Interaction-assisted topological pumping in few- and many-atom Rydberg arrays

Abstract

Topology can imbue lattice systems with special properties, notably the presence of robust eigenstates living at their boundary. Through dimensional reduction, the robust bulk band topology of, e.g., the integer quantum Hall system can be mapped onto similarly robust charge-pumping dynamics of a topological pump living in one lower dimension. Recent studies have uncovered a rich influence of interactions on the dynamics of topological pumps in nonlinear systems, including the robust pumping of self-bound solitons. These striking observations in classical nonlinear photonics have raised a number of questions, chiefly if and how this phenomenology persists in strongly correlated quantum systems and in the few-body limit. Here, using few- and many-atom arrays, we explore how dipolar interactions impact the dynamics of topological population pumping along a Rydberg synthetic dimension. In the few-body limit, we find that dipolar interactions lead to self-bound states that are efficiently pumped along the synthetic dimension, described by an emergent pair-state topological pump. We find that this interaction-assisted pumping persists in many-atom arrays, with a sharpened dependence on the dipolar interaction strength that stems from the enhanced spatial connectivity. These Rydberg-based studies on interaction-assisted topological pumping help connect observations from classical nonlinear photonics to the few-body quantum limit and pave the way for studies of new strongly correlated quantum pumping phenomena.

Figures (12)

• Figure 1: Topological pumping along a Rydberg synthetic lattice with dipolar interactions.(a) Multiple microwave tones are applied to Rydberg atoms (left) to create an effective tight-binding model (right) of resonantly-coupled internal states. (b) Depiction of the effective single-particle Rice-Mele model (Eq. \ref{['eqn:sRM']}) with staggered intra- ($J_1$) and inter-cell ($J_2$) hopping and potential landscape modulation $\Delta$. For atoms in nearby tweezer traps, dipolar interactions ($V_{\rm{dd}}$) lead to the correlated anti-hopping of Rydberg electrons along the synthetic dimension. The Rice-Mele lattice parameters are controlled as $J_{1/2}(\varphi) = J_0 (1\pm\cos(\varphi))$ and $\Delta(\varphi) =\Delta_0\sin(\varphi)$, where $\varphi$ is the pump phase. (c) Pumping trajectory as depicted in the $(J_1 - J_2)$ vs. $\Delta$ parameter space, enclosing the gap-closing condition at the origin. (d) The instantaneous one-atom energy band structure plotted against the pump phase $\varphi$, shown for $\Delta_0 = 2 J_0$.
• Figure 2: Influence of dipolar interactions on two-body pumping dynamics.(a) Pumping dynamics are simulated with 50-site systems and initiated at the center. Plots from left to right correspond to interaction-to-hopping ratios of $V/J_0 = -3, 0, 3$. Gray dashed lines indicate the center of mass position over time, and the corresponding line should have a slope of 2 for an ideal pump. All three cases show directional transport, but population spreads across the system faster for $V/J_0 = 0$. (b) Interaction dependence of the simulated pumping behavior of an atom pair, characterized at a fixed time $t = 4T$. Left: The tendency to pump is captured by the center of mass position $\lambda$, plotted vs. $V/J_0$. The solid line is for preparing both atoms at site $0$, while the dashed line assumes perfect preparation of the single-particle lower-band Wannier state. Center: The tendency to stay localized, characterized by the inverse partition ratio (IPR). The tendency to both pump and remain localized can be captured by the population $2n$ sites ($n$ unit cells) away from the initial site after $n$ pumping periods. Right: The population at site 8, $P_8$, plotted vs. $V/J_0$.
• Figure 3: Measured pumping dynamics in a 5-site lattice. Pump parameters [$J_0/h = 0.75(1)$ MHz, $\Delta_0/h = 1.5(2)$ MHz, and $\omega = 0.75$$\rm{MHz}$] are the same as for the 50-site simulations of Fig. 2. Time evolution of the site-wise populations for (a,b) non-interacting and (c,d) a system of interacting atoms. Measurements for $V/J_0 = 0, 3$ are acquired simultaneously and based on post-selection of singly and doubly occupied dimer arrays. Numerical simulations use the exact $C_3$ coefficients for each transition and include state preparation and measurement (SPAM) errors. At each time step and site, 100 shots were taken (for arrays of five separated dimers). This corresponds, on average, to $\sim$250 samples for singles and $\sim$150 samples for pairs, giving a statistical uncertainty of $\sim$0.06 for each experimental $P_n$ value.
• Figure 4: Measured interaction dependence of two-body pumping. Interaction dependence of the probability for atoms to be pumped away from the initial site after one-half (a,b) and one (c,d) pumping period, explored for both positive and negative values of the interaction-to-hopping ratio $V/J_0$ based on utilizing different sets of Rydberg states [inset in (a)]. The site-specific probability for atoms to pump one site away at time $t=T/2$ is presented in (a) and the probability to pump two sites away at time $t=T$ is presented in (c). Both curves show the asymmetric behavior described in Fig. \ref{['FIG:fig1']}. (b,d) Site-wise population maps at fixed $t=T/2$ and $t = T$ as a function of $V/J_0$, with mean-values of the experimentally measured data (bottom) along with SPAM-included simulation (top). Pump parameters and conditions are the same as in Fig. \ref{['FIG:fig2b']}. Error bars are the standard error from multiple independent datasets.
• Figure 5: Pumping dynamics as projected onto the instantaneous eigenstate energy structure. Simulations are calculated on a 50-site lattice under periodic boundary conditions for 1 period, under initial states $|0\rangle$ [panel (a)] or the pair product state $|00\rangle$ [panels (b,c)]. Colors indicate the overlap between the time-evolved state vector and the instantaneous energy eigenstates of the system Hamiltonian. (a) For the single particle pump, the initial state partially populates both the lower and upper energy bands, with a lower band overlap of $\sum|\langle \Psi_{l}|00\rangle|^2\approx 0.82$. (b) With intermediate interaction $V/J_0 = 3$, the initial two-particle state mainly populates one energy sub-band of the two-atom eigenenergy structure. (c) For an increased interaction strength of $V/J_0 = 9$, the initialized two-particle state again mainly projects onto a single energy sub-band at time $t=0$, but a reduced energy band gap (to symmetry-relevant states) leads population of the time-evolved state to exhibit transfer to another energy sub-band at $t\approx T/4$, signaling a breakdown in adiabaticity. To note, in panel (c) there are additional energy bands centered at energies $\pm 9 J_0$, out of the range of the plot.