Non-equilibrium dynamics expands our understanding on physical processes based on the conventional equilibrium physics. In particular, non-equilibrium steady states with continuous flow among them have drawn much interest related to various biochemical processes, biomolecular motors, and high-temperature quantum entanglement as well as Bose-Einstein condensates. Here we report observation of a non-equilibrium steady states of atoms achieved in a hybrid of a moving optical lattice and a surrounding cold atom cloud in a phasestabilized magneto-optical trap. A part of atoms are localized and transported in the moving optical lattice and the rest are not localized in the lattice while trapped as a cold cloud of atoms. These motional states coexist with continuous transition between them. Our model calculations well reproduce the key features of the experimental observations including stepwise transitions, confirming the existence of a non-equilibrium steady state with characteristics of asymmetric simple exclusion process in the cold atom system. A collection of cold atoms in a periodic optical potential 1,2 is a useful tool for metrological applications as well as fundamental studies. Atomic clocks using optical lattices are reported to have ultrahigh resolution 3 . Studies on nonlinear dynamics and chaotic motion due to photon recoil and lattice amplitude modulation [4][5][6] have been proposed based on the atomic motion corresponding to classically well-understood harmonic oscillators in the optical lattice. Josephson junction array of cold atoms 7 in optical lattice, Landau-Zener tunneling 8 by lattice acceleration, and Mott insulator-metal transition 9 by using periodic modulation of the lattice amplitude have been investigated. As seen in these examples, cold atom systems have experimental advantages in realizing ideal lattice models. They are much more controllable than real electron systems 10 .Recently, non-equilibrium dynamics of cold atoms has become an active research topic 11,12 , expanding our understanding based on the existing equilibrium physics. In particular, nonequilibrium steady states (NESSs), the stationary states with continuous flows among them, have drawn much interest among various non-equilibrium phenomena. For example, biochemical reactions such as ATP hydrolysis and other biomolecular motors are described by a stochastic NESS theory 13 . In quantum physics, NESS is suggested as a possible pathway to entanglement at high temperature 14 and generation of high-temperature Bose-Einstein condensates 15 . Associated with an array of particles, a particular interest lies in asymmetric simple exclusion process (ASEP) 16 , describing a driven diffusive system of one-dimensional lattice of particles hopping to other sites at a certain rate along the lattice. A model of ASEP with the Langmuir kinetics, which includes absorption and desorption of particles in a lattice connected to a reservoir, is suggested 17 to describe the NESS system of mRNA translation 18 , for example. Related to cold atom sy...

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