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Cavités Fabry-Perot supraconductrices
We use high quality Fabry Perot Niobium superconducting cavity. We have devoted considerable efforts for the improvement of these resonators in the past years. They reach now extremely long photon storage times, in the second range (0.13 s). We recall here the important steps in this development.
Very long damping times can be obtained straightforwardly with closed superconducting cavities. 
values up to 
have been reported in the GHz frequency range, and cavity field lifetimes of a fraction of a second obtained at 21 GHz in micromaser experiments.
However, circular Rydberg atoms require a weak directing electric field to avoid admixture with other states in the hydrogenic manifold. They are not compatible thus with the high closed cavities, which are obviously an equipotential volume.
We used instead Fabry Perot cavities, made up of two spherical mirrors facing each other (figure above). The mirrors have a 50 mm diameter and a 40 mm radius of curvature. The cavity sustains a gaussian TEM
mode, corresponding to nine antinodes of the standing wave between the two mirrors. The mode waist is 6 mm and the mode volume 700 mm
.
A d.c. voltage can be applied across the mirrors, provinding a rather homogeneous directing electric field. This voltage, under computer control, is used in the experimental sequences to control in real time the atom-cavity resonance condition via the Stark effect.
The cavity lifetime is very sensitive to the diffusion/diffraction losses due to mirrors surface imperfections, since photons can easily escape in the outside world through the centimeter gap between the mirrors. Obtaining a long enough storage time has been a long and painful process.
This figure presents the lifetime of the mode, 
, as a function of time (right scale). The left scale presents a simple factor of merit for a cavity QED experiment :
is the vacuum Rabi frequency, measuring the rate of the coherent atom-field interaction.
The factor 
roughly estimates the maximum number of coherent atom-cavity operations that can be performed before decoherence sets-in (due to various overheads, the actual number of achievable quantum logic operations is close to 
). It is also related to the maximum size of a Schrödinger cat state which can be prepared in the cavity before it decoheres.
At the onset of these experiments, in the 90’s, 
was limited to 2 
s by the mirrors roughness. The typical atom-cavity interaction time being of the order of the Rabi period (20 s), no coherent atom-field operation was allowed. We used these very limited cavities to measure the Lamb shift of the atomic levels in an empty cavity, an effect clearly impervious to relaxation.
An improvement in the mirrors preparation, using electropolishing techniques, led us to a lifetime of 150 s in ’96. This was long enough to allow for a couple of interactions with the mode. We were able to realize quantum memory and EPR atom pair experiments and to prepare and probe Schrödinger kittens with a few photons.
The next step, raising the damping time to 1 ms, was realized by surrounding the gap between the mirrors by a nearly closed aluminum ring. It efficiently recirculated the lost photons inside the mode and raised its lifetime by nearly an order of magnitude. The atoms entered the cavity-ring structure through 3 mm diameter holes.
The stray fields in these holes badly affected the atomic coherences. All coherent atomic state manipulations had to be performed inside the structure. The Ramsey pulses were fed by a side waveguide and coupled into low standing waves. This arrangement puts very strong constaints on the experimental timing.
We were nevetheless able to prepare triplets of entangled particules, the most complex quantum information sequence at the time, to study the efficient generation of Schrödinger cat states with a few tens of photons during the resonant interaction of a single atom with a mesoscopic coherent field.
The last decisive step has been taken with a totally new mirrors technology.
We have reached a lifetime of 0.13s, comparable to what is achieved with closed cavities, and close to the theoretical optimum for an open cavity with this geometry. This corresponds to 
. Hundreds of logic operations become feasible within the cavity lifetime.
We have, as a first step, realized the QND measurement of a single photon field, repeated up to a few hundred times. This major improvement opens the way to decoherence studies with cats made up of hundreds of photons.
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