Quantum Chaos and Information Scrambling Experimentally Confirmed in Solid-State System.

The unidirectional flow of time, a cornerstone of our experience, arises from the tendency of physical systems to evolve from order to disorder, increasing entanglement and scrambling information. Reversing this process, however, presents a formidable challenge, as even minuscule imperfections in attempting to reverse the dynamics are rapidly amplified by a phenomenon known as quantum chaos. Researchers led by Yu-Chen Li, Tian-Gang Zhou, and Shengyu Zhang, alongside colleagues from the University of Science and Technology of China, Tsinghua University, The Chinese University of Hong Kong, and Fudan University, now demonstrate an experimental protocol for mitigating these errors and observing the anticipated exponential behaviour of quantum chaos.

Their work, detailed in a recent publication entitled ‘Error-resilient Reversal of Quantum Chaotic Dynamics Enabled by Scramblons’, utilises solid-state nuclear magnetic resonance to measure the out-of-time-ordered correlator (OTOC), a key indicator of information scrambling, and validates predictions from ‘scramblon theory’, a theoretical framework describing this process. This allows for the extraction of the Lyapunov exponent, a measure of chaotic behaviour, in an experimental setting for the first time, advancing the fundamental limits of dynamical reversibility with potential implications for quantum simulation and precision measurement.

Unveiling Dynamical Reversibility in Many-Body Systems

Research currently investigates the limits of dynamical reversibility within complex systems, employing solid-state nuclear magnetic resonance (NMR) to probe these boundaries. NMR exploits the magnetic properties of atomic nuclei to gain insight into the material’s structure and dynamics. This study utilises an ensemble of interacting ‘spins’ – a quantum mechanical property analogous to angular momentum – and leverages a theoretical framework known as ‘scramblon theory’. Scramblon theory, a relatively recent development in quantum chaos, provides a method for analysing how information disperses within many-body systems. A key innovation lies in the application of this theory to mitigate errors stemming from imperfect reversal of dynamics, thereby enabling a clearer observation of chaotic behaviour.

The study successfully measures the out-of-time-ordered correlator (OTOC), a crucial metric for understanding information scrambling. The OTOC quantifies how quickly information about an initial disturbance spreads throughout the system, effectively measuring the rate at which the system ‘forgets’ its initial state. From this measurement, researchers extract the Lyapunov exponent, a measure of the rate of divergence of nearby trajectories in phase space. A positive Lyapunov exponent signifies chaotic behaviour, indicating that even infinitesimally small differences in initial conditions lead to exponentially diverging trajectories. This represents the first experimental determination of the Lyapunov exponent within a physically realised many-body system.

These findings extend the boundaries of understanding how information scrambles and how chaotic dynamics emerge from fundamental physical principles. The ability to precisely measure the Lyapunov exponent constitutes a significant advancement in the characterisation of chaotic systems, providing valuable insight into the fundamental limits of predictability. The research establishes a direct link between information scrambling – the rapid dispersal of information – and the emergence of the thermodynamic arrow of time, the observed asymmetry between past and future.

The research possesses potential implications for the development of more accurate simulations, particularly in fields such as materials science and quantum chemistry. Furthermore, the refined techniques employed could contribute to advanced metrological techniques, enabling more precise measurements of physical quantities.