Quantum thermalization and the dynamics of entanglement

Adam M. Kaufman

S. Lepoutre, Johannes Schachenmayer, Lucas Gabardos +7 more

Understanding quantum thermalization through entanglement build up in isolated quantum systems addresses fundamental questions on how unitary dynamics connects to statistical physics. Spin systems made of long-range interacting atoms offer an ideal experimental platform to investigate this question. Here, we study the spin dynamics and approach towards local thermal equilibrium of a macroscopic ensemble of S = 3 chromium atoms pinned in a three dimensional optical lattice and prepared in a pure coherent spin state, under the effect of magnetic dipole-dipole interactions. Our isolated system thermalizes under its own dynamics, reaching a steady state consistent with a thermal ensemble with a temperature dictated from the system's energy. The build up of quantum correlations during the dynamics is supported by comparison with an improved numerical quantum phase-space method. Our observations are consistent with a scenario of quantum thermalization linked to the growth of entanglement entropy.

S. Lepoutre, Johannes Schachenmayer, Lucas Gabardos +7 more

Understanding quantum thermalization through entanglement build-up in isolated quantum systems addresses fundamental questions on how unitary dynamics connects to statistical physics. Here, we study the spin dynamics and approach towards local thermal equilibrium of a macroscopic ensemble of S = 3 spins prepared in a pure coherent spin state, tilted compared to the magnetic field, under the effect of magnetic dipole-dipole interactions. The experiment uses a unit filled array of 104 chromium atoms in a three dimensional optical lattice, realizing the spin-3 XXZ Heisenberg model. The buildup of quantum correlation during the dynamics, especially as the angle approaches pi/2, is supported by comparison with an improved numerical quantum phase-space method and further confirmed by the observation that our isolated system thermalizes under its own dynamics, reaching a steady state consistent with the one extracted from a thermal ensemble with a temperature dictated from the system's energy. This indicates a scenario of quantum thermalization which is tied to the growth of entanglement entropy. Although direct experimental measurements of the Renyi entropy in our macroscopic system are unfeasible, the excellent agreement with the theory, which can compute this entropy, does indicate entanglement build-up.

Prasenjit Deb, Abhishek Banerjee, Pratapaditya Bej +1 more

Tanmay Saha, Pratik Ghosal, Pratapaditya Bej +2 more

Alexander Lukin

Classical statistical mechanics relies on the ergodic hypothesis, which states that a system explores the entire allowed phase space during its time evolution. Pure quantum states are at odds with this concept as they remain in a single quantum state even if the system's parameters are suddenly altered. However, in a generic many-body system, coherent dynamics drive local thermalization of its subsystems. In this case, any local observable appears thermal and can be described by a statistical ensemble even though the full state remains pure. The key to understanding the phenomenon of quantum thermalization lies in the entanglement properties of the system: The presence of entanglement creates local entropy that validates the use of statistical physics.\nIn this thesis, we experimentally study the emergence of statistical mechanics in a quantum state and observe the fundamental role of quantum entanglement in facilitating this emergence. We perform microscopy on an evolving quantum system, and we see thermalization occur on a local scale while we measure that the full quantum state remains pure.\nThe only known robust exception from the paradigm of quantum thermalization is provided by disordered systems. In this case, the particle transport ceases through the system, preventing the formation of a sufficient amount of entanglement required for thermalization. However, if the many-body system is interacting, the state develops non-local quantum correlations that are inaccessible to any local observable. These correlations spread exponentially slowly in time throughout the entire system and are considered a hallmark feature of many-body-localized states.\nIn order to study the interplay between thermalization and localization in our system, we develop novel methods for high fidelity state preparation and readout. We achieved an exquisite isolation of our system from the environment, which allows us to monitor coherent many-body dynamics over multiple decades of time evolution.\nWe experimentally realize such a many-body localized system and observe the formation of non-local quantum correlations, while the particle transport is frozen in the system. Our work experimentally establishes many-body localization as a qualitatively distinct phenomenon from localization in non-interacting, disordered systems.