Metastable confinement in Rydberg lattice gauge theories

Abstract

Confinement and string breaking are two fundamental phenomena in gauge theories. Signatures of both are currently pursued in quantum-simulator experiments, opening a new angle on strongly interacting dynamics of gauge fields out of equilibrium, complementary to traditional particle-physics settings. In this work, we report the emergence of metastable confinement dynamics in a U(1) lattice gauge theory, originating from the competition between string tension and four-Fermi coupling - a competition that naturally arises in Rydberg atom arrays. We show that the initial string state can be resonantly melted through controlled energy matching, a phenomenon we identify as resonant string breaking. We demonstrate this mechanism for both static and Floquet-driven systems, where periodic modulation generates a spectrum of tunable sideband resonances. Our work provides new insights into the mechanisms of confinement and string breaking driven by long-range interactions and time-dependent fields, which are available in current quantum simulators on a variety of platforms.

Figures (5)

• Figure 1: Schematics of LGTs description and resonant string breaking of Rydberg atom arrays. (a) Mapping between Rydberg atoms (with $|0\rangle,|1\rangle$ being the ground and Rydberg state, respectively) and a U(1) quantum link model. The Néel states map into string states. (b) Schematic of stable and metastable confinement regimes. When the chosen initial state (Néel state shown in red solid line) lies at the extreme of the spectrum, the dynamics mimic the thermal equilibrium in the blockade Hilbert space, and both states show confinement. Conversely, when the initial state lies in the middle of the spectrum, the confinement will break in the thermal equilibrium. (c) Schematic of a resonant melting process starting from a Néel state where the resonance condition $(n+1)V_{2}=n\delta_{0}$ with $n=2$ is satisfied. (d) Time evolution of the average occupation $\langle n_{j}\rangle$ away from resonance ($\delta_{0}=0$, left) and at resonance ($\delta_{0}\approx 3V_{2}/2$, right).
• Figure 2: Thermal equilibrium and time average of local observables. (a) Upper panel: the effective temperature of the initial state. Lower panel: the thermal expectation values of the nearest-neighbor correlation $\hat{O}_{ZZ}$ in the blockade subspace (red, therm. 1) and in the resonant subspace (green, therm. 2), and the time-averaged expectation value of the observable (blue, aveg.). The blockade radius is $R_{\mathrm{b}}/a=2.8$ (corresponding to $V_{2}/\Omega\approx8.11$). The light green (purple) area denotes the stable (metastable) confinement regime. (b) The nearest-neighbor correlation $\hat{O}_{ZZ}$ as a function of the staggered detuning $\delta_{0}$ and the blockade radius $R_{\mathrm{b}}$. The white dashed line corresponds to the resonant condition $3V_{2}\approx 2\delta_{0}$, and the red dashed line denotes the cut $R_{\mathrm{b}}/a=2.8$. (c) The time evolution of $\hat{O}_{ZZ}$ at the three characteristic points in (b). The number of atoms is $N=20$.
• Figure 3: Resonant string breaking in the eigenstates and dynamics. (a) Maximal overlap between the eigenstates $|\psi_{i}\rangle$ and the initial state $|Z_{2}\rangle$. The three triangles denote the three resonances at $(n+1)V_{2}= n\delta_{0}$ for $n=1,2,3$, corresponding to the three lines of the same colors in (b) and (c). (b),(c) The overlaps between the dynamical state $|\psi(t)\rangle$ and the initial state $|Z_{2}\rangle$ in (b) or the one-island excitation state $|\phi^{n}\rangle$ in (c). $n$ denotes the number of quark-antiquark pairs in an isolated island. The number of atoms is $N=28$.
• Figure 4: Floquet resonances from periodic modulation of global detuning $\Delta=\Delta_{\mathrm{m}}\cos(\omega t)$. (a) The nearest-neighbor correlation $\hat{O}_{ZZ}$ as a function of the staggered detuning $\delta_{0}$ and the modulation frequency $\omega$. (b) The detailed resonance structure for $\delta_{0}/\Omega=9$, corresponding to the red dashed line in (a). The number of atoms is $N=20$.
• Figure 5: Maximal overlap between the eigenstates $|\psi_{i}\rangle$ and the initial state $|Z_{2}\rangle$ for two different atom numbers $N$.