated in space. After these interactions, they enter the detection region where the transition probability from the lower quantum state to the upper one is measured by light induced fluorescence using 2 laser beams. In the first beam, only atoms in the internal state F=4 are detected and in the second beam only atoms in state F=3. The fluorescence is collected by 2 photodiodes and the resulting signal is processed by the controlling system.
Ramsey Fringes
This completes one cycle of operation of PHARAO. Repeating this cycle while scanning the microwave field around the caesium resonance produces the well-known Ramsey fringe pattern: the transition probability oscillates as cos²(-0)T/2 = cos²(-0)D/2v around the caesium hyperfine frequency 0. The period of the fringes is inversely proportional to the time T = D/v between two Ramsey interactions. In microgravity this time can be made 5 to 10 times longer than in an Earth fountain. For instance, the following figure displays the expected signal in PHARAO for v = 5 cm/s in comparison with a fountain signal and a thermal beam resonance.
PHARAO's expected signal versus the one of a fountain.
The gain in resolution obtained in microgravity conditions
a)The resonance in thermal beam Cs clock : width 100 Hz.
b) The resonance in a fountain : width 1 Hz.
c) The PHARAO resonance : width 0.1 Hz for launch velocity 5 cm/s.
Not only the interaction time can be longer in PHARAO but the constant atomic velocity in the device also brings a number of advantages with respect to the accuracy of the clock: low cavity phase shift and low collisional shift. The design parameters for PHARAO are a frequency stability of 10-13
-½ where is the measurement time in seconds, and an accuracy of 10-16. Averaged over one day, the stability will reach 2-3 10-16 and about 10-16 over 10 days. This stability crucially depends on the performance of the interrogation oscillator (Ultra Stable Quartz oscillator). PHARAO should be able to operate at a level of 3 10-14-½ with a cryogenic sapphire oscillator such as developed by the University of Western Australia (UWA) or the superconducting oscillator developed by Stanford University for test on the ISS (SUMO project). An optical communication link between the two experiments has been assessed.
Laser Beam Generation
Laser light is provided by an all-diode laser system. The optical bench includes 4 frequency stabilized diode lasers, some acousto-optic modulators to precisely tune the beam frequencies and control the beam intensities and mechanical shutters to turn off the light. The laser beams are injected into the ultra-vacuum tube with ten optical fibres.
Microwave Generation
The selection and the interrogation field which feed the microwave cavities are synthesized by a frequency chain. The main oscillator of the chain is a 10 MHz quartz oscillator whose frequency is multiplied and mixed with a programmable synthesizer to reach the 9.192... GHz. It is important that the phase correlation between the two fields (selection and interrogation) cancel in the mean term to avoid a frequency shift of the atomic resonance induced by an initial atomic coherence. The operating controlling system manages the operation of the clock. It provides all sequential signals, drives the power and the frequency of the synthesizer chain and processes both detection signals in order to derive the frequency correction to be applied to the programmable synthesizer of the frequency chain.
