Magnetic field control
The transition is shifted by 1.4 MHz in a 1 Gauss field. It is thus essential for a good contrast of the Ramsey interferometer to control the stray magnetic fields.
All the experimental core is made of non-magnetic materials (copper, niobium and brass). All stainless steel parts nearby are carefully demagnetized. The assembly is realized with amagnetic bronze tools to prevent remagnetization. All screws, plugs, cables are individually tested for their residual magnetic field.
Five levels of magnetic shielding are used. Three coils around the cryostat assembly reduce the lab magnetic field amplitude at the few 100 mG level. Two -metal high permeability shieds surround the nitrogen reservoir and shield in the cryostat assembly. The inner part of the 0.6 K shield is plated with Indium, superconducting at this low temperature. It does not screen the magnetic field, but reduces its fluctuations. Finally, the rectangular box enclosing the three Ramsey zones and the two cavities is completely covered with 10 layers of high permeability Vitrovac alloy.
We have cheched that the residual magnetic field in this assembly is in the 10 G range, with very low gradients. We thus think that magnetic field fluctuations do not contribute to any Ramsey interferometer contrast reduction.
Electric field control
The circular states are stable only in a directing electric field. This field is applied in a controlled way all along the atomic field path (across the cavity mirrors, between the gold plate and the graphite mirror in the Ramsey zones). The shape of the conductors and guard rings have been designed to optimize the field homogeneity along the atomic path.
We have checked the field map with position-resolved spectroscopy of Stark-sensitive lines between low angular momentum Rydberg states. It agrees very well with numerical simulations of the field performed with the Simion sofware.
Of course, the voltages applied on the field-generating electrodes take into account the contact potentials between the metals (mainly gold and niobium). We have determined precisely these potentials by Rydberg states spectroscopy.
It is also important that the atoms never get close to any metallic surface. The patch effect contact potentials create strong inhomogeneous electric fields in the immediate vicinity of these surfaces. The atoms are never closer than 5 mm from any surface in their path trough the atomic apparatus.
As illustrated in this figure (cut through the set-up, with the circular states preparation box on the right and the field-ionization detectors on the left), the atoms are never closer than 5 mm from any surface in their path trough the Ramsey atomic interferometer. They enter and exit the shielding box through small diameter holes, but atomic coherences need not be preserved then. Strong fields preseve only the atomic populations.
Blackbody radiation control
The hundreds of thermal photons per mode at room temperature must not leak into the core of the experiment. The central rectangular box enclosing the atomic Ramsey interferometer has only two small entry and exit holes, with a 3 mm diameter, below cut-off for the 51.1 GHz transition frequency.
All signal lines use stainless steel coaxial cables, with a very strong attenuation in the millimeter-wave range. All waveguides getting inside the box include strong attenuators cooled at 0.8 K. Microwave absorbers are installed inside the 0.6 K shield to trap any residual photons, coming from instance from the electrostatic lenses used to route the electrons to the electron multipliers. The lasers and atomic beams are fed through circular waveguides below cut-off for the millimeter-waves.
The measured residual photon number in the cavity mode is then, within the experimental errors, equal to the thermodynamical limit, 0.05 photons on the average at 0.8 K.