Correlations due to localization in quantum eigenfunctions of disordered microwave cavities

Area of Science:

• Quantum chaos
• Disordered systems
• Microwave cavities

Background:

• Eigenfunctions in quantum chaotic and disordered systems exhibit unique statistical properties.
• Localization effects can lead to nonuniversal correlations, deviating from standard predictions.
• Understanding these properties is crucial for fields ranging from condensed matter physics to quantum computing.

Purpose of the Study:

• To experimentally investigate the statistical properties of eigenfunctions in quantum chaotic and disordered microwave cavities.
• To explore the influence of localization on nonuniversal correlations.
• To determine the spatial decay characteristics of eigenfunctions and their relationship to theoretical models.

Main Methods:

• Experimental tuning of energy (E) and mean free path (l) to transition between localized and delocalized states.
• Measurement of level-to-level inverse participation ratio (I2) and its fluctuations.
• Analysis of spatial density autocorrelations of eigenfunctions.

Main Results:

• Observed nonuniversal correlations in eigenfunctions attributed to localization.
• Demonstrated large, asymmetric fluctuations in the inverse participation ratio (I2) for disordered billiards.
• Experimentally determined exponential spatial decay of eigenfunction densities with characteristic decay lengths.
• Quantitative agreement between experimental findings and nonlinear sigma model calculations.

Conclusions:

• Localization significantly impacts eigenfunction correlations in quantum chaotic and disordered systems, leading to nonuniversal behavior.
• Experimental results align with theoretical predictions from nonlinear sigma models, validating the models' applicability.
• The study provides a comprehensive experimental characterization of eigenfunction properties in these complex systems.