#nonequilibriumdynamics

Quantum Phase Transition Squeeze

OSU physicists identified a universal “Squeezing Phase Transition,” which introduces new dynamical phases of matter and improves our understanding of how complex quantum systems originate entanglement. Postdoctoral researcher Samuel Begg, assistant professor Dr. Thomas Bilitewski, and graduate student Arman Duha studied this occurrence.

Non-Equilibrium Dynamics and Entanglement

Nonequilibrium dynamics of quantum spins interacting over long distances are studied using power-law interacting spin-1/2 bilayer XXZ models. In quantum metrology, entangled states are essential, especially through spin squeezing, which lowers quantum noise below the conventional quantum limit for quantum-enhanced sensing.

Starting dynamics with two layers polarized in opposite directions is simple and easily generated. The dynamic production of entangled pairs of excitations by interlayer spin-exchange interactions causes two-mode squeezing. The system goes out of equilibrium, therefore new nonequilibrium phases of matter are categorized by their universal properties.

Different Dynamic Phases

The OSU group found a drastic transition between two dynamical regimes, which they called phases of matter due to their similarities:

Fully Collective Phase

The system achieves Heisenberg-limited scaling, the theoretical maximum for quantum-enhanced sensing, at this phase. He contrasted the fully collective regime to a swarm of fireflies synchronizing their flashes, where all spins function together.

This phase's main feature is the squeezed observable's low variance relative to system size. The minimal variance scales with zero exponent in the fully collective phase, independent of system size. This collective behavior optimizes quantum sensor precision.

Partially Collective Phase

However, the partially collective phase has scalable squeezing. Although spins in this domain do not work together, the system allows quantum-enhanced sensing, which improves with system scale.

The variance scaled positively with system size in a two-dimensional case. The minimal variance is more than a constant and increases with system size in this phase. This regime reveals that quantum information persists even amid powerful local interactions that could otherwise cause chaos in the complicated, many-body system.

Phase Transition Nature

When these two regimes switch from entirely collective to partially collective, a new dynamical phase transition occurs. These regimes are established as discrete dynamical phases within non-equilibrium critical events because the change occurs during the system's time evolution rather than as an equilibrium phase transition (like ice melting).

The aspect ratio (layer spacing to layer length scale) and interaction power-law exponent determine the changeover point. Systems having a large power-law exponent in proportion to dimension are totally collective above a critical aspect ratio and partially collective below it.

It was found that the partially collective phase dynamics followed universal laws similar to those governing systems near equilibrium phase transitions. Squeezing dynamics scaling is characterized by system parameters and divergent time scale. A scaling ansatz that links the least variance to system size and aspect ratio captures universal scaling.

The critical exponents for this transition are the same even for square, triangular, and hexagonal lattices in two dimensions, supporting universality and implying that the phenomena are not affected by system configuration details.

Accessing Excitation Modes

The physical origin of these phases can be inferred from the system's excitation spectrum. Only the collective momentum mode (k=0 mode) is unstable in the entirely collective phase, and it expands exponentially to form the two-mode squeezing entanglement. No other momentum modes change.

However, numerous finite-momentum modes become unstable in partially collective regimes. Unchecked growth of these modes would drastically decrease the collective spin length and depolarize the system. Thus, interactions are needed to prevent these finite momentum excitations, indicating that the partially collective phase exists and that basic quadratic theory cannot explain it.

Impacts on Quantum Technology

Identification of the universal Squeezing Phase Transition and its critical size will substantially effect future quantum technology. The discoveries improve our understanding of dependable entanglement creation, which is critical for developing quantum systems with a significant advantage over classical ones.

In particular, this study promotes quantum sensing, which leverages entanglement to achieve unprecedented measurement accuracy for basic science, medical imaging, and navigation.

Non-Equilibrium Dynamics in Quantum Reservoirs for Science and Machine Learning Bringing machine learning and quantum physics together, the "quantum reservoir" offers a new paradigm for information processing and accelerates scientific processes, especially materials discovery. This approach solves difficult computational tasks using quantum systems' complex dynamics, surpassing standard quantum algorithms.

Quantum Reservoir Computing Principles

Quantum Reservoir Computing (QRC) uses a complex quantum reservoir for machine learning. This paradigm states that quantum systems dynamically process input signals.

Instead of training the complete complex quantum system, QRC trains a simple readout layer to achieve the goal. This is its main benefit. This reliance on the reservoir's spontaneous evolution emphasizes the need of using quantum system dynamics instead of conventional quantum techniques. Investigators are using quantum reservoirs to solve machine learning problems like time series prediction, pattern recognition, and categorization. Also being studied are hybrid classical-quantum systems that combine quantum reservoirs with classical machine learning. AI-compatible frameworks aim to bridge the gap between AI and quantum computing by making quantum reservoirs easier to integrate into machine learning pipelines. Non-Equilibrium Dynamics and System robustness Quantum reservoirs work best in non-thermal equilibrium systems. Non-equilibrium dynamics are important because they produce richer system dynamics. Quantum reservoirs include many-body localized (MBL) systems and discrete time crystals. These non-equilibrium quantum systems may store and process data differently than traditional systems due to their unique properties. Robust quantum systems like MBL and discrete time crystals improve stability and noise resistance. QRC can be used in future quantum devices because to its durability. Application: Quantum Phase Transition Unsupervised Detection The quantum reservoir concept can find topological phase transitions in complex materials without supervision, demonstrating its promise. Phase transition characterization has traditionally required complex observations and computationally intensive simulations. Li Xin, Da Zhang, and Zhang-Qi Yin developed a “quantum reservoir” method to detect these transitions without complex computations or system characterization. This unique approach can detect phase transitions even in noise, enabling quantum gadget development and materials discovery.

Using Many-Body Localization to Find Phase Boundaries