Local emergence of thermal correlations in an isolated quantum many-body system

Abstract

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 ...

Nonequilibrium dynamics of a noisy quantum Ising chain: Statistics of work and prethermalization after a sudden quench of the transverse field

“…This type of ligt-cone spreading of correlations has been observed experimentally (without noise) in the quench dynamics of the Bose-Hubbard model [35] and in the coherent split of 1D Bose gases, characterizing the wave front associated to the pre-thermal state [36].…”

Experimental characterization of a quantum many-body system via higher-order correlations

“…1) [21]. Matter-wave interferometry [22][23][24] gives direct access to the spatially resolved relative phase ϕ(z) between the superfluids (see Methods).…”

“…We extract this relative phase by fitting a sinusoidal function to each pixel line in the interference pattern [24]. This allows to determine ϕ(z) modulo 2π.…”

Light-cone effect and supersonic correlations in one- and two-dimensional bosonic superfluids

“…On the other hand, the spreading of correlations in dimensions higher than one constitutes an almost unexplored land, where t-DMRG approaches do not apply. This question is particularly relevant in view of the possibility of extending the experimental results [11,12] in higher dimensions.…”