Sufficient progress towards redefining the International System of Units (SI) in terms of exact values of fundamental constants has been achieved. Exact values of the Planck constant h, elementary charge e, Boltzmann constant k, and Avogadro constant N A from the CODATA 2017 Special Adjustment of the Fundamental Constants are presented here. These values are recommended to the 26th General Conference on Weights and Measures to form the foundation of the revised SI.

We study the transport of ultra cold atoms in a tight optical lattice. For identical fermions the system is insulating under an external force while for bosonic atoms it is conducting. This reflects the different collisional properties of the particles and reveals the role of inter-particle collisions in establishing a macroscopic transport in a perfectly periodic potential. Also in the case of fermions we can induce a transport by creating a collisional regime through the addition of bosons. We investigate the transport as a function of the collisional rate and we observe a transition from a regime in which the mobility increases with increasing collisional rate to one in which it decreases. We compare our data with a theoretical model for electron transport in solids introduced by Esaki and Tsu. The motion of particles in periodic potentials is the underlying process for fundamental transport phenomena like electric current in metals. Quantum mechanically, particles in a periodic potential can be described with Bloch states. Without an external force, the particles can move freely through the potential and in the case of a non-interacting sample the system acts like a perfect conductor. Under a constant external force, the periodic potential is tilted and the new stationary states are localized Wannier-Stark states [1]. In the absence of interactions the particles cannot change their quantum state and the latter system behaves like an insulator for DC currents. Instead, in the presence of interactions collisions can change the quantum state of the particles and a macroscopic current is established. At the onset of interactions an increasing collisional rate is therefore expected to favor a current through the potential whereas at high collisional rate the current is hindered by collisions. The latter regime is well known from solids where scattering with phonons and impurities provide an extremely large collisional rate and the conductivity decreases linearly with increasing collisional rates [2]. However the limit of low collisonal rate, where the role of collisions is reversed, is experimentally not accessible in solids. With the development of semi-conductor superlattices [3], this regime could be entered and phenomena like negative electric conductivity could be observed [4,5,6], but a completely non-interacting system is not achievable even in superlattices.In this work we use ultra cold atoms in an optical lattice to investigate the transport in periodic potentials induced by an external force starting from the limit of zero interaction. Such kind of systems have already been used with success to study solid state phenomena like the Wannier-Stark ladder [7] or Josephson junctions [8]. Here we take advantage of the unique possibility of controlling both the scattering process and the parameters of the lattice to study the transition from an ideal insulator to a real conductor in a perfectly periodic potential. The use of indistinguishable fermionic atoms allows us to create a completely non-interacting sy...

We realize an interferometer with an atomic Fermi gas trapped in an optical lattice under the influence of gravity. The single-particle interference between the eigenstates of the lattice results in macroscopic Bloch oscillations of the sample. The absence of interactions between fermions allows a time-resolved study of many periods of the oscillations, leading to a sensitive determination of the acceleration of gravity. The experiment proves the superiority of noninteracting fermions with respect to bosons for precision interferometry and offers a way for the measurement of forces with microscopic spatial resolution.

We investigate theoretically and experimentally the center-of-mass motion of an ideal Fermi gas in a combined periodic and harmonic potential. We find a crossover from a conducting to an insulating regime as the Fermi energy moves from the first Bloch band into the bandgap of the lattice. The conducting regime is characterized by an oscillation of the cloud about the potential minimum, while in the insulating case the center of mass remains on one side of the potential.

We report a new experimental scheme which combines atom interferometry with Bloch oscillations to provide a new measurement of the ratio h/m Rb . By using Bloch oscillations, we impart to the atoms up to 1600 recoil momenta and thus we improve the accuracy on the recoil velocity measurement. The deduced value of h/m Rb leads to a new determination of the fine structure constant α −1 = 137.035 999 45 (62) with a relative uncertainty of 4.6 × 10 −9 . The comparison of this result with the value deduced from the measurement of the electron anomaly provides the most stringent test of QED. To test them, other determinations of α, independent of QED, are required. The most precise are deduced from the measurement of the ratio h/m between the Planck constant and the mass of an atom thanks to the relation deduced from the ionization energy of hydrogen:where m e is the electron mass. The limiting factor is the ratio h/m: the uncertainty of the Rydberg constant R ∞ is 7 × 10 −12 [5,6] and that of the mass ratio m/m e 4.8 × 10