Understanding relaxation processes is an important unsolved problem in many areas of physics. A key challenge is the scarcity of experimental tools for the characterization of complex transient states. We used measurements of full quantum mechanical probability distributions of matter-wave interference to study the relaxation dynamics of a coherently split one-dimensional Bose gas and obtained comprehensive information about the dynamical states of the system. After an initial rapid evolution, the full distributions reveal the approach toward a thermal-like steady state characterized by an effective temperature that is independent from the initial equilibrium temperature of the system before the splitting process. We conjecture that this state can be described through a generalized Gibbs ensemble and associate it with prethermalization.

Understanding the dynamics of isolated quantum manybody systems is a central open problem at the intersection between statistical physics and quantum physics. Despite important theoretical effort 1 , no generic framework exists yet to understand when and how an isolated quantum system relaxes to a steady state. Regarding the question of how, it has been conjectured 2,3 that equilibration must occur on a local scale in systems where correlations between distant points can establish only at a finite speed. Here, we provide the first experimental observation of this local equilibration hypothesis. In our experiment, we quench a one-dimensional Bose gas by coherently splitting it into two parts. By monitoring the phase coherence between the two parts we observe that the thermal correlations of a prethermalized state 4,5 emerge locally in their final form and propagate through the system in a light-cone-like evolution. Our results underline the close link between the propagation of correlations 2,3,6,7 and relaxation processes in quantum many-body systems.It has been theoretically suggested that relaxation in generic isolated quantum many-body systems proceeds through the dephasing of the quantum states populated at the onset of the non-equilibrium evolution 8,9 . It is generally believed that this dynamically leads to relaxed states that can be well described either by the usual thermodynamical ensembles or by generalized Gibbs ensembles that take into account dynamical constraints 10 . However, it remains an open question how these relaxed states form dynamically, and in particular, whether they emerge gradually on a global scale, or appear locally and then spread in space and time 3 .Ultracold atomic gases offer an ideal test bed to explore such quantum dynamics. Their almost perfect isolation from the environment and the many available methods to probe their quantum states make it possible to reveal the dynamical evolution of a many-body system at a very detailed level 4,7,11-16 .In our experiment, a phase-fluctuating ultracold onedimensional (1D) Bose gas 17 is split coherently 18 . The splitting creates a non-equilibrium state consisting of two gases with almost identical phase profiles. Interactions in the many-body system drive the relaxation of this highly phase-correlated state to a prethermalized state, characterized by thermal phase correlations 4,19 . The dynamics is monitored by time-resolved measurements of the relative phase field using matter-wave interferometry 20 .The experimental procedure starts with a 1D degenerate gas of 4,000-12,000 87 Rb atoms trapped at temperatures between 30-110 nK in a magnetic trap, formed 100 µm below the trapping wires of an atom chip 21 . By applying radiofrequency fields through additional wires on the chip, we rapidly transform the initial harmonic trapping potential into a double well, thereby realizing the matter-wave analogue of a coherent beamsplitter 18 (see Methods).The system is allowed to evolve in the double well for a variable time t , before the gases are ...

The description of the non-equilibrium dynamics of isolated quantum many-body systems within the framework of statistical mechanics is a fundamental open question. Conventional thermodynamical ensembles fail to describe the large class of systems that exhibit nontrivial conserved quantities, and generalized ensembles have been predicted to maximize entropy in these systems. We show experimentally that a degenerate one-dimensional Bose gas relaxes to a state that can be described by such a generalized ensemble. This is verified through a detailed study of correlation functions up to 10th order. The applicability of the generalized ensemble description for isolated quantum many-body systems points to a natural emergence of classical statistical properties from the microscopic unitary quantum evolution.

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The complexity of interacting quantum many-body systems leads to exceedingly long recurrence times of the initial quantum state for all but the smallest systems. For large systems, one cannot probe the full quantum state in all its details. Thus, experimentally, recurrences can only be determined on the level of the accessible observables. Realizing a commensurate spectrum of collective excitations in one-dimensional superfluids, we demonstrate recurrences of coherence and long-range order in an interacting quantum many-body system containing thousands of particles. Our findings will enable the study of the coherent dynamics of large quantum systems even after they have reached a transient thermal-like state.

The dynamics and prethermalization of one-dimensional quantum systems probed through the full distributions of quantum noise Takuya Kitagawa, Adilet Imambekov, Jörg Schmiedmayer et al. Abstract. We detail the experimental observation of the non-equilibrium many-body phenomenon prethermalization. We study the dynamics of a rapidly and coherently split one-dimensional Bose gas. An analysis based on the use of full quantum mechanical probability distributions of matter wave interference contrast reveals that the system evolves toward a quasi-steady state. This state, which can be characterized by an effective temperature, is not the final thermal equilibrium state. We compare the evolution of the system to an integrable Tomonaga-Luttinger liquid model, and show that the system dephases to a prethermalized state rather than undergoing thermalization toward a final thermal equilibrium state.

We study the nonequilibrium dynamics of a coherently split one-dimensional Bose gas by measuring the full probability distribution functions of matter-wave interference. Observing the system on different length scales allows us to probe the dynamics of excitations on different energy scales, revealing two distinct length-scale-dependent regimes of relaxation. We measure the crossover length scale separating these two regimes and identify it with the prethermalized phase-correlation length of the system. Our approach enables a direct observation of the multimode dynamics characterizing one-dimensional quantum systems. The nonequilibrium dynamics of many-body quantum systems and their pathway towards equilibrium is of fundamental importance in vastly different fields of physics. Open questions appear, for example, in high-energy physics for understanding quark-gluon plasma [1][2][3], in cosmology for describing preheating of the early Universe [4], or in the comprehension of relaxation processes in condensed-matter systems [5,6].Because of their isolation from the environment and their tunability, ultracold atom systems have triggered many studies of nonequilibrium dynamics in closed interacting quantum systems, with particular interest drawn to quantum quenches [7,8]. Important questions are related to systems where the dynamics is constrained by several constants of motion [9] and to the possible description of nonequilibrium states by generalized statistical mechanics ensembles [10,11].Recently, we reported the experimental observation of prethermalization in a coherently split one-dimensional (1D) ultracold Bose gas [12], made possible by a characterization of the dynamical states through measurements of full distribution functions [13,14]. Prethermalization [15] was understood as the rapid relaxation to a steady state exhibiting thermal-like properties but differing from the true thermal equilibrium that is eventually expected to occur on longer time scales [16][17][18][19][20].In this Letter, we study the relaxation process [21] leading to the prethermalized state by measuring the full (probability) distribution functions (FDFs) of phase and contrast of matter-wave interference. We probe the 1D system on different length scales to investigate its multimode dynamics, which reveals two distinct regimes separated by a characteristic crossover length scale. We measure this characteristic length scale and identify it with the effective thermal phase-correlation length of the prethermalized system.We prepare a quasi-1D Bose gas of several thousand 87 Rb atoms in an elongated (along the z direction) magnetic microtrap on an atom chip [22] at a (tunable) temperature between 20 and 120 nK. The gas is coherently split along the radial (x) direction using a symmetric radio-frequency dressed-state double-well potential [23], creating two uncoupled 1D gases separated by a distance of 3:1 m [ Fig. 1(a)]. The longitudinal and radial trap frequencies in the double well are 7 Hz and 1.4 kHz, respectively, and the size of the...

We experimentally study the dynamics of a degenerate one-dimensional Bose gas that is subject to a continuous outcoupling of atoms. Although standard evaporative cooling is rendered ineffective by the absence of thermalizing collisions in this system, we observe substantial cooling. This cooling proceeds through homogeneous particle dissipation and many-body dephasing, enabling the preparation of otherwise unexpectedly low temperatures. Our observations establish a scaling relation between temperature and particle number, and provide insights into equilibration in the quantum world.