Probing entanglement in a many-body-localized system (1805.09819v2)

Abstract: An interacting quantum system that is subject to disorder may cease to thermalize due to localization of its constituents, thereby marking the breakdown of thermodynamics. The key to our understanding of this phenomenon lies in the system's entanglement, which is experimentally challenging to measure. We realize such a many-body-localized system in a disordered Bose-Hubbard chain and characterize its entanglement properties through particle fluctuations and correlations. We observe that the particles become localized, suppressing transport and preventing the thermalization of subsystems. Notably, we measure the development of non-local correlations, whose evolution is consistent with a logarithmic growth of entanglement entropy - the haLLMark of many-body localization. Our work experimentally establishes many-body localization as a qualitatively distinct phenomenon from localization in non-interacting, disordered systems.

• The paper demonstrates that many-body localization in a disordered Bose-Hubbard model suppresses thermalization through a slow, logarithmic growth of entanglement entropy.
• It employs site-resolved imaging with digital micromirror devices to precisely measure particle fluctuations and density correlations, confirming spatial localization.
• The findings suggest that preserving non-local entanglement in MBL systems could enable robust quantum memory by retaining information in near-equilibrium states.

Probing Entanglement in a Many-Body-Localized System

The research paper titled "Probing Entanglement in a Many-Body-Localized System" by Lukin et al. provides an intricate paper of many-body localization (MBL) and its distinguishing characteristics from Anderson localization in quantum systems. The work utilizes a disordered Bose-Hubbard model to examine the breakdown of thermalization, focusing on the system's entanglement properties.

Overview

The paper demonstrates that MBL systems exhibit behaviors incompatible with classical thermalization processes due to the presence of disorder and interactions. Disorder in a quantum system can halt transport, leading to localization, which prevents thermal equilibration of subsystems. The paper highlights how non-local correlations evolve, consistent with a logarithmic growth of entanglement entropy, the haLLMark of MBL.

Experimental Methodology

The authors implement an experimental setup using a one-dimensional Bose-Hubbard chain, employing quasiperiodic potentials to introduce disorder. Characterization of entanglement properties is accomplished by measuring particle fluctuations and correlations among particles, which exhibit a stationary particle distribution indicative of localization.

Significant aspects of the experimentation include:

• The utilization of DMDs (Digital Micromirror Devices) for potential modulation and site-resolved imaging.
• Measurement of the single-site von Neumann entropy indicates suppressed entropy growth in strong disorder cases, highlighting a lack of thermalization.
• Analysis of density-density correlations reveals exponential decay that correlates with the localization length of particles suffused by disorder strength.

Key Findings

1. Breakdown of Thermalization: The data shows a suppressed growth of the number entropy, $S_\text{n}$, attributing to transport inhibition, an expected consequence of many-body localization.
2. Spatial Localization: The results illustrate an exponential decay in density-density correlations for strong disorder, confirming the particles' spatial localization.
3. Entanglement Dynamics: Examination of configurational entanglement, quantified via configurational correlators, $C$, indicates a slow, logarithmic growth despite saturation in number entanglement.
4. Scaling of Entropy: The paper presents a volume-law scaling of configurational entanglement over subsystem sizes, suggesting non-local correlation formation.

Theoretical Implications

The paper suggests that MBL systems may be understood by examining local integrals of motion, representing conserved quantities in localization. This view aligns MBL with the behavior of integrable, non-thermalizing systems.

Practical Implications

The findings endorse potential uses for MBL systems in developing quantum memory, where retained memory of initial conditions allows information storage at near-equilibrium states that are resistant to external perturbations tied to thermalization.

Future Directions

The research hints at various directions for further investigation:

• Expanding the paper to larger systems could reveal critical properties at the thermal-MBL transition.
• Exploring the interplay between interacting MBL states with thermal regions to paper Griffiths dynamics.
• Practical examination of MBL states as candidates for quantum storage solutions, leveraging the Rydberg atom platform's native properties.

This document serves to expand understanding of entanglement dynamics in disordered quantum systems, providing critical insights into when and how they diverge from conventional thermodynamic behavior, and framing the discussion for exploring complex phenomena in quantum mechanics.