Atom interferometry with Bose-Einstein condensate in optical beat note superlattices

Optical lattices represent a fundamental tool in the field of ultra-cold atoms that allow to simulate a large variety of quantum phenomena like the conduction of electrons in solids, to explore the physics of quantum particles in low dimensions and to implement spin models to simulate quantum magnetism. In addition optical lattices allow manipulation of ultra-cold atoms in atomic clocks and atom interferometry experiments for the precise measurement of time, gravity, fundamental constants and for fundamental physics tests. Optical lattices of wavelength λ, created by retro-reflecting a laser beam on a mirror, show useful stability properties, since the lattice period is exactly λ/2, so the position of the minima of the potential depends only on the frequency. With current technologies it is possible to stabilize frequencies below the Hz level. Moreover, this configuration is strongly immune to beam pointing instabilities, vibrations of the mirror can be reduced and, as for the residual intensity noise, they can only induce common-mode fluctuations of the site potentials. There is strong interest in many of the research fields mentioned above in creating periodic potentials with larger separations between the different sites, which is limited to fraction of µm due to the available narrow-linewidth laser sources. During my PhD we have realized an innovative, large-spacing optical superlattice based on the beating note between two retroreflected optical lattices with commensurate wavelengths, nλ2 =(n+1)λ1. Choosing n≫1 we demonstrated that the resulting potential is periodic and, for sufficiently low lattice depths, the energy spectrum of the superlattice is equal to the one of an optical lattice with wavelength nλ2, so with lattice spacing n time larger than standard retroreflecting lattice. We refer to it as Beat-note Super Lattice (BNSL). In the framework of atom interferometry, we implemented the BNSL technique in different ultra-cold trapped atom interferometry experiments showing its flexibility. In the first one, we used a 10µm spacing BNSL to realize a spatial Bloch oscillation interferometer which operate in presence of small external forces. When cancelling the interatomic interactions by means of a magnetic Feshbach resonance, the dynamics exhibits a coherence up to 1 s, demonstrating how BNSL provides very stable potentials with a large spatial periodicity. The second interferometer relies on a multimode configuration in an harmonic trap, where the coherent splitting and recombination of a BEC into multiple momentum components are realized by means of Kapitza-Dirac (KD) diffraction from a pulsed 5 µm BNSL. Here the harmonic trap closes the trajectories of the momentum components, and the BNSL pulses allow to reduce their recoil velocity, hence the oscillation amplitude. This is important, since we need to keep the dynamics in the harmonic region of our optical harmonic trap. A third kind of interferometer, we are currently working on, is based on BEC optically trapped in array of double well potentials. To realize such array we exploit two collinear BNSLs with a periodicity of one twice the other (10µm and 5µm), and to do this I need only three commensurate wavelengths. Each one of this double well represents a sensor I can exploit to realize a Mach-Zehnder interferometer. A preliminary set of measurements, with no external perturbation applied, show correlations between the outputs of each Mach-Zehnder. Having more the one correlated interferometers is possible to perform differential analysis between the outputs to subtract common noise and to realise a trapped atom gradiometer. Our studies are focusing on that goal. A last series of measures performed with our array of double wells potential concerns the possibility to introduce repulsive interaction during the input state preparation to reduce the large noise we are actually observing in the measurements. This goes in the direction of realizing non-classical states (number squeezed state) to enhance the sensitivity of the sensor beyond the standard quantum limit.