Controlling quantum transport through an external driving field is a basic issue in quantum mechanics, yet with relevance to fundamental physics tests and precision measurements as well as to applications devices. Quantum transport control has gained a renewed interest with the advent of optical lattices for ultra-cold atoms. These are increasingly employed to realize laboratory models for solid state crystals. In our lab we experimentally demonstrate for Wannier-Stark intraband transitions in lattice potentials.

As previously a sample of cold 88Sr atoms is loaded into vertical standing wave potential. The wavefunctions of trapped atoms are Wannier-Stark wavefunction, which are localized in the lattice side. Periodically modulating the lattice potential phase with frequency ?B we can transfer atomic wavefunctions into delocalized state. In particular intraband transitions between Wannier-Stark levels give rise to coherent delocalization effects (V. V. Ivanov et al., Phys. Rev. Lett. 100, 043602 (2008)).

Fig. 1: Intraband site-to-site tunneling

In order to modulate the phase of the lattice potential, the retro-reflecting mirror is mounted on a piezoelectric transducer. Delocalization is directly observed through a coherent broadening of an initially well-localized atomic wave packet. Than we measure in situ the spatial distribution of the sample by absorption imaging.

Fig. 2: Resonance spectrum

We observe a resonance of broadening of the atomic sample around multiple Bloch frequencies. The line-width of these resonances is Fourier limited up to 15 seconds, this suggests that the delocalization dynamics is determined by coherent tunneling. Spurious incoherent processes may limit the coherence time of the system on a timescale longer than 15 s. The narrow resonance of the broadening of atomic wavefunctions allow us to accurately measure the Bloch frequency of our system, and thus to measure gravity acceleration with a sensitivity better than 10-6 g.

Further we coherently control the spatial extent of the atomic wavefunctions over a millimeter distance. We can reversibly stretch and shrink the wavefunction by modulating the phase of the lattice potential with a certain detuning.

Fig. 3: Revivals of the spatial distribution of the atoms in the lattice potential under strong and non-resonant driving.

We observe revivals of the spatial distribution of the atoms in the lattice potential under strong and non-resonant driving. Setting the frequency detuning of the driving to about 250 mHz we demonstrated a revival in time of 3.8 seconds. Remarkably the atomic wavefunctions stretch over distance large than 1 mm, and then it shrinks almost to an initial size.

Another impressive results is a self-interference of the atomic wavenctions during TOF. While in absence of driving the thermal sample expands following the usual gaussian profile, applying the driving we clearly observe the appearing of a non-Gaussian distribution. There we can distinguish two components: the first one is directly related to the expansion in absence of modulation, while the second one has a spatial extent and relative weight related to the broadening. This distribution directly results from the self-interference of the wavefunction in free expansion.