Proposal for realizing Heisenberg-type quantum-spin models in Rydberg-atom quantum simulators

TL;DR

This work addresses realizing Heisenberg-type quantum-spin models in Rydberg-atom simulators using static magnetic fields to tune the XXZ interaction between dressed Rydberg states $|nS_{1/2},m_J\rangle$ and $|(n+1)S_{1/2},m_J\rangle$. By analyzing the magnetic-field dependence of the anisotropy parameter $\delta$, the authors identify Heisenberg points $\delta=1$ near Förster resonances and propose experimental realizations of a tunable $J_1$-$J_2$ spin-1/2 chain and a spin-1 Heisenberg model without Floquet engineering. The perturbative derivation yields an effective bilinear-biquadratic spin-1 Hamiltonian and a mechanism to implement longer-range interactions through geometric arrangements such as zigzag ladders and Gelfand ladders, with realistic parameters yielding MHz-scale exchange and feasible magnetic-field stability. These results enable exploration of rich quantum many-body phenomena, including the Haldane phase and related dynamics, in Rydberg-atom platforms and can be extended to other atomic species and higher dimensions.

Abstract

We investigate the magnetic-field dependence of the interaction between two Rydberg atoms, $|nS_{1/2}, m_J\rangle$ and $|(n+1)S_{1/2}, m_J\rangle$. In this setting, the effective spin-1/2 Hamiltonian takes the form of an {\it XXZ} model. We show that the anisotropy parameter of the {\it XXZ} model can be tuned by applying a magnetic field and, in particular, that it changes drastically near the Förster resonance points. Based on this result, we propose experimental realizations of spin-1/2 and spin-1 Heisenberg-type quantum spin models in Rydberg atom quantum simulators, without relying on Floquet engineering. Our results provide guidance for future experiments of Rydberg atom quantum simulators and offer insight into quantum many-body phenomena emerging in the Heisenberg model.

Figures (17)

• Figure 1: Definition of the positions of two Rydberg atoms. One atom is placed at the origin, and the other is placed at the position $\bm{R} \equiv R(\sin\theta \cos\varphi, \sin\theta \sin\varphi, \cos\theta)$, where $R$ is the distance between the atoms, and $\theta$ and $\varphi$ are the polar and azimuthal angles, respectively.
• Figure 2: Magnetic field and principal quantum number dependence of the anisotropy parameter of the pair $|nS_{1/2},m_J=-1/2\rangle$ and $|(n+1)S_{1/2},m_J=-1/2\rangle$ for $\theta=\pi/2$.
• Figure 3: Magnetic field dependence of various quantities of ${}^{87}$Rb atoms for $n = 65$ and $m_J = -1/2$. (a) $\delta$ vs $B$. The blue dotted line represents $\delta=1$. (b) Pair energy vs $B$. We plot the pair energy relative to $E_0 \simeq -h \times 1691.81~{\rm GHz}$, which is the pair energy of $\left|65S_{1/2},-1/2\right\rangle\left|66S_{1/2},-1/2\right\rangle$ at $B=0$. The red solid line represents $E_{\uparrow\downarrow}$. The blue dotted, green dashed, purple dash-dotted, orange dash-dot-dotted, and thin solid red lines represent the pair energies of $\left|\psi_1\right\rangle\equiv |\widetilde{65P_{3/2},1/2}\rangle |\widetilde{65P_{3/2},1/2}\rangle$, $\left|\psi_2\right\rangle\equiv |\widetilde{65P_{3/2},-1/2}\rangle|\widetilde{65P_{3/2},-1/2}\rangle$, $\left|\psi_3\right\rangle\equiv |\widetilde{65P_{3/2},1/2}\rangle|\widetilde{65P_{1/2},1/2}\rangle$, $\left|\psi_4\right\rangle\equiv|\widetilde{65P_{3/2},-3/2}\rangle|\widetilde{65P_{3/2},1/2}\rangle$, and $\left|\psi_5\right\rangle\equiv |\widetilde{65P_{3/2},-3/2}\rangle|\widetilde{65P_{3/2},-3/2}\rangle$, respectively. The black circles, squares, and triangles indicate the Förster resonance points. (c) $C_6$ vs $B$. The blue dotted line represents $C_6 = 0$. (d) $R_{\rm c}$ vs $B$.
• Figure 4: (a) Atom configuration for the spin-1/2 $J_1$-$J_2$ model. Black circles represent the positions of Rydberg atoms. Here, $\theta_0$ denotes the angle between the vertices of the same length. (b) Atom configuration for the spin-1 Heisenberg model. Two atoms enclosed by the red solid line represent an effective spin-1 degree of freedom.
• Figure S1: Magnetic field and principal quantum number dependence of the anisotropy parameter of the pair $|nS_{1/2},m_J=1/2\rangle$ and $|(n+1)S_{1/2},m_J=1/2\rangle$ for $\theta=\pi/2$. (a) ${}^7$Li atom, (b) ${}^{23}$Na atom, (c) ${}^{39}$K atom, (d) ${}^{87}$Rb atom, (e) ${}^{133}$Cs atom.