Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator (1809.05540v2)

Abstract: Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations. These fluctuations play a dominant role in the quantum critical region surrounding the transition point, where the dynamics are governed by the universal properties associated with the QPT. While time-dependent phenomena associated with classical, thermally driven phase transitions have been extensively studied in systems ranging from the early universe to Bose Einstein Condensates, understanding critical real-time dynamics in isolated, non-equilibrium quantum systems is an outstanding challenge. Here, we use a Rydberg atom quantum simulator with programmable interactions to study the quantum critical dynamics associated with several distinct QPTs. By studying the growth of spatial correlations while crossing the QPT, we experimentally verify the quantum Kibble-Zurek mechanism (QKZM) for an Ising-type QPT, explore scaling universality, and observe corrections beyond QKZM predictions. This approach is subsequently used to measure the critical exponents associated with chiral clock models, providing new insights into exotic systems that have not been understood previously, and opening the door for precision studies of critical phenomena, simulations of lattice gauge theories and applications to quantum optimization.

• The paper experimentally confirms the quantum Kibble-Zurek mechanism by demonstrating power-law scaling in an Ising quantum phase transition using a programmable Rydberg atom array.
• It employs precise control of laser detuning and Rabi frequency to verify universal scaling laws with a measured exponent of 0.50(3), consistent with Ising universality.
• The study further explores transitions to Z3 and Z4 ordered phases, uncovering more intricate dynamics that pave the way for future investigations in quantum simulations.

Quantum Kibble-Zurek Mechanism and Critical Dynamics in a Rydberg Atom Simulator

The paper presented in the paper explores the critical dynamics of quantum phase transitions (QPTs) using a programmable Rydberg atom quantum simulator. The central focus lies in the experimental examination of the quantum Kibble-Zurek mechanism (QKZM), which is an extension of the classical Kibble-Zurek theory to quantum systems. This mechanism describes the nonequilibrium dynamics that occur as a system crosses a QPT, particularly focusing on the scaling behavior of domains of correlated regions formed during the phase transition.

The experimental setup involves a one-dimensional array of 51 $^{87}$Rb atoms configured with programmable interatomic interactions. This system allows precise control over parameters such as the detuning and Rabi frequency of the coupling laser, facilitating the paper of different QPTs into ordered phases characterized by different spatial symmetries ($\mathbb{Z}_2$, $\mathbb{Z}_3$, and $\mathbb{Z}_4$).

Key Findings and Methodology

1. Verification of QKZM in Ising QPT: Experimentally, the authors confirmed the QKZM by demonstrating a power-law scaling of the correlation length with respect to the sweep rate of the control parameter across the critical point in a $\mathbb{Z}_2$-phase transition. The correlation length followed $\xi(s) = \xi_{0}(s_{0}/s)^{\mu}$, with an experimentally determined scaling exponent of $\mu = 0.50(3)$, consistent with the predictions for an Ising-type transition in one dimension.
2. Exploration of Universality: Rescaled spatial correlations demonstrated a universality in the transition behavior, characteristic of the Ising universality class with critical exponents $z = \nu = 1$. This observation lends strong credence to the universal applicability of QKZM in isolated quantum systems beyond mean-field approximations.
3. Extensions to More Complex Systems: The paper extends to transitions into $\mathbb{Z}_3$ and $\mathbb{Z}_4$ ordered phases. Particularly in the $\mathbb{Z}_3$ phase, deviations from simple QKZM predictions were observed, suggesting more intricate dynamics possibly governed by the chiral clock model universality class. For the $\mathbb{Z}_4$ ordered phase, results suggest a more complex transition, possibly involving intermediate gapless incommensurate phases.
4. Numerical Simulations: Results from experimental observations are supplemented by matrix product state simulations, which, although broadly in line with experimental findings, highlight discrepancies that point to the complexity of simulating nonequilibrium dynamics in interacting quantum many-body systems.

Implications and Future Research

The reported experimental findings mark a significant step in the paper of quantum critical dynamics using analogue quantum simulation. The ability to verify universal scaling laws in isolated quantum systems breaks ground for more precise examinations of complex quantum phenomena. Potential future directions may include:

• Large-scale dynamics of QPTs in two and three dimensions, which could uncover new universality classes pertinent to uncharted quantum phenomena.
• Application of the observed behaviors in quantum information science, especially towards optimization problems and lattice gauge theories.
• Integrating improvements in coherence and control to facilitate simulations of more exotic phases in quantum materials.

Overall, this research contributes to a deeper understanding of the dynamic processes involved in QPTs, paving the way for significant advancements in both theoretical approaches and practical applications within quantum technologies.