Probing many-body dynamics on a 51-atom quantum simulator

TL;DR

This work demonstrates a scalable quantum simulator based on defect-free arrays of neutral atoms excited to Rydberg states, realizing a programmable Ising-like Hamiltonian with tunable interactions and blockade. By adiabatically sweeping detuning, the team observes Z2, Z3, and Z4 crystalline orders and maps the quantum phase transition in up to 51 qubits, while fully coherent simulations validate the observed dynamics. A sudden quench reveals robust, long-lived crystal oscillations and constrained, non-thermal dynamics consistent with quantum dimer-like behavior, highlighting slow thermalization despite long-range couplings. The results establish a versatile platform for exploring large-scale quantum many-body phenomena, non-equilibrium dynamics, and potential quantum optimization applications.

Abstract

Controllable, coherent many-body systems can provide insights into the fundamental properties of quantum matter, enable the realization of new quantum phases and could ultimately lead to computational systems that outperform existing computers based on classical approaches. Here we demonstrate a method for creating controlled many-body quantum matter that combines deterministically prepared, reconfigurable arrays of individually trapped cold atoms with strong, coherent interactions enabled by excitation to Rydberg states. We realize a programmable Ising-type quantum spin model with tunable interactions and system sizes of up to 51 qubits. Within this model, we observe phase transitions into spatially ordered states that break various discrete symmetries, verify the high-fidelity preparation of these states and investigate the dynamics across the phase transition in large arrays of atoms. In particular, we observe robust manybody dynamics corresponding to persistent oscillations of the order after a rapid quantum quench that results from a sudden transition across the phase boundary. Our method provides a way of exploring many-body phenomena on a programmable quantum simulator and could enable realizations of new quantum algorithms.

Figures (16)

• Figure 1: Experimental platform.a, Individual $^{87}{\rm Rb}$ atoms are trapped using optical tweezers (vertical red beams) and arranged into defect-free arrays. Coherent interactions $V_{ij}$ between the atoms (arrows) are enabled by exciting them (horizontal blue and red beams) to a Rydberg state, with strength $\Omega$ and detuning $\Delta$ (inset). b, A two-photon process couples the ground state $\left|g\right\rangle=\left|5S_{1/2}, F=2, m_F=-2\right\rangle$ to the Rydberg state $\left|r\right\rangle=\left|70S_{1/2}, J=1/2, m_J=-1/2\right\rangle$ via an intermediate state $\left|e\right\rangle=\left|6P_{3/2}, F=3, m_F=-3\right\rangle$ with detuning $\delta$, using circularly polarized 420 nm and 1013 nm lasers with single-photon Rabi frequencies of $\Omega_B$ and $\Omega_R$, respectively. Typical experimental values are $\delta\approx 2\pi \times 560 \text{MHz} \gg \Omega_B, \Omega_R \approx 2\pi \times 60, 36\,\text{MHz}$. c, The experimental protocol consists of loading the atoms into a tweezer array (1) and rearranging them into a preprogrammed configuration (2). After this, the system evolves under $U(t)$ with tunable parameters $\Delta(t),\Omega(t)$ and $V_{ij}$. This evolution can be implemented in parallel on several non-interacting sub-systems (3). We then detect the final state using fluorescence imaging (4). Atoms in state $\left|g\right\rangle$ remain trapped, whereas atoms in state $\left|r\right\rangle$ are ejected from the trap and detected as the absence of fluorescence (indicated with red circles). d, For resonant driving ($\Delta = 0$), isolated atoms (blue circles) display Rabi oscillations between $\left|g\right\rangle$ and $\left|r\right\rangle$. Arranging the atoms into fully blockaded clusters of $N=2$ (green circles) and $N=3$ (red circles) atoms results in only one excitation being shared between the atoms in the cluster, while the Rabi frequency is enhanced by $\sqrt{N}$. The probability of detecting more than one excitation in the cluster is $\leq5\%$. Error bars indicate 68% confidence intervals (CI) and are smaller than the marker size.
• Figure 2: Phase diagram and build-up of crystalline phases.a, A schematic of the ground-state phase diagram of the Hamiltonian in equation (\ref{['eq:Rydberg-Hamiltonian']}) displays phases with various broken symmetries depending on the interaction range $R_b/a$ ($R_b$, blockade radius; $a$, trap spacing) and detuning $\Delta$ (see main text). Shaded areas indicate potential incommensurate phases (diagram adapted from Fendley2004). Here we show the experimentally accessible region; further details can be found in Fendley2004Sachdev2002Schachenmayer2010. b,The build-up of Rydberg crystals on a 13-atom array is observed by slowly changing the laser parameters, as indicated by the red dashed arrows in a (see also Fig. \ref{['fig:preparation_fidelity']}a). The bottom panel shows a configuration in which the atoms are $a=5.74\,\mu$m apart, which results in a nearest neighbour interaction of $V_{i,i+1}=2\pi\times24\,$MHz and leads to a Z$_2$ order whereby every other atom is excited to the Rydberg state $\left|r\right\rangle$. The bar plot on the right displays the final, position-dependent Rydberg probability (error bars denote 68% confidence intervals). The configuration in the middle panel ($a = 3.57\,\mu$m, $V_{i,i+1}=2\pi\times414.3\,$MHz) results in Z$_3$ order and the top panel ($a=2.87\,\mu$m, $V_{i,i+1}=2\pi\times1536\,$MHz) in Z$_4$ order. For each configuration, we show a single-shot fluorescence image before (left) and after (right) the pulse. Red circles highlight missing atoms, which are attributed to Rydberg excitations.
• Figure 3: Comparison with a fully coherent simulation.a, The laser driving consists of a square shaped pulse $\Omega(t)$ (blue) with a detuning $\Delta(t)$ (red) that is chirped from negative to positive values. b, The data show the time evolution of the Rydberg excitation probability for each atom in a 7-atom cluster (colored points), obtained by varying the stopping time $t_{\rm stop}$ of laser excitation the laser-excitation pulse $\Omega(t)$. The corresponding curves are theoretical single atom-trajectories obtained from an exact simulation of quantum dynamics with equation (\ref{['eq:Rydberg-Hamiltonian']}), the functional form of $\Delta(t)$ and $\Omega(t)$ used in the experiment, and finite detection fidelity. c, Evolution of the seven most probable many-body states (data). The target state is reached with $54(4)$% probability ($77(6)$% when corrected for finite detection fidelity). Solid lines are theoretical (simulated) many-body trajectories. Error bars in b and c denote 68% confidence intervals.
• Figure 4: Scaling behavior.a, Preparation fidelity of the crystalline ground state as a function of cluster size. The red circles are the measured values and the blue circles are corrected for finite detection fidelity (Methods). Error bars denote 68% confidence intervals. b, Number of observed many-body states per number of occurrences out of 18439 experimental realizations in a 51-atom cluster. The most frequently occurring state $\left|r_1 g_2 r_3 \cdots r_{49} g_{50} r_{51}\right\rangle$ is the ground state of the many-body Hamiltonian.
• Figure 5: Quantifying Z$_2$ order in a 51-atom array after a slow detuning sweep.a, Single-shot fluorescence images of a 51-atom array before applying the adiabatic pulse (top row) and after the pulse (bottom three rows correspond to three separate instances). Red circles mark missing atoms, which are attributed to Rydberg excitations. Domain walls are identified as either two neighbouring atoms in the same state or a ground state atom at the edge of the array (Methods), and are indicated with blue ellipses. Long Z$_2$ ordered chains between domain walls are observed. b, Blue points show the mean of the domain-wall density as a function of detuning during the sweep. Error bars show the standard error of the mean and are smaller than the marker size. The red circles are the corresponding variances, and the error bars represent one standard deviation. The onset of the phase transition is indicated by a decrease in the domain-wall density and a peak in the variance (see main text for details). Each point is obtained from about $1000$ realizations. The solid blue curve is a fully coherent matrix product state (MPS) simulation without free parameters (bond dimension $D=256$), taking measurement fidelities into account. c, Domain wall number distribution for $\Delta = 2\pi\times14\,$MHz, obtained from 18439 experimental realizations (blue bars, top). Error bars indicate 68% confidence intervals. Owing to the boundary conditions, only even numbers of domain walls can appear (Methods). Green bars (bottom) show the distribution obtained by correcting for finite detection fidelity using a maximum-likelihood method (Methods), which results in an average number of $5.4$ domain walls; red bars show the distribution of a thermal state with the same mean domain wall density (Methods). d, Measured correlation function (\ref{['eq:corr_function']}) in the Z$_2$ phase.