The manipulation of matter waves had an important role in the history of quantum mechanics. The first experimental validation of matter-wave behaviour was the observation of diffraction of matter by crystals 1 , followed by interference experiments with electrons, neutrons, atoms and molecules using gratings and Young's double slit [2][3][4][5] . More recently, matter-wave manipulation has become a building block for quantum devices such as quantum sensors 6 and it has an essential role in a number of proposals for implementing quantum computers 7,8 . Here, we demonstrate the coherent control of the spatial extent of an atomic wavefunction by reversibly stretching and shrinking the wavefunction over a distance of more than one millimetre. The quantum-coherent process is fully deterministic, reversible and in quantitative agreement with an analytical model. The simplicity of its experimental implementation could ease applications in the field of quantum transport and quantum processing.Cold atomic gases trapped in optical lattices (large and periodic ensembles of optical microtraps created by interfering optical laser beams) provide ideal tools for studying quantum transport in different regimes 9,10 and quantum many-body systems in periodic potentials [11][12][13][14][15] . One of the challenges in this field is to coherently transfer matter waves between macroscopically separated sites. This would provide a mechanism to couple distant quantum bits and ultimately would lead to scalable quantum-information processing with cold atoms in optical lattices 16 . Recently, it was demonstrated that spatially driven lattice potentials in the presence of a linear potential can induce a coherent delocalization of a matter wave 17 when the driving is applied at the Bloch frequency ν B , that is, the linear potential between adjacent sites expressed in frequency units. The delocalization occurs at integer multiples of ν B because of the resonant coupling between Wannier-Stark levels within the same band. The resonances are characterized by a sinc 2 (π t ν) spectral profile, where t is the driving time and ν is the detuning of the driving from the resonant frequency. The sinc response here arises from the influence on the tunnelling current of the relative phase φ between the driving and the site-to-site quantum phase in the broadened wavefunction. When φ lies between 0 and π the wavefunction expands, whereas when it lies between π and 2π the wavefunction shrinks. In particular, when φ = 2π the wavefunction returns to the starting point. Such a reversible behaviour is expected provided that the evolution of the wavefunction is fully coherent.Any mechanism introducing loss of coherence would in fact lead to a non-reversible broadening. However, in a decoherence-free regime, it should be possible to engineer the spatial extension of the wavefunction using the frequency offset and the amplitude of the driving as tuning knobs. Here, we experimentally demonstrate this new technique of matter-wave manipulation by showing that coher...

Atomic wave packets loaded into a phase-modulated vertical optical-lattice potential exhibit a coherent delocalization dynamics arising from intraband transitions among Wannier-Stark levels. Wannier-Stark intraband transitions are here observed by monitoring the in situ wave-packet extent. By varying the modulation frequency, we find resonances at integer multiples of the Bloch frequency. The resonances show a Fourier-limited width for interrogation times up to 2 s. This can also be used to determine the gravity acceleration with ppm resolution. devices. Quantum transport control has, however, gained a renewed interest with the advent of optical lattices for ultracold atoms. These are, in fact, increasingly employed to realize laboratory models for solid state crystals. The accurate tunability of atomic parameters such as the temperature, the strength of interaction, and the dimensionality bring ultracold atoms samples within the extreme quantum regime sought for precise quantum transport control [5], gravity measurements [6 -8], and metrology [9].Atom transport control in optical lattices depends in general on the form of the external driving field [10] and, in particular, on its strength and frequency whose values may be chosen so as to span from transport enhancement [11] to suppression [12]. Within this context Bloch oscillations [13], Landau-Zener tunneling [14], and resonant tunneling enhancement in tilted optical lattices [15] are certainly worth mentioning. Likewise important manifestations comprise transport in the well-known kicked-atom model where quantum transport could actually be engineered both by semiclassical [16] and by purely quantum [17,18] effects.In this Letter we experimentally demonstrate for the first time Wannier-Stark intraband transitions in lattice potentials, a phenomenon which has been studied theoretically [19,20] but has never been observed before. Our lattice potential has the form:where mgz is the gravity potential, U 0 is the lattice depth, k L is the optical-lattice wave vector, while z 0 and M are, respectively, the phase-modulation amplitude and frequency (see Fig. 1).Intraband transitions between Wannier-Stark levels give rise to coherent delocalization effects, which we observe through a coherent ballistic expansion of an initially welllocalized atomic wave packet. Wannier-Stark intraband tunneling, unlike the more familiar Landau-Zener tunneling occurring between different bands [14,15], is not affected by typical decoherence mechanisms occurring in the Landau-Zener interband case, such as line broadening due to the transverse profile of the lattice potential. Furthermore we work with an atomic species remarkably robust against decoherence processes [21,22], which enables us to observe transitions up to five neighboring Wannier-Stark levels, corresponding to coherently driven tunneling across five neighboring sites. Owing to such a quantum robustness the resonance spectra exhibit Fourier-limited widths over excitation times of the order of seconds. Such a highresolution ...

We have produced a quantum degenerate mixture of fermionic alkali-metal 6 Li and bosonic spin-singlet 174 Yb gases. This was achieved using sympathetic cooling of lithium atoms by evaporatively cooled ytterbium atoms in a far-off-resonant optical dipole trap. We observe the coexistence of Bose-condensed (T /T c 0.8) 174 Yb with 2.3 × 10 4 atoms and Fermi degenerate (T /T F 0.3) 6 Li with 1.2 × 10 4 atoms. Quasipure Bose-Einstein condensates of up to 3 × 10 4 174 Yb atoms can be produced in single-species experiments. Our results mark a significant step toward studies of few-and many-body physics with mixtures of alkali-metal and alkaline-earthmetal-like atoms, and for the production of paramagnetic polar molecules in the quantum regime. Our methods also establish a convenient scheme for producing quantum degenerate ytterbium atoms in a 1064 nm optical dipole trap.

We report on the realization of a stable mixture of ultracold lithium and ytterbium atoms confined in a far-off-resonance optical dipole trap. We observe sympathetic cooling of 6Li by 174Yb and extract the s-wave scattering length magnitude |a(6Li-174Yb)|=(13±3)a0 from the rate of interspecies thermalization. Using forced evaporative cooling of 174Yb, we achieve reduction of the 6Li temperature to below the Fermi temperature, purely through interspecies sympathetic cooling.

We report on the realization of dynamical control of transport for ultra-cold 88 Sr atoms loaded in an accelerated and amplitude-modulated 1D optical lattice. We tailor the energy dispersion of traveling wave packets and reversibly switch between Wannier-Stark localization and driven transport based on coherent tunneling. Within a Loschmidt-echo scheme where the atomic group velocities are reversed at once, we demonstrate a novel mirror for matter waves working independently of the momentum state and discuss possible applications to force measurements at micrometric scales.