• atom interferometer
• interactions

We have studied the effect of interactions on the sensitivity with which an atom interferometer is able to measure an energy offset $\delta$ between the two wells. The latter may be proportional, for instance, to the gravity constant $g$ or to an acceleration/rotation to be measured.
The main finding of this investigation is that, holding the particles for specific time intervals during the phase accumulation stage, it is possible to reach a better sensitivity (up to ~ 50% in the cases analysed) with respect to the non interacting case.
Atom interferometry is a technique aimed to give high precision measurements. Indeed atoms beams have some features that make them a very different tool with respect to photons: (i) they have short de Broglie wavelengths
(~ 10 pm for thermal atoms, up to ~ 1 μm for ultracold ones) and very short coherence lengths ~ 100 pm for thermal atoms, up to ~ 10 μm for ultracold ones), (ii) they interact among themselves, property that allows for non linearity, needed to reach particular useful states (as squeezed states) in order to get better measurements, without looking for some medium that can give the required non linearity for an optical interferometer (see, i.e. the Kerr effect), (iii) atoms can be trapped, giving rise to a new class of interferometer. Moreover, ultracold atoms show quantum effects that can be used for interferometric purpose.
These features make ultracold atom interferometers excellent tools for precision measurements of various physical quantity, such as accelerations and rotations, and to test basic quantum mechanics and general relativity.
In our work we have analysed the behaviour of atoms in a double-welll potential, with the possibility to tune the height of the barrier and the energy difference between the wells. This simple set-up gives rise to an interferometer, where the splitting process is realized by letting the barrier high enough for the atoms in the two wells to be isolated, in order to accumulate a phase difference. After a phase difference is accumulated, the recombination procedure is conducted by a second beam splitter, performed by lowering the barrier again.
This kind of double-welll potential interferometers are currently available and realized both in optical traps and on atom chip.
In our investigation we have found that in presence of interactions a better sensitivity with respect to the non interacting case is found even in the simplest interferometric protocol proposed. Indeed such improvement has been experimentally demonstrated but with high engineered measurements.