Trimer Dynamics in Floquet-driven arrays of Rydberg Atoms

TL;DR

This work addresses realizing mobile three-body bound states (trimers) in Floquet-engineered Rydberg spin arrays. It employs the WAHUHA pulse sequence and a high-frequency expansion to derive beyond-leading-order effective Hamiltonians, revealing an approximate $SO(2)$ magnetization-conserving regime and new trimer-transport channels. The second-order Floquet terms introduce correlated hopping and multispin interactions that markedly enhance trimer mobility, with long-range dipolar couplings and two-dimensional geometries further stabilizing trimers by energetically separating them from other excitations. The findings establish a practical route to observing mobile multiparticle bound states in programmable quantum simulators and motivate experimental exploration in Rydberg and related platforms.

Abstract

We analyze the WAHUHA Floquet protocol recently applied to arrays of Rydberg atoms and derive beyond-leading-order corrections in the high-frequency expansion of the effective spin theory. We find that an appropriate choice of the pulses times can enforce an approximate symmetry corresponding to the conservation of the total magnetization. The interaction channels emerging from higher-order Floquet terms affect three-body bound states (\emph{trimers}), which gain a significant mobility. We estimate the corresponding enhancement in 1D spin chains and conclude that their dynamics is within experimental reach. Detrimental effects due to the proliferation of particles outside of the trimer magnetization sector are found to occur and spread on time-scales slower than the trimer propagation. Moreover, these can be suppressed in higher dimensional lattices, e.g. in 2D triangular lattices, as the lattice geometry brings these processes off resonance. Our results establish a concrete route to realizing mobile multiparticle bound states in Floquet-engineered Rydberg platforms.

Figures (7)

• Figure 1: Floquet pulse scheme and trimer dynamics. (a) Schematic representation of the WAHUHA Floquet driving sequence, consisting of four $\pi/2$ pulses applied at times $t_1, t_2, t_3, t_4$ with phases $\phi = 0, -\pi/2, \pi/2, \pi$, separated by intervals $\tau_1, \tau_2, 2\tau_3$, such that $\tau_1 + \tau_2 + \tau_3 = T/2$. This protocol effectively engineers anisotropic spin interactions by averaging out undesired terms. (b) Illustration of a trimer (three adjacent spin excitations forming a bound state) propagating coherently along a one-dimensional spin chain.
• Figure 2: Trimer properties in the XXZ model and its Floquet corrections. (a) Energy spectrum of the 1D XXZ model (with closed boundary conditions) in the $N_\uparrow = 3$ sector for $L = 50$ sites as a function of $h/\Delta$. The trimer band appears as a narrow, high-energy band separated from lower-energy scattering states for $h/\Delta \lesssim 2/3$. The vertical dashed black line marks the reference value $h/\Delta = 0.5$, corresponding to the value for the leading order XXZ terms in Eq. \ref{['eq:effective_1d_nn']}. (b) Comparison of the highest-energy bands of the XXZ model at $h/\Delta = 0.5$ across different magnetization sectors ($N_\uparrow = 1$, 2, and 3) highlighting the different dispersion of magnons, dimers and trimers. (c) Schematic illustration of the correlated third-neighbor hopping process contributing to trimer propagation in the effective Hamiltonian. (d) Bandwidth of the trimer band from Eq. \ref{['eq:effective_1d_nn']} as a function of the Floquet parameter $\Gamma$. The black star marks the choice of $\Gamma = 0.01$, used throughout the main text.
• Figure 3: Time-resolved diagnostics of trimer propagation in a 17-site chain under the exact driven Hamiltonian with $\Gamma = 0.01$ and closed boundary conditions. (a) Local magnetization as a function of time, showing a clear light-cone structure emerging from a central trimer excitation. The effective light-cone (white dashed line) is obtained from the bound-state dispersion by extracting the maximum slope via finite differences over three adjacent $k$-points in the exact spectrum. (b) Time evolution of the trimer correlator $\mathcal{T}_i(t)$ showing ballistic behavior. The dashed dark line marks the effective light-cone velocity for $\Gamma = 0.01$ ($v \approx 0.173$), while the dotted red line shows the velocity for $\Gamma \to 0$ ($v \approx 0.130$) for comparison. (c) Time evolution of the magnetization $m=\sum_i n_i$ inside the light cone (green), outside of the cone (orange) and the total one (blue). The step-like structure of the curves arises the discrete nature of the lattice. (d) Magnetization profile of a propagating single-spin magnon and (e) of a dimer.
• Figure 4: (a) Maximum trimer velocity $v_{\text{max}} = \frac{\partial E_T(k)}{\partial k}$ evaluated from the exact-diagonalization spectrum of the generic $H_\text{eff}$ up to $\mathcal{O}(1/\omega^2)$, see Eqs. \ref{['eq:twospins_ham']}, \ref{['eq:fourspin_ham']}, including long-range couplings $J_{ij}\sim 1/r_{ij}^\alpha$ for $L=17$, closed boundary conditions in the sector $N_\uparrow=3$. The distance $r_{ij}$ is taken as the minimal distance on the periodic chain. The lower cutoff $\alpha = 3$ corresponds to the dipolar case. The black star marks the choice of $\Gamma$ and $\alpha$ used in section \ref{['sec:long-range']}. (b) Time evolution under the exact driven Hamiltonian of the trimer projection operator $\mathcal{T}_i(t)$ for $\Gamma = 0.01$ and $\alpha = 3$ (dipolar couplings). We observe an increase of $\sim60\%$ in the speed of the excitations with respect to the $\Gamma\rightarrow 0$ case (red dotted line).
• Figure 5: (a) Schematic representation of trimeric bound state geometries on a triangular lattice. (b) The spectrum of the effective Hamiltonian (see Eq. \ref{['eq:general_hamiltonian']} in the Appendices) with $\Gamma = 0.015$ in a 2D triangular lattice of 36 sites with first neighbors couplings and closed boundary conditions along both directions. The plot shows energy levels in the $N_\uparrow = 3$ sector (blue squares) and the $N_\uparrow = 7$ sector (red crosses) along a momentum-space path in the 2D Brillouin zone. The trimer bands correspond to the 11 most energetic ones in the $N_\uparrow = 3$ sector. The highest trimer band appears as an isolated, high-energy branch, energetically well separated from both other $N_\uparrow = 3$ excitations and from higher-spin sectors like $N_\uparrow = 7$.