Interplay of Unidirectional Quantum Strings in Kagome Rydberg Atom Array

Abstract

Leveraging the rapid development of quantum simulators, the intriguing phenomena of quantum string are observed across various quantum simulation platforms. However, the complex interplay between the quantum strings cannot be well analyzed due to the limited system size in real quantum simulators. Here, with the help of a newly developed quantum Monte Carlo method, we can simulate a larger-scale Kagome Rydberg atom array, providing an ideal playground for studying quantum strings. By introducing a novel edge pinning method, the ends of a quantum string can be attached to edges so that the flexible manipulation of the quantum string becomes possible. Due to the geometric constraint, the quantum strings are unidirectional, which strongly complicates their interplay. To quantitatively describe the quantum string, we built a one-dimensional effective model. With both analytic and numerical methods, rich physics can be found, including ``geometric breaking", heart-like superposition state of quantum strings, and the attractive inter-string interactions. This work can benefit the comprehension of quantum strings and may also shed light on the simulation of high-energy physics.

Figures (8)

• Figure 1: The schematic diagram of (a) different gauge charges (yellow: negative; blue: positive) with special ones highlighted with dashed rectangle and "electric field" marked with red arrows, (b) the effect of $\sigma^x$ including creating and moving gauge charges, (c) the ring exchange process highlighted by the recycling symbol arrow, and (d) the "free" and "fixed" quantum string (connected red arrows) pinned by the edge defect (hand) in the background of the stripe phase. The repulsive interactions $V_{ij}$ are highlighted by different colored solid lines.
• Figure 2: The density distribution of the atom in the Rydberg state (black dot) and the resonant configuration (red hexagon) for (a) single free quantum string, and double free quantum strings attached with (b) same side and (c) different sides. The blue lines mark the possible region of the string's fluctuation, and the inset of (a) is the snapshot from the QMC simulation after transforming the states in the C sublattice. The number of lattice sites is $561$ with $L_x=15$ and $L_y=13$. (d) Schematic picture of the interplay between free quantum strings, where the red crosses mean the gauge charges can not annihilate with each other.
• Figure 3: (a-d) The density distribution of the atom in the Rydberg state (black dot) and the resonant configuration (red hexagon) calculated by QMC (left) and EM (right) for different defect distances with $L_x=15$ and $L_y=13$. (e) The schematic pictures of quantum string excitations presented in (a) (blue) and (d) (red), respectively. The arrows on both sides correspond to the effective spin configuration in the effective theory. (f) The energy difference calculated by QMC and EM, and the energy reference is set to $E(\delta x)$ at $\Delta x=7$, where two free quantum strings are irrelevant.
• Figure 4: (a) The density distribution and (b) the snapshot for three defects on different sides. (c) Schematic pictures of the superposition of free and fixed quantum strings. (d) The density distribution and (e) the snapshot for two fixed quantum strings with string distance $\Delta x=2$. (f) The corresponding energy difference of two fixed quantum strings with different distances calculated by QMC, and the dashed black line labels the energy reference $E(\Delta x)$ at $\Delta x=5$, where inter-string interaction is extremely weak.
• Figure 5: Schematic pictures for analyzing (a-d) the tension energy and (e) the ring exchange interaction of the quantum string. The blue double arrows highlight the Rydberg repulsive interactions considered. White arrows mark the change of positions of excited Rydberg atoms.