Statistical mechanics relies on the maximization of entropy in a system at thermal equilibrium. However, an isolated quantum many-body system initialized in a pure state remains pure during Schrödinger evolution, and in this sense it has static, zero entropy. We experimentally studied the emergence of statistical mechanics in a quantum state and observed the fundamental role of quantum entanglement in facilitating this emergence. Microscopy of an evolving quantum system indicates that the full quantum state remains pure, whereas thermalization occurs on a local scale. We directly measured entanglement entropy, which assumes the role of the thermal entropy in thermalization. The entanglement creates local entropy that validates the use of statistical physics for local observables. Our measurements are consistent with the eigenstate thermalization hypothesis.
A logarithmic signature Some one-dimensional disordered interacting quantum systems have been theoretically predicted to display a property termed many-body localization (MBL), where the system retains the memory of its initial state and fails to thermalize. However, proving experimentally that something does not occur is tricky. Instead, physicists have proposed monitoring the entanglement entropy of the system, which should grow logarithmically with evolution time in an MBL system. Lukin et al. observed this characteristic logarithmic trend in a disordered chain of interacting atoms of rubidium-87. This method should be generalizable to other experimental platforms and higher dimensions. Science , this issue p. 256
The interplay between magnetic fields and interacting particles can lead to exotic phases of matter that exhibit topological order and high degrees of spatial entanglement. Although these phases were discovered in a solid-state setting, recent innovations in systems of ultracold neutral atoms-uncharged atoms that do not naturally experience a Lorentz force-allow the synthesis of artificial magnetic, or gauge, fields. This experimental platform holds promise for exploring exotic physics in fractional quantum Hall systems, owing to the microscopic control and precision that is achievable in cold-atom systems. However, so far these experiments have mostly explored the regime of weak interactions, which precludes access to correlated many-body states. Here, through microscopic atomic control and detection, we demonstrate the controlled incorporation of strong interactions into a two-body system with a chiral band structure. We observe and explain the way in which interparticle interactions induce chirality in the propagation dynamics of particles in a ladder-like, real-space lattice governed by the interacting Harper-Hofstadter model, which describes lattice-confined, coherently mobile particles in the presence of a magnetic field. We use a bottom-up strategy to prepare interacting chiral quantum states, thus circumventing the challenges of a top-down approach that begins with a many-body system, the size of which can hinder the preparation of controlled states. Our experimental platform combines all of the necessary components for investigating highly entangled topological states, and our observations provide a benchmark for future experiments in the fractional quantum Hall regime.
Phase transitions are driven by collective fluctuations of a system's constituents that emerge at a critical point [1]. This mechanism has been extensively explored for classical and quantum systems in equilibrium, whose critical behavior is described by a general theory of phase transitions. Recently, however, fundamentally distinct phase transitions have been discovered for out-ofequilibrium quantum systems, which can exhibit critical behavior that defies this description and is not well understood [1]. A paradigmatic example is the many-body-localization (MBL) transition, which marks the breakdown of quantum thermalization [2][3][4][5][6][7][8][9][10][11]. Characterizing quantum critical behavior in an MBL system requires the measurement of its entanglement properties over space and time [4,5,7], which has proven experimentally challenging due to stringent requirements on quantum state preparation and system isolation. Here, we observe quantum critical behavior at the MBL transition in a disordered Bose-Hubbard system and characterize its entanglement properties via its quantum correlations. We observe strong correlations, whose emergence is accompanied by the onset of anomalous diffusive transport throughout the system, and verify their critical nature by measuring their systemsize dependence. The correlations extend to high orders in the quantum critical regime and appear to form via a sparse network of many-body resonances that spans the entire system [12,13]. Our results unify the system's microscopic structure with its macroscopic quantum critical behavior, and they provide an essential step towards understanding criticality and universality in nonequilibrium systems [1,7,13].
We propose a quantum information based scheme to reduce the temperature of quantum manybody systems, and access regimes beyond the current capability of conventional cooling techniques. We show that collective measurements on multiple copies of a system at finite temperature can simulate measurements of the same system at a lower temperature. This idea is illustrated for the example of ultracold atoms in optical lattices, where controlled tunnel coupling and quantum gas microscopy can be naturally combined to realize the required collective measurements to access a lower, virtual temperature. Our protocol is experimentally implemented for a Bose-Hubbard model on up to 12 sites, and we successfully extract expectation values of observables at half the temperature of the physical system. Additionally, we present related techniques that enable the extraction of zero-temperature states directly.
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