An electron gas in a one-dimensional periodic potential can be transported even in the absence of a voltage bias if the potential is slowly and periodically modulated in time. Remarkably, the transferred charge per cycle is sensitive only to the topology of the path in parameter space. Although this so-called Thouless charge pump was first proposed more than thirty years ago 1 , it has not yet been realized. Here we report the demonstration of topological Thouless pumping using ultracold fermionic atoms in a dynamically controlled optical superlattice. We observe a shift of the atomic cloud as a result of pumping, and extract the topological invariance of the pumping process from this shift. We demonstrate the topological nature of the Thouless pump by varying the topology of the pumping path and verify that the topological pump indeed works in the quantum regime by varying the speed and temperature.Topology manifests itself in physics in a variety of ways 2-4 , with the integer quantum Hall effect (IQHE) being one of the best-known examples in condensed matter systems. There, the Hall conductance of a two-dimensional electron gas is quantized very precisely in units of fundamental constants 5 . As discussed in the celebrated Thouless-Kohmoto-Nightingale-den Nijs paper 6 , this quantized value is given by a topological invariant, the sum of the Chern numbers of the occupied energy bands.In 1983, Thouless considered a seemingly different phenomenon of quantum transport of an electron gas in an infinite onedimensional periodic potential, driven in a periodic cycle 1 . This seems to be similar to the famous Archimedes screw 7 , which pumps water via a rotating spiral tube. However, whereas the Archimedes screw follows classical physics and the pumped amount of water can be changed continuously by tilting the screw, the charge pumped by the Thouless pump is a topological quantum number and not affected by a smooth change of parameters 1 . Interestingly, this quantization of pumped charge shares the same topological origin as the IQHE. The charge pumped per cycle can be expressed by the Chern number defined over a (1 + 1)-dimensional periodic Brillouin zone formed by quasimomentum k and time t. Although several single-electron pumping experiments have been implemented in nanoscale devices, such as quantum dots with modulated gate voltages 8-10 or surface acoustic waves to create a potential periodic in time 11 , the topological Thouless pump, which should have the spatial periodicity to define the Bloch wavefunction as well as the temporal periodicity, has not been realized in electron systems.In this Letter, we report a realization of Thouless' topological charge pump by exploiting the controllability of ultracold atoms in an optical superlattice. Differently from recent realizations of topological bands in two (spatial or synthetic) dimensions 12-17 , our experiment explores the topology of a (1 + 1)-dimensional adiabatic process, in which a dynamically controllable onedimensional optical superlattice is implemente...

Thermodynamic properties of matter generally depend on the details of interactions between its constituent parts. However, in a unitary Fermi gas where the scattering length diverges, thermodynamics is determined through universal functions that depend only on the particle density and temperature. By using only the general form of the equation of state and the equation of force balance, we measured the local internal energy of the trapped gas as a function of these parameters. Other universal functions, such as those corresponding to the Helmholtz free energy, chemical potential, and entropy, were calculated through general thermodynamic relations. The critical parameters were also determined at the superfluid transition temperature. These results apply to all strongly interacting fermionic systems, including neutron stars and nuclear matter.

Matter-wave dynamics reveals a flat energy band engineered in a novel optical lattice.

We engineer the on-site dissipation to reveal its impact on the quantum phase transition from Mott insulator to superfluid.

We observed an enhanced atom-dimer loss due to the existence of Efimov states in a three-component mixture of 6Li atoms. We measured the magnetic-field dependence of the atom-dimer loss in the mixture of atoms in state |1> and dimers formed in states |2> and |3>, and found two peaks corresponding to the degeneracy points of the energy levels of |23> dimers and the ground and first excited Efimov trimers. We found that the locations of these peaks disagree with universal theory predictions, in a way that cannot be explained by nonuniversal two-body properties. We constructed theoretical models that characterize the nonuniversal three-body physics of three-component 6Li atoms in the low-energy domain.