HOW AN ATOMIC CLOCK WORKS

How an atomic clock works 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 a microwave cavity with two zones fed with a 9.2-GHz signal tuned around the caesium hyperfine transition at frequency 0. A highly homogeneous 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 sequential mode

This sequence comprises 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 launching velocity. The sequence is driven by the onboard management unit (UGB) monitored by the ground control centre.

Caesium atom handling cycle

First, about 10⁸ atoms are captured and cooled in an 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 to 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 spatially separated Ramsey zones. 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 two 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. Fluorescence is measured by two photodiodes and the resulting signal is processed by the control 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 five to ten 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 that of a fountain.
Gain in resolution obtained in microgravity conditions
a) Resonance in thermal beam Cs clock: width 100 Hz.
b) Resonance in a fountain: width 1 Hz.
c) PHARAO resonance: width 0.1 Hz for launch velocity 5 cm/s.

Not only can the interaction time can be longer in PHARAO, but the constant atomic velocity in the device also affords a number of advantages with respect to the clock’s accuracy: 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 (ultrastable quartz oscillator). PHARAO should be able to operate at a level of 3 10^-14 -½ with a cryogenic sapphire oscillator such as that developed by the University of Western Australia (UWA) or the superconducting oscillator developed by Stanford University for tests 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 four frequency-stabilized diode lasers, 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 by ten optical fibres.

Microwave Generation

The selection and interrogation fields that feed the microwave cavities are synthesized by a frequency chain. The main oscillator in the chain is a 10-MHz quartz oscillator whose frequency is multiplied and mixed with a programmable synthesizer to reach 9.192... GHz. It is important that the phase correlation between the two fields (selection and interrogation) cancels out in the medium term to avoid a frequency shift of the atomic resonance induced by an initial atomic coherence. The control 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.