Quantum thermalization through entanglement in an isolated many-body system (1603.04409v3)

Abstract: The concept of entropy is fundamental to thermalization, yet appears at odds with basic principles in quantum mechanics. Statistical mechanics relies on the maximization of entropy for a system at thermal equilibrium. However, an isolated many-body system initialized in a pure state will remain pure during Schr\"{o}dinger evolution, and in this sense has static, zero entropy. The underlying role of quantum mechanics in many-body physics is then seemingly antithetical to the success of statistical mechanics in a large variety of systems. Here 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. We directly measure entanglement entropy and observe how it assumes the role of the thermal entropy in thermalization. Although the full state remains measurably pure, entanglement creates local entropy that validates the use of statistical physics for local observables. In combination with number-resolved, single-site imaging, we demonstrate how our measurements of a pure quantum state agree with the Eigenstate Thermalization Hypothesis and thermal ensembles in the presence of a near-volume law in the entanglement entropy.

• The paper reveals that local systems reach thermal equilibrium through entanglement while the overall quantum state remains pure.
• The paper employs cold atom experiments and single-site imaging to measure entanglement entropy that scales linearly with subsystem volume.
• The paper validates the Eigenstate Thermalization Hypothesis, bridging quantum mechanics with macroscopic thermodynamics for isolated systems.

Quantum Thermalization through Entanglement in an Isolated Many-Body System: An Analysis

This paper presents an experimental investigation into the emergence of thermalization in isolated quantum systems, with a highly specific focus on the role of quantum entanglement. The authors address the longstanding question in statistical mechanics of how thermal behavior emerges from isolated quantum systems undergoing unitary evolution, remaining in a globally pure state throughout.

Isolated many-body quantum systems traditionally appear to contradict the statistical mechanics framework that hinges on entropy maximization, given that such systems initialized in a pure state retain zero entropy through time. This paper investigates how local thermalization arises when the global quantum state retains its purity, leveraging entanglement as the mechanism responsible for this phenomenon.

Key Observations and Results

1. Entangled Thermalization: The researchers utilize an array of cold atoms to create a highly controllable Bose-Hubbard system, effectively simulating a quantum many-body system. The experiment demonstrates that while the global state remains pure according to the Schrödinger evolution, local observables equilibrate and exhibit properties consistent with a thermal ensemble.
2. Measurement of Entanglement Entropy: A notable methodological advancement is the direct measurement of entanglement entropy, utilizing number-resolved, single-site imaging techniques. Through these measurements, the entanglement entropy reflects the thermal entropy for localized subsystems of the entire quantum state, suggesting entanglement's role as the creator of local entropy.
3. Entanglement Propagation: The experiments show dynamics consistent with theoretical predictions wherein entanglement spreads in the system effectively forming an 'entanglement light cone'. The entanglement entropy reaches a steady-state value where it scales linearly with the subsystem's volume, thus exhibiting a near 'volume law' behavior, a haLLMark of extensive thermal-like entanglement in contrast to the area law typical for ground states.
4. Saturation and Local Thermalization: At long timescales, the system was observed to equilibrate locally, with entanglement entropy and single-site observables matching closely with those predicted by canonical thermal ensembles, confirming the Eigenstate Thermalization Hypothesis (ETH). This finding underscores that entangled pure states can emulate statistical thermal states for observables localized within subsystems.

Theoretical and Practical Implications

The experimental results corroborate the key tenants of the ETH by demonstrating that thermal-like behavior in isolated quantum systems can indeed emerge due to the system's inherent quantum entanglement. Practically, these insights are critical for understanding thermalization processes in quantum simulators or quantum computing architectures where isolation from thermal baths is engineered.

Moreover, the paper contributes to the broader theoretical discourse by highlighting the critical role entanglement plays in bridging the microscopic quantum description and the macroscopic statistical mechanics framework. It poses new questions regarding the limit on subsystem size to maintain local thermality and the related issue of system integrability.

Future Directions

The research opens several avenues for future theoretical and experimental exploration. From scaling studies in larger lattices for deeper insights into thermalization transitions to exploring entanglement properties in different quantum phases, this work sets a foundation. Additionally, research into systems that fail to thermalize, such as those exhibiting many-body localization, could benefit from the methodological tools refined in this paper.

In conclusion, this paper sets a significant precedent for using entanglement as a quantitative conduit for understanding thermalization in isolated, non-equilibrium quantum systems, paving the way for both theoretical developments and practical applications in quantum technologies.